Table of contents

The 5th International Conference on Mathematical Modeling in Physical Sciences (IC- MSQUARE) took place at Athens, Greece, from Monday, 23^th of May, to Thursday, 26^th of May 2016.

The Conference was attended by more than 130 participants and hosted about 170 oral, poster, and virtual presentations while counted more than 500 pre-registered authors. The 5^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 since after the Keynote and Invited Talks in the morning, three parallel oral and one poster session were running every day. However, according to all attendees, the program was excellent with high level talks and the scientific environment was fruitful, thus all attendees had a creative time.

We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee.

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

We present the stochastic model of the galactic cosmic ray (GCR) particles transport in the heliosphere. The model is created based on the numerical solution of the Parker transport equation (PTE) describing the non-stationary transport of charged particles in the turbulent medium. We present the numerical schemes for the strong order integration of the set of the stochastic differential equations (SDEs) corresponding to the non-stationary PTE. Among the employed methods are the strong order Euler-Maruyama, Milstein and stochastic Runge- Kutta methods. We perform the selection of the method resulting in the highest agreement of the model of the 27-day variation of the GCR intensity with the experimental observations.

The present paper evaluates the axial strain and stress of a thermo-mechanically loaded non-uniform bar by using a numerical method based on a variational principle. The solutions are obtained up to the elastic limit of the material based on the assumptions that material properties are independent of temperature variation and plane cross-sections remain plane maintaining axisymmetry. This approximation is carried out by Galerkin's principle, using a linear combination of sets of orthogonal co-ordinate functions which satisfy prescribed boundary conditions. The solution algorithm is implemented with the help of MATLAB^® computational simulation software. Some numerical results of thermoelastic field are presented and discussed for different bar materials such as mild steel, copper, aluminium alloy 6061 (Al alloy 6061), aluminium alloy 7075 (Al alloy 7075) and diamond. The effect of geometry parameters like aspect ratio, slenderness ratio and the type of taperness is investigated and the relevant results are obtained in dimensional form. The term bar used in this paper is in generic sense and hence the formulation is applicable for all one dimensional elements, e.g., rods, pipes, truss members, etc.

Let be an abstract space and a denumerable (finite or infinite) alphabet. Suppose that is a family of functions such that for all we have and a family of transformations . The pair ((S_a)_a, (p_a)_a) is termed an iterated function system with place dependent probabilities. Such systems can be thought as generalisations of random dynamical systems. As a matter of fact, suppose we start from a given ; we pick then randomly, with probability p_a (x), the transformation S_a and evolve to S_a (x). We are interested in the behaviour of the system when the iteration continues indefinitely.

Random walks of the above type are omnipresent in both classical and quantum Physics. To give a small sample of occurrences we mention: random walks on the affine group, random walks on Penrose lattices, random walks on partially directed lattices, evolution of density matrices induced by repeated quantum measurements, quantum channels, quantum random walks, etc.

In this article, we review some basic properties of such systems and provide with a pathfinder in the extensive bibliography (both on mathematical and physical sides) where the main results have been originally published.

In this work the new multivariate discrete probability model of distribution of processes distortion of radiation from remote sensing data is proposed and studied. Research was performed on a full cycle adopted in mathematical statistics, namely, the model was constructed and investigated, various methods for estimating the parameters was proposed and test the hypothesis that the model adequacy observations, was considered.

The Fokker-Planck equation describes the evolution of a probability distribution towards equilibrium-the flow parameter is the equilibration time. Assuming the distribution remains normalizable for all times, it is equivalent to an open hierarchy of equations for the moments. Ways of closing this hierarchy have been proposed; ways of explicitly solving the hierarchy equations have received much less attention. In this paper we show that much insight can be gained by mapping the Fokker-Planck equation to a Schrodinger equation, where Planck's constant is identified with the diffusion coefficient.

We propose a drift-diffusion model for systems which obey fractional exclusion statistics (FES), in a framework where the species include classical degrees of freedom such as positions. The transition rates are calculated and the relation between the step and acceptance probabilities on one hand and the diffusion and drift processes on the other hand are established. A Monte Carlo scheme is implemented on a prototypical double-junction system of particles with screened Coulomb interactions. In our approach the properties of interacting quantum gases are locally included using the FES methodology. The model is suitable to describe transient as well as stationary regimes.

The freezing property for a family of models involving Gaussian Random Fields is studied in a unified manner and it is related to the behaviour of the entropy of the Gibbs measure in terms of the variational principle. The analysis includes the Gaussian Multiplicative Chaos, Random Energy Model, Spin Glass Mean-Field, and the Random Polymers models.

The article presents the results of a study of road safety indicators that influence the development and operation of the transport system. Road safety is considered as a continuous process of risk management. Authors constructed a model that relates the social risks of a major road safety indicator - the level of motorization. The model gives a fairly accurate assessment of the level of social risk for any given level of motorization. Authors calculated the dependence of the level of socio-economic costs of accidents and injured people in them. The applicability of the concept of socio-economic damage is caused by the presence of a linear relationship between the natural and economic indicators damage from accidents. The optimization of social risk is reduced to finding the extremum of the objective function that characterizes the economic effect of the implementation of measures to improve safety. The calculations make it possible to maximize the net present value, depending on the costs of improving road safety, taking into account socio-economic damage caused by accidents. The proposed econometric models make it possible to quantify the efficiency of the transportation system, allow to simulate the change in road safety indicators.

The article explains the use of the human capital sustainable development index (HCSDI) to assess the quality of the reproduction of human capital. The paper provides the algorithm for calculating HCSDI and its components. Authors estimated cross-country differences of HCSDI and developed econometric model of the impact of corruption on HCSDI. The use of this model has allowed to reveal the mechanism and assess the impact of corruption on HCSDI and its components. The results of econometric analysis revealed a negative multiplier effect: an increase in the corruption of the socio-economic system of the state by 1% caused HCSDI reduce by more than 1%. The results and conclusions may be proxy-assessments of the socio-economic consequences of violations of the stability of reproduction of human capital in the conditions of the growth of corruption in the country

The issue of edge determination of a single object in reconstructed nuclear medicine images has been examined thoroughly in the past, nevertheless most of the investigation has focused on the concepts of either numerical sinogram differentiation or segmentation. This work aims to develop an automated method for determining the contour of a single convex object in PET and SPECT reconstructed images, which can be used for computing body edges for attenuation correction, as well as for eliminating streak artifacts outside the specific object. This was accomplished by implementing a modified cumulative sums (CUSUM) scheme in the sinogram. Our method can automatically detect the object's boundary in the reconstructed image. This approach has been tested in simulated as well as real phantoms and it performed efficiently for all convex objects. We were able to detect the contour of a single object in the image space, which in turn enabled us to eliminate streak artifacts outside and thus to obtain body edges necessary for attenuation correction.

Different network models have been proposed along the last years inspired by real-world topologies. The characterization of these models implies the understanding of the underlying network phenomena, which accounts structural and dynamic properties. Several mathematical tools can be employed to characterize such properties as Cellular Automata (CA), which can be defined as dynamical systems of discrete nature composed by spatially distributed units governed by deterministic rules. In this paper, we proposed a method based on the modeling of one specific CA over distinct network topologies in order to perform the classification of the network model. The proposed methodology consists in the modeling of a binary totalistic CA over a network. The transition function that governs each CA cell is based on the density of living neighbors. Secondly, the distribution of the Shannon entropy is obtained from the evolved spatio-temporal pattern of the referred CA and used as a network descriptor. The experiments were performed using a dataset composed of four different types of networks: random, small-world, scale-free and geographical. We also used cross-validation for training purposes. We evaluated the accuracy of classification as a function of the initial number of living neighbors, and, also, as a function of a threshold parameter related to the density of living neighbors. The results show high accuracy values in distinguishing among the network models which demonstrates the feasibility of the proposed method.

We present results concerning the dynamics and the structure of adsorbed layers of molten polyethylene (PE) between two graphite surfaces. The molecular weight of the monodisperse PE chains reaches the entanglement regime. We study three cases of interwall distances, equal to two, three and four times the unperturbed radius of gyration (R_g) of PE chains. The confined system is equilibrated by use of efficient Monte Carlo (MC) algorithms. Conducting molecular dynamics (MD) simulations, we reveal the distribution of relaxation times as a function of distance from the graphite walls at the temperature of 450 K. From the atomic-level stresses we calculate a realistic estimate of the adhesion tension, which is not affected significantly by the width of the pore. Although the distance between the two walls is comparable to the width of the adsorbed layer, we do not record the formation of 'glassy bridges' under the studied conditions. The diffusion of polymer chains in the middle layer is not inhibited by the existence of the two adsorbed layers. Extreme confinement conditions imposed by the long range wall potentials bring about an increase in both the adsorption and desorption rates of chains. The presented results seem to cohere with a reduction in the calorimetric (heat capacity step) glass transition temperature (T_g).

Density function theory, a subfield of quantum mechanics (QM), in combination with molecular mechanics (MM) has opened the way to engineer new artificial enzymes. Herein, we report theoretical calculations done using QM/MM to examine whether the regioselectivity and rate of chlorination of the enzyme chloroperoxidase can be improved by replacing the vanadium of this enzyme with niobium through dialysis. Our calculations show that a niobium substituted chloroperoxidase will be able to enter the initial steps of the catalytic cycle for chlorination. Although the protonation state of the niobium substituted enzyme is calculated to be different from than that of the natural vanadium substituted enzyme, our calculations show that the catalytic cycle can still proceed forward. Using natural bond orbitals, we analyse the electronic differences between the niobium substituted enzyme and the natural enzyme. We conclude by briefly examining how good of a model QM/MM provides for understanding the mechanism of catalysis of chloroperoxidase.

