Table of contents

The 10^th International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) due to the international conditions regarding the pandemic Covid-19 was held online and in addition to the lectures and presentations that took place in real time, it also had a large collection of pre-recorded presentations that were available to the participants through the conference website.

The Conference was attended by more than 180 participants and hosted about 250 oral and virtual presentations while counted more than 600 pre-registered authors. The 10^th IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc.

The scientific program was rather heavy, however, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time.

The Conference Chairman

Dimitrios Vlachos

University of Peloponnese

List of International Scientific Committee, Organizing Committee are available in the pdf.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

• Type of peer review: Single-blind

• Describe criteria used by Reviewers when accepting/declining papers. Was there the opportunity to resubmit articles after revisions?

• Conference submission management system: IDAS Conference management System

• Number of submissions received: 336

• Number of submissions sent for review: 315

• Number of submissions accepted: 189

• Acceptance Rate (Number of Submissions Accepted / Number of Submissions Received X 100): 56.25%

• Average number of reviews per paper: 2

• Total number of reviewers involved: more than 600

• Any additional info on review process (ie plagiarism check system): We use Turnitin system for plagiarism checking

• Contact person for queries:

Dimitrios Vlachos

Associate Professor, University of Peloponnese

Email: dvlachos@uop.gr

Tel: +30 6944 371526

Effective visualisation of railway tunnel subsurface features (e.g. voids, utilities) provides critical insight into structural health and underpins planning of essential targeted predictive maintenance. Subsurface visualisation here utilises a rotating ground penetrating radar antenna system for 360° point cloud data capture. This technology has been constructed by our industry partner Railview Ltd, and requires the development of complimentary signal processing algorithms to improve feature localisation. The main novelty of this work is extension of Shrestha and Arai's Combined Processing Method (CPM) to 360° Ground Penetrating Radar (360GPR) datasets, for first-time application in the context of railway tunnel structural health inspection. Initial experimental acquisition of a sample rotational transect for CPM enhancement is achieved by scanning a test section of tunnel sidewall - featuring predefined target geometry - with the rotating antenna. Next, frequency data separately undergo Inverse Fast Fourier Transform (IFFT) and Multiple Signal Classification (MUSIC) processing to recover temporal responses. Numerical implementation steps are explicitly provided for both MUSIC and two associated spatial smoothing algorithms, addressing an identified information deficit in the field. Described IFFT amplitude is combined with high spatial resolution of MUSIC via the CPM relation. Finally, temporal responses are compared qualitatively and quantitatively, evidencing the significant enhancement capabilities of CPM.

Information technologies of biotechnological processes are based on the use of mathematical models to describe microbiological synthesis. Application of digital technologies in analysis of microbial growth patterns is mainly determined by the ability of modern programming languages to numerically integrate systems of differential equations describing the development of the microbial process in time. In Jupyter Notebook environment in the R programming language, the solution of the kinetic growth model of the E.coli microbial population was shown. Two solution methods were used - the one-step Runge-Kutta method of the fourth order of accuracy and the universal solver ODE (General Solver for Ordinary Differential Equations). Initial data of the problem in question: $\frac{{K}_{s}}{{S}_{0}}=2$ (K_s is substrate affinity S₀ constant for the biomass (microorganism), S₀ is initial concentration of substrate); replicating cells m_a0 = 0.01; total number of cells m₀ = 0.05; stoichiometric ratio Y_s = 0.5; various ratios 1) $1) \frac{\lambda }{{\mu }_{m}}=0.0357; 2) \frac{\lambda }{{\mu }_{m}}=0.0714; 3) \frac{\lambda }{{\mu }_{m}}=0.1071; 4) \frac{\lambda }{{\mu }_{m}}=0.1428;5) \frac{\lambda }{{\mu }_{m}}=0.2142$ (λ is specific growth rate of dividing cells, μ_m is inactivation rate constant). As a result, the simulation and verification of microbial biomass growth process - its visual representation in the form of tabular and graphical data were carried out. In the process of simulation of E.coli growth the following peculiarity was revealed. In addition to cell division, a fairly intensive loss of their ability to divide occurs. This process is supposedly determinant in population development and limits the growth and ultimate density of the culture. Thus, information technology will help the researcher not only in studying the process, establishing patterns and predicting results, but also in making reasoned decisions.

The main object of the research given in this paper is modelling the water droplet movements on the leaf surface which is an important factor in realising how pesticide, nutrient or water engrossed through the surface. Therefore, a physical model based on mathematics proposed here for producing a realistic trajectory of droplet traversing a leaf surface. A vital feature of our methodology is to build the leaf surface using a recently developed method, by the author, so-called a hybrid CloughTocher cubic polynomial interpolation (CT-CPI) method. The leaf surface consisted of a mesh of triangles over which the hybrid CT-CPI method is build from 3D real life data gathered using a laser scanner. The droplet motion in our model affected by friction, resistance and gravity forces. The model verified using Matlab programming; the outcomes are promising and seem to capture reality well.

Increasing the quality and reliable reproducibility of large-size composite structures molding using the vacuum infusion method, which is gaining popularity in various industries, is achieved in practice through numerous tests by try and errors that require significant costs and time. The purpose of these tests is to determine the layout of the ports for the resin injection and vacuum supply, as well as the temperature regime that ensures the absence of isolated non-impregnated zones, the minimum porosity and the required reinforcement volume fraction in the composite. The proposed approach removes the simplifying assumptions used in commercial software for modeling the process, which reduce the accuracy of reconstruction of its dynamics and the sensitivity to the formation of unrepairable defects such as dry spots. It involves multiphysics modeling of resin filling in a porous preform by describing the resin front dynamics by the phase field equation, pressure distribution in an unsaturated porous medium by the Richards equation, the evolution of the degree of cure by the convection / diffusion / thermokinetics equation, and thermal processes by the heat transfer equation using modified models of viscosity, the diffusion coefficient of the degree of cure, the boundary condition for the vacuum port. To reduce the finite element computation time of the investigated variants of the process, which is necessary for its computer optimization, the predictive partial sub-criteria were used, which give a reliable prediction before the beginning of the resin gel and solidification. Due to this, a gain in computation time is 30-50% with a significant prediction accuracy of quality objectives and the presence of possible defects.

The aim of the work is to create a new design of electrodes for renal denervation. In standard RFA systems, monopolar heating is most often used, by introducing an RF electrode inside the vessel. This approach leads to the need to interrupt blood flow during the procedure. In addition, the monopolar mode of operation requires the contact of the inserted electrode with the vessel walls, which greatly complicates the design of the electrode system. Point contact of the electrode system with the vessel can damage the inner walls of the artery. It is proposed to use a multi-electrode structure for external stimulation by creating a hollow cylindrical thermal field for effective treatment. It has been established that external heating will create the required thermal field without direct contact with the walls of the artery. The external arrangement of the electrodes makes it possible to regulate the temperature on the external surface of the vessel. With such heating, it is not necessary to block the blood flow, and due to the symmetry of the arrangement, continuous heating can be obtained without moving the electrodes during the procedure. Mathematical modeling confirms the possibility of vascular denervation during external heating.

The paper describes a new system of integrated modelling SIEMNED (Software and Information Environment for Modelling and Numerical support of Experiments on complex Devices) designed for numerical support of experiments on tokamak installations. Also discussed are the results of its application to the modelling of discharge scenarios at the T-15 MD installation, which is currently being prepared for the physical launch.

A convectional reaction-diffusion is the main process causing a stable distribution of nutrients in biological objects. Indeed, the boundary problems for PDE are always used to describe this phenomenon. The spatial structure of biological objects is usually complex and non-uniform. Therefore, the creation of a digital phantom where gradients will be estimated becomes an especial procedure taking both a computational time and the resources. Recently, a simplified method of time dependent concentration gradient evaluation has been introduced. It represents the final spatial-time distribution as a superposition of the sphere sources diffusion fields. Using such an approximation, one can avoid preliminary reconstruction of digital mech-objects simulating a biological structure. In the present study the introduced approach is validated using the finite element method (FEM). It was shown that the exactness of coincidence is determined by the reciprocal distance of the sources and the scale of the considered area. The symmetry of a mutual boundary position plays an essential part in a validation conformity. A sphere sources formed field differs from the finite element method estimation on 7% under the most appropriate conditions. Other possible applications of the introduced approach to concentration gradient modelling in biological objects are discussed.

Oscillators with a Duffing-type restoring force and quadratic damping are dealt with in this paper. Four characteristic cases of this restoring force are analysed: hardening, softening, bistable and a pure cubic one. Their energy-displacement relationships are considered, and the corresponding closed-form exact solutions are obtained in terms of the incomplete Gamma function, which represent new results. Such results provide insight into damped dynamics of the class of system, including finding the phase trajectories as well as the comparison between these cases from the viewpoint of the energy loss per cycle.

The essential part of mathematical modelling of nutrients convectional reaction-diffusion is creation of a digital phantom of considered biological object. This process becomes an especial problem which needs to be solved before numerical calculations of the concentration gradients will be done. There are two principal ways to get the solution in this case. The first approach is the reconstruction of a digital phantom on the base of the experimental data directly. The second one is the creation of a virtual object according to the experimental evidence and the known principals de novo. The main advantage of the created phantom is a high adaptability to modelling demands and a physical problem formulation. In the present study a new algorithm of a digital phantom creation has been established. The principles of the claimed procedures are demonstrated by the example of a nervous tissue. Initially, one needs to create N 3D objects according to Voronoi diagrams. Each object has 144 edges and 69 boundaries on average. Having chosen M rear objects, a long 3D structure mimicking neurons axons is created according to a loft procedure from the start boundaries to the end ones. Then, the set of Boolean operations has been applied to form continuous smooth objects. The remain (N-(M+s)) objects are combined into several whole bodies using the loft procedures between the closet neighbours. The final structure has a good conformity with a nervous tissue architecture. Furthermore, the obtained phantom is correct to the mesh application and further numerical calculations.

Numerical modeling of time series of observations of Yakutsk meteorological station was used for the first time to construct a model of heat and moisture climate variability over the course of a century cycle of solar activity (SA). The lag of precipitation relative to temperature for ¼ of the rhythmic wave was revealed. Consecutive change of climatic phases: cold-wet (CW) warm-wet (WW), cold-dry (CD) and warm-dry (WD) has been established. The nonlinearity of the solar-tropospheric relations at level of intra- and secular oscillations is confirmed. The trends and anomalies of climate changes and permafrost response for the next decades and the current century as a whole are determined.

The paper presents the derivation of the synthesis method for the algorithm of the time-optimal controller for a third order dynamic system. A model with an extreme second-order transient response with delay was adopted as an object of research. The constant speed actuator is represented by an integrator. The synthesis is based on using the Pontryagin's maximum principle and describing the dynamics of a system in the state space using canonical variables. The verification of the correctness of the result obtained by the theorem of Feldbaum A.A. on the number of switchings of the direction of movement of the regulating body during the control interval has been executed. To calculate the canonical state variables, it is proposed to use the position of the regulator, the controlled value and the derivative calculated from its values, measured on real objects.

The features of the mathematical model of multi-criteria optimization of the distribution of current thermal and electrical loads at a combined heat and power plant with a mixed composition of equipment based on traditional heating units and a heating CCGT are considered. The previously proposed mathematical apparatus for solving the problem of multi-criteria optimization at a thermal power plant is analyzed. It is shown that with a mixed composition of equipment, along with the criteria of efficiency and environmental friendliness, it is also necessary to take into account the factors of reliability and mobility (maneuverability). The substantiation of the choice of reliability and mobility criteria for optimizing the operation modes of a thermal power plant is given. Approaches to solving the multi-criteria task are considered. The description of the features of the algorithm for solving the optimization problem is given in relation to thermal power plants with a mixed composition of equipment, including heating turbines of the T type and PGU.

The features of a mathematical model for optimizing the distribution of heat and electricity at a large thermal power plant with a complex composition of equipment as part of traditional heating units and a heating CCGT are considered. The selection and justification of optimization criteria at different stages of preparation and entry of the station to the electricity and capacity market is given. The disadvantages of the previously proposed optimal distribution algorithms are analyzed in relation to thermal power plants with a complex composition of equipment and with a complex scheme for the supply of electricity and heat. A method and algorithm for solving the problem are proposed based on the equivalence of the CHP equipment and the decomposition of the problem taking into account the schemes of electricity and heat output. The description of mathematical optimization methods is given, taking into account the peculiarities of the CCGT operating modes at reduced loads. The requirements for information support when integrating the developed algorithm into the application software of the automated process control system based on the PTC are given.

The features of a mathematical model for optimizing the distribution of heat and electricity at a large thermal power plant with a complex composition of equipment as part of traditional heating units and a heating CCGT are considered. The selection and justification of optimization criteria at different stages of preparation and entry of the station to the electricity and capacity market is given. The disadvantages of the previously proposed optimal distribution algorithms are analyzed in relation to thermal power plants with a complex composition of equipment and with a complex scheme for the supply of electricity and heat. A method and algorithm for solving the problem are proposed based on the equivalence of the CHP equipment and the decomposition of the problem taking into account the schemes of electricity and heat output. The description of mathematical optimization methods is given, taking into account the peculiarities of the CCGT operating modes at reduced loads. The requirements for information support when integrating the developed algorithm into the application software of the automated process control system based on the PTC are given.

Modern electric grid companies are focused on minimum economically feasible costs and are aimed at improving the efficiency of financial and economic activities through the rational use of resources. The digital twin structure is proposed for the management of field service teams in the event of accidents and technological failures in an electric grid company. The digital twin includes an agent model, a system dynamics model, a geographic information system component, and modules with experiments. The description of the simulation model of management of field service teams in the event of accidents and technological failures is formalized, the input and output information on the model components is highlighted, the information is structured, and the scheme of the system dynamics model is created. Experiment designs for the digital twin of the management of field service teams in the event of accidents and technological failures in order to determine the best reliability and cost indicators are developed. The developed approach can be used to create digital twins of the management process of field service teams in the event of accidents and technological failures for various electric grid companies by selecting the parameters of simulation models according to the statistical reports by electric grid companies and connecting the appropriate GIS modules.

In this article, a referential study of the sequential importance sampling particle filter with a systematic resampling and the ensemble Kalman filter is provided to estimate the dynamic states of several synchronous machines connected to a modified 14-bus test case, when a balanced three-phase fault is applied at a bus bar near one of the generators. Both are supported by Monte Carlo simulations with practical noise and model uncertainty considerations. Such simulations were carried out in MATLAB by the Power System Toolbox, whereas the evaluation of the Particle Filter and the Ensemble Kalman Filter by script files developed inside the toolbox. The results obtained show that the particle filter has higher accuracy and more robustness to measurement and model noise than the ensemble Kalman filter, which helps support the feasibility of the method for dynamic state estimation applications.

The rapid developments and innovations in technology have created unlimited opportunities for private and public organizations to collect, store and analyze the large and complex information about users and their online activities. Data mining, data publishing, and sharing sensitive data with third parties help organizations improve the quality of their products and services and raise significant individuals' privacy concerns. Privacy of personal information remains subject to considerable controversy. The problem is that big data analytics methods allow user's data to be unlawfully generated, stored, and processed by leaving users with little to no control over their personal information. This quantitative correlational study measures the effect of privacy concerns, risk, control, and trust on individuals' decisions to share personal information in the context of big data analysis. The key research question aimed to examine the relationship among the variables of perceived privacy concerns, perceived privacy risk, perceived privacy control, and trust. Drawing on Game Theory, the study explores all the game players' actions, strategies, and payoffs. Correlation analysis was used to test these variables based on the research model with 418 internet users of e-services in the United States. The overall correlation analysis showed that the variables were significantly related. Recommendations for future studies are to explore e-commerce, e-government, and social networking separately, and data should be collected in different regions where many factors can affect the privacy concerns of the individuals.

In this study is presented a mathematical approach that can be used to estimate the variability of the growth rate coefficient (λ), the total number of cases, and the midpoint of maximum infection due to the COVID-19 pandemic. The different parameters are quantified using one-year data set reported for Ecuador (from March 2020 to February 2021) and the (discrete or differential) logistic model. In particular, the results evidence that the most critical months of the pandemic in Ecuador were March and April 2020. In the following months, the outbreak continues with low growth rate values but in a variable way, which can be attributed to state health policies and the social behavior of the population. The estimated number of confirmed cases is around 409 K agrees with the data reported at the end of May 2021, validating the proposed mathematical approach.

We analyzed herein the new covid-19 daily positive cases recorded in Albania. We observed that the distribution of the daily new cases is non-stationary and usually has a power law behavior in the low incidence zone, and a bell curve for the remaining part of the incidence interval. We qualified this finding as the indicator intensive dynamics and as proof that up now, the heard immunity has not been reached. By parallelizing the preferential attachment mechanisms responsible for a power law distribution in the social graphs elsewhere, we explain the low daily incidence distribution as result of the imprudent gatherings of peoples. Additionally, the bell-shaped distribution observed for the high daily new cases is agued as outcome of the competition between illness advances and restriction measures. The distribution is acceptably smooth, meaning that the management has been accommodated appropriately. This behavior is observed also for two neighbor countries Greece and Italy respectively, but was not observed for Turkey, Serbia, and North Macedonia. Next, we used the multifractal analysis to conclude about the features related with heterogeneity of the data. We have identified the local presence self-organization behavior in some separate time intervals. Formally and empirically we have identified that the full set of the data contain two regimes finalized already, followed by a third one which started in July 2021.

The paper is devoted to the results of numerical modelling of non-stationary effects during the spread of a viral infection in a small group of individuals. We are considering the case of the spread of a viral infection by airborne droplets. Two consecutive stages of infection of the body are considered. At the first stage, virions enter the lungs and as a result of viremia are transported to the affected organs. In the second stage, the virions actively replicate in the affected organs. Random movement of individuals in the group changes the local concentration of virions near the selected individual. The random level of virion concentration may be greater than a certain critical value after which the infection of the selected individual will go into an irreversible stage. The main purpose of our work is to illustrate qualitatively new effects that occur in nonlinear systems in a random environment.

We analyze the evolution of the COVID19 infections in the first months of the pandemics and show that the basic compartmental SIR model cannot explain the data, some characteristic time series being by more than an order of magnitude different from the fit function over significant parts of the documented time interval. To correct this large discrepancy, we amend the SIR model by assuming that there is a relatively large population that is infected but was not tested and confirmed. This assumption qualitatively changes the fitting possibilities of the model and, despite its simplicity, in most cases the time series can be well reproduced. The observed dynamic is only due to the transitions between two infected compartments, which are the unconfirmed infected and the confirmed infected, and the rate of closing the cases (by recovery or death) in the confirmed infected compartment. We also discuss some relevant extensions of this model, to improve the interpretation and the fitting of the data. These findings qualitatively and quantitatively evidences the "iceberg phenomenon" in epistemology.

In the end of 2019, the emergence of COVID-19 was reported and confirmed for the first time, and it triggered an international pandemic. In Japan, the strong tendency to spread of infection is still continuing. The Japanese Government has been raised two concepts to overcome this difficulty. One is the thorough measures to control of the spread of infection and the other is the economic recovery. The government has carried out the corresponding two policies: the use of COVID-19 Contact-Confirming Application (COCOA) and the application of "GoTo Travel Campaign". We focus on these two policies and study an ideal situation, which enables us to balance more economic recovery and control of the spread of infection. To pursue this goal, we propose a mathematical model to estimate these policies's effects and conduct simulations of 28 scenarios. In addition, we analyze each result of the simulation and investigate characteristics of each situation. As a result, we clearly find that it required that not only the increasing the using rate of COCOA but also a positive change of people's behaviors and awareness.

Treatments to combat cancer seek to reach specific regions to ensure maximum efficiency and reduce the possible adverse effects that occur in the treatment. One of these strategies include the treatment with magnetic nanoparticles (NPM), which has presented promising results, however, aspects involved in the trajectory of the nanoparticles are not yet known. The aim of this work is estimating the behavior of NPM through supervised neural networks, for this, artificial neural networks were implemented, such as multilayer perceptron, with optimization algorithms in which the Levenberg Marquardt algorithm stands out, different trajectories of NPM were simulated, including parameters such as time, position in X and Y, the speed that the nanoparticles can reach and physical factors that interact in the distribution were considered, such as the gravitational field, the magnetic field, the Stokes force, the force of pushing and dragging with different values of viscosity in the blood, generating a database with optimized reaction times that allows a more accurate prediction. The architecture obtained with the artificial neural the network that contains the optimization algorithm [5 4 3 2], presented the best performance with a training MSE of 1.763E-07, a validation uRMSE of 0.0049, and trend probabilities of X 0.62 % and 0.576 % in Y.

We present a traffic model inspired by the motion of molecular motors along microtubules, represented by particles moving along a one-dimensional track of variable length. As the particles move unidirectionally along the track, several processes can occur: particles already on the track can move to the next open site, additional particles can attach at unoccupied sites, or particles on the track can detach. We study the model using mean-field theory and Monte Carlo simulations, with a focus on the steady-state properties and the time evolution of the particle density and particle currents. For a specific range of parameters, the model captures the microtubule instability observed experimentally and reported in the literature. This model is versatile and can be modified to represent traffic in a variety of biological systems.

We present analytical solutions and Monte Carlo simulation results for a one-dimensional modified TASEP model inspired by the interplay between molecular motors and their cellular tracks of variable lengths, known as microtubules. Our TASEP model incorporates rules for changes in the length of the track based on the occupation of the first two sites. Using mean-field theory, we derive analytical results for the particle densities and particle currents and compare them with Monte Carlo simulations. These results show the limited range of mean-field methods for models with localized high correlation between particles. The variability in length adds to the complexity of the model, leading to emergent features for the evolution of particle densities and particle currents compared to the traditional TASEP model.

To describe the propagation of radiation in biological tissue, it is crucial to know the tissue's optical characteristics. Integrating spheres method is widely used for experimental determination of optical properties of biological tissues. In this method, radiation scattered by the test sample in forward and backward directions is detected by the integrating spheres, along with the radiation that passed through the sample without scattering. In order to increase information content of the measurements, a moveable integrating spheres method was proposed, allowing one to register scattered radiation at different distances from sample surface to sphere ports. In this work, using the multilayer Monte Carlo method a numerical simulation of radiation propagation in a turbid medium was carried out under the conditions of detecting scattered radiation by moveable and stationary integrating spheres. Random errors were added to the direct problem solution in order to simulate experimental inaccuracies. The corresponding inverse problems were solved and the errors arising in the determination of optical properties (albedo, scattering anisotropy, optical depth) were compared in the cases of moveable and fixed spheres. It is shown that the same error in the inverse problem input data leads to smaller root-mean-square deviation from the true values when reconstructing albedo and anisotropy with the moveable spheres method, compared to the classical stationary spheres approach.

The release of hazardous materials in urbanized areas is a considerable threat to human health and the environment. Therefore, it is vital to detect the contamination source quickly to limit the damage. In systems localizing the contamination source based on the measured concentrations, the dispersion models are used to compare the simulated and registered point concentrations. These models are run tens of thousands of times to find their parameters, giving the model output's best fit to the registration. Artificial Neural Networks (ANN) can replace in localization systems the dispersion models, but first, they need to be trained on a large, diverse set of data. However, providing an ANN with a fully informative training data set leads to some computational challenges. For example, a single simulation of airborne toxin dispersion in an urban area might contain over 90% of zero concentration in the positions of the sensors. This leads to the situation when the ANN target includes a few percent positive values and many zeros. As a result, the neural network focuses on the more significant part of the set - zeros, leading to the non-adaptation of the neural network to the studied problem. Furthermore, considering the zero value of concentration in the training data set, we have to face many questions: how to include zero, scale a given interval to hide the zero in the set, and include zero values at all; or limit their number? This paper will try to answer the above questions and investigate to what extend zero carries essential information for the ANN in the contamination dispersion simulation in urban areas. For this purpose, as a testing domain, the center of London is used as in the DAPPLE experiment. Training data is generated by the Quick Urban & Industrial Complex (QUIC) Dispersion Modeling System.

Photosynthetic pigment-protein complexes are the essential parts of thylakoid membranes of higher plants and cyanobacteria. Besides many organic and inorganic molecules they contain pigments like chlorophyll, bacteriochlorophyll, and carotenoids, which absorb the incident light and transform it into the energy of the excited electronic states. The semiclassical theories such as molecular exciton theory and the multimode Brownian oscillator model allows us to simulate the linear and nonlinear optical response of any pigment-protein complex, however, the main disadvantage of those approaches is a significant amount of effective parameters needed to be found in order to reproduce the experimental data. To overcome these difficulties we used the Differential evolution method (DE) that belongs to the family of evolutionary optimization algorithms. Based on our preliminary studies of the linear optical properties of monomeric photosynthetic pigments using DE, we proceed to more complex systems like the reaction center of photosystem II isolated from higher plants (PSIIRC). PSIIRC contains only eight chlorophyll pigments, and therefore it is potentially a very promising subject to test DE as a powerful optimization procedure for simulation of the optical response of a system of interacting pigments. Using the theoretically simulated linear spectra of PSIIRC (absorption, circular dichroism, linear dichroism, and fluorescence), we investigated the dependence of the algorithm convergence on DE settings: strategies, crossover, weighting factor; eventually finding the optimal mode of operation of the optimization procedure.

It is known that during the flow, if the displacing fluid can chemically react with the components of porous medium and with the release of a gas phase, then such a flow regime can be unstable. During this process, pressure fluctuations can be observed, and the displacing fluid will move in "waves". In the course of our research, a simple mathematical model was proposed that provides a qualitative explanation of the reasons for the emergence of such a phenomenon; laboratory modeling was carried out, and the criterion of the "waves" formation was found, depending on the concentration of chemically active components. The proposed model can predict the emergence of the wave instabilities in a laboratory experiment, which will allow to carry out a future experiment on a larger scale.

The geomagnetic field is among the most striking features of the Earth. By far the most important ingredient of it is generate in the fluid conductive outer core and it is known as the main field. It is characterized by a strong dipolar component as measured on the Earth's surface. It is well established the fact that the dipolar component has reversed polarity many times, a phenomenon dubbed as dipolar field reversal (DFR). There have been proposed numerous models focused on describing the statistical features of the occurrence of such phenomena. One of them is the domino model, a simple toy model that despite its simplicity displays a very rich dynamic. This model incorporates several aspects of the outer core dynamics like the effect of rotation of Earth, the appearance of convective columns which create their own magnetic field, etc. In this paper we analyse the phase space of parameters of the model and identify several regimes. The two main regimes are the polarity changing one and the regime where the polarity remains the same. Also, we draw some scaling laws that characterize the relationship between the parameters and the mean time between reversals (mtr), the main output of the model.

The fractional calculus gains wide applications nowadays in all fields. The implementation of the fractional differential operators on the partial differential equations make it more reality. The space-time-fractional differential equations mathematically model physical, biological, medical, etc., and their solutions explain the real life problems more than the classical partial differential equations. Some new published papers on this field made many treatments and approximations to the fractional differential operators making them loose their physical and mathematical meanings. In this paper, I answer the question: why do we need the fractional operators?. I give brief notes on some important fractional differential operators and their Grünwald-Letnikov schemes. I implement the Caputo time fractional operator and the Riesz-Feller operator on some physical and stochastic problems. I give some numerical results to some physical models to show the efficiency of the Grünwald-Letnikov scheme and its shifted formulae.

MSC 2010: Primary 26A33, Secondary 45K05, 60J60, 44A10, 42A38, 60G50, 65N06, 47G30,80-99

Melting is a common phenomenon in our daily life, and although it is understood in thermodynamic (macroscopic) terms, the transition itself has eluded a description from the point of view of microscopic dynamics. While there are studies of metastable states in classical spin Hamiltonians, cellular automata, glassy systems and other models, the statistical mechanical description of the microcanonical superheated solid state is lacking.

Our work is oriented to the study of the melting process of superheated solids, which is believed to be caused by thermal vacancies in the crystal or by the occupation of interstitial sites. When the crystal reaches a critical temperature, it becomes unstable and a collective self-diffusion process is triggered. These studies are often observed in a microcanonical environment, revealing long-range correlations due to collective effects, and from theoretical models using random walks over periodic lattices. Our results suggest that the cooperative motion made possible by the presence of vacancy-interstitial pairs (Frenkel pairs) above the melting temperature can induce long-range effective interatomic forces even beyond the neighboring fourth layer. From microcanonical simulations it is also known that an ideal crystal needs a random waiting time until the solid phase collapses. Regarding this, our results also point towards a description of these waiting times using a statistical model in which there is a positive quantity X that accumulates from zero in incremental steps, until it exceeds a threshold value.

Quantum teleportation is a notable basement of quantum processing. It has been experimentally tested with outstanding growing success by introducing improvements and applied advances in the last two decades. Its quantum non-local properties have let to discover and introduce novel implementations based on it in quantum processing, cryptography, quantum resources generation among others. In the current work, we develop a scheme performing double teleportation on two different virtual receivers, while the sender is still able to post-select the final target of teleportation. This process can be then used to generate non-local resources in a coordinated way. Those resources can be transferred to one of the receivers in the form of the non-local resource desired. They are analysed in terms of their parametric behavior, and properties derived from the CHSH inequality.

This study aims to answer through a mathematical model and its numerical simulation the question whether the kinetic rate constants of chemical reactions are influenced by the strength of gravitational field. In order to calculate the effects of gravity on the kinetic rate constants, the model of kinetic rate constants derived from collision theory is amended by introducing the mass and length corrections provided by general relativity. Numerical simulations of the model show that the rate constant is higher where the gravitational field is more intense.

This study presents an asymptotic stability analysis of a model of a bioreactor converting carbon monoxide (CO) gas into ethanol through a C. autoethanogenum biocatalyst. The configuration is a bubble column reactor with co-current gas-liquid flows where gas feed is introduced by a gas distributor placed at the bottom of the column. A pure culture of C. autoethanogenum is subsequently injected at the bottom of the column; therein, cells are dispersed in the liquid and consume the dissolved gas and release by-products such as ethanol and acetic acid. Cellular growth and byproduct secretion are affected by spatially varying dissolved gas concentrations due to advection-diffusion mass transports which are induced by the effect of the injection pressure and gravitational force. The model accounts for four species representing the biomass, the CO substrate in the liquid phase, and two by-products - ethanol and acetic acid. Substrate dynamics is described by an advection-diffusion equation.

We investigate the asymptotic stability of the biomass dynamics that is a requirement for the system's controllability, i.e. for the possibility to steer a dynamical system from an arbitrary initial state to an arbitrary final state using a set of controls. The concept of stability of the controls is extremely relevant to controllability since almost every workable control system is designed to be stable. If a control system is not stable, it is usually of no use in practice in industrial processes. In the case of a bioreactor, the control is the biomass and controllability is the possibility of modulating through this control the ethanol production. We present a test for asymptotic stability, based on the analysis of the properties of the dynamic function defining its role as storage function.

We soften the non zero y-boundary on a Bunimovich like quarter-stadium. The smoothing procedure is performed via an exponent monomial potential, the system becomes partially reflective, preserving the particle's translation and rotational motion. By increasing the exponent value, the stadium's boundaries become rigid and the system's dynamics reaches a chaotic regime. We set a leaking soft stadium family by opening a limited region located at some place of its basis's boundary, throughout which the particles can leak out. This work is an extension of our recently reported paper on this matter. We chase the particle's trajectory and focus on the stadium transient behavior by means of the statistical analysis of the survival probability on the marginal orbits that never leave the system, the so called bouncing ball orbits. We compare these family orbits with the billiard's transient chaos orbits.

In this article, we will first discuss the completeness of real numbers in the context of an alternate definition of the straight line as a geometric continuum. According to this definition, points are not regarded as the basic constituents of a line segment and a line segment is considered to be a fundamental geometric object. This definition is in particular suitable to coordinatize different points on the straight line preserving the order properties of real numbers. Geometrically fundamental nature of line segments are required in physical theories like the string theory. We will construct a new topology suitable for this alternate definition of the straight line as a geometric continuum. We will discuss the cardinality of rational numbers in the later half of the article. We will first discuss what we do in an actual process of counting and define functions well-defined on the set of all positive integers. We will follow an alternate approach that depends on the Hausdorff topology of real numbers to demonstrate that the set of positive rationals can have a greater cardinality than the set of positive integers. This approach is more consistent with an actual act of counting. We will illustrate this aspect further using well-behaved functionals of convergent functions defined on the finite dimensional Cartezian products of the set of positive integers and non-negative integers. These are similar to the partition functions in statistical physics. This article indicates that the axiom of choice can be a better technique to prove theorems that use second-countability. This is important for the metrization theorems and physics of spacetime.

We construct the explicit form of higher-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The matrix potential entries can depend arbitrarily on the two variables. Our construction is based on results for coupled Korteweg-de Vries equations [27].