In this work, we have studied the adsorption of a single flexible star polymer chain by a flat surface. The molecular dynamics simulation has been validated for the case of a free star polymer chain using the diffusion experiment. The scaling laws found are in agreement with the Flory theory predictions and the Rouse model. For the adsorption, preliminary results were obtained for chains of different sizes N=31 to N=199 and different functionalities (f=3,4,6,8,10). For the case of semi-flexible star polymer chains, further investigation is needed to locate the critical point of adsorption when varying the potential interaction strength between the chain and the surface.

The HuLiS program is presented as a tool to decompose a delocalized wave function as a linear combination of localized electronic structures. The principles of the energy based HL-CI and the overlap based schemes HL-P are developed. The results obtained for a set of 10 relevant organic molecules are shown to compare very well with high level quantum chemistry calculations. A trust factort is introduced and its use is shown on the allyl radical case where symmetry must be taken into account.

We considered the new equation of distribution of optical impulses in silica fibers. We also found its exact solitonic solution and analyzed extreme cases.

Nonlinear mathematical model of free surface fluid film is presents. Increment, frequency, phase velocity for thin layers of viscous liquids at low Reynolds numbers are calculated. The instability region is found. Optimal flow regimes of films of water and alcohol, corresponding to the maximum values of increment, are calculated.

In this paper, we consider the (2+1)-dimensional complex modified Korteweg-de Vries and Maxwell-Bloch (cmKdVMB) equations. Lax pairs of cmKdVMB equations are presented. Using the Lax pair, we construct a Darboux transformation and namely one-fold transformations. The soliton solutions are obtained from the different "seeds" by using this Darboux transformation.

This study concerns atomistic and coarse-grained Molecular Dynamics simulations of pristine hexabenzocoronene (HBC) molecular crystals. HBC is a symmetric graphene flake of nanometric size that falls in the category of polyaromatic hydrocarbons, finding numerous applications in the field of organic electronics. The HBC molecule is simulated in its crystalline phase initially by means of an all-atom representation, where the molecules self- organize into well aligned molecular stacks, which in turn create a perfect monoclinic molecular crystal. The atomistic model reproduces fairly well the structural experimental properties and thus can be used as a reliable starting point for the development of a coarsegrained model following a bottom-up approach. The coarse-grained model is developed by applying Iterative Boltzmann Inversion, a systematic coarse-graining method which reproduces a set of target atomistic radial distribution functions and intramolecular distributions at the coarser level of description. This model allows the simulation of HBC crystals over longer time and length scales. The crystalline phase is analyzed in terms of the Saupe tensor and thermomechanical properties are probed at the atomistic level.

The momentum distribution of charge carriers in two-dimensional FeAs-clusters modeling iron-based superconductors was calculated within the limits of the two-orbital model. The calculation was implemented by use of quantum world-line Monte Carlo algorithm. Matsubara Green's function was calculated for clusters with sizes up to 10x10 FeAs-cells. Profiles of the distributions are presented for the entire Brillouin zone. The data indicate the presence of a jump near the Fermi level, which is the evidence of the Fermi-type distribution. The influence on the momentum distribution of the value of the interaction parameter is discussed.

The local structure, segmental dynamics, topological analysis of entanglement networks and mechanical properties of atactic polystyrene - amorphous silica nanocomposites are studied via molecular simulations using two interconnected levels of representation: (a) A coarse - grained level. Equilibration at all length scales at this level is achieved via connectivity - altering Monte Carlo simulations. (b) An atomistic level. Initial configurations for atomistic Molecular Dynamics (MD) simulations are obtained by reverse mapping well- equilibrated coarse-grained configurations. By analyzing atomistic MD trajectories, the polymer density profile is found to exhibit layering in the vicinity of the nanoparticle surface. The dynamics of polystyrene (in neat and filled melt systems) is characterized in terms of bond orientation. Well-equilibrated coarse-grained long-chain configurations are reduced to entanglement networks via topological analysis with the CReTA algorithm. Atomistic simulation results for the mechanical properties are compared to the experimental measurements and other computational works.

The small-angle scattering (SAS) structure factor from a new model of a 3D deterministic fractal in which the relative positions and the number of structural units vary with fractal iteration number is calculated. It is shown that, depending on the relative positions of scattering units inside the fractal, we can obtain various types of power-law successions, such as: convex/concave - when the absolute value of the scattering exponent of the first power-law decay is higher/smaller than that of the subsequent power- law decay, or any combination of them (i.e. convex-concave or concave-convex). The obtained results can explain experimental SAS (neutron or X-rays) data which are characterized by a succession of power-law decays of arbitrary length.

In this paper, we consider the coherent component of the electromagnetic wave field inside random media. The subject of our interest concerns a random medium, consisting of a statistical ensemble of different scattering species and artificial material structures developed on base of dielectric or metallic resonant or non-resonant particles. The starting point of our theory is the multiple scattering theory, the averaged electric field satisfies a Dyson equation with a mass operator related to the effective dielectric permittivity of the homogenized structure. Quantum multiple scattering theory has been transposed into this electromagnetic case. We give a formal solution for the mass operator by introducing the T-matrix formalism. We show that the T-matrix satisfies a Lippman-Schwinger equation. Then, we introduce the Quasi-Crystalline Coherent Potential Approximation (QC-CPA), which takes into account the correlation between the particles with a pair-distribution function. The mass operator includes geometric effects, caused by resonant behavior due to the shape and size of particles, cluster effects because of correlations between particles. Significant modifications of particle scattering properties can be observed.

The Computational Fluid Dynamics (CFD) is used to numerically simulate the behavior of fluid flow, and all the laws that rule the study of fluids, both the energy and mass transfer, chemical reactions, hydraulic behavior, and other applications. Among these innumerable applications, the local behavior of a mixing tank can be estimated using the CFD techniques. In order to follow-up studies in the literature giving them increased credibility, this project aimed to determine whether both the scheduling Potency/Volume and Torque/Volume maintain the necessary level of agitation in the mix tank to extrapolate the volume 10 times and 100 times, using an axial impeller blades inclined at 45 degrees type (PBT 45), and a radial impeller (Rushton turbine) with the use of the CFD. With the results, was analyzed if a criterion is superior to the other in terms of maintaining the level of agitation in scheduling. The case study made it possible to achieve the main objective, deepen studies in Computational Fluid Dynamics. Therefore, managed to the largest domain in tools offered by CFX-ANSYS 14.0 software, allowing future work to be conducted.

Influence of the size effect on the magnetic phase transition's temperature and magnetic moment of the nanowires was modelled based on "average spin" method. As it was shown that Curie temperature was increased with nanowires' sizes increase. The calculated value of the critical exponent of the spin-spin correlations v = 0.737 is close to experimental value.

Challenged with the high rate of leakage from water supply systems, these managers are committed to identify control mechanisms. In order to standardize and control the pressure Pressure Reducing Valves (VRP) are installed in the supply network, shown to be more effective and provide a faster return for the actual loss control measures. It is known that the control pressure is while controlling the occurrence of leakage. Usually the network is sectored in areas defined by pressure levels according to its topography, once inserted the VRP in the same system will limit the downstream pressure. This work aims to show the importance of VRP as loss reduction for tool.

The hybrid graphene - hexagonal boron nitride (G-hBN) systems offer new routes in the design of nanoscale electronic devices. Using ab initio density functional theory calculations we investigate the dynamics of zig-zag nanoribbons a few interatomic distances wide. Several structures are analyzed, namely pristine graphene, hBN and G-hBN systems. By passivating the nanoribbon edges with hydrogen and different halogen atoms, one may tune the electronic and mechanical properties, like the band gap energies and the natural frequencies of vibration.

We have implemented a unitary, numerically exact, Fourier split step method, based on a proper Suzuki-Trotter factorization of the quantum evolution operator, to propagate a two-body complex in arbitrary external potential landscapes taking into account exactly the internal structure. We have simulated spatially indirect Wannier-Mott excitons - optically excited electron-hole pairs with the two charges confined to different layers of a semiconductor heterostructure with prototypical 1D and 2D potentials emphasizing the effects of the internal dynamics and the insufficiency of mean-field methods in this context.

The stochastic variational method has proven to be a very efficient and accurate tool to calculate especially bound states of quantum-mechanical few-body systems. It relies on the Rayleigh-Ritz variational principle for minimizing real eigenenergies of Hermitian Hamiltonians. From molecular to atomic, nuclear, and particle physics there is actually a great demand of describing also resonant states to a high degree of reliance. This is especially true with regard to hadron resonances, which have to be treated in a relativistic framework. So far standard methods of dealing with quantum chromodynamics have not yet succeeded in describing hadron resonances in a realistic manner. Resonant states can be handled by non-Hermitian quantum Hamiltonians. These states correspond to poles in the lower half of the unphysical sheet of the complex energy plane and are therefore intimately connected with complex eigenvalues. Consequently the Rayleigh-Ritz variational principle cannot be employed in the usual manner. We have studied alternative selection principles for the choice of test functions to treat resonances along the stochastic variational method. We have found that a stationarity principle for the complex energy eigenvalues provides a viable method for selecting test functions for resonant states in a constructive manner. We discuss several variants thereof and exemplify their practical efficiencies.

We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT for short) and Noncommutative Floer Homology (NCFH for short). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we define some new invariants for 3-manifolds using the space of taut codim-1 foliations modulo coarse isotopy along with various techniques from noncommutative geometry.

Two dimensional (2D) analogue of vacuum sector of the Brans Dicke (BD) gravity [1] is studied to obtain dynamics of anisotropic spherically symmetric perfect fluid. Our obtained static solutions behave as dark matter with state equation but in non-static regimes behave as regular perfect fluid with barotropic index ϒ > 0. Positivity property of total mass of the fluid causes that the BD parameter to be ω >2/3 and/or ω < —1. Locations of the event and apparent horizons of the collapsing fluid are obtained in its static regime. In case ω > 0 the apparent horizon is covered by event horizon where the cosmic censorship hypothesis is still valid. According to the model [1], we obtain de Broglie pilot wave of our metric solution which describes particles ensemble which become distinguishable via different values of ω. Incident current density of particles ensemble on the horizons is evaluated which describe the 'Hawking radiation'. The de Brogle-Bohm quantum potential effect is calculated also on the event (apparent) horizon which is independent (dependent) to values of ω.