Previously, the basic laws and equations of electrodynamics, atomic nuclei, elementary particles theory and gravitation theory were derived from the equations of compressible oscillating ether. In this work, the theory of atomic structure for all chemical elements is constructed. A formula for the values of the energy levels of the electrons of an atom, which are the values of the energies of binding of electrons with the nucleus of an atom in the ground unexcited state, is derived from the equations of the ether. Based on experimental data on the ionization energies of atoms and ions, it is shown that the sequence of values of the energy levels of electrons has jumps, exactly corresponding to the periods of the table of chemical elements. It is concluded that it is precisely these jumps, and not quantum-mechanical rules, prohibitions and postulates that determine the periodicity of the properties of chemical elements. Ethereal correction of the table of chemical elements is presented which returns it to the form proposed by D.I. Mendeleev.

We discuss the results of numerical modeling of forming optical-terahertz bullets at the process of optical rectification. Our calculations are based on a generalization of the well-known Yajima - Oikawa system, which describes the nonlinear interaction of short (optical) and long (terahertz) waves. The generalization relates to situations when the optical component is close to a few-cycle pulse. We study the influence of the number of optical pulse oscillations on the formation of an optical-terahertz bullet. We develop original nonlinear conservative pseudo-spectral difference scheme approximating the generalization of the Yajima-Oikawa system. It is realized with the help of FFT algorithm. Mathematical modeling demonstrates scheme efficiency.

The theory of nonlinear spectroscopy on randomly oriented molecules leads to the problem of averaging molecular quantities over random rotation. We solve this problem for arbitrary tensor rank by deriving a closed-form expression for the rotationally invariant tensor of averaged direction cosine products. From it, we obtain some useful new facts about this tensor. Our results serve to speed the inherently lengthy calculations of nonlinear optics.

There are several types of exterior ballistic models used to calculate projectile's flight trajectories. The most complex 6 degree of freedom rigid body model has many disadvantages to using it to create firing tables or rapid calculations in fire control systems. Some of ballistic phenomena can be simplified by empirical equations without significant loss of accuracy. This approach allowed to create standard NATO ballistic model for spin stabilized projectiles named Modified Point of Mass Model (PM Model). For fin (aerodynamically) stabilized projectiles like mortar projectiles simple Point of Mass Model is commonly used. The PM Model excludes many flight phenomena in calculations. In this paper authors show the mean pitch theory as an approximation of the natural fin stabilised projectile pitch during flight. The theory allows for simple improvement of accuracy of the trajectories calculation. In order to validate the theory data obtained from shooting of supersonic mortar projectiles were used. The comparison of accuracy between simple PM Model and PM Model including mean pitch theory were shown. Results were also compared with the angle of response theory.

It is for the most part expected that dark matter is important to clarify the rotation of the galaxy, It has effectively been seen that the non-commutative geometry background can achieve this objective similarly. The objective of this study is to investigate a relationship between non-commutative geometry and certain aspect of dark matter. We are relying on a basic mathematical expression argument that indicates that the appearance of dark matter in galaxies and galaxy clusters with regard to flat rotation curves is similarly a result of non commutative geometry.

Without stating any assumptions or making postulates we show that the electromagnetic quantum vacuum plays a primary role in quantum electrodynamics, particle physics, gravitation and cosmology. Photons are local oscillations of the electromagnetic quantum vacuum field guided by a non-local vector potential wave function. The electron-positron elementary charge emerges naturally from the vacuum field and is related to the photon vector potential. We establish the masse-charge equivalence relation showing that the masses of all particles (leptons, mesons, baryons) and antiparticles have electromagnetic origin. In addition, we deduce that the gravitational constant G is an intrinsic property of the electromagnetic quantum vacuum putting in evidence the electromagnetic nature of gravity. We show that Newton's gravitational law is equivalent to Coulomb's electrostatic law. Furthermore, we draw that G is the same for matter and antimatter but gravitational forces could be repulsive between particles and antiparticles because their masses bear naturally opposite signs. The electromagnetic quantum vacuum field may be the natural link between particle physics, quantum electrodynamics, gravitation and cosmology constituting a basic step towards a unified field theory.

The system of governing equations for the dynamics of the compressible viscous ideal gas is considered in the 3D bounded domain with the inflow and outflow boundary conditions. The cylinder is located in the domain. Such problem is simulated using the high order WENO-scheme for inviscid part of the equations and using 4-th order central approximation for the viscous tensor part with the third order temporal discretization.

The method of Proper Orthogonal Decomposition (POD) is applied to the problem at hand in order to extract the most active nodes. Cascades of bifurcations of periodic orbits and invariant tori are found that correspond to the excitation in different POD modes. The approximation of the reduced order model is analyzed and it is shown that one cannot make parameter extrapolations for the reduced order model to capture the same dynamics as is observed in the original full size model.

The extension of the classical A.N. Kolmogorov's flow problem for the stationary 3D Navier-Stokes equations on a stretched torus for velocity vector function is considered. A spectral Fourier method with the Leray projection is used to solve the problem numerically. The resulting system of nonlinear equations is used to perform numerical bifurcation analysis. The problem is analyzed by constructing solution curves in the parameter-phase space using previously developed deflated pseudo arc-length continuation method. Disconnected solutions from the main solution branch are found. These results are preliminary and shall be generalized elsewhere.

Working with ever growing datasets may be a time consuming and resource exhausting task. In order to try and process the corresponding items within those datasets in an optimal way, de Bruijn sequences may be an interesting option due to their special characteristics, allowing to visit all possible combinations of data exactly once. Such sequences are unidimensional, although the same principle may be extended to involve more dimensions, such as de Bruijn tori for bidimensional patterns, or de Bruijn hypertori for tridimensional patterns, even though those might be further expanded up to infinite dimensions. In this context, the main features of all those de Bruijn shapes are going to be exposed, along with some particular instances, which may be useful in pattern location in one, two and three dimensions.

The numerical model of the diffuse reflection of Gaussian beam from the surface of biological tissue is introduced. The two-dimensional fractional Brownian motion (fBm) with the Hurst index H and the scale parameter σ was used for the simulations of the tissue surface relief. For the surfaces described by fixed σ = 0.1 and H = 0.55, H = 0.803 (corresponds to the surface of a banana fruit), H = 0.9, the angular distributions of the reflected radiation intensity were calculated using a Kirchhoff integral approach. The resulting distributions considerably differ from each other. Therefore, the introduced model can be used for the solution of the inverse problem of finding the fBm parameters of tissue surfaces employing the experimentally measured distribution of the reflected radiation intensity.

The mathematical model that describes the local heating of biological tissues by optical radiation is introduced. Changes of the electric properties of biological tissues in such process can be used as a reliable tool for analyzing heating and damage degrees of tissues.

We present a derivation of a manifestly symmetric form of the stress-energy-momentum using the mathematical tools of exterior algebra and exterior calculus, bypassing the standard symmetrizations of the canonical tensor. In a generalized flat space-time with arbitrary time and space dimensions, the tensor is found by evaluating the invariance of the action to infinitesimal space-time translations, using Lagrangian densities that are linear combinations of dot products of multivector fields. An interesting coordinate-free expression is provided for the divergence of the tensor, in terms of the interior and exterior derivatives of the multivector fields that form the Lagrangian density. A generalized Leibniz rule, applied to the variation of action, allows to obtain a conservation law for the derived stress-energy-momentum tensor. We finally show an application to the generalized theory of electromagnetism.

At present, there are different treatments against cancer, however, some of them, such as chemotherapy, are very invasive for the human body, since they affect healthy tissues. Magnetic targeting of drugs by means of magnetic nanoparticles is one of the alternative techniques that has emerged in the last decade, it is based on the targeting of drug delivery to the tumor without affecting healthy tissues, via of injected nanoparticles with diamagnetic properties directly into the bloodstream, driven by external magnetic fields produced by permanent magnets. This technique in literature is often come upon as MTD for its acronym in English. In this work, a numerical model was developed in order to quantify the loss of nanoparticles in the process of interaction with the walls of the bloodstream. For this model, the Kinetic technique was used, quantifying the probability of adsorption and absorption taking into account the following parameters: diameter of the nanoparticle (200 nm), density of the nanoparticle (6450 kg · m^-3), diameter of the cell endothelial (0.1 μm - 1 μm), transcellular pores of the fenestrated endothelium (70 nm) and modulus of elasticity of the endothelium (4.1 ± 1.7 kPa).

We study how the explicit symmetry breaking, through a continuous parameter in the Lagrangian, can actually lead to the creation of different types of symmetries. As examples we consider the motion of a relativistic particle in a curved background, where a nonzero mass breaks the symmetry of the conformal algebra of the metric, and the motion in a Bogoslovsky-Finsler space-time, where a Lorentz violation takes place. In the first case, new nonlocal conserved charges emerge in the place of those which were previously generated by the conformal Killing vectors, while in the second, rational in the momenta integrals of motion appear to substitute the linear expressions corresponding to those boosts which fail to be symmetries.

Blade coaters are most commonly used for coating of paper and paperboard with higher efficiency. The efficiency of short-dwell blades coaters depends on many factors such as the properties of the coating material, design of the coating reservoir, the types of flow behaviour taking place inside the reservoir, etc. In this work, we have proposed an optimal design of the reservoir to improve the efficiency of short-dwell coaters. The reservoir has been modeled as flow inside a two-dimensional rectangular cavity. Incompressible Navier-Stokes equations in primitive variable formulation have been solved to obtain the flow fields inside the cavity. Spatial derivatives present in the momentum, and continuity equations are evaluated using a sixth-order accurate compact scheme whereas the temporal derivatives are calculated using the fourth-order Runge-Kutta method. The actual rate of convergence of the numerical scheme has been discussed in detail. In addition, the accuracy and stability of the used numerical method are also analysed in the spectral plane with the help of amplification factor and group velocity contour plot. The obtained numerical solutions have been validated with the existing literature. Four different aspect ratio cases (L/H = 3/4,4/3,4/5 and 5/4) have been considered for the simulations including the case of square cavity. It has been observed that L/H = 5/4 case provides best results among all others.

In this work, it is shown that the equations of motion of the scalar field for spatially flat, homogeneous, and isotropic space-time Friedmann-Robertson-Walker have a form-invariance symmetry, which is arising from the form invariance transformation. Form invariance transformation is defined by linear function ρ = n²ρ in general case. It is shown the method of getting potential and the scalar field for the power law scale factor. The initial model is always stable at exponent of the scale factor α > 1, but stability of the transformation model depends on index n. Slow roll parameters and spectral induces is obtained and at large α they agree with Planck observation data.

A method for the group classification of differential equations we recently proposed is applied to the classification of a family of generalized Klein-Gordon equations. Our results are compared with other classification results of this family of equations labelled by an arbitrary function. Some conclusions are drawn with regards to the effectiveness of the proposed method.

The mechanical properties of additively fabricated metallic parts are closely correlated with their microstructural texture. Knowledge about the grain evolution phenomena during the additive manufacturing process is of essential importance to accurately control the final structural material properties. In this work, a two-dimensional model based on the cellular automata method was developed to predict the grain evolution in the selective laser melting process. The effectiveness of this presented model is proven by comparing the simulated and reported results. The influence of process parameters, like the scanning strategy, laser power, and scanning speed, on the microstructural grain morphology, are numerically evaluated.

A theoretical study of the behaviour of atomic planes in an elastic single-crystal rod under the action of volumetric forces such as the inertial force and the force of gravity has been carried out. The regularity of the linear distribution density of atomic planes in a single-crystal rod has been established in frames of continuous and discrete approaches. The obtained distribution function is of independent interest, and it can be used, for example, in studying the behaviour of a metal rod under conditions of an external induced electric field.

In this work, we consider a homogeneous and isotropic cosmological model of the universe in f (T, B) gravity with non-minimally coupled fermionic field. In order to find the form of the coupling function F(Ψ), the potential function V (Ψ) of the fermionic field and the function f (T, B), we found through the Noether symmetry approach. The results obtain are coincide with the observational data that describe the late-time accelerated expansion of the universe.

We propose a method for generating a wide variety of increasingly complex microscopic temperature expressions in the form of functional polynomials in thermodynamic temperature. The motivation for study of such polynomials comes from thermostat theory. The connection of these polynomials with classical special functions, in particular, with Appell sequences, is revealed.

The physical processes that form the saturated absorption resonance spectra on the atomic transition with level momenta J= 1/2 in the field of unidirectional waves of arbitrary intensities are investigated both analytically and numerically. It is shown that the narrow structures of the nonlinear resonance spectra (resonances of electromagnetic-induced transparency and absorption) and the processes forming them are determined by the direction of the light wave polarizations, degree of openness of the atomic transition, and the saturating wave intensity. The conditions under which the nonlinear resonance is exclusively coherent, due to the magnetic coherence of transition levels, are revealed.

In this paper we research the (1+1)-dimensional system of Schrodinger-Maxwell-Bloch equations (NLS-MBE), which describes the optical pulse propagation in an erbium doped fiber and find PT-symmetric and reverse space-time Schrodinger-Maxwell-Bloch equations, i.e. the kinds of nonlocal Schrodinger-Maxwell-Bloch equations. In particular case, the system of Schrödinger-Maxwell-Bloch equations is integrable by the Inverse Scattering Method as shown in the work of M.A blowitz and Z. Musslimani. Following this method we prove the integrability of the nonlocal system of Schröodinger-Maxwell-Bloch equations by Lax pairs. Also the explicit and different seed solutions are constructed by using Darboux transformation.

In this work, the generalized nonlinear Schrödinger equation is investigated. This equation is integrable and admits Lax pair. To obtain travelling wave solutions the extended tanh method is applied. This method is effective to obtain the exact solutions for different types of nonlinear partial differential equations. Graphs of obtained solutions are presented. The derived solutions are found to be important for the explanation of some practical physical problems.

We investigated the gravity model F (R, T), which interacts with a fermion field in a uniform and isotropic at spacetime FLRW. The main idea and purpose of the work donewas to create a mathematical model and find a particular solution for the scale factor a, since it describes the dynamics of the evolution of the Universe. The solutions for this universe are obtained using the Noether symmetry method. With its help, a specific form of the Lagrangian is obtained. And the possible types of the scale factor were found. The evolution of the resulting cosmological model has been investigated.

The paper presents a new approximate deconvolution subgrid model for Large Eddy Simulation in which corrections to implicit filtering due to spatial discretization are integrated explicitly. The top-hat filter implied by second-order central finite differencing is a key example, which is discretised using the discrete Fourier transform involving all the mesh points in the computational domain. This discrete filter kernel is inverted by inverse Wiener filtering. The inverse filter obtained in this way is used to deconvolve the resolved scales of the implicitly filtered velocity field on the computational grid. Subgrid stresses are subsequently calculated directly from the deconvolved velocity field. The model was applied to study decaying two-dimensional turbulence. Results were compared with predictions based on the Smagorinsky model and the dynamic Germano model. A posteriori testing in which Large Eddy Simulation is compared with filtered Direct Numerical Simulation obtained with a Fourier spectral method is included. The new model presented strictly speaking applies to periodic problems. The idea of recovering a high-order inversion of the numerically induced filter kernel can be extended to more general non-periodic problems, also in three spatial dimensions.

In this article, we examine a gravitational theory including a fermion field that is non-minimally coupled to metric f (R) gravity in (2+1) dimensions. We give the field equations for fermion fields and Friedmann equations. In this context, we study cosmological solutions of the field equations using these forms obtained by the existent of Noether symmetry.

In this note we compute all deformations of the 4-dimensional classical Galilei algebra &. In particular, we find examples of quadratic, cubic and quartic Lie algebra deformations.

In this note, we give examples of S—expansions of Lie algebras of finite and infinite dimension. For the finite dimensional case, we expand all real three-dimensional Lie algebras. In the case of infinite dimension, we perform contractions obtaining new Lie algebras of infinite dimension.

In this paper, we study the generalized Heisenberg ferromagnet equation, namely, the M-CVI equation. This equation is integrable. The integrable motion of the space curves induced by the M-CVI equation is presented. Using this result, the Lakshmanan (geometrical) equivalence between the M-CVI equation and the two-component Camassa-Holm equation is established.

For constructing physical science based models in irregular numerical grids, an easy-to-implement method for solving partial differential equations has been developed and its accuracy has been evaluated by comparison to analytical solutions that are available for simple initial and boundary conditions. The method is based on approximating the local average gradients of a field by fitting equation of plane to the field quantities at neighbouring grid positions and then calculating an estimate for the local average gradient from the plane equations. The results, comparison to analytical solutions, and accuracy are presented for 2-dimensional cases.