We consider a charged Brownian particle bounded by an harmonic potential, embedded in a Markovian heat bath and driven from equilibrium by external electric and magnetic fields. We develop a quaternionic-like (or Pauli spinor-like) representation, hitherto exploited in classical Lorentz related dynamics. Within this formalism, in a very straight forward and elegant fashion, we compute the exact solution for the resulting generalized Langevin equation, for the case of a constant magnetic field. For the case the source electromagnetic fields satisfy Maxwell's equations, yielding spinor-like Mathieu equations, we compute the solutions within the JWKB approximation. With the solutions at hand we further compute spatial, velocities and crossed time correlations. In particular we study the (kinetically defined) nonequilbrium temperature. Therefore, we can display the system's time evolution towards equilibrium or towards non equilibrium (steady or not) states.

We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70's by Smith and Tassie, and Bell and Ruegg. As relativistic symmetries, they have been extensively researched and applied to several physical systems for the last 18 years. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrödinger-like equations, i.e, without a matrix structure. In this paper we use the original formalism of Bell and Ruegg to derive general requirements for the Lorentz structures of potentials in order to have these SU(2) symmetries in the Dirac equation, again allowing for the suppression of the matrix structure of the second-order equation of either the upper or lower components of the Dirac spinor. Furthermore, we derive equivalent conditions for spin and pseudospin symmetries with 2- and 1-dimensional potentials and list some possible candidates for 3, 2, and 1 dimensions. We suggest applications for physical systems in three and two dimensions, namely electrons in graphene.

We present our proposal of the supervised binary divergence decision tree with nested separation method based on the generalized linear models. A key insight we provide is the clustering driven only by a few selected physical variables. The proper selection consists of the variables achieving the maximal divergence measure between two different classes. Further, we apply our method to Monte Carlo simulations of physics processes corresponding to a data sample of top quark-antiquark pair candidate events in the lepton+jets decay channel. The data sample is produced in pp̅ collisions at √S = 1.96 TeV. It corresponds to an integrated luminosity of 9.7 fb^-1 recorded with the D0 detector during Run II of the Fermilab Tevatron Collider. The efficiency of our algorithm achieves 90% AUC in separating signal from background. We also briefly deal with the modification of statistical tests applicable to weighted data sets in order to test homogeneity of the Monte Carlo simulations and measured data. The justification of these modified tests is proposed through the divergence tests.

A model of turbulent galactic magnetic fields was developed in which, the type of turbulence were considered to be Kolmogorov. We tested the effect of this model on an isotropically distributed flux of ultra high energy cosmic ray in the extragalactic space. To do this, a giant Galactic halo (radius of ∼⃒ 100Mpc) was considered. Regular and random components of the Galactic Magnetic Fields were considered to have the mean observed relevant values and also satisfy a Kolmogorov field type. The deviation from isotropy then were calculated considering the propagation of ultra high energy protons in such a magnetic field and results were discussed to show how isotropic is the flux of ultra high energy cosmic rays in the extragalactic space. It is seen that considering an isotropic flux of ultra high energy cosmic rays in the intergalactic space for different choices of galactic magnetic field is not consistence with the distribution of observed ultra high energy events.

We determine active gravitational mass operator of the simplest composite quantum body - a hydrogen atom - within the semiclassical approach to the Einstein equation for a gravitational field. We show that the expectation value of the mass is equivalent to energy for stationary quantum states. On the other hand, it occurs that, for quantum superpositions of stationary states with constant expectation values of energy, the expectation values of the gravitational mass exhibit time-dependent oscillations. This breaks the equivalence between active gravitational mass and energy and can be observed as a macroscopic effect for a macroscopic ensemble of coherent quantum states of the atoms. The corresponding experiment could be the first direct observation of quantum effects in General Relativity.

We propose a model for an active Brownian system that exhibits one-dimensional directed motion. This system consists of two Brownian spherical particles that interact through an elastic potential and have time-dependent radii. We suggest an algorithm by which the sizes of the particles can be varied, such that the center of mass of the system is able to move at an average constant speed in one direction. The dynamics of the system is studied theoretically using a Langevin model, as well as from Brownian Dynamics simulations.

In re-parametrization invariant systems, such as mini-superspace Lagrangians, the existence of constraints can lead to the emergence of additional non-local integrals of motion defined in phase space. In the case of a FLRW flat/non-flat space-time minimally coupled to an arbitrary scalar field, we manage to use such conserved quantities to completely integrate the system of equations of motion. This is achieved without constraining the potential in any way. Thus, obtaining the most general solution that encompasses all possible cosmological scenarios which can be based on the existence of a scalar field.

We present a local Bäcklund Wahlquist-Estabrook (WE) transformation for a supersymmetric Korteweg-de Vries (KdV) equation. As in the scalar case, such type of transformation generates infinite hierarchies of solutions and also implicitly gives the associated (local) conserved quantities. A nice property is that every of such hierarchies admits a nonlinear superposition principle, starting for an initial solution, including as a particular case the multisolitonic solutions of the system. We discuss the symmetries of the system and we present in an explicit way its local conserved quantities with the help of the associated Gardner transformation.

For a one dimensional system tight binding models are described by sparse tridiagonal matrices which describe interactions between nearest neighbors. In this report, we construct open and closed random tight-binding models based in the tridiagonal matrices of the so-called,β-ensembles of random matrix theory.

We study static spherically symmetric solutions of the nonprojectable Hořava theory with and without cosmological constant. The solutions we find are two-side wormholes and (single-side) naked singularities. Interestingly, in the case of negative cosmological constant we find that in the exterior side the wormhole acquires an asymptotic scaling between space and time equal to the scaling of the Lifshitz solution, which was previously found to be a vacuum solution of the same theory. This result leads us to pose the question whether in the case of negative cosmological constant the asymptotic anisotropic Lifshitz scaling is a generic feature of the vacuum field equations rather than the asymptotic AdS-like scaling.

CP violation in the charm quark sector has not been examined very well as the case for strange and beauty ones. Some novel insights into the issue on the CP violation in D meson decay are discussed. Specifically, i) the T-violating observables in D → VV decays are constructed. Assuming CPT invariance T violation implies CP violation. This is a new idea and an alternative way for probing CP violation in D decays; ii) the decay of quantum correlated DD̅ pair to vector mesons (denoted by V) is explored, which offers the new CP violating observables that have not been noticed before;

Searching for the New Physics (NP) phenomenon beyond Standard Model (SM) is still a main focus in particle physics. Here we propose to search for Λ — ⊼ oscillation in the decay J/ψ → Λ⊼ AA using BES detector. With one-year luminosity at BESIII, we can put a constraint that the Λ — ⊼ oscillation mass is smaller than 10^-15 MeV at 90% confidence level, corresponding to the oscillation time of 10^-6 second around, in case of non-observation of any signals. These measurements should provide very precious informations besides the neutron oscillation experiment. Also it would be the first-time access by experiment for Λ — ⊼ oscillation.

In this study we have obtained non-extensive entropies and have showed that these entropies satisfy the non-extensive uncertainty relation for the wave function corresponding to the modified Pöschl-Teller potential. We have also computed statistical complexity depending on entropic index q for the same wave function and we have showed that complexity decreases by increasing of q.

We report on our attempts of treating excited hadron states as true quantum resonances. Hitherto the spectroscopy of mesons, usually considered as quark-antiquark systems, and of baryons, usually considered as three-quark systems, has been treated through excitation spectra of bound states (namely, confined few-quark systems), corresponding to poles of the quantum-mechanical resolvent at real negative values in the complex energy plane. As a result the wave functions, i.e. the residua of the resolvent, have not exhibited the behaviour as required for hadron resonances with their multiple decay modes. This has led to disturbing shortcomings in the description of hadronic resonance phenomena. We have aimed at a more realistic description of hadron resonances within relativistic constituent-quark models taking into account explicitly meson-decay channels. The corresponding coupled-channels theory is based on a relativistically invariant mass operator capable of producing hadron ground states with real energies and hadron resonances with complex energies, the latter corresponding to poles in the lower half-plane of the unphysical sheet of the complex energy plane. So far we have demonstrated the feasibility of the coupled-channels approach to hadron resonances along model calculations producing indeed the desired properties. The corresponding spectral properties will be discussed in this contribution. More refined studies are under way towards constructing a coupled-channels relativistic constituent-quark model for meson and baryon resonances.

Neutrino-nucleus reactions, involving both neutral current (NC) and charged current (CC) interactions are important probes in modern neutrino physics searches. In the present work, we study the concrete CC reactions ¹³⁰Te(v_ℓ,ℓ⁻)¹³⁰I and ¹³⁰Te(_ℓ,ℓ⁺)¹³⁰Sb which are of current experimental interest for the CUORE and COBRA experiments operating at Gran Sasso underground laboratory in Italy. The nuclear wave functions for the required initial and final nuclear states are derived by employing the proton-neutron (p-n) quasi-particle random phase approximation (QRPA) which has been previously tested in our neutral-current v-nucleus studies for Te isotopes.

The complete understanding of the phenomenological process related to the evolution of the ternary multiphase system is still lacking. In this paper the ternary interdiffusion process in multiphase system is discussed by means of numerical modeling. The entropy production principle is proposed to chose the proper diffusion path during the process (e.g. internal oxidation). The bi-velocity method of the three-component multi-phase system is presented. The simulations show the local entropy production curve that determines the thickness of the two-phase zone.

Relativity Theory and the corresponding Relativistic Quantum Mechanics are the fundamental theories of physics. Special Relativity (SR) relates the frames of Relativistic Inertial observers (RIOs), through Linear Spacetime Transformation (LSTT) of linear spacetime. Classic Special Relativity uses real spacetime endowed with Lorentz metric and the frames of two RIOs with parallel spatial axes are always related through Lorentz Boost (LB). This cancels the transitive attribute in parallelism, when three RIOs are related, because LB is not closed transformation, causing Thomas Rotation. In this presentation, we consider closed LSTT of Complex Spacetime, so there is no necessity for spatial axes rotation and all the frames are chosen having parallel spatial axes. The solution is expressed by a 4x4 matrix (Λ) containing components of the complex velocity of one Observer wrt another and two functions depended by the metric of Spacetime. Demanding isometric transformation, it emerges a class of metrics that are in accordance with the closed LSTT and the transformation matrix contains one parameter ω depended by the metric of Spacetime. In case that we relate RIOs with steady metric, it emerges one steady number (ω_I) depended by the metric of Spacetime of the specific SR. If ω_I is an imaginary number, the elements of the Λ are complex numbers, so the corresponding spacetime is necessarily complex and there exists real Universal Speed (U_I). The specific value ω_I=±i gives Vossos transformation (VT) endowed with Lorentz metric (for g_ii=1) of complex spacetime and invariant spacetime interval (or equivalently invariant speed of light in vacuum), which produce the theory of Euclidean Complex Relativistic Mechanics (ECRMs). If ω_I is a real number (ω_I#0) the elements of the Λ are real numbers, so the corresponding spacetime is real, but there exist imaginary U_I. The specific value ω_I=0 gives Galileo Transformation (GT) with the invariant time, in which any other closed LSTT is reduced, if one RIO has small velocity wrt another RIO. Thus, we have infinite number of closed LSTTs, each one with the corresponding SR theory. In case that we relate accelerated observers with variable metric of spacetime, we have the case of General Relativity (GR). For being that clear, we produce a generalized Schwarzschild metric, which is in accordance with any SR based on this closed complex LSTT and Einstein equations. The application of this kind of transformations to the SR and GR is obvious. But, the results may be applied to any linear space of dimension four endowed with steady or variable metric, whose elements (four- vectors) have spatial part (vector) with Euclidean metric.

Various studies have confirmed that only a small number of incident field directions are needed to apply the topological derivative in inverse scattering problem. In this paper, we consider a topological derivative-based technique with a small number of such directions for imaging thin, curve-like dielectric inhomogeneities embedded in a homogeneous domain, and explore a suitable condition via various numerical simulation results.

Anand constitutive relation of SnAgCu and SnAgCu-nano Al solders were studied under uniaxial tension, and the constitutive model was used in the finite element simulation to analyze the stress-strain response of lead-free solder joints in 3D IC devices. The results showed that the nine parameters of the Anand model can be determined from separated constitutive relations and experimental results. Based on Anand model, the finite element method was selected to calculate the stress-strain response of lead-free solder joints, it was found that in the 3D IC device the maximum stress-strain concentrated in the concern solder joints, the stress-strain of SnAgCu-nano Al solder joints was lower than that of SnAgCu solder joints, which represented that the addition of nano Al particles can enhance the reliability of lead-free solder joints in 3D IC devices.

In this paper we present the Monte Carlo entropic sampling (MCES) applied to an Ising-like model for 2D and 3D system in order to show the interaction influence of the edge molecules of the system with their local environment. We show that, as for the 1D and the 2D spin crossover (SCO) systems, the origin of multi steps transition in 3D SCO is the effect of the edge interaction molecules with its local environment together with short and long range interactions. Another important result worth noting is the co-existence of step transitions with hysteresis and without hysteresis. By increasing the value of the edge interaction, L, the transition is shifted to the lower temperatures: it means that the role of edge interaction is equivalent to an applied negative pressure because the edge interaction favours the HS state while the applied pressure favours the LS state. We also analyse, in this contribution, the role of the short- and long-range interaction, J respectively G, with respect to the environment interaction, L.

We used the atom-phonon coupling model to explain and illustrate the behaviour of a linear nano-chain of molecules. The analysis of the system's behaviour was performed using Free Energy method, and by applying Monte Carlo Metropolis (MCM) method which take into account the phonon contribution. In particular we tested both the MCM algorithm and the dynamic-matrix method and we expose how the thermal behaviour of a 1D spin crossover system varies as a function of different factors. Furthermore we blocked the edge atoms of the chain in its high spin state to study the effect on the system's behaviour.

A wide variety of systems may be described by specific dependence, which is known as logistic curve, or S-curve, between the internal characteristic and the external parameter. Linear feedback between these two values may be suggested for a wide set of systems also. In present paper, we suggest a bifurcation behavior for systems with both features, and discuss it for two cases, which are the Ising magnet in external field, and the development of manufacturing enterprise.

Nowadays, there is a huge necessity to generate novel strategies for social-ecological systems analyses for resolving global sustainability problems. This paper has as main purpose the application of the formal concept analysis to formalize the theory of Augusto Ángel Maya, who without a doubt, was one of the most important environmental philosophers in South America; Ángel Maya proposed and established that Ecosystem-Culture relations, instead Human-Nature ones, are determinants in our understanding and management of natural resources. Based on this, a concept lattice, formal concepts, subconcept-superconcept relations, partially ordered sets, supremum and infimum of the lattice and implications between attributes (Duquenne-Guigues base), were determined for the ecosystem-culture relations.

Atmospheric jets and vortices which, together with inertia-gravity waves, constitute the principal dynamical entities of large-scale atmospheric motions, are well described in the framework of one- or multi-layer rotating shallow water models, which are obtained by vertically averaging of full "primitive" equations. There is a simple and physically consistent way to include moist convection in these models by adding a relaxational parameterization of precipitation and coupling precipitation with convective fluxes with the help of moist enthalpy conservation. We recall the construction of moist-convective rotating shallow water model (mcRSW) model and give an example of application to upper-layer atmospheric vortices.

The study of processes associated with vegetation grow is very important to understand the dynamics of flooded ecosystems and their sustainable management. We present a cell-centered individual-based probabilistic model for the dynamics of tree-populations, that is further tailored towards the environmental conditions present in the Amazon floodplains.

While the properties of conductive fibres and coatings on textiles can easily be measured and calculated, magnetic coatings of fibres, yarns and fabrics still lack descriptions of their physical properties. Since magnetic textiles can be used for a variety of applications, from magnetic filters to invisible water-marks to magnetic coils and sensors, simulations would be supportive to understand and utilize their properties. The article gives an overview of different coatings on textile fibres, varying the magnetic materials as well as the fibre composition, giving rise to the interactions between neighbouring coated fibres. In this way, it is possible to understand the strong shape anisotropy which must be taken into account when the magnetic properties of textiles are to be tailored. Additionally, the differences between several possible magnetic coating materials become visible. This study can help adjusting the magnetic properties of textile fabrics to a desired application.

Magnetic nano-structures can be used for various applications. Examinations of nano-structured systems often aim at decreasing pattern sizes due to their possible utilization in data storage media, in order to enhance the possible information density in a given area. This scaling process, however, is limited by the resolution of the lithography process which is used to produce the nano-particles. Thus the influence of shape modifications on the magnetic properties is important to be examined, especially the correlation between small form changes and magnetization reversal processes or coercive fields. In a recent project, square nanoparticles from permalloy were simulated using Magpar. Simulations were performed for the ideal geometric shape used in the lithography process, for the realistic shape of the produced nano-particles as obtained by SEM, and for intermediate steps between these extreme shapes. This study allows for estimation of the reliability of magnetic properties of nano-structures with respect to shape modifications in the lithography process.

Software was developed for quick numerical calculations and graphic display of the absorption, reflection and transmittance spectra of two-dimensional systems of small conductive particles. It allowed us to make instant comparison of calculation results and experimental data. A lattice model was used to simulate nearly distributed particles, and the coherent-potential approximation was applied to obtain a solution to the problem of interacting particles. The Delphi programming environment was used.

Measurements of the optical reflection spectra from periodic structures with two quantum wells in the elementary cell have been done. The dependencies of the light reflection on the angle of the light incidence, polarization and temperature were studied. An analysis of the experimental data showed that the pattern with 60 cells is a good Bragg reflector with reflectivity more than 90% in the maximum of the spectral band.

The main goal of this work is to add and analyze an equation that represents the volume in a dynamical model of the mammalian cell cycle proposed by Gérard and Goldbeter (2011) [1]. The cell division occurs when the cyclinB/Cdkl complex is totally degraded (Tyson and Novak, 2011)[2] and it reaches a minimum value. At this point, the cell is divided into two newborn daughter cells and each one will contain the half of the cytoplasmic content of the mother cell. The equations of our base model are only valid if the cell volume, where the reactions occur, is constant. Whether the cell volume is not constant, that is, the rate of change of its volume with respect to time is explicitly taken into account in the mathematical model, then the equations of the original model are no longer valid. Therefore, every equations were modified from the mass conservation principle for considering a volume that changes with time. Through this approach, the cell volume affects all model variables. Two different dynamic simulation methods were accomplished: deterministic and stochastic. In the stochastic simulation, the volume affects every model's parameters which have molar unit, whereas in the deterministic one, it is incorporated into the differential equations. In deterministic simulation, the biochemical species may be in concentration units, while in stochastic simulation such species must be converted to number of molecules which are directly proportional to the cell volume. In an effort to understand the influence of the new equation a stability analysis was performed. This elucidates how the growth factor impacts the stability of the model's limit cycles. In conclusion, a more precise model, in comparison to the base model, was created for the cell cycle as it now takes into consideration the cell volume variation

A sigmoidal curve y(t) is a monotone increasing curve such that all derivatives vanish at infinity. Let t_n be the point where the nth derivative of y(t) reaches its global extremum. In the previous work on sol-gel transition modelled by the Susceptible-Infected- Recovered (SIR) system, we observed that the sequence {t_n} seemed to converge to a point that agrees qualitatively with the location of the gel point [2]. In the present work we outline a proof that for sigmoidal curves satisfying fairly general assumptions on their Fourier transform, the sequence {t_n} is convergent and we call it "the critical point of the sigmoidal curve". In the context of phase transitions, the limit point is interpreted as a junction point of two different regimes where all derivatives undergo their highest rate of change.