This model consists of a periodic structure formed by solid beams equidistant from each other submerged in a fluid. The beams are clamped at both ends. The distance between the beams, the elastic properties of the solid and the fluid; and the geometric parameters of the beams determine a relationship between the frequencies of the mechanical waves that can propagate through the structure and the wave vector. Analysis within the first Brillouin zone with the Bloch periodicity condition gives rise to frequency bands in which there is the propagation of mechanical waves and bands in which no waves are propagated. Some propagation bands and forbidden regions were found in the examined frequency ranges for various geometric configurations.

Estimation of stress distribution on the parts of a weapon is one of the most important stages of designing and optimization of firearms. The paper describes the finite element numerical model of the short recoil operated weapon and results of parametric analysis of the stress distribution on weapon parts. Considered changes in loading courses can be the result of differences in applied ammunition (produced in accordance with various standards or self-elaborated rounds). Conducted works allowed for estimation of approximate critical value of propellant gas pressure, which can be dangerous for pistol structure. Moreover, the paper presents the results of the kinematic characteristics investigation of the weapon using the finite element method and by way of the experimental tests, which proves the correctness of the assumptions made for the numerical model.

Around the world, Covid-19 outbreak caused a sudden and forced migration from face-to-face education to online education generating an unprecedented phenomenon in the history of education. In Mexico, the most affected Education level was Basic Public Education, the least unprepared while Private Higher Education has experienced by years alternative models using technology. Despite, around the world, new findings arose evidencing that students could require emotional support under the confinement due to the extended lockdown and an intense effort to follow their new educative plans revealing behavioral issues as success factors of that extended online education in the emergent strategy. Based on a statistical model of exploratory factor analysis of data applied to Freshman and Sophomore engineering students, this work presents a roadmap of statistical modelling and testing for the analysis of several dimensions of more effective causal in the success of the forced online education paradigm implementation. Obtaining a Cronbach α value of 0.817, it points to meaningful internal reliability to discriminate and rearrange those causal and dimensions into a more comprehensive education ecosystem.

In this work we study the system of the votes, the mechanism of the electoral support formation, and also the elements of its dynamics, by analyzing the data from several election processes in Albania. Firstly, we evidence the specific features and the characteristics of the distributions of votes through a descriptive approach, and next we use those findings to identify the nature of the elementary processes of the agreement, the defects of the system and dynamical issues. The distributions of the votes for the majority or majority-like election as by polling stations reference results a two-parts function. The part of the distribution located in the small vote fraction fits to a power law or to a q-exponential function, therefore the foremost factor of the electoral support for the subjects populating this zone is based in the preferential attachment rule, with some modification. Consequently, the small subjects or independent candidates, realize their electoral attractiveness based on the individual performance. Also, their voters act rationally and usually gather sufficient information before deciding to support them. The bell-shaped part of the distribution which describes the votes of the candidates of the main parties, fits better to the q-gaussian functions. In this case, electoral support is affected strongly by the political activists (militants) which harvest local influences to convict people producing an extra support for the candidates of big parties, regardless of their performance and electoral values. This physiognomy is characteristic for all legislative and administrative majority voting or other majority-like elections as practically behave the closed-lists elections of 2009, 2013, 2017 and also the semi-opened list of the 2021. The distributions of the closed-list votes in the administrative elections are mostly of the exponential or q-exponential type. Also, the distributions based on the data from electoral constituencies which include many polling stations resulted q-exponentials for all types of elections. We connected the q-exponential form of the distribution with the electoral network failures, system deficiencies and heterogeneity effects. In 2021, the distributions of the votes for subjects is obtained similar to the typical recent majority voting distribution, a mix of the power law and q-gaussian functions. The distribution of the votes for the candidates on the semi-open list for those elections resulted a mix of two q-exponentials. We associated this last with the difficulties of the voters to understand new electoral rules and additional other causes of the non-electoral nature. Also, the electorate network might have suffered extra irregularity issues due to the inadequate sizes of elections units, etc. The distributions of the votes for the two main parties are found q-gaussians with q ∼ 1.32 and q ∼ 1.57 for the right and the left wing respectively. Based on the non-stationarity level measured by the q-value, significant redistribution events are expected for the left-wing network, whereas the right-wing network would experience fewer changes in ceteris paribus socio-electoral conditions. Interestingly, the mix of the votes for two main political parties has produced a q-gaussian with q=1.004, and subsequently, the joint system is found in a more relaxed state. Therefore, the compound network including two main parties is likely to not undergo significant redistribution of the votes in the near future. This means that the small subjects or the fresh-born ones are not likely to cause changes on the system. Based on the deductions for electoral agreement formation, we used our recently introduced q-opinion approach to model the electoral opinion formation. In this model, the q-opinion produces an additional term that multiplies the modified preferential attachment probability for the link establishment. Herein, the q-parameter is calculated by using an ad-hoc formula involving the performance of the candidate as utility function, which associates the agreement behavior as the response, with the candidate performance as the offer or the cause factor. The quantity q henceforth acts as activation-inhibition switch of the extra utility involved in the q-opinion model, and particularly it provides a nonzero voter's support for the high-performance opponent candidates. The model has reproduced the distributions analyzed in this study. It resulted that many voters in this electorate system act rationally, despite their affiliations.

This article deals with the problem of modeling the assessment of the level of integrity of the content of the physics course learned by students. The need for such modeling is due to the need to bring education courses to online format. The degree of integrity of learning is proposed to be established by modeling the percolation of intradisciplinary connections established in the course structure. The model uses the graph model of intradisciplinary connections (T. N Gnitetskaya) and the principles of percolation theory (P-theory). The article provides a few practical solutions for the use of P-theory. An algorithm has been developed that allows forming the topics of the physics course into the studied structure.

We found a crossover from a Berezinskii-Kosterlitz-Thouless (BKT, logarithmic-rough surface to a Kardar-Parisi-Zhang (KPZ, algebraic)-rough surface for growing/recessing vicinal crystal surfaces in the non-equilibrium steady state using the Monte-Carlo method. We also found that the crossover point from a BKT-rough surface to a KPZ-rough surface is different from the kinetic roughening point for the (001) surface. Multilevel islands and negative islands (island-shaped holes) on the terrace formed by the two-dimensional nucleation process are found to block surface fluctuations, which contributes to making a BKT-rough surface.

We propose a one-dimensional model for the dilute aqueous solution of NaCl which is treated as an incompressible fluid placed in the external electric field. This model is based on the Poisson-Nernst-Planck system of equations, which also contains the constant flow velocity as a parameter and considers the dissociation and the recombination of ions. We study the steady-state solution analytically and prove that it is a stable equilibrium. Analyzing the numerical solutions, we demonstrate the importance of dissociation and recombination for the physical meaningfulness of the model.

We propose a method of determining the parameters of systems with serialized characteristics, which may suggest the existence of symmetry in the system. The method is demonstrated in extracting the parameters of a metal-semiconductor in the presence of significant series resistance, which is itself important but limits the accuracy of the existing methods in the determination of the other calculated parameters such as barrier height and ideality factor. We show the steps involved in establishing whether symmetry exists, and show that some functional interrelations between the parameters and the independent variables can readily be established. We use actual measurement data from an experimental diode and show that the results outperform the popular Cheung-Cheung approach. This general approach, therefore, represents a significant advancement in the analysis of serialized empirical data.

In this paper we investigated the calculation of the anodic limit of two anions of ionic liquids, largely used as electrolyte of lithium batteries. Starting from a model based on calculations performed on single ions at the MP2 level of theory, we showed that the matching between calculation and experiments decreases while using more expanded basis set with respect to 6-31G**, possibly because of the destabilization of the neutral species when larger basis sets are considered. Additionally, in order to decrease the computational time, the performances for the calculation of the anodic limit obtained by means of a series of DFT functionals with increasing level of complexity (from the Generalized Gradient Approximation to the Range Separated Hybrid meta-Generalized Gradient Approximation) were compared. Overall, the best performing functionals are BMK, ωB97M-V and MN12-SX, while acceptable results can be obtained by M06-2X, M11, M08-HX and M11-L. Some less computationally expensive functionals, like CAM-B3LYP and ωB97X-D, also provide reasonable values of the anodic limit.

The accurate prediction of the thermodynamic properties of oligomeric blends and, in general, binary liquid mixtures from atomistic simulations is a challenging task. In this work we develop a methodology for the full thermodynamic analysis of oligomeric blends and the extraction of the Flory-Huggins interaction parameter from the Gibbs energy of mixing, combining Flory-Huggins thermodynamics with Kirkwood-Buff theory of solutions. We perform a series of Molecular Dynamics (MD) simulations of 2-methylpentane/n-heptane mixtures, at various mole fractions. Firstly we validate the forcefield we apply in our MD simulations, comparing the density and excess volume we obtain against the corresponding experimental estimates found in the literature. Then we calculate the Kirkwood-Buff integrals in the isothermal-isobaric (NpT) ensemble, applying the particle fluctuations method, and we extract the component activity coefficients, the excess Gibbs energy, the excess enthalpy, and the excess entropy of mixing as functions of the mole fraction. Finally we calculate the Flory-Huggins interaction parameter χ by interpreting the Gibbs energy of mixing in the framework of Flory-Huggins theory, and explore its dependence on composition. All results are compared against experimental measurements in order to evaluate our methodology. Agreement is found to be very good.

We study the stability/instability of skyrmions under mechanical stresses by Monte Carlo simulations in a 3D disk composed of tetrahedrons. Skyrmions emerge in chiral magnetic materials, such as FeGe and MnSi, under the competition of ferromagnetic interaction (FMI) and Dzyaloshinskii-Moriya interaction (DMI) and are stabilized by the external magnetic field. Recent experimental studies show that skyrmions are also stabilized/destabilized by uniaxial compressive stress perpendicular to or along the magnetic field direction. These phenomena are studied by using a 3D Finsler geometry (FG) model. In this 3D FG model, the DMI coefficient is automatically anisotropic by a geometrically implemented coupling of strains and electronic spins. We find that skyrmions are stabilized (destabilized) by extension (compression) stress along the direction of the applied magnetic field consistent with reported experimental data. This consistency implies that the 3D FG model successfully implements the magnetostrictive or magneto-elastic effect of external mechanical stresses on chiral magnetic orders, including the skyrmion configuration.

Simulations of the magnetic heat capacity of some (Pr, Tb)Al₂ compounds were performed using the mean-field approach. The developed routine aims to optimize the set of mean-field parameters. The proposed algorithm calculates the sum of squared differences between the experimental points and the simulated curve and then changes the parameters in order to minimize this sum. This searching leads to consistent values that can reproduce the experimental data. The parameters found in this work reproduced the heat capacities curves of the Pr_xTb_(1−x)Al₂ compounds, x=0.25, x=0.50 and x=0.75, with good agreement. The physical limitations of the mean-field approach do not preclude analysing the results. These parameters are important because they can help to understand and calculate the magnetocaloric effect these materials can present.

As many molecules have their rotovibrational resonance frequencies in the mid-infrared or terahertz regime, efficient generation of corresponding frequency combs may lead to large progress in gas spectroscopy and sensing. Quantum cascade lasers (QCLs) are among the most promising candidates for a compact and cheap radiation source in this frequency range. This contribution presents a full-wave numerical solution of the Maxwell-Liouville-von Neumann equations, thus avoiding the limited applicability of the rotating wave approximation to moderate field strengths and spectral bandwidths. We include losses and chromatic dispersion of the optically active material in the QCL. The semiclassical approach uses the finite-difference time-domain (FDTD) method to derive update equations for the electric field, starting from the one-dimensional Maxwell equations. There, the optical full-wave propagation is coupled to the electronic quantum system via a polarization term that arises from the evolution of the density matrix. Furthermore, dispersion effects are considered through a classical polarization term and losses are introduced by a finite material conductivity. This work mainly focuses on the integration of group velocity dispersion (GVD) due to the bulk material and, if applicable, the waveguide geometry into the update equations. It is known to be one of the main degradation mechanisms of terahertz frequency combs, but has not yet been added to the existing full-wave solver. The implementation is carried out as Lorentz model and is applied to an experimentally investigated QCL frequency comb setup from the literature. The reported results are in good agreement with the experimental data. Especially, they confirm the need for dispersion compensation for the generation of terahertz frequency combs in QCLs.

Rutherford's formula for the scattering of charged α-particles in the Coulomb field can be easily generalized to the case of gravitational scattering. The extended Rutherford formula for the gravitational scattering is presented. One of the types of the gravitational scattering in the Solar system is the gravity assist maneuvers. In this paper, an effective gravitational scattering cross-section is introduced by analogy for them and the generalized Rutherford formula for gravitational scattering is presented out when performing gravity assists. Modern methods of the ballistic design of the interplanetary space flights using gravity assist maneuvers around planets [1-3] are associated with the need to calculate a lot of trajectories (i.e. of the phase beams). For their effective use it is necessary to study the structure of non-linear flyby gravitational scattering using the Rutherford' formula and to construct the corresponding effective modelling using according regularized phase beams. It is shown that with using of such approach, it is possible to significantly increase the efficiency of the recurrent procedure for the gravity assists chains searching for ballistic scenarios of the modern interplanetary flights.

One of the types of gravitational scattering in the Solar system within the framework of the model of the restricted three-body problem (R3BP) is gravity assist maneuvers of the "particles of insignificant mass" [1] (spacecraft, asteroids, comets, etc.). For their description, a physical analogy with the beam scattering of charged α particles in a Coulomb field is useful. However, unlike the scattering of charged particles, there are external restrictions for the possibility of gravity assists executing related from the restricted size of planet's sphere of influence. At the same time, internal restrictions for the gravity assists performance estimated by the effective radii of planets are known from the literature on R3BP [2] (gravitational capture by the planet, falling into it). They depend from the particle asymptotic velocity relative the planet. For obvious reasons, their influence cuts off the possibility of effective gravity assists performance [3]. In this work the generalized estimates of the sizes of the near-planetary regions ("perturbation rings"), falling into which is a necessary condition for the implementation of gravity assists, are presented. The detailed analysis shows that Neptune and Saturn have the characteristic "perturbation rings" of the largest sizes in the Solar system, and Jupiter occupies only the fourth place in this checklist.

Tree graphs such as Cayley trees provide a stage to support the self-organization of fractal networks by the flow of walkers from the root vertex to the outermost shell of the tree graph. This network model is a typical example that demonstrates the ability of a random process on a network to generate fractality. However, the finite scale of the tree structure assumed in the model restricts the size of fractal networks. In this study, we removed the restriction on the size of the trees by introducing a lifetime τ (number of steps of random walks) of walkers. As a result, we successfully induced a size-independent fractal structure on a tree graph without a boundary. Our numerical results show that the mean number of offspring d_b of the original tree structure determines the value of the fractal box dimension d_b through the relation d_b — 1 = (n_b — 1)^-θ. The lifetime τ controls the presence or absence of small-world and scale-free properties. The ideal fractal behaviour can be maintained by selecting an appropriate value of τ. The numerical results contribute to the development of a systematic method for generating fractal small-world and scale-free networks while controlling the value of the fractal box dimension. Unlike other models that use recursive rules to generate self-similar structures, this model specifically produces small-world fractal networks with scale-free properties.

In state-recurrence analysis, recurrences are considered either in the space that constitutes of the observed quantities, or in an embedding space that is manufactured by time-delayed variables. An alternative approach is proposed here. In the so-called energy-variation analysis, the complexity of an orbit is quantified in terms of the statistics of the constant-speed geodesic condition. Energy-variation analysis requires significantly less operations than state-recurrence analysis, in particular, for multivariate time-series, while numerical experiments demonstrate that the resulting energy-recurrence matrix encodes information that is sufficient for quantifying the complexity of orbits.

This work describes various methods of time series prediction. It illustrates the differences between machine learning methods, nonlinear algorithms, and statistical methods in their approach to prediction, and tries to explain in depth the principles of some of the most widely used representatives of these types of prediction methods. All of these methods are then tested on a time series from the real world: the course of power consumption of a supercomputer infrastructure. The reader is gradually acquainted with data analysis, preprocessing, the principle of the methods, and finally with the prediction itself. The main benefit of the work is the final comparison of the results of this testing in terms of the accuracy of the predictions, and the time needed to calculate them.