A new methodology and the corresponding C++ code for mesoscopic simulations of elastomers are presented. The test system, crosslinked ds-1'4-polyisoprene' is simulated with a Brownian Dynamics/kinetic Monte Carlo algorithm as a dense liquid of soft, coarse-grained beads, each representing 5-10 Kuhn segments. From the thermodynamic point of view, the system is described by a Helmholtz free-energy containing contributions from entropic springs between successive beads along a chain, slip-springs representing entanglements between beads on different chains, and non-bonded interactions. The methodology is employed for the calculation of the stress relaxation function from simulations of several microseconds at equilibrium, as well as for the prediction of stress-strain curves of crosslinked polymer networks under deformation.

The n -vicinities method for approximate calculations of the partition function of a spin system was proposed previously. The equation of state was obtained in the most general form. In the present publication these results are adapted to the Ising model on the D - dimensional cubic lattice. The state equation is solved for an arbitrary dimension D and the behavior of the free energy is analyzed. For large values of D (D > 2) the obtained results are in good agreement with the ones obtained by means of computer simulations. For small values of D, there are noticeable discrepancies with the exact results.

The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.

Approximants for the modified Bessel function I₁(x) has been found using the multi-point quasi-rational technique. The approximations here determined has good accuracy for any positive value of the variable, and it seems to be adequate for most of the works where this function are used. Furthermore, the approximants are simple to calculate numerically in a direct way or using any usual MAPLE or MATLAB software.

The motivation for this work came from an attempt to give an alternative definition for the meter, the SI unit for measuring length. As a starting point towards this goal we present the underlying theory behind our approach which uses ideas from quantum field theory and non-commutative geometry, in particular the notion of an odd K-cycle which is based on the Dirac operator (and its inverse, the Dirac propagator). Using physics terminology, the key point in our strategy is this: instead of measuring ordinary length in space-time we measure the "algebraic (or spectral) length" in the space of quantum states of some fermion acted upon by the Dirac propagator.

The Ising like model, taking into account short-, long-range interaction as well as surface effects is used to investigate size and shape effects on the thermal behaviour of 2D and 3D spin crossover (SCO) nanoparticles embedded in a matrix. We analyze the role of the parametert, representing the ratio between the number of surface and volume molecules, on the unusual thermal hysteresis behaviour (appearance of the hysteresis and a re-entrance phase transition) at small scales.

Stratified flows in open channels arise as a result of density or surface level differences. If the channel is connected to a basin at one or both ends, strong winds originating from the basin cause the "wind setup" effect that increases the water level at the entrance of the channel. On the other hand, along the channel, persistent winds in the upper layer flow direction lead to an increase of the drift velocity and to a decrease in upper layer flow depth. The Istanbul Strait (Bosphorus) connecting the Black and the Marmara Seas, is characterized by a stratified flow caused by the surface level and salinity difference between these basins, consisting of a southward upper layer flow and a northward lower layer flow. Along the strait, there are three hydraulic control points; the north sill, a midway contraction reach and the south sill. Under wind effects, the northern and southern entrances of the strait behave as an estuary whereas the midway reach to the south of the contraction acts as as an open channel. In winter, when the sea level difference is relatively low, the wind setup due to southerly winds may cause a blockage and even reversal of the upper layer flow. On the other hand in spring when there is excessive river discharge, northerly winds increase the influx of Black Sea waters into the strait and may lead to a blockage of the lower layer. We claim that strong northerly winds may cause a decrease of the upper layer depth beyond the contraction and we propose a simple model for its estimation in terms of the wind and water flow speeds.

Analyzing the dynamics of the photospheric magnetic field of the Sun is one of the most important problems in Solar Physics. Different estimates of the complexity of magnetograms of the Sun Active Regions (AR) are used to predict the time and the strength of the solar flares, but the quality of the forecasts are still insufficient. A magnetogram is a highly variable discrete image with a very large number of local extrema. We use an idea of extraction of stable critical points within a framework of the scale-space theory. Two sequential convolutions of the image with the same Gaussian kernel and calculating the difference between the produced images allow to get a stable estimation of the Laplacian of the image. A critical graph is constructed using maxima and minima of the Laplacian. Dynamics of critical graphs can be used for diagnostics of dynamical regimes of ARs. The so-called spectral gap is proposed to be used as a numerical descriptor. This is the difference between the two largest eigenvalues of the discrete Laplacian of the graph constructed on critical networks. We investigated several ARs and found that there was a sudden increase in the spectral gap values one or two days before the flares.

In this work we present the results of analytical modeling and 3D computer simulation of microfluidic Wheatstone bridge, which is used for high-accuracy measurements and precision instruments. We propose and simulate a new method of a bridge balancing process by changing the microchannel geometry. This process is based on the "etching in microchannel" technology we developed earlier (doi:10.1088/1742-6596/681/1/012035). Our method ensures a precise control of the flow rate and flow direction in the bridge microchannel. The advantage of our approach is the ability to work without any control valves and other active electronic systems, which are usually used for bridge balancing. The geometrical configuration of microchannels was selected based on the analytical estimations. A detailed 3D numerical model was based on Navier-Stokes equations for a laminar fluid flow at low Reynolds numbers. We investigated the behavior of the Wheatstone bridge under different process conditions; found a relation between the channel resistance and flow rate through the bridge; and calculated the pressure drop across the system under different total flow rates and viscosities. Finally, we describe a high-precision microfluidic pressure sensor that employs the Wheatstone bridge and discuss other applications in complex precision microfluidic systems.

The energy levels of CO₂ in the small (s) and large (l) nano-cages of cubic sI clathrates are calculated in the Born-Oppenheimer approximation using pairwise atom-atom interaction potentials. In the s cage, the centre of mass of CO₂ oscillates with small amplitudes, asymmetrically about the cage center with harmonic frequencies around 100 cm^-1. In the l cage, oscillations are anharmonic with large amplitude motions in a plane parallel to the hexagonal faces of the cage and the corresponding frequencies are calculated to be 55 cm^-1 and 30 cm^-1. Librational harmonic frequencies are calculated at 101.7 cm^-1 and 56.0 cm^-1 in the 5 cage and at 27.9 cm^-1 and 46.4 cm^-1 in the l cage. Results show that the coupling between the CO₂ molecule and the nano-cage is quite different for the low frequency translational, rotational or librational modes and the high frequency vibrational modes, which consequently leads to different relaxation channels.

A Monte Carlo (MC) simulation of a 2D microscopic ABV (metal A, metal B and void V) Ising model of an interconnect alloy is performed by taking into account results of Finite Element methods (FEM) calculations on correlated void-thermal effects. The evolution of a homogeneous structure of a binary alloy containing a small percentage of voids is studied with temperature cycling. The diffusion of voids and segregation of A type or B type metals is a function of the relative interaction energy of the different pairs AA, BB, AB, AV and BV, the initial concentrations of A, B and V and local heating effect due to the presence of clusters of voids. Voids segregates in a matrix of A type, of B type or AB type and form large localized clusters or smaller delocalized ones of different shapes.

Dynamic of the three-dimensional vortex system in layered high-temperature superconductors with internal nanosized ferromagnetic defects has been studied by using Monte Carlo simulations. Magnetization processes in the array of ferromagnetic defects under the field of Abrikosov vortices have been taken into account. The current-voltage characteristics under applying of external dc magnetic field have been obtained. It has been shown that S-type nonlinearity of E(J) curve which have been obtained previously for twodimensional vortex system also appears in this more realistic anisotropic three-dimensional case. The effect of vortex-vortex inter-layer coupling on the S-nonlinearity has been analyzed.

Developing (underdeveloped) countries are territories of slow economic growth (catch-up growth). Perspectives of their economic growth largely depend on developing and introducing financial and technological innovations in the sphere of the financial markets. The level and quality of those innovations should enable provision of faster growth of the financial sector of the national economy by rising stability and effectiveness of the financial institutions. Powerful and stable financial sector is the basic element for attracting investments and upsurge of liquidity in the economic system of a developing country that aims to have developed economy. Intellectual capital is the most important of the fundamental factors of production in the financial sphere. It is a catalytic element of the process of the economic development. From this position, the researchers' collective develops and presents a mathematical model which characterizes the connection between the intellectual capital and financial results of the commercial activity of financial institutions. The model is applied in the analysis of the activity of financial institutions that are part of the EEU.

We have assessed the potential applications of the neutron monitor hardware as random number generator for normal and uniform distributions. The data tables from the acquisition channels with no extreme changes in the signal level were chosen as the retrospective model. The stochastic component was extracted by fitting the raw data with splines and then subtracting the fit. Scaling the extracted data to zero mean and variance of one is sufficient to obtain a stable standard normal random variate. Distributions under consideration pass all available normality tests. Inverse transform sampling is suggested to use as a source of the uniform random numbers. Variational Monte Carlo method for quantum harmonic oscillator was used to test the quality of our random numbers. If the data delivery rate is of importance and the conventional one minute resolution neutron count is insufficient, we could always settle for an efficient seed generator to feed into the faster algorithmic random number generator or create a buffer.

We study stock market instability by using cross-correlations constructed from the return time series of 366 stocks traded on the Tokyo Stock Exchange from January 5, 1998 to December 30, 2013. To investigate the dynamical evolution of the cross-correlations, crosscorrelation matrices are calculated with a rolling window of 400 days. To quantify the volatile market stages where the potential risk is high, we apply the principal components analysis and measure the cumulative risk fraction (CRF), which is the system variance associated with the first few principal components. From the CRF, we detected three volatile market stages corresponding to the bankruptcy of Lehman Brothers, the 2011 Tohoku Region Pacific Coast Earthquake, and the FRB QE3 reduction observation in the study period. We further apply the random matrix theory for the risk analysis and find that the first eigenvector is more equally de-localized when the market is volatile.

The characterization of the statistical distributions of observed weather data is of crucial importance both for the construction and for the validation of weather models, such as weather generators (WG's). An important class of WG's (e.g., the Richardson-type generators) reduce the time series of each variable to a time series of its residual elements, and the residuals are often assumed to be normally distributed. In this work we propose an approach to investigate if the shape assumed for the distribution of residuals is consistent or not with the observed data of a given site. Specifically, this procedure tests if the same distribution shape for the residuals noise is maintained along the time. The proposed approach is an adaptation to climate time series of a procedure first introduced to test the shapes of distributions of growth rates of business firms aggregated in large panels of short time series. We illustrate the procedure by applying it to the residuals time series of maximum temperature in a given location, and investigate the empirical consistency of two assumptions, namely i) the most common assumption that the distribution of the residuals is Gaussian and ii) that the residuals noise has a time invariant shape which coincides with the empirical distribution of all the residuals noise of the whole time series pooled together.

In this paper the information model of intradisciplinary connections and semantic structures method are described. The information parameters, which we use in information model, are introduced. The question we would like to answer in this paper is - how to optimize the Physics Course' content. As an example, the differences between entropy values in the contents of physics lecture with one topic but different logics of explanations are showed.

We compute analytically the masses, binding energies and hamiltonians of gravitationally bound Bohr-type states via the rotating relativistic lepton model which utilizes the de Broglie wavelength equation in conjunction with special relativity and Newton's relativistic gravitational law. The latter uses the inertial-gravitational masses, rather than the rest masses, of the rotating particles. The model also accounts for the electrostatic charge- induced dipole interactions between a central charged lepton, which is usually a positron, with the rotating relativistic lepton ring. We use three rotating relativistic neutrinos to model baryons, two rotating relativistic neutrinos to model mesons, and a rotating relativistic electron neutrino - positron (or electron) pair to model the W^± bosons. It is found that gravitationally bound ground states comprising three relativistic neutrinos have masses in the baryon mass range (∼⃒ 0.9 to 1 GeV/c²), while ground states comprising two neutrinos have masses in the meson mass range (∼⃒ 0.4 to 0.8 GeV/c²). It is also found that the rest mass values of quarks are in good agreement with the heaviest neutrino mass value of 0.05 eV/c² and that the mass of W^± bosons (∼⃒ 81 GeV/c²) corresponds to the mass of a rotating gravitationally confined e^± — v_e pair. A generalized expression is also derived for the gravitational potential energy of such relativistic Bohr-type structures.

Demand for clean and treated water is increasing all over the world. Therefore it is crucial to conserve water for better use and to avoid unnecessary, excessive consumption or wastage of this natural resource. Classification of excessive domestic water consumption is a difficult task due to the complexity in determining the amount of water usage per activity, especially as the data is known to vary between individuals. In this study, classification of excessive domestic water consumption is carried out using a well-known Fuzzy C-Means (FCM) clustering algorithm. Consumer data containing information on daily, weekly and monthly domestic water usage was employed for the purpose of classification. Using the same dataset, the result produced by the FCM clustering algorithm is compared with the result obtained from a statistical control chart. The finding of this study demonstrates the potential use of the FCM clustering algorithm for the classification of domestic consumer water consumption data.

In this article, algorithms of non-linear filtering of Poisson time series are tested using statistical modelling. The objective is to find a representation of a time series as a wavelet series with a small number of non-linear coefficients, which allows distinguishing statistically significant details. There are well-known efficient algorithms of non-linear wavelet filtering for the case when the values of a time series have a normal distribution. However, if the distribution is not normal, good results can be expected using the maximum likelihood estimations. The filtration is studied according to the criterion of maximum likelihood by the example of Poisson time series. For direct optimisation of the likelihood function, different stochastic (genetic algorithms, annealing method) and deterministic optimization algorithms are used. Testing of the algorithm using both simulated series and empirical data (series of rare words frequencies according to the Google Books Ngram data were used) showed that filtering based on the criterion of maximum likelihood has a great advantage over well-known algorithms for the case of Poisson series. Also, the most perspective methods of optimisation were selected for this problem.

Epidemics are an extremely important matter of study within the Mathematical Modeling area and can be widely found in the literature. Some epidemiological models use differential equations, which are very sensible to parameters, to represent and describe the diseases mathematically. For this work, a variation of the SIR model is discussed and applied to a certain epidemic scenario, wherein vaccination is introduced through two different strategies: constant vaccination and vaccination in pulses. Other epidemiological and population aspects are also considered, such as mortality/natality and infection rates. The analysis and results are performed through numerical solutions of the model and a special attention is given to the discussion generated by the paramenters variation.

The Computational Fluid Dynamics (CFD) is a tool used to numerically simulate fluid flow behavior, and all the laws that govern the study of fluids is the mass transfer and energy, chemical reactions, hydraulic behaviors, among others applications. This tool mathematical equation solves the problem in a specific manner over a region of interest, with predetermined boundary conditions on this region. This work is to study the flow channel through the CFD technique.

The issue of water pollution has worsened in recent times due to releases, intentional or not, of pollutants in natural water bodies. This causes several studies about the distribution of pollutants are carried out. The water quality models have been developed and widely used today as a preventative tool, ie to try to predict what will be the concentration distribution of constituent along a body of water in spatial and temporal scale. To understand and use such models, it is necessary to know some concepts of hydraulic high on their application, including the longitudinal dispersion coefficient. This study aims to conduct a theoretical and experimental study of the channel dispersion coefficient, yielding more information about their direct determination in the literature.

In this paper, we propose an algorithm for computation of the transport coefficients of rarefied gas, which is based on stochastic modeling of phase trajectories considered molecular system. The hard spheres potential is used. The number of operations is proportional to the number of used molecules. Naturally in this algorithm the conservation laws are performed. The efficiency of the algorithm is demonstrated by the calculation of the viscosity and diffusion coefficients of several noble gases (argon, neon, xenon, krypton). It was shown that the algorithm accuracy of the order of 1-2% can be obtained by using a relatively small number of molecules. The accuracy dependence on the number of used molecules, statistics (number of the used phase trajectories) and calculation time was analyzed.

A single phase heat and mass model has always been used to represent the moisture and temperature distribution during the drying of food. Several effects of the drying process, such as physical and structural changes, have been considered in order to increase understanding of the movement of water and temperature. However, the comparison between the heat and mass equation with and without structural change (in terms of shrinkage), which can affect the accuracy of the prediction model, has been little investigated. In this paper, two mathematical models to describe the heat and mass transfer in food, with and without the assumption of structural change, were analysed. The equations were solved using the finite difference method. The converted coordinate system was introduced within the numerical computations for the shrinkage model. The result shows that the temperature with shrinkage predicts a higher temperature at a specific time compared to that of the non-shrinkage model. Furthermore, the predicted moisture content decreased faster at a specific time when the shrinkage effect was included in the model.

We describe a smooth structure, called Frolicher space, on CW complexes and spaces of triangulations. This structure enables differential methods for e.g. minimization of functionnals. As an application, we exhibit how an optimized triangulation can be obtained in order to get an optimized H¹ approximation in a prescribed a class of triangulations.

Applying appropriate electric pulses to a nematic liquid crystal confined between plates, the bulk order reconstruction can occur, a mechanism allowing the switching between topologically different nematic textures without any director rotation. Using a moving mesh finite element method we describe the order tensor dynamics for a nematic inside an asymmetric n-cell, putting in evidence as textural distortions induced by strong asymmetries can be relaxed via both bulk and surface order reconstruction, occurring close to a confining plate with different time duration.

The lattice Boltzmann method (LBM) is a suitable tool for solving transport phenomena that occur in gas- and liquid phases at different length scales, especially when complex geometries such as porous media are involved. However, investigations about applications of LBM in the solid electrical conducting material have not been carried out yet. Since in fuel cells (FCs) the multifunctional layers play an important role during the energy conversion process, and such layers consist of porous material, the ohmic resistance of porous materials represents a crucial characteristic to be studied to predict the internal ohmic losses. The purpose of this paper is to show the feasibility of LBM to determine the ohmic resistance of electrical conducting materials whose dimensions are modified considering the crosssectional area and length. Characteristics, limitations and recommendations of LBM applied to solid electrical conducting materials calculating the ohmic resistance are presented considering the coupling of the methodology with the Ohm's Law. Additionally, the behavior of the ohmic resistance for a given porous material is presented.

Among the people moving as a group there appear social and psychological forces together with physical forces such as friction and resistance. With the definition that the field of the crowd is the region of those forces continuously extending with varying strength, and with the pre-requisite that the spatial distribution of the crowd, i.e., the distribution of the field, varies according to the hydrodynamic rule by the Navier-Stokes equation, a methodology was proposed to describe the behavior of the crowd composed of many agent particles as the movement of a compressible, turbulent fluid. A numerical calculation was exemplified for the dynamic behavior and spatial distribution of crowds during movements when there appears a conflict between groups with different characters, imaging for instance the medieval battle of Breitenfeld.

The following will introduce the A.I.E.S model, in which nonlinear maps determine the evolution of an inanimate substance to form an organic substance (Biopoiesis). We will demonstrate that when relating this model to a window of coherence that appears in the chaotic bifurcation diagram, a biological characteristics of warm-blood animate systems appears. Our model provides a mathematical platform in understanding Biopoiesis, that is, the process by which living organisms develop from inanimate matter.