Recent microgravity experiments have demonstrated that Faraday waves can arise in a secondary instability over the primary columnar patterns that develop after the frozen wave instability. While some numerical studies have investigated this phenomenon, theoretical analyses are only found in the works of Shevtsova et al. (2016) [1] and Lyubimova et al. (2019) [2]. Here, we extend these efforts by analysing the stability of a three-layer system, and derive the critical onset of Faraday waves, which appear via Hopf bifurcation. Numerical simulations — based on a model that reproduces the frozen wave mode with lowest wavenumber — are carried out to test this result and to analyse the character of the bifurcation. The predicted Hopf bifurcation is confirmed, which constitutes the first observation of modulated secondary Faraday waves. The abrupt growth of these modulated waves above onset indicates that the primary bifurcation is subcritical and is accompanied by a saddle-node bifurcation of periodic orbits that stabilises the (branch of) unstable solutions created in the subcritical Hopf bifurcation. Further above onset, these modulated waves are destroyed via a saddle-node heteroclinic bifurcation. Results for an N-layer configuration, which represents a more general frozen wave pattern, are also presented and compared with the three-layer case.

A new toy model with interacting N agents is proposed in this paper. The agents in this model possess quantity, and have an interaction radius depending on the quantity. They exchange a part of the quantity with agents belonging to within their interaction radii. The cumulative distribution function about observing the quantity in a stationary state exhibits a power law, and the exponent is universally close to –1 if the density of agents is sufficiently small.

In this paper we will show the algebraic and graphic expressions, that were obtained through the Euler method and Lagrange interpolation by means of GeoGebra software for some linear second order differential equations. This teaching material was designed for the course of differential equations, and as a complement of support for the numerical calculation course for the engineering careers of the Universidad de Antofagasta.

In this paper we will show the visualization of the approximations that can be obtained by means of the order 1 spline method for Hermite differential equations with well-interactive examples of GeoGebra applets.

Here, we will dedicate ourselves to publisize, the great benefit that can be obtained, in the process of generating new mathematical knowledge for learning and teaching the numerical solutions of differential equations.

Let us consider $\frac{{d}^{2}y}{d{x}^{2}}+y=Q(x,a), y(0)=y(1)=0,x,a\in (0,1).$.

In the following paper, various differential equations will be displayed, which willbe solved using Galerkin's numericla method and where formal solutions and their numerical approximations can be seen with GeoGebra animated Apptles.

Spherical Bessel functions have many important applications in engineering, optic and science. In this work, wich is a continuation of the error function in fractional differential equations, it is shown how solve the fractional differential equation $\frac{{d}^{\alpha }y}{d{x}^{\alpha }}={j}_{0}(x),{y}^{(k)}(0)=0,k=0, \mathrm{...} m-1, \text{with}\, m-1\lt \alpha \le m, m\in {\rm N},$ where the nonhomogenous part is the function Bessel spherical J₀(x).

The paper examines the Fractional Fourier Transform (FRFT) based technique as a tool for obtaining the probability density function and its derivatives; and mainly for fitting stochastic model with the fundamental probabilistic relationships of infinite divisibility. The probability density functions are computed, and the distributional proprieties are reviewed for Variance-Gamma (VG) model. The VG model has been increasingly used as an alternative to the Classical Lognormal Model (CLM) in modelling asset prices. The VG model was estimated by the FRFT. The data comes from the SPY ETF historical prices. The Kolmogorov-Smirnov (KS) goodness-of-fit shows that the VG model fits better the cumulative distribution of the sample data than the CLM. The best VG model comes from the FRFT estimation.

A family of differential dynamic systems is considered on a real plane of their phase variables x, y. The main common feature of systems under consideration is: every particular system includes equations with polynomial right parts of the third order in one equation and of the second order in another one. These polynomials are mutually reciprocal, i.e., their decompositions into forms of lower orders do not contain common multipliers. The whole family of dynamic systems has been split into subfamilies according to the numbers of different reciprocal multipliers in the decompositions and depending on an order of sequence of different roots of polynomials. Every subfamily has been studied in a Poincare circle using Poincare mappings. A plan of the investigation for each selected subfamily of dynamic systems includes the following steps. We determine a list of singular points of systems of the fixed subfamily in a Poincare circle. For every singular point in the list, we use the notions of a saddle (S) and node (N) bundles of adjacent to this point semi trajectories, of a separatrix of the singular point, and of a topo dynamical type of the singular point (its TD – type). Further we split the family under consideration to subfamilies of different hierarchical levels with proper numbers. For every chosen subfamily we reveal topo dynamical types of singular points and separatrices of them. We investigate the behavior of separatrices for all singular points of systems belonging to the chosen subfamily. Very important are: a question of a uniqueness of a continuation of every given separatrix from a small neighborhood of a singular point to all the lengths of this separatrix, as well as a question of a mutual arrangement of all separatrices in a Poincare circle Ω. We answer these questions for all subfamilies of studied systems. The presented work is devoted to the original study. The main task of the work is to depict and describe all different in the topological meaning phase portraits in a Poincare circle, possible for the dynamical differential systems belonging to a broad family under consideration, and to its numerical subfamilies of different hierarchical levels. This is a theoretical work, but due to special research methods it may be useful for applied studies of dynamic systems with polynomial right parts. Author hopes that this work may be interesting and useful for researchers as well as for students and postgraduates. As a result, we describe and depict phase portraits of dynamic systems of a taken family and outline the criteria of every portrait appearance.

In this note, we study the action of the rational quantum Calogero-Moser system on polynomials rings. This a continuation of our paper [Ibrahim Nonkan 2021 J. Phys.: Conf. Ser. 1730 012129] in which we deal with the polynomial representation of the ring of invariant differential operators. Using the higher Specht polynomials we give a detailed description of the actions of the Weyl algebra associated with the ring of the symmetric polynomial C[x₁,..., x_n]^Sn on the polynomial ring C[x₁,..., x_n]. In fact, we show that its irreducible submodules over the ring of differential operators invariant under the symmetric group are its submodules generated by higher Specht polynomials over the ring of the symmetric polynomials. We end up studying the polynomial representation of the ring of differential operators invariant under the actions of products of symmetric groups by giving the generators of its simple components, thus we give a differential structure to the higher Specht polynomials.

In this note, we study the polynomial representation of the quantum Olshanetsky-Perelomov system for a finite reflection group W of type B_n. We endowed the polynomial ring C[x₁,..., x_n] with a structure of module over the Weyl algebra associated with the ring C[x₁,..., x_n]^W of invariant polynomials under a reflections group W of type B_n. Then we study the polynomials representation of the ring of invariant differential operators under the reflections group W. We make use of the theory of representation of groups namely the higher Specht polynomials associated with the reflection group W to yield a decomposition of that structure by providing explicitly the generators of its simple components.

In this note, we study the actions of rational quantum Olshanetsky-Perelomov systems for finite reflections groups of type D_n. we endowed the polynomial ring C[x₁,..., x_n] with a differential structure by using directly the action of the Weyl algebra associated with the ring C[x₁,..., x_n]^W of invariant polynomials under the reflections groups W after a localization. Then we study the polynomials representation of the ring of invariant differential operators under the reflections groups. We use the higher Specht polynomials associated with the representation of the reflections group W to exhibit the generators of its simple components.

In the present work, a method for magnetometer calibration through least squares fitting is presented. This method has been applied over the magnetometer's data set obtained during the integration tests of the Attitude Determination and Control Subsystem (ADCS) of UPMSat-2. The UPMSat-2 mission is a 50-kg satellite designed and manufactured by the Technical University of Madrid (Universidad Politécnica de Madrid), and finally launched in September 2020. The satellite has three fluxgate magnetometers (one of them experimental) whose calibration is critical to obtain correct measurements to be used by the ADCS. Among several mathematical methods suitable to obtain the calibration parameters, an ordinary least squares fitting algorithm is selected as a first step of the calibration process. The surface estimated is an ellipsoid, surface represented by the magnetometer's measures of the Earth magnetic field in a point of the space. The calibration elements of the magnetometers are related to the coefficients of the estimated ellipsoid.

This paper investigates smoke movement and its stratification in a lay-by of a 900 m long road tunnel by computer simulation using Fire Dynamics Simulator. The lay-by is located upstream of the fire in its vicinity. The influence of lay-by geometry on smoke spread is evaluated by comparison with a fictional tunnel without lay-by. Several fire scenarios with various tunnel slopes and heat release rates of fire in the tunnels without and with the lay-by are considered. The most significant breaking of smoke stratification and decrease of visibility in the area of the lay-by can be observed in the case of zero slope tunnel for more intensive fires with significant length of backlayering. Several other features of smoke spread in the lay-by are analysed as well. The parallel calculations were performed on a high-performance computer cluster.

In the present work, the effect of the friction forces at bearings on cup anemometer performance is studied. The study is based on the classical analytical approach to cup anemometer performance (2-cup model), used in the analysis by Schrenk (1929) and Wyngaard (1981). The friction torque dependence on temperature was modelled using exponential functions fitted to the experimental results from RISØ report #1348 by Pedersen (2003). Results indicate a logical poorer performance (in terms of a lower rotation speed at the same wind velocity), with an increase of the friction. However, this decrease of the performance is affected by the aerodynamic characteristics of the cups. More precisely, results indicate that the effect of the friction is modified depending on the ratio between the maximum value of the aerodynamic drag coefficient (at 0° yaw angle) and the minimum one (at 180° yaw angle). This reveals as a possible way to increase the efficiency of the cup anemometer rotors. Besides, if the friction torque is included in the equations, a noticeable deviation of the rotation rate (0.5-1% with regard to the expected rotation rate without considering friction) is found for low temperatures.

Let G be an graph simple, undirected, connected and unweighted graphs. The Reciprocal distance energy of a graph G is equal to the sum of the absolute values of the reciprocal distance eigenvalues. In this work, we find a lower bound for the Harary energy, reciprocal distance Laplacian energy and reciprocal distance signless Laplacian energy of a graph. Moreover, we find relationship between the Harary energy and Reciprocal distance Laplacian energies.

The distance between two vertices is equal to the number of edges on the shortest path connecting them. The Harary matrix of a simple, undirected, connected and unweighted graph of n vertices is an nonnegative matrix of order n, such that the (i, j)-entry is equal to the reciprocal distance between the vertices v_i and V_j if the vertices are different and zero if are equal. In this work we found bounds for the spectral radius of the Harary matrix of the join product of regular graphs.

Numerical Methods have attracted of research community for solving engineering problems. This interest is due to its practicality and the improvement of highspeed calculations done on current century processors. The increase in numerical method tools in engineering software, such as Matlab, is an example of the increased interest. In this paper, we are present a new improved numerical integration method, that is based on the well-known trapezoidal rule. The proposed method gives a great enhancement to the trapezoidal rule and overcomes the issue of the error value when dealing with some higher order functions even when solving for a single interval. After literature review, the proposed system is mathematically explained along with error analysis. Few examples are illustrated to prove improved accuracy of the proposed method over traditional trapezoidal method.

At the dawn of the research on waveguides the propagation by electrical conduction through transmission lines was compared with the general transmission theory of plane electromagnetic waves. After the invention of lasers we wonder whether the impedance concept can allow a seamless shift from the geometric rendering of received electromagnetic signals to the understanding of simple arguments on power transfer. Perhaps, the impedance concept could help noticing the occurrence of radiation-matter interactions and give hints as to how some phenomena could be enhanced by exposing matter to specific non-ionizing radiations.

The following offers a new axiomatic basis of mechanics and physics in their most important dynamics domain, i.e. a principle (axiom) of completeness intended to generalize Newton's second law of motion for the case of a non-stationary variable-mass point (system) that varies with time. This generalization leads to hyperdynamic dependencies describing such motion from new accurate qualitative standpoints.

Characterization of digital X-ray imaging devices is very important because it can be used to measure and compare the performance of detectors used in Diagnostic Radiology. This characterization is usually made through the calculation of Modulation Transfer Function (MTF), Noise Power Spectrum (NPS) and Detective Quantum Efficiency (DQE). These parameters, especially the DQE, are very important because they quantify the effect of spatial resolution, contrast and noise on Radiographic image quality (IQ). The IEC 62220-1-1:2015 International Standard provides comprehensive guidelines how to capture and analyze X-ray images to characterize digital X-ray detectors. A novel, fast and free MATLAB-based software was developed, named RAD_IQ, to calculate the Signal Transfer Property (STP), perform Noise Component Analysis (NCA), and calculate the parameters MTF, NPS & DQE of X-ray detectors based on the novel IEC 62220-1-1:2015 International Standard for General Radiography and IEC 62220-1-1:2007 for Digital Mammography. Our results were validated against well-established software products used for quantitative image analysis of digital X-ray detectors. The calculated parameters were within 5% difference compared to available software products. The conclusion of our study was that RAD_IQ can be easily used from Medical Physicists, Biomedical Engineers and researchers without any programming experience to characterize the performance of digital X-ray detectors used in Diagnostic Radiology.

In this work, we propose a modeling formulation and controller design for a class of hybrid dynamical systems. In this formulation, a switching dynamical system is modeled as a dynamical system with discontinuous right hand side. More specifically, the system is transformed to a nonlinear system with discontinuous nonlinearities. Then, a synthesis of feedback linearization and sliding mode control is employed for output tracking control problem. Application and implementation of this approach is illustrated via a chemical process example.

In the analysis of physical systems, the forces and mechanics of all system changes as codified in the Newtonian laws can be redefined by the methods of Lagrange and Hamilton through an identification of the governing action principle as a more general framework for dynamics. For the living system, it is the dimensional and relational structure of its biologic continuum (both internal and external to the organism) that creates the signature informational metrics and course configurations for the action dynamics associated with any natural systems phenomena. From this dynamic information theoretic framework, an action functional can be also derived in accordance with the methods of Lagrange. The experiential process of acquiring information and translating it into actionable meaning for adaptive responses is the driving force for changes in the living system. The core axiomatic procedure of this adaptive process should include an innate action principle that can determine the system's directional changes. This procedure for adaptive system reconciliation of divergences from steady state within the biocontinuum can be described by an information metric formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of the Kullback's Principle of Minimum Discrimination Information powered by the mechanics of survival replicator dynamics. This entropic driven trajectory naturally minimizes the biocontinuum information gradient differences like a least action principle and is an inference procedure for directional change. If the mathematical expression of this process is the Lagrangian integrand for adaptive changes within the biocontinuum, then it is also considered as an action functional for the living system.

Studies indicate the mass death of a significant number of biological groups on Earth, in particular - dinosaurs, at the end of the Cretaceous period 66 million years ago. Currently, there are two main theories: large-scale volcanic eruptions and the asteroid impact that formed the Chicxulub crater (Mexico). The production of sulfur-containing gases from the Earth's surface layers vapors during impact is considered a main source of climatic effects, as they form stratospheric sulfate aerosols that block sunlight and thus cool the Earth's atmosphere and interfere with photosynthesis. It is presented an application of the 3-D coupled global hydrodynamic climate model of intermediate complexity, including ocean model, sea ice evolution model and energy - moisture balance atmosphere model to study this asteroid impact effects on the Earth's climate. The model continents and ocean depths distribution corresponds to Cretaceous period. A series of calculations with different residence times and deposition times of the stratosphere aerosol have been carried out. It was found that, depending on the stratosphere aerosol time parameters, the global annual average surface air temperature decreased by 18°C - 27°C, remained below zero for 4 - 30 years, and a recovery time of more than 30 years was observed.

This paper describes the modelling and simulation of the Electrical Power Subsystem (EPS) of the Thermal Analysis Support and Environment Characterization Laboratory (TASEC-Lab). TASEC-Lab is a university experiment on board a sub-orbital platform. It is designed to measure the convection heat transfer in high-altitude balloon missions. The EPS provides, regulates, and distributes electric power to the different systems, parts, and sensors that compose the TASEC-Lab (e.g., On Board Computer (OBC), temperature and pressure sensors, cup anemometer, GPS, heaters... ). It mainly consists of a Li-ion battery and two DC-DC converters, and they have been characterized by conducting laboratory tests and fitting to experimental data. A real power consumption profile of the first TASEC-Lab's mission (designed by Universidad Politecnica de Madrid) is used as input to simulate the EPS. The mathematical model is validated by comparison with experimental results.

Considering constant development of the interior ballistics, along with new gun and ammunition designs, the necessity of in-depth analysis of the shot event is continuously increasing. Numerical simulations of interior ballistics problems are useful for optimising new designs or explaining complex issues, regarding performance instabilities and catastrophic failures. With the rise of the computing power, there is a significant urge to drive the numerical errors towards machine zero. This goal demands using methods of high order of accuracy in both space and time. Current methods allow to achieve an arbitrary order of numerical accuracy, thus allowing to shift the focus towards sophistication of the mathematical model of the studied phenomenon. Therefore, in this work, some numerical schemes, in context of finite volume method, are reviewed and studied using well established test problems. The results of the presented analysis are meant to become the basis for future development of a high order numerical scheme for simulation of interior ballistics problems.