An application of the graph model of inter-subject links to University courses of Physics and Chemistry is presented in this article. A part of inter-subject space with directions of inter-subject links from Physics to Chemistry in the group of physical concepts has been shown. The graph model of inter-subject links includes quantitative indicators. Its numerical values are given in the article. The degree of connectedness between the data of Physics and Chemistry courses is discussed for the courses considered. The effect of the courses placement within a curriculum on the value of their connectedness is shown. The placement of courses within a curriculum can provide the study of the courses at the same time or consecutive study, when one course precedes another.

This article discusses a numerical model describing optimization of fibres winding process on open and closed frame. The quality production of said type of composite frame depends primarily on the correct winding of fibers on a polyurethane core. It is especially needed to ensure the correct angles of the fibers winding on the polyurethane core and the homogeneity of individual winding layers. The article describes mathematical model for use an industrial robot in filament winding and how to calculate the trajectory of the robot. When winding fibers on the polyurethane core which is fastened to the robot-end-effector so that during the winding process goes through a fibre-processing head on the basis of the suitably determined robot-end-effector trajectory. We use the described numerical model and matrix calculus to enumerate the trajectory of the robot-end-effector to determine the desired passage of the frame through the fibre-processing head. The calculation of the trajectory was programmed in the Delphi development environment. Relations of the numerical model are important for use a real solving of the passage of a polyurethane core through fibre-processing head.

In this work, we propose a non-linear differential equation of Riccati-type, where the standard partition function Z(T) is taken as its particular solution leading to their generalization Z_g(T); from there, other related statistical thermodynamic functions are generalized. As an useful application of our proposal, other thermodynamic functions, namely, the internal energy, heat capacity, Helmholtz free energy and entropy, associated to the model of the ideal monatomic gas in D-dimensions are generalized. According to our results, thermodynamic properties derived from the standard partition functions by means of ordinary statistical mechanics are incomplete. In fact, although asymptotically with the increasing of temperature the generalized statistical thermodynamic functions reduce to the standard ones, these contain an extra term which is dominant at very low temperature indicating that standard findings should be corrected.

The dynamics of the director reorientation in nematic liquid crystals (NLC) confined by cylindrical cavities of porous polymeric films under strong electric field E with has been investigated theoretically. The main attention was paid to the specific mode of field application characterized by abrupt changes of the applied voltage's polarity. In experiments with porous films filled with a liquid crystal 5CB such mode resulted in appearance of strong peak -like decreasing of an optical transparence of the films. Two mechanisms of such unusual response based on assumption of electrically induced motion of ions and overall motion of a liquid were considered and applied to explain experimental results.

We examine the relationship between trading volumes, number of transactions, and volatility using daily stock data of the Tokyo Stock Exchange. Following the mixture of distributions hypothesis, we use trading volumes and the number of transactions as proxy for the rate of information arrivals affecting stock volatility. The impact of trading volumes or number of transactions on volatility is measured using the generalized autoregressive conditional heteroscedasticity (GARCH) model. We find that the GARCH effects, that is, persistence of volatility, is not always removed by adding trading volumes or number of transactions, indicating that trading volumes and number of transactions do not adequately represent the rate of information arrivals.

The dynamics of the periodic distortions in confined nematic liquid crystals (LCs) has been investigated theoretically basing on the hydrodynamic theory including the director motion with appropriate boundary and initial conditions. Analysis of the numerical results for the turn-on process provides an evidence for the appearance of the spatially periodic patterns in confined LC film, only in response to the suddenly applied strong electric field. It has been shown that there is a threshold value of the amplitude of the thermal fluctuations of the director over the LC sample which provides the nonuniform rotation mode rather than the uniform one, whereas the lower values of the amplitude dominate the uniform mode. During the turn-off process the reorientation of the director to the direction preferred by the surfaces is characterized by the complex destruction of the initially periodic structure to a monodomain state.

The quantization procedure of the vector potential is enhanced at a single photon state revealing the possibility for a simultaneous representation of the wave-particle nature of the photon. Its relationship to the quantum vacuum results naturally. A vector potential amplitude operator is defined showing the parallelism with the Hamiltonian of a massless particle. It is further shown that the quantized vector potential satisfies both the wave propagation equation and a linear time-dependent Schrödinger-like equation.

For a hybrid discrete-continual model describing a system which consists of a substrate and polymer coating, we provide computer simulation of its mechanical properties for various levels of deformations. For the substrate, we apply the elastic model with the Hooke law while for the polymeric coating, we use a discrete model. Here we use the Stockmayer potential which is a Lennard-Jones potential with additional term which describes the dipole interactions between neighbour segments of polymer chains, that is Keesom energy. Using Monte-Carlo method with Metropolis algorithm for a given temperature the equilibrium state is determined. We obtain dependencies of the energy, force, bending moment and Young's modulus for various levels of deformations and for different values of temperature. We show that for the increase of the deformations level the influence of surface coating on the considered material parameters is less pronounced. We provide comparison of obtained results with experimental data on deformations of crystalline polymers (gutta-percha, etc.)

The behavior of LC systems in alternating external fields is investigated; hysteresis curves are calculated. The dependencies of the area of the hysteresis curves on the frequency of the external field, at various values of temperature, amplitude of external field and of intermolecular interactions constants are discussed. The position of maximum and the peak height depending on the temperature and the of interactions constants are investigated.

This paper describes a mathematical model of the main fracture isolation in porous media by water-based mature gels. While modeling injection, water infiltration from the gel pack through fracture walls is taking into account, due to which the polymer concentration changes and the residual water resistance factor changes as a consequence. The salutation predicts velocity and pressure fields of the non-Newtonian incompressible fluid filtration for conditions of a non-deformable formation as well as a gel front trajectory in the fracture.

The mathematical model of agent injection into the main fracture is based on the fundamental laws of continuum mechanics conservation describing the flow of non-Newtonian and Newtonian fluids separated by an interface plane in a flat channel with permeable walls. The mathematical model is based on a one-dimensional isothermal approximation, with dynamic parameters pressure and velocity, averaged over the fracture section.

Experimental studies of estimation the mutual influence of humidity and flux of cosmic rays in first approximation were carried out. Normalized cross-correlation function of time series of neutron monitors count rate and level of relative atmosphere humidity near cosmic rays registration point is studied. Corrected and uncorrected on pressure minute and hour data of 6NM64 neutron monitor count rate were used for the study. Neutron monitor is located in Al-Farabi Kazakh National University, at an altitude of 850 m above sea level. Also, data from NM64 neutron monitor of Tien Shan mountain research station of Institute of Ionosphere, located at an altitude of 3340 m above sea level were used. Uncorrected on pressure cosmic rays intensity better reflects the changes in relative atmosphere humidity. Average and sometimes strong relationship is often observed by time changes of atmosphere humidity near the point of cosmic rays detection and their intensity: the value of normalized cross-correlation function of respective signals, even in case of their long duration and a large number of data (eg, for minute changes at intervals of up to several months) covers 0.5 - 0.75 range, sometimes falling to ∼⃒ 0.4.

At Helmholtz-Zentrum Berlin (HZB) the end-station PEAXIS (Photo Electron Analysis and X-ray resonant Inelastic Spectroscopy) combining Angle-dependent X-ray Photoelectron Spectroscopy (AdXPS) and Resonant Inelastic X-ray Scattering (RIXS) is currently built. The latter method uses a spherical variable line space (VLS) grating to focus the beam onto the detector. Working in first-order diffraction allows resolving photon energy by transferring the energy-dependent signal to a position-dependent focal spot on the detector. Focusing requires a precise combination of various parameters of the VLS grating and the geometry of the RIXS spectrometer. The VLS grating was optimized by calculating the geometry parameters for different photon energies, simulating the instrument and evaluating the pattern on the detector. As figure of merit we chose the intensity times the square of the resolving power averaged over the photon energies.

One of the major contradictions in subject teaching is the contradiction between the unity of the world and the discrete separated generalized content of natural sciences that study natural phenomena. These are physics, chemistry, biology and more. One can eliminate the conflict if opens the content's interdisciplinary links set by the events that are studied by different disciplines. The corresponding contexts of the phenomenon content arise depending on the discipline, and they are not enough coordinated. Obviously, we need a mechanism that allows establishing interdisciplinary links in the content quickly and without losing the logic of the material and assess their coherence in academic disciplines. This article uses a quantitative method of coherence assessment elaborated by T.N. Gnitetskaya. The definition of the concept of the semantic state introduced by the authors is given in this article. The method is applied to coherence assessment of physics and chemistry textbooks. The coherence of two pairs of chemistry and physics textbooks by different authors in different combinations was calculated. The most cohered pairs of textbooks (chemistry-physics) were identified. One can recommend using the pair of textbooks for eighth grade that we offered that favors the development of holistic understandings of the world around us.

The anomalous diffusion of a particle that moves in complex environments is analytically studied by means of the time fractional diffusion equation. The influence on the dynamics of a random moving particle caused by a uniform external field is taken into account. We extract analytical solutions in terms either of the Mittag-Leffler functions or of the M- Wright function for the probability distribution, for the velocity autocorrelation function as well as for the mean and the mean square displacement. Discussion of the applicability of the model to real systems is made in order to provide new insight of the medium from the analysis of the motion of a particle embedded in it.

Although chemo- and radiotherapy can annihilate tumors on their own. they are also used in coadjuvancy: improving local effects of radiotherapy using chemotherapy as a radiosensit.izer. The effects of radiotherapy are well described by current radiobiological models. The goal of this work is to describe a discrete radiotherapy model, that has been previously used describe high radiation dose response as well as unusual radio-responses of some types of tumors (e.g. prostate cancer), to obtain a model of chemo+radiotherapy that can describe how the outcome of their combination is a more efficient removal of the tumor. Our hypothesis is that, although both treatments haven different mechanisms, both affect similar key points of cell metabolism and regulation, that lead to cellular death. Hence, we will consider a discrete model where chemotherapy may affect a fraction of the same targets destroyed by radiotherapy. Although radiotherapy reaches all cells equally, chemotherapy diffuses through a tumor attaining lower concentration in its center and higher in its surface. With our simulations we study the enhanced effect of combined therapy treatment and how it depends on the tissue critical parameters (the parameters of the lion-extensive radiobiological model), the number of "targets" aimed at by chemotherapy, and the concentration and diffusion rate of the drug inside the tumor. The results show that an equivalent, cliemo-radio-dose can be computed that allows the prediction of the lower radiation dose that causes the same effect than a radio-only treatment.