Porosity and permeability are important properties of porous materials, such as rocks and concrete. This paper presents the physical-mathematical modelling of a novel test, based on one previously developed by one of the authors (standardized in Switzerland, Japan and China) for measuring the air-permeability of concrete structures. In the present case, a cylindrical specimen is placed inside an air-tight cell, subjected to an initial vacuum pressure P₀, which is afterwards isolated from the pump. The rate of pressure increase (due to the extraction of air originally at atmospheric pressure P_a) is related to the coefficient of permeability of the material whilst the final pressure attained is a function of the porosity (total amount of air extracted). The analysis assumes a unidirectional radial flow of air, which can be achieved by a special serial three-chamber vacuum cell (with pressure regulation of the external chambers) or by an air-tight sealing of the extreme faces of the cylinder. The analysis is developed under the assumption of viscous laminar flow. To account for the molecular diffusion flow, the test can be performed under vacuum (P₀ ≪ Pa) and under overpressure (P₀ ≫ P_a), enabling the application of the Klinkenberg correction to get the intrinsic coefficient of permeability.

In this investigation we propose several generalized first-order integral-boundary-layer (IBL) models to simulate the two-dimensional gravity-driven flow of a thin fluid layer down an incline. Various cases are considered and include: isothermal and non-isothermal flows, flat and wavy bottoms, porous and non-porous surfaces, constant and variable fluid properties, and Newtonian and non-Newtonian fluids. A numerical solution procedure is also proposed to solve the various model equations. Presented here are some results from our numerical experiments. To validate the generalized IBL models comparisons were made with existing results and the agreement was found to be reasonable.

It is presented a machine learning approach to find the optimal anisotropic SPH kernel, whose compact support consists of an ellipsoid that matches with the convex hull of the self-regulating k-nearest neighbors of the smoothing particle (query).

Attitude determination represents a fundamental task for most of the spacecrafts. It relies on three basic aspects: 1) sensors selection, 2) relevant environmental conditions estimation, and 3) algorithms that relate the sensor measurements to the expected conditions in the reference frame. Each one has its own impact on the accuracy that the system can achieve. Besides, two factors stand out above the others in terms of accuracy: 1) sensor quality (calibration, range, etc), and 2) precision of the environmental models. The computation of the satellite attitude needs at least two independent measurements (magnetometers, solar sensors...), whit their corresponding simulated measurements in the reference frame. Nevertheless, the number of measurements can be reduced to one if the satellite attitude is constrained. This paper describes a procedure to calculate satellites' attitude and the main environmental models used (Earth magnetic model, Sun position model, Albedo model), including orbit propagation. This methodology can be extended to measure the performance of a sensor if the satellite attitude can be derived from other measurements and satellite constrains. The methodology is checked with data from the UPMSat-2 mission (launched in September 2020 within the VEGA VV16 mission). This is a 50-kg satellite designed and developed at the Universidad Politécnica de Madrid (UPM).

We consider a class of abstract nonlinear wave equations with memory and linear dissipation. We give sufficient conditions in terms of the nitial data to prove the nonexistence of global solutions. We improve recent results that have studied this problem for viscoelastic wave, Kirchhoff and Petrovsky equations with positive initial energy values.

Energy conversion in nanosized devices is studied in the framework of state-space models. We use a network representation of the underlying master equation to describe the dynamics by a graph. Particular segments of this network represent input and output processes that provide a way to introduce a coupling to several heat reservoirs and particle reservoirs. In addition, the network representation scheme allows one to decompose the stationary dynamics as cycles. The cycle analysis is a convenient tool for analyse models of machine operations, which are characterized by different nanoscale energy conversion processes. By introducing the cycle affinity, we are able to calculate the zero-current limit. The zero-current limit can be mapped to the zero-affinity limit in a network representation scheme. For example, for systems with competing external driving forces the open-circuit voltage can be determined by setting the cycle affinity zero. This framework is used to derive open-circuit voltage with respect to microscopic material energetics and different coupling to particle and temperature reservoirs.

This article focuses on a mathematical description of the emotional phenomenon. The key concept is to consider emotions as an energy, and to rely on the analogy with the electromagnetic waves. Our aim is to provide a mathematical approach to characterize the emergence of emotional fluxes in the human psyche. This goes beyond classical pscychological approaches. In this setting, specific emotions correspond to specific frequencies and our psychic state results from the summation of different characteristic frequencies. Our general model of psychic state is a dynamical system whose evolution results from interactions between external inputs and internal reactions. The model provides both qualitative (frequencies) and quantitative (intensity) components. It aims to be applied to real life situations (in particular in work environments) and we provide a typical example which naturally leads to a problem of control.

The ability to accurately predict the operation of a particular mechanism and, on the basis of this, estimate the equipment life is a very important task. The amount of losses of the enterprise can depend on such study, as well as the health of many people whose lives depend on the health of the working installation. As part of this work, the main time series models were considered and the most suitable for the study was selected. The operation of a gas turbine was studied and a forecast was made. On the basis of the study, linear regression, ARIMA and moving average models were built and evaluated.

The article discusses topical issues of analysis of the state and improving the quality of management of the structure of fixed and working capital of enterprises of the petrochemical complex. Evaluation of indicators affecting the efficiency of their use made it possible to determine the directions for improving the process of forming the value of fixed and circulating assets of petrochemical enterprises. In conclusion, the authors highlight the successful practices of enterprise asset management.

The applications of multi-agent systems (MAS) are growing increasingly in the industrial field due to the advantages inherent to their characteristics and properties, the use of distributed automation architectures, which have satisfactorily solved control problems that its complexity and dynamic behavior have not been properly resolved with other approaches under these conditions, intelligent agents must meet the requirements of current automation systems, such as autonomy, flexibility, reconfiguration, in concurrent and collaborative systems, which traditionally do not have been designed to satisfy these characteristics. In the present work, a distributed architecture is proposed for the design of an intelligent agent in a Human-Machine Interface (HMI) for the supervision of the filtering stage of a water purification plant, characterized by the ability to collaborate with the other agents that make up the entire plant. For the projection and design of the system, the Unified Modeling Language (UML) and Petri nets (PN) are used for the simulation and validation of the system, and the implementation of the agent from macros in C language, starting from a methodology of multi-agent design that is applied in this document. The implementation of the intelligent agent in an HMI associated with multi-agent architecture, which allowed to evaluate its behavior through the analysis of the properties of the PN and experimental tests, demonstrating the correct operation of the device, response times and its dynamic behavior based on of the functional requirements of the water purification plant and comparisons with similar works.

An approach guided by physical consistency in determining the general forms of D-dimensional kinetic energy density functionals (KEDF) has been demonstrated previously, producing an expansion which contains the majority of the known one-point KEDF forms. It is known that any noninteracting KEDF shall necessarily have a homogeneity degree of 2 in coordinate scaling. This paper demonstrates that this condition is already satisfied in the general expansion despite not being conceived with the scaling as a constraint.

The rapid development of Information and Communication Technologies (ICT) and high-capacity hardware components make it necessary to achieve a strong integration of automatic systems based on new paradigms on intelligent distributed architectures, where require highly complex supervision and control tasks, due to the generated requirements of the new production systems, the high number of variables to control and the advancement of technologies, especially in industries where continuous processes have been established. In the present work, a distributed hierarchical modular architecture is proposed for a supervision system, based on multi-agent systems (MAS), oriented to the management of processes in the filtration stage of a water purification plant, using a methodology to the implementation of intelligent agents that allow to project, design, verify and validate the system. This methodology is fundamentally based on the use of the Unified Modeling Language (UML) for its projection and Petri nets (PN) for the simulation and validation of properties, which allows to guarantee the modularity, flexibility, and robustness of the proposed system. The architectures of the intelligent agents in the different programmable devices are modeled and simulated to achieve an adequate interaction and collaboration, allowing to reduce the conflicts that may be generated between them. The evaluation of the distributed architecture focuses on the fulfillment of the functional requirements and evaluation metrics, which, through the analysis of the properties of the Petri net, allows to determine the correct operation of the system and its dynamic behavior in the face of unforeseen situations at different levels of automation.

The impact of the generalized pattern search algorithm (GPSA) on power system complete observability utilizing synchrophasors is proposed in this work. This algorithmic technique is an inherent extension of phasor measurement unit (PMU) minimization in a derivative-free framework by evaluating a linear objective function under a set of equality constraints that is smaller than the decision variables in number. A comprehensive study about the utility of such a system of equality constraints under a quadratic objective has been given in our previous paper. The one issue studied in this paper is the impact of a linear cost function to detect optimality in a shorter number of iterations, whereas the cost is minimized. The GPSA evaluates a linear cost function through the iterations needed to satisfy feasibility and optimality criteria. The other issue is how to improve the performance of convergence towards optimality using a gradient-free mathematical algorithm. The GPSA detects an optimal solution in a fewer number of iterations than those spent by a recursive quadratic programming (RQP) algorithm. Numerical studies on standard benchmark power networks show significant improvement in the maximum observability over the existing measurement redundancy generated by the RQP optimization scheme already published in our former paper.

Modern trends towards the expansion of online services lead to the need to determine the location of customers, who may also be on a moving object (vessel or aircraft, others vehicle – hereinafter the "Vehicle"). This task is of particular relevance in the fields of medicine – when organizing video conferencing for diagnosis and/or remote rehabilitation, e.g., for post-infarction and post-stroke patients using wireless devices, in education – when organizing distance learning and when taking exams online, etc. For the analysis of statistical materials of the accuracy of determining the location of a moving object, the Gaussian normal distribution is usually used. However, if the histogram of the sample has "heavier tails", the determination of latitude and longitude's error according to Gaussian function is not correct and requires an alternative approach. To describe the random errors of navigation measurements, mixed laws of a probability distribution of two types can be used: the first type is the generalized Cauchy distribution, the second type is the Pearson distribution, type VII. This paper has shown that it's possible obtaining the decomposition of the error distribution density using orthogonal Hermite polynomials, without having its analytical expression. Our numerical results show that the approximation of the distribution function using the Gram-Charlier series of type A makes it possible to apply the orthogonal decomposition to describe the density of errors in navigation measurements. To compare the curves of density and its orthogonal decomposition, the density values were calculated. The research results showed that the normalized density and its orthogonal decomposition practically coincide.

A tree is a connected acyclic graph. A tree is called a starlike if exactly one of its vertices has degree greater than two. Let λι be the largest eigenvalue of the adjacency matrix of a starlike tree. In this work, we obtain a lower bound for the spectral radius of a starlike tree. This bound only depends of the maximum degree of the vertices.

The energy graph was defined by Gutman, in 1978, as the sum of the absolute values of the eigenvalues of the adjacency matrix. In this work, we obtain a upper bound for the energy of a starlike tree. This bound is obtained in function of the number of vertices and the maximum degree of the vertices.

The article presents the results of the high-speed camera test of newly developed igniter's charges for artillery rounds. The test was performed to take a closer look at the ignition process of mixtures, that is, to check the time-to-ignition of samples, and to assess the presence and quantity of solid igniting particles (if any). Five compositions were tested: Three of them contained the new igniter's charges developed by the Military Institute of Armament Technology, and the other two contained black powder in different granularity classes as a comparison mixture. This article presents the collated test results.

The choice of material, type of braid and rope parameters are a broad issue of great importance in the designing process. An equally important issue is the proper selection of knot type used for attaching the rope to the other elements of a structure, as this is a critical point accumulating major stresses. Inappropriate tying of a rope may decrease its tensile strength by over 50%; therefore, it is an important issue in terms of structural strength. This article investigates different tying configurations of the same rope and shows the influence of knot types on rope static tensile strength.

In this paper, we consider the generalized fractional Volterra integro-differential equations with the regularized Prabhakar derivative and represent the solution of this type of equations in the form of Bromwich integral in the complex plane. Then we select the hyperbolic contour as an optimal contour to approximate the Bromwich integral. Further, an example to show absolute errors for various parameters by using our numerical scheme on hyperbolic contour is given.

We have implemented the basic steps for the FDK backprojecting algorithm in computed tomography. Application works from the set of preloaded projections and uses OpenCV libraries for FFT, convolution, frequency space image filtering, image's brightness, contrast and quality manipulation. Compared to the desktop implementation, the calculation-intensive part of the application was moved to the asynchronous background task hosted by an android fragment. This allows the task to survive the application's configuration changes and to run in the background even if the main activity was destroyed. The minimalistic interface with the access to all main backprojecting parameters was implemented. The result of backprojection is saved as an image in the download folder of the phone. The user also has the control over the reconstructed slice location along the Z axis.

A banyan-type network is a switching network, which is constructed by placing unit switches with two inputs and two outputs in s (s > 1) stages. In each stage, 2^{n – 1} (n > 1) unit switches are aligned. Past studies conjecture that this network becomes rearrangeable when s ≥ 2n-1. Although a considerable number of theoretical analyses have been done, the rearrangeability of the banyan-type network with 2n – 1 or more stages is not completely proved. As a tool to assess the rearrangeability, this study presents a CNF-SAT (conjunctive normal form - satisfiability) modelling scheme for banyan-type networks. In the proposed scheme, the routing is formulated to a SAT problem represented in CNF. By feeding the problem to a SAT solver, it is found whether the problem is satisfiable or unsatisfiable. If the problem is unsatisfiable for a certain request, the network is not rearrangeable. By contrast, if the problem is satisfiable for any requests, the network is rearrangeable. This study applies the CNF-SAT modelling scheme to various configurations of 2n – 1 stage banyan-type networks. These networks are assessed for rearrangeability by solving the SAT problems. The proposed method will be helpful to conduct future theoretical studies on banyan-type networks.

In this paper, we discuss when the solution to the initial value problem for a linear matrix time-varying differential equation is symmetric on a given interval. By symmetry, we mean that the solution does not change when transposed. Throughout the paper, we assume that the equation has coefficients of finite order of smoothness. We demonstrate that, in order to verify whether the solution to the initial value problem is symmetric on a given interval, it can be useful to construct two matrix sequences associated to the equation. Using these sequences, we prove a sufficient condition for the solution symmetry on a given interval. Assuming that the initial value problem for a linear matrix time-varying differential equation satisfies this condition, we derive a formula for a symmetric solution to this problem.

The execution of the so-called extinction tests represents the classical experimental method used to estimate the damping of an oscillatory system. For the specific case of ship roll motion, the roll decay tests are carried out at model-scale in a hydrodynamic basin. During these tests, the vessel is posed in an imbalance condition by an external moment and, after the release, the motion decays to the equilibrium condition. When the damping is far below the critical one, the transient decay is oscillatory. Here a new methodology is presented to determine the damping coefficients by fitting the roll decay curves directly, using a least-square fitting through a differential evolution algorithm of global optimisation. The results obtained with this methodology are compared with the predictions from standard methods. This kind of approach seems to be very promising when the motion model of the system under investigation is established with any level of non-linearities included. The usage of the fitting procedure on the approximate analytic solution of the differential equation of motion demonstrates the flexibility of the method. As a benchmark example, two experimentally measured roll extinction curves have been considered and suitably fitted. The newly predicted results, compared with the ones obtained from standard roll decay analysis, show that the algorithm is capable to perform a good regression on the experimental data.

Surface charges accumulating on dielectrics during long-time operation of Gas Insulated High Voltage Direct Current (HVDC-GIS) equipments may affect the stable operation and could possibly trigger surface flashovers. In industrial applications, to quantify and identify the location of the surface charge accumulation from experimental measurements, the surface potential distribution is evaluated using, e.g., electrostatic probes, then the charge density is determined by solving an electrostatic problem based on an inversion procedure known as Charge Inversion Algorithm. The major practical limitation of such procedure is the inversion and the storage of the fully dense matrix arising from the representation via Integral Equations of the electrostatic phenomenon, resulting in O(N³) computational complexity and O(N²) memory requirement. In this paper it is shown how hierarchical matrices can be efficiently used to accelerate the charge inversion algorithm and, more importantly, reduce the overall memory requirement.

In this paper, a comparison between two current-based Integral Equations approaches for eddy current problems is presented. In particular, the very well-known and widely adopted loop-current formulation (or electric vector potential formulation) is compared to the less common J-φ formulation. Pros and cons of the two formulations with respect to the problem size are discussed, as well as the adoption of low-rank approximation techniques. Although rarely considered in the literature, it is shown that the J-φ formulation may offer some useful advantages when large problems are considered. Indeed, for large-scale problems, while the computational efforts required by the two formulations are comparable, the J-φ formulation does not require any particular attention when non-simply connected domains are considered.

Mathematical models of phase behavior are widely used to describe multiphase oil and gas-condensate systems during hydrocarbon recovery from natural petroleum reservoirs. Previously a non-equilibrium phase behavior model was proposed as an extension over generally adopted equilibrium models. It is based on relaxation of component chemical potentials difference between phases and provides accurate calculations in some typical situations when non-instantaneous changing of phase fractions and compositions in response to variations of pressure or total composition is to be considered. In this paper we present a thermodynamic analysis of the relaxation model. General equations of non-equilibrium thermodynamics for multiphase flows in porous media are considered, and reduced entropy balance equation for the relaxation process is obtained. Isotropic relaxation process is simulated for a real multicomponent hydrocarbon system with different values of characteristic relaxation time using the non-equilibrium model implemented in the PVT Designer module of the RFD tNavigator simulation software. The results are processed with a special algorithm implemented in Matlab to calculate graphs of the total entropy time derivative and its constituents in the entropy balance equation. It is shown that the constituents have different signs, and the greatest influence on the entropy is associated with the interphase flow of the major component of the mixture and the change of the total system volume in the isotropic process. The characteristic relaxation time affects the rate at which the entropy is approaching its maximum value.

Inverse problem solution is an integral part of data interpretation for well testing in petroleum reservoirs. In case of two-phase well tests with water injection, forward problem is based on the multiphase flow model in porous media and solved numerically. The inverse problem is based on a misfit or likelihood objective function. Adjoint methods have proved robust and efficient for gradient calculation of the objective function in this type of problems. However, if time-lapse electrical resistivity measurements during the well test are included in the objective function, both the forward and inverse problems become multiphysical, and straightforward application of the adjoint method is problematic. In this paper we present a novel adjoint algorithm for the inverse problems considered. It takes into account the structure of cross dependencies between flow and electrical equations and variables, as well as specifics of the equations (mixed parabolic-hyperbolic for flow and elliptic for electricity), numerical discretizations and grids, and measurements in the inverse problem. Decomposition is proposed for the adjoint problem which makes possible step-wise solution of the electric adjoint equations, like in the forward problem, after which a cross-term is computed and added to the right-hand side of the flow adjoint equations at this timestep. The overall procedure provides accurate gradient calculation for the multiphysical objective function while preserving robustness and efficiency of the adjoint methods. Example cases of the adjoint gradient calculation are presented and compared to straightforward difference-based gradient calculation in terms of accuracy and efficiency.

In this study, we are to present that a one-dimensional equation for vertically averaged temperature, modeled on a vertically thin, two-dimensional heat exchanger with variable top solid-fluid interface, recovers the two-dimensional thermal information, i.e. steady temperature and flux distribution on the top and temperature-fixed bottom faces. The relative error of these quantities is less than 5% with the maximum gradient of the height kept approximately below 0.5, while the computational time is reduced to 0.1–5%, when compared with direct two-dimensional computations, depending on the shape of the top face. The model equation, derived by the vertical averaging of the two-dimensional thermal conduction equation, is closed by an approximation that the heat exchanger is sufficiently thin in the sense that the second derivative of temperature with respect to the horizontal coordinate depends only on the coordinate. In this model equation, the fluid equation above the exchanger is decoupled by a conventional equation for the normal heat flux on the top surface. In principle, however, the coupling of the model and the fluid equation is possible through the temperature and heat flux on the top interface, recovered by the model equation. The type of mathematical modeling can be applicable to a wide variety of bodies with extremely small dimensions in some (coordinate-transformed) directions.

Representation of wells in numerical simulation of petroleum reservoirs is a challenging task due to large difference in typical scales of grid blocks (tens to hundreds meters) and wells (~0.1 m), with high pressure and saturation gradients around wells. Although a variety of grid refinement techniques can be used for local simulations, they have limited application in field-scale problems due to huge model dimensions. Thus, auxiliary quasi-stationary local solutions (so-called inflow performance relations) are used to relate well flow rate with well and grid block pressures. These auxiliary solutions are strictly derived for linear cases and generalized to non-linear problems by using grid-block averaged values of fluid and reservoir properties. In the case of hot water injection for heavy oil recovery, this results in significant errors in well injectivity calculations due to large temperature and saturation gradients dynamically influencing viscosity and relative permeability distributions around the well. In this paper we propose a method which combines a semi-analytical solution of the hyperbolic Entov-Zazovsky problem for non-isothermal oil displacement with integration for pressure distribution taking into account nonlinear dependencies of fluid viscosities and relative permeabilities on temperature and saturations. Both constant injection rate and constant well pressure cases are considered. Example calculations demonstrate that the method helps to avoid underestimation of well injectivity in non-isothermal problems caused by grid-block averaging of fluid and reservoir properties in conventional inflow performance relations.

The advection-diffusion-reaction equation is used for describing the dispersion of a quasi-passive contaminant from industrial point sources in a limited area. The conditions established on the open boundary ensure that the problem is correct in the sense of Hadamard, that is, its solution exists, is unique, and is stable to initial perturbations. The Lagrange identity is used to construct the adjoint operator and formulate an adjoint problem. Equivalent direct and adjoint estimates are derived to assess the concentration of the pollutant at monitoring sites of the area. Formulas obtained on the basis of adjoint estimates are useful in analysing the sensitivity of the model to both variations in the intensity of pollution sources and variations in the initial distribution of the pollutant concentration in the area. New optimal emission control strategies based on using the adjoint estimates are developed in order to prevent violations of existing sanitary standards by timely reduction of emission rates of operating sources. Optimal control here lies in minimizing these reductions. In addition, this control is primarily aimed at reducing the intensity of emissions from sources that most pollute the monitoring site. Also, new methods are proposed for identifying the main parameters of an unknown point source that arose as a result of a dangerous incident (accident, explosion, etc.). These methods allow determining the location and intensity of a constant or non-stationary point source, as well as the moment of emission of a pollutant in the case of an instantaneous point source. This helps to quickly assess the scale of the incident and its consequences. Numerical results show the effectiveness of the methods.

The real capacitors' behaviour in electric circuits modelled by a single capacity deviates from the ideal one. In order to find better compromises between precision and simplicity, different C-R-L models are used. In these models, C, R, L are called equivalent parameters and take constant values. Under these assumptions, the capacitors are modelled as lumped parameter subsystems although it is well known that the real capacitors are essentially distributed parameter systems. As highlighted in this paper, the capacitors are also time-variant subsystems. To prove this, we use two types of experimental data: data measured during the capacitor's discharge process and data obtained from frequency characteristics. The article proposes two estimation methods of equivalent values for the model parameters C and R based on their time variance highlighted by the experimental data. The estimation methods use a system of equations associated with the discharging of capacitors, respectively, with the frequency characteristics via polynomial regression. The experiments were carried out with an electrolytic polymer capacitor rated 220 μF, 25 V, 2.5 A rms, 85 °C, designed mainly for energy storage and filtering, the results being confirmed by experiments performed on other similar capacitors.

This study presents the impact of seasonal variation in air density on the operating tip-speed ratio of small wind turbines. The air density, which varies depending on the temperature, atmospheric pressure, and relative humidity, has an annual amplitude of about 5% in Tokyo, Japan. This study quantified this impact using the rotational speed equation of motion in a small wind turbine informed by previous work. This governing equation has been simplified by expanding the aerodynamic torque coefficient profile for a wind turbine rotor to the tip-speed ratio. Furthermore, this governing equation is simplified by using nondimensional forms of the air density, inflow wind velocity, and rotational speed with their characteristic values. In this study, the generator's load is set to be constant based on a previous analysis of a small wind turbine. By considering the equilibrium between the aerodynamic torque and the load torque of the governing equation at the optimum tip-speed ratio, the impact of the variation in the air density on the operating tip-speed ratio was expressed using a simple mathematical form. As shown in this derived form, the operating tip-speed ratio was found to be less sensitive to a variation in air density than that in inflow wind velocity.

This study presents the impact of the difference between the implicit and explicit time integration methods on a steady turbulent flow field. In contrast to the explicit time integration method, the implicit time integration method may produce significant kinetic energy conservation error because the widely used spatial difference method for discretizing the governing equations is explicit with respect to time. In this study, the second-order Crank-Nicolson method is used as the implicit time integration method, and the fourth-order Runge-Kutta, second-order Runge-Kutta and second-order Adams-Bashforth methods are used as explicit time integration methods. In the present study, both isotropic and anisotropic steady turbulent fields are analyzed with two values of the Reynolds number. The turbulent kinetic energy in the steady turbulent field is hardly affected by the kinetic energy conservation error. The rms values of static pressure fluctuation are significantly sensitive to the kinetic energy conservation error. These results are examined by varying the time increment value. These results are also discussed by visualizing the large scale turbulent vortex structure.

In this work, we consider the inverse source recovery problem from sEEG, EEG and MEG point-wise data. We regard this as an inverse source recovery problem for L² vector-fields normally oriented and supported on the grey/white matter interface, which together with the brain, skull and scalp form a non-homogeneous layered conductor. We assume that the quasistatic approximation of Maxwell's equation holds for the electro-magnetic fields considered. The electric data is measured point-wise inside and outside the conductor while the magnetic data is measured only point-wise outside the conductor. These ill-posed problems are solved via Tikhonov regularization on triangulations of the interfaces and a piecewise linear model for the current on the triangles. Both in the continuous and discrete formulation the electric potential is expressed as a linear combination of double layer potentials while the magnetic flux density in the continuous case is a vector-surface integral whose discrete formulation features single layer potentials. A main feature of our approach is that these contributions can be computed exactly. Due to the consideration of the regularity conditions of the electric potential in the inverse source recovery problem, the Cauchy transmission problem for the electric potential is inadvertently solved as well. In the problem, we propagate only the electric potential while the normal derivatives at the interfaces of discontinuity of the electric conductivities are computed directly from the resulting solution. This reduces the computational complexity of the problem. There is a direct connection between the magnetic flux density and the electrical potential in conductors such as the one we explore, hence a coupling of the sEEG, EEG and MEG data for solving the respective inverse source recovery problems simultaneously is direct. We treat these problems in a unified approach that uses only single and/or double layer potentials. We provide numerical examples using realistic meshes of the head with synthetic data.

After being introduced to approximate two-dimensional geographical surfaces in 1971, the multivariate radial basis functions (RBFs) have been receiving a great amount of attention from scientists and engineers. Over decades, RBFs have been applied to a wide variety of problems. Approximation, interpolation, classification, prediction, and neural networks are inevitable in nowadays science, engineering, and medicine. Moreover, numerically solving partial differential equations (PDEs) is also a powerful branch of RBFs under the name of the 'Meshfree/Meshless' method. Amongst many, the so-called 'Generalized Multiquadric (GMQ)' is known as one of the most used forms of RBFs. It is of (ɛ² + r²)^β form, where r = ║x-x^Θ║₂ for x, x^Θ ∈ ⁿ represents the distance function. The key factor playing a very crucial role for MQ, or other forms of RBFs, is the so-called 'shape parameter ɛ' where selecting a good one remains an open problem until now. This paper focuses on measuring the numerical effectiveness of various choices of ɛ proposed in literature when used in image reconstruction problems. Condition number of the interpolation matrix, CPU-time and storage, and accuracy are common criteria being utilized. The results of the work shall provide useful information on selecting a 'suitable and reliable choice of MQ-shape' for further applications in general.

The great interest about out of plane behavior of masonry infill walls has recently increased since it is a key point in the seismic modelling of framed structures. Their contribute to the whole seismic resistance of a framed building cannot be skipped. After a review of the literature on the subject, this paper presents a trilinear constitutive model for the out of plane behavior of masonry infills based on the tensile strength of the constituents. Comparisons with literature model are provided and the identification of the model is based on experimental tests.

The most important meteorological data are:ambient temperature, precipitation quantity, air humidity, amount and type of clouds, atmospheric pressure, wind direction and speed, visibility, weather phenomena. These coefficients impact the effectiveness of various combat activities, especially those conducted in an open space. Knowledge of future weather conditions is essential for planning the location, calculating times, choice of means, and other aspects relevant to the upcoming operations. Taking weather conditions into account is vital, specifically when it comes to planning combat operations, where the accuracy in cooperation is of paramount importance. Rocket forces and artillery is a particular type of armed forces where weather conditions are critical. The effectiveness of artillery depends on ballistic calculation precision, and so knowledge of atmospheric conditions is fundamental. Atmospheric data are collected from sounding using a single probe attached to a balloon. It is generally known that particular meteorological parameters change in a smooth spatial manner depending on various coefficients. Information about the atmosphere collected by a single probe may be insufficient, due to the possibility of a balloon drifting away from the area of interest, and the calculations are based on data received from its probe. In this paper, I will suggest a method for preparing artillery use meteorologically, which takes into account the distribution of particular meteorological coefficients over a given area.

An analytical method using Green's Functions for obtaining solutions in bio-heat transfer problems, modeled by Pennes' Equation, is presented. Mathematical background on how treating Pennes' equation and its μ²T term is shown, and two contributions to the classical numbering system in heat conduction are proposed: inclusion of terms to specify the presence of the fin term, μ²T, and identify the biological heat transfer problem. The presentation of the solution is made for a general multi-layer domain, deriving and showing general approaches and Green's Functions for such n number of layers. Numerical examples are presented to simplify human skin as a two-layer domain: dermis and epidermis, accounting metabolism as a heat source, and blood perfusion only at the dermis. Time-independent summations in the series-solution are written in closed forms, leading to better convergence along the boundaries. Details on obtaining the two-layer solution and its eigenvalues are presented for boundary conditions of prescribed temperature inside the body and convection at the surface, such as its intrinsic verification.

The parity violation in nuclear reactions led to the discovery of the new class of toroidal multipoles. Since then, it was observed that toroidal multipoles are present in the electromagnetic structure of systems at all scales, from elementary particles, to solid state systems and metamaterials. The toroidal dipole T (the lowest order multipole) is the most common. This corresponds to the toroidal dipole operator $\hat{T}$ in quantum systems, with the projections ${\hat{T}}_{i}$ (i = 1, 2, 3) on the coordinate axes. These operators are observables if they are self-adjoint, but, although it is commonly discussed of toroidal dipoles of both, classical and quantum systems, up to now no system has been identified in which the operators are self-adjoint. Therefore, in this paper we use what are called the "natural coordinates" of the ${\hat{T}}_{3}$ operator to give a general procedure to construct operators that commute with ${\hat{T}}_{3}$. Using this method, we introduce the operators ${\hat{p}}^{(k)}, {\hat{p}}^{(k1)}$, and ${\hat{p}}^{(k2)}$, which, together with ${\hat{T}}_{3}$ and ${\hat{L}}_{3}$, form sets of commuting operators: $({\hat{p}}^{(k)}, {\hat{T}}_{3,} {\hat{L}}_{3})$ and $({\hat{p}}^{(k1)}, {\hat{p}}^{(k2)}, {\hat{T}}_{3})$. All these theoretical considerations open up the possibility to design metamaterials that could exploit the quantization and the general quantum properties of the toroidal dipoles.

Diabetes is the eight-cause death worldwide. The cause of death of patients with diabetes is mostly the long-term complications, that are not easy to detect opportunely. In previous studies, we applied photoacoustic spectroscopy (PAS), a non-destructive technique, to detect several components of blood. The goal of the study was to apply the phase-resolved method (PRM), on blood optical absorption spectra obtained by PAS, to analyse blood components in experimental type 1 diabetes. Diabetes was produced in male Wistar rats through the administrations of streptozotocin (STZ). Venous blood samples were obtained one, two, four and eight weeks after STZ. PRM applied to spectra allowed to detect p450 cytochrome. There was a significant and positive correlation between glycaemia and p450 cytochrome (p=0.001). Since p450 cytochrome participates in detoxification function, results indicate that glycaemia could affect detoxification. It will be important in future studies to study the implications of those results on the development of diabetes complications. The novelty of the study was to use PAS to find out if there was any correlation between spectroscopy variables and glycaemia. It is concluded that PRM applied to PAS is a suitable technology to study p450 cytochrome in diabetes.

In this work we have considered the study of the exchange rate series for the specific case where the formal financial market is not active. In those situations, we would be interested in the parallelization of the exchange rate with financial indexes for stabilized financial market. We observed that the stationarity of the distribution for some the exchange rate of currencies traded in the country differs significantly. The time dynamics shows the presence of the elements of local critical behavior, but those tendencies attenuate and fade away in an a periodic fashion. Next, we considered and evidenced the correlation distances and dissimilarity between exchange rates of national currencies versus euro and dollar and golden prices. It resulted that two exchange rates do have different distance from golden price taken for references. The correlation distance between the series of the return in different period has evidenced that there is not a regular behavior in this respect.

The article discusses the influence of geometric parameters (the presence and magnitude of the radius of curvature) at the junction of the toneholes with the main bore of the air column on the frequency characteristics of woodwind musical instruments. A theoretical calculation of the eigenfrequencies of an air column with one tonehole in the case of sharp edges has been carried out. The resonance frequencies were also found using computer simulation in the COMSOL Multiphysics 5.5 program for the case of sharp edges and joints with a radius of curvature. An empirical dependence of the frequency of the main tone of the air column on the radius of curvature of the edges of the tonehole is obtained. All simulation were carried out for two models: excluding and including viscous drag and thermal exchange losses.

Hybrid modeling, the combination of first principle and machine learning models, is an emerging research field that gathers more and more attention. Even if hybrid models produce formidable results for academic examples, there are still different technical challenges that hinder the use of hybrid modeling in real-world applications. By presenting NeuralFMUs, the fusion of a Functional Mock-up Unit (FMU), a numerical ODE solver and an artifical neural network, we are paving the way for the use of a variety of first principle models from different modeling tools as parts of hybrid models. This contribution handles the hybrid modeling of a complex, real-world example: Starting with a simplified 1D-fluid model of the human cardiovascular system (arterial side), the aim is to learn neglected physical effects like arterial elasticity from data. We will show that the hybrid modeling process is more comfortable, needs less system knowledge and is therefore less error-prone compared to modeling solely based on first principle. Further, the resulting hybrid model has improved in computation performance, compared to a pure first principle white-box model, while still fulfilling the requirements regarding accuracy of the considered hemodynamic quantities. The use of the presented techniques is explained in a general manner and the considered use-case can serve as example for other modeling and simulation applications in and beyond the medical domain.

Nowadays, the active safety systems that control the dynamics of passenger cars usually rely on real-time monitoring of vehicle side-slip angle (VSA). The VSA can't be measured directly on the production vehicles since it requires the employment of high-end and expensive instrumentation. To realiably overcome the VSA estimation problem, different model-based techniques can be adopted. The aim of this work is to compare the performance of different model-based state estimators, evaluating both the estimation accuracy and the computational cost, required by each algorithm. To this purpose Extended Kalman Filters, Unscented Kalman Filters and Particle Filters have been implemented for the vehicle system under analysis. The physical representation of the process is represented by a single-track vehicle model adopting a simplified Pacejka tyre model. The results numerical results are then compared to the experimental data acquired within a specifically designed testing campaign, able to explore the entire vehicle dynamic range. To this aim an electric go-kart has been employed as a vehicle, equipped with steering wheel encoder, wheels angular speed encoder and IMU, while an S-motion has been adopted for the measurement of the experimental VSA quantity.

Interferometric gravitational wave detectors (IGWD) are a very complex detector, the need to lock the detector in a dark fringe condition besides the vibrations that affect the mirrors, creates the necessity of using active suspension systems. These active systems make the system reach the desired sensitivity but make the calibration of such detectors much more difficult. To solve this problem a calibrator is proposed, a resonant mass gravitational wave detector could be used to detect the same signal in a narrower band and use the measured amplitude to calibrate the IGWD, as resonant mass gravitational wave detectors are easily calibrated. This work aims to design the mechanical antenna of such a calibrator. The main difficulty is to design the calibrator is the frequencies required to make the detection. These massive detectors usually were made in frequencies close to 1 kHz and the frequency range to operate for better sensitivity is around 100 Hz. The antenna is modelled in finite elements method and a design of such an antenna is presented.

Interferometric gravitational wave detectors (IGWD) are a very complex detector, the need to lock the detector in a dark fringe condition besides the vibrations that affect the mirrors, creates the necessity of using active suspension systems. These active systems make the system reach the desired sensitivity but make the calibration of such detectors much more difficult. To solve this problem a calibrator is proposed, a resonant mass gravitational wave detector could be used to detect the same signal in a narrower band and use the measured amplitude to calibrate the IGWD, as resonant mass gravitational wave detectors are easily calibrated. This work aims to obtain the expected sensitivity of such a calibrator by using lumped modelling in such mechanical detectors. The calibrator is modelled as a spring mass system and the sensitivity curve is presented calculated in by a matlab program. The curve shows that using state of art parameters for the detector the final sensitivity is close to the quantum limit and can be used to calibrate the IGWDs.

Within the spectrum of radio waves, the Ku band (12 - 18 GH_z) stands out for the wide range of instruments available and for its relative ease of acquisition, given that satellite television operates in this band. This situation offers a great opportunity for the development of radio astronomy in countries with unfavorable climatic conditions for optical astronomy, since this band is only affected by dense masses of water vapor. In this article we present a methodology for the calibration of the receiver system of compact Ku-band radio telescopes, and its application in the determination of the brightness temperature of the Moon. Our methodology involves modeling the influence of the atmosphere of the Earth on the response of the radioreceptor, which minimizes the error in the calculation of the brightness temperature of the observed object. We applied the proposed methodology in the monitoring of the Lunar cycle using the Ku-band radio telescope of the Observatorio Astronomico of Universidad Tecnológica de Pereira, Colombia (OAUTP). After observing during May, June, and July of 2021, we obtained an average temperature of 213.15 K, with maximum and minimum values of 275.55 K and 150.75 K, respectively. In addition, we evidenced a delay of 5.75 days between the phase in which the maximum temperature is presented and the phase of the full Moon, which is consistent with the frequency of observation. The results show that our methodology is useful to optimize the calibration of compact Ku-band radio telescopes, and expand the potential of this type of instrument for the scientific study of radio sources other than the Sun, in this case the Moon.

An experiment to measure the speed of gravitational signals in short distances has been developed with the intention to study its behavior when a medium different from air is allocated between the emitter and the detection and check if the speed of the interaction changes. The experiment is composed of three sapphire bars that vibrates, and as they vibrate its creates a tidal gravitational wave signal that interacts with another sapphire bar, this bar is monitored by a very pure microwave signal and its amplitude and phase are measured and the gravity speed is calculated, all system is cooled to a temperature of 4.2 K to increase sensitivity and kept in high vacuum. The sapphire bar needs to be suspended to avoid seismic noise and other interference. This work models the sapphire bar with the suspension, a wire that suspends the bar by its center and has its performance calculated in a finite element modelling. The final result shows that the mechanical behavior of the sapphire bar is not affected by the suspension.

The resonant-mass gravitational wave detector SCHENBERG is a spherical detector that operates with a central frequency close to 3200 Hz and a bandwidth around 200 Hz. It has a spherical mass that works as an antenna whose weight is 1150 kg and is connected to the outer environment by a suspension system designed to attenuate local noise due to seism as well as other sources; the sphere is suspended by its center of mass. When a gravitational wave passes by the detector, the antenna is expected to vibrate. This motion should be monitored by six parametric microwave transducers whose output signals will be digitally analyzed. In order to determine the detector performance better, it is necessary to obtain the vibration frequencies of the sphere with a better precision. To achieve such a goal the sphere with the holes to mount the transducers and the central hole from which the sphere is suspended is simulated in a finite element method program when the gravity is applied to the sphere and the deformation is kept. After that the vibration normal modes of the sphere are calculated and they are compared to the experimental results.

In the world today, civil infrastructure plays a major role in the advancement of the modern age. They are huge in scale, complex in their behaviour and create great impact in everyday life. To ensure safety of these structures, assessment of their structural integrity is an important and challenging task. The sole purpose of structural health monitoring is to detect damage in the structures and suggest suitable rehabilitation measures. Various sensors are employed to achieve the task of damage detection and establish a warning system to avoid failure of the structures. For large structures, long-gauge Fibre Bragg Grating (FBG) sensors which are sensitive to the global behaviour, can be suitably used for this purpose. However, health monitoring of a structure with large number of sensors is expensive and hence there is a need to optimize the number of sensors deployed to minimize the cost of the exercise without compromising on performance assessment. For this purpose, several optimization algorithms are available in literature. In this study, the Effective Independence Method (EIM) which optimizes the response of the structure based on modal analysis, is used to derive the Optimum sensor placement (OSP) protocol for a reinforced concrete (RC) bridge-deck in Poland, the geometry of which has been taken from literature. This will enable the placement of 40 long gauge FBG sensors in regions for efficient damage response in the bridge-deck. Further, the optimum orientation of the sensors is further validated with a finite element model of the bridge-deck, where a moving load is applied, and strains are recorded in the sensing fibre in both longitudinal (along length) and transverse (along breadth) alignments. It has been found that long gauge FBG sensors placed in the transverse direction are more efficient in damage detection than when they are placed longitudinally.

The issue of elements remaining in the barrel after firing is crucial both for the safe use of munition, and its reliability. These elements maybe categorized as being part of a metal case or a projectile (for example, fragments of broken connectors between a metal band and a projectile), or those associated with a propelling charge (like unburnt propellant grains). Both groups are undesirable and reflect the ammunition improper work. During own shooting tests of a 120 mm mortar ammunition the problem of unburnt elements remaining in the barrel occurred. The collected material was tested using one of the thermal analysis techniques - Differential Scanning Calorimetry - to characterize and to identify the tested sample.

Grid-characteristic method (GCM) is a fast and reliable numerical method that allows to model wave effects in viscoelastic media with high accuracy, including surface and contact waves. This research is dedicated to the application of GCM to the problem of medical ultrasound. Calculations for High-Intensity Focused Ultrasound (HIFU) were performed on 3D model statements for homogenous and inhomogeneous media, and a qualitative correspondence with experimental data was achieved. Numerical results include estimation of consumed energy (based on Maxwell viscosity model), velocity vector and stress tensor components. Various material parameters were considered, including relaxation time and inclusions of different types.

The exactly solvable Position Dependent Mass Schrödinger Equation (PDMSE) for Mie-type potentials is presented. To that, by means of a point canonical transformation the exactly solvable constant mass Schrödinger equation is transformed into a PDMSE. The mapping between both Schrödinger equations lets obtain the energy spectra and wave functions for the potential under study. This happens for any selection of the O von Roos ambiguity parameters involved in the kinetic energy operator. The exactly solvable multiparameter exponential-type potential for the constant mass Schrödinger equation constitutes the reference problem allowing to solve the PDMSE for Mie potentials and mass functions of the form given by m(x) = skx^s-1/(x^s + 1))². Thereby, as a useful application of our proposal, the particular Lennard-Jones potential is presented as an example of Mie potential by considering the mass distribution m(x) = 6kx⁵/(x⁶ + 1))². The proposed method is general and can be straightforwardly applied to the solution of the PDMSE for other potential models and/or with different position-dependent mass distributions.

We analyze the chain fountain effect-the chain siphoning when falling from a container onto the floor. We argue that the main reason for this effect is the inertia of the chain, whereas the momentum received by the beads of the chain from the bottom of the container (typically called "kicks") plays no significant role. The inertia of the chain leads to an effect similar to pulling the chain over a pulley placed up in the air, above the container. In another model (the so called "scientific consensus"), it was assumed that up to half of the mechanical work done by the tension in the chain may be wasted when transformed into kinetic energy during the pickup process. This prevented the chain to rise unless the energy transfer in the pickup process is improved by the "kicks" from the bottom of the container. Here we show that the "kicks" are unnecessary and both, energy and momentum are conserved-as they should be, in the absence of dissipation-if one properly considers the tension and the movement of the chain. By doing so, we conclude that the velocity acquired by the chain is high enough to produce the fountain effect. Simple experiments validate our model and certain configurations produce the highest chain fountain, although "kicks" are impossible.

The Haken-Kelso-Bunz (HKB) system of equations is a well-developed model for dyadic rhythmic coordination in biological systems. It captures ubiquitous empirical observations of bistability – the coexistence of in-phase and antiphase motion – in neural, behavioral, and social coordination. Recent work by Zhang and colleagues has generalized HKB to many oscillators to account for new empirical phenomena observed in multiagent interaction. Utilising this generalization, the present work examines how the coordination dynamics of a pair of oscillators can be augmented by virtue of their coupling to a third oscillator. We show that stable antiphase coordination emerges in pairs of oscillators even when their coupling parameters would have prohibited such coordination in their dyadic relation. We envision two lines of application for this theoretical work. In the social sciences, our model points toward the development of intervention strategies to support coordination behavior in heterogeneous groups (for instance in gerontology, when younger and older individuals interact). In neuroscience, our model will advance our understanding of how the direct functional connection of mesoscale or microscale neural ensembles might be switched by their changing coupling to other neural ensembles. Our findings illuminate a crucial property of complex systems: how the whole is different than the system's parts.

A weak correlation between the diffusion-exponent fluctuations and the temperature fluctuations is discussed based on recent experimental observations for protein diffusion inside bacteria. Its existence is shown to be essential for describing the statistical properties of the fluctuations. It is also quantified how largely the fluctuations are modulated by the weak correlation.

The availability of a robust approach that describe the hidden features of flood events in regulated rivers is of great importance. The key goal of this research is to utilize some of information and complexity measures to assess and rank flood patterns within a regulated river system. To meet this goal, the Metric Entropy (ME) as measure of information content and Rényi Complexity (CR) as a quantification for complexity content were employed. To examine the role of river regulation on flood risk control, river stage records of two monitoring stations located at downstream of two different dams were considered in this research. The findings show that information and complexity metrics offer an image of the randomness embedded in dataset and the presence of internal patterns in studied data records. In general, this research shows that natural environmental risks and disasters can be assessed and ranked using a promising physical scheme based on information and complexity measures.

Training Deep Learning (DL) models with missing labels is a challenge in diverse engineering applications. Missing value imputation methods have been proposed to try to address this problem, but their performance is affected with Massive Proportion of Missing Labels (MPML). This paper presents a approach for handling MPML in Multivariate Long-Term Time Series Forecasting. It is an two-step process where interpolation (using Gaussian Processes Regression (GPR) and domain knowledge from experts) and prediction model are separated to enable the integration of prior domain knowledge. First, a set of samples of the possible interpolation of the missing outputs are generated by the GPR based on the domain knowledge. Second, the observed input sensor data and interpolated labels from GPR are used to train the prediction model. We evaluated our approach with the development of a soft-sensor with one real datasets to forecast the biomass during recombinant adeno-associated virus (rAAV) production in bioreactors. Our experimental results demonstrate the potential of the approach through quantitative evaluation of the generated forecasts in a case that would be extremely difficult to train a DL model due to MPML.

The paradigm of Quantum computing and artificial intelligence has been growing steadily in recent years and given the potential of this technology by recognizing the computer as a physical system that can take advantage of quantum mechanics for solving problems faster, more efficiently, and accurately. We suggest experimentation of this potential through an architecture of different quantum models computed in parallel. In this work, we present encouraging results of how it is possible to use Quantum Processing Units analogically to Graphics Processing Units to accelerate algorithms and improve the performance of machine learning models through three experiments. The first experiment was a reproduction of a parity function, allowing us to see how the convergence of a given Quantum model is influenced significantly by computing it in parallel. For the second and third experiments, we implemented an image classification problem by training quantum neural networks and using pre-trained models to compare their performances with the same experiments carried out with parallel quantum computations. We obtained very similar results in the accuracies, which were close to 100% and significantly improved the execution time, approximately 15 times faster in the best-case scenario. We also propose an alternative as a proof of concept to address emotion recognition problems using optimization algorithms and how execution times can be positively affected by parallel quantum computation. To do this, we use tools such as the cross-platform software library PennyLane and Amazon Web Services to access high-end simulators with Amazon Braket and IBM quantum experience.

We report on a preliminary investigation of the non linear optical (NLO) properties and in particular dipole polarizability. The target species are two perfect tetrahedral nanoclusters Nb₄B₁₈ and Ta₄B₁₈, along with their nanofullerene counterpart that is C₂₈. Our study based on density functionals (DFs) that have gained popularity among the scientific community. In addition we performed Hartree-Fock calculations known for not including dynamic electron correlation. The DF obtained values are characterized by some dispersion, with maximal differences to be around 5 %, in all three cases. Given that the DFT introduces a fuzzy percentage of electron correlation sets the observed convergence of HF values to DFT ones is at least surprising. Furthermore, it should be said that though the values can be characterized as accurate their reliability should not be taken for granted. Last, we note the smooth convergence of LC-BLYP, LC-BP86, LC-BPW91 to LC-whPBE.