Oscillations of a dislocation segment dependence on the external forces are considered. Expressions are obtained for matrix elements which are expressed by means of the generalized susceptibilities matrix of dislocation oscillators. Elimination of non-physical features in the range of large wave numbers was made within the Peierls dislocation model. An expression was obtained describing the low-frequency asymptotic behavior of the diagonal and non-diagonal elements of the generalized susceptibilities matrix of dislocation oscillators.

The system of equations describing the bending vibrations of the dislocation in the ferromagnetic crystal is written. Elastic and magnetostrictive properties of the ferromagnetic crystals are considered isotropic. The linearization of the resulting system produced a relatively small contribution to the magnetization from the influence of dislocation. In the linear approximation of the dislocation displacement system of equation describing vibrations of a ferromagnetic crystal with an edge dislocation is obtained. The equation of motion of an edge dislocation in a ferromagnetic crystal is found.

Ion channel systems are a class of proteins that reside in the membranes of all biological cells and forms conduction pores that regulate the transport of ions into and out of cells. They can be investigated theoretically in the microcanonical formalism since the number of accessible states can be easily evaluated by using the Stirling approximation to deal with factorials. In this work, we have used gamma function (Γ (n)) to solve the two-state or open-close channel model without any approximation. New values are calculated for the open probability (p₀) and the relative error between our numerical results and the approximate one using Stirling formula is presented. This error (p₀^app — p₀)/p₀ is significant for small channel systems.

The amplitude of the electric fields around the vibrating edge dislocation on the distance from the dislocation line in long-wave and short-wave cases is found. The laws of decrease modulus of the amplitude of the electric fields at the distance from the dislocation line are determined.

This work presents the numerical solution of laminar incompressible viscous flow in a three dimensional branching channel with circle cross section for generalized Newtonian fluids. The governing system of equations is based on the system of balance laws for mass and momentum. Numerical solution is based on cetral finite volume method using explicit Runge- Kutta time integration. In the case of unsteady computation artificial compressibility method is considered.

The problem of probability density function estimation for a random process is one of the most common in practice. There are several methods to solve this problem. Presented laboratory work uses methods of the mathematical statistics to detect patterns in the realization of random process. On the basis of ergodic theory, we construct algorithm for estimating univariate probability density distribution function for a random process. Correlational analysis of realizations is applied to estimate the necessary size of the sample and the time of observation. Hypothesis testing for two probability distributions (normal and Cauchy) is used on the experimental data, using χ2 criterion. To facilitate understanding and clarity of the problem solved, we use ELVIS II platform and LabVIEW software package that allows us to make the necessary calculations, display results of the experiment and, most importantly, to control the experiment. At the same time students are introduced to a LabVIEW software package and its capabilities.

We have developed an analytical dual-frequency model, which results in accurate dual-peaks of the ion energy distributions (IEDs) for the given control parameters. The model can analytically calculate and predict the IEDs dual peaks and energy width with necessary plasma parameters. This model can also predict the IEDs from dual frequencies' drives at any voltage, the associated results are compared with particle-in-cell (PIC) simulations. The IED at a surface is an important parameter for processing in dual radio frequencies driven capacitive couple discharges. The computing model is developed for the IED in a low pressure discharge based on a linear transfer function that relates the time-varying sheath voltage to the time- varying ion energy response at the surface. This model is in good agreement with PIC simulations over a wide range of dual frequencies driven capacitive couple discharge excitations.

The present work accounts centrifugal stiffening effect on the nonlinear vibration response of an FGM Timoshenko beam. Analysis is carried out for a cantilever beam fixed with a rotating hub. Material is assumed to have a gradation relation along the depth of the beam. Centrifugal force and axial displacement raised due to the rotating hub is incorporated in the strain energy equations. Subsequent to this, an iterative technique is employed to obtain amplitude dependent vibration response of a rotating Timoshenko beam while material follows a gradation relation along the beam depth. Main objective of the work is to obtain the effects of rotational speeds, hub radius, and different gradation relations on the linear as well as nonlinear frequencies and mode shapes.

The present work considers analysis of adhesive friction of rough surfaces using n- point asperity concept for statistical definition of surface roughness features, and accurate finite element analysis of elastic-plastic deformation of single asperity contact. Well defined adhesion index and plasticity index are used to study the prospective contact situations arising out of variation in material properties and surface roughness features. From the present results it is possible to locate the combinations of adhesion index and plasticity index that may yield very low coefficient of friction. Thus suitable choice of surface and material parameters for the contact of two rough surfaces can be made in order to minimize friction typically at low load and micro scale roughness situations.

This paper studies the non-negativity and stability properties of the solutions of a newly proposed SEIADR model which incorporates asymptomatic and dead-infective subpopulations to those defining the standard SEIR model and, in parallel, it incorporates feedback vaccination and antiviral treatment controls.

The article deals with one-dimensional problem of rise-time distortion signal without carrying signal, that appears in the starting point intermittently, that is signal distortion at front edge or one of its derivative. The authors show that front edge of signal isn't distorted in case of propagation in unrestricted (including absorbing) area (amplitude of starting signal step or of one of its derivatives doesn't change) and move with the accuracy of vacuum light speed. The paper proves that it is the time interval shortage that causes signal loss with the route extension, but not the reduction of its starting amplitude, during which front edge of signal retains its starting value. The research presents new values for this time interval.

The article presents the results of a study of the transfer functions of a construction machine as a complex dynamic system. Authors constructed a dynamic model of a construction machine. The paper formulates and solves a system of nonlinear differential equations of motion of the chassis system of a construction machine on the basis of the d'Alembert- Lagrange equation. The numerical values of the transfer function coefficients for the construction machines were determined from the experimentally obtained curves of acceleration, processed by area method. Authors determined the experimental curves of the transition process of chassis system of a construction machine. The results of the study show that the difference of source curves ordinates and calculation of transients is less than 4% on average, which indicates a fairly accurate description of the process. The resulting expressions of transfer system functions of the chassis with sufficient precision can be used for practical purposes in the design and development of new construction machines.

Composite shell structures are extensively used in aerospace, civil, marine and other engineering applications. In practical civil engineering applications, the necessity of covering large column free open areas is often an issue and hyperbolic paraboloid shells are used as roofing units. Quite often, to save weight and also to provide a facility for inspection, cutouts are provided in shell panels. The paper considers free vibration characteristics of stiffened composite hyperbolic paraboloid shell panel with cutout in terms of natural frequency and mode shapes. A finite element code is developed for the purpose by combining an eight noded curved shell element with a three noded curved beam element. The size of the cutouts and their positions with respect to the shell centre are varied for different edge conditions to arrive at a set of inferences of practical engineering significances.

Classification of aircraft targets from scattered electromagnetic waves is a challenging application, which suffers from aspect angle dependency. In order to eliminate the adverse effects of aspect angle, various strategies were developed including the techniques that rely on extraction of several features and design of suitable classification systems to process them. Recently, a hierarchical method, which uses features that take advantage of waveform structure of the scattered signals, is introduced and shown to have effective results. However, this approach has been applied to the special cases that consider only a single planar component of electric field that cause no-cross polarization at the observation point. In this study, two small scale aircraft models, Boeing-747 and DC-10, are selected as the targets and various polarizations are used to analyse the cross-polarization effects on system performance of the aforementioned method. The results reveal the advantages and the shortcomings of using waveform structures in time-domain target identification.

Multi-dimensional transfer functions (MDTF) are occasionally designed as two-step approaches. At the first step, the constructed domain is modelled coarsely using global volume statistics and an initial transfer function (TF) is designed. Then, a finer classification is performed using local information to refine the TF design. In this study, both a new TF domain and a novel two-step MDTF strategy are proposed for visualization of abdominal organs. The proposed domain is generated by aligning the histograms of the slices, which are reconstructed based on user aligned majority axis/regions through an interactive Multi-Planar Reconstruction graphical user interface. It is shown that these user aligned histogram stacks (UAHS) exploit more a priori information by providing tissue specific inter-slice spatial domain knowledge. For initial TF design, UAHS are approximated using a multi-scale hierarchical Gaussian mixture model, which is designed to work in quasi real time. Then, a finer classification step is carried out for refinement of the initial result. Applications to several MRI data sets acquired with various sequences demonstrate improved visualization of abdomen.

Optical character recognition is one of the important issues in the field of pattern recognition. This paper presents a method for recognizing handwritten digits based on the modeling of convolutional neural network. The integrated fuzzy logic module based on a structural approach was developed. Used system architecture adjusted the output of the neural network to improve quality of symbol identification. It was shown that proposed algorithm was flexible and high recognition rate of 99.23% was achieved.

Railway bed gravel foundation has a constant permanent impact on urban ecology and ground surface. It is only natural that larger objects, such as railway stations, make broader impact. Surface run-off waters polluted by harmful substances existing in railroad track body (ballast section) flow along railroad tracks and within macadam, go down into subterranean ground flow and then enter neighbouring rivers and water basins. This paper presents analytic calculations and characteristics of surface run-off liquid filtration which flows through gravel multiple layers (railroad track ballast section). The authors analyse liquids with various density and viscosity flowing in multi-layer porous medium. The paper also describes liquid stationary and non-stationary weepage into gravel foundation of railroad tracks.

Minimum-phase (MP) filters have all zeros inside and/or unit circle. As a consequence, the group delay of an MP system is always less than that of non-minimum phase systems, having the equal magnitude responses. Minimum-phase (MP) filters find applications where it is necessary to have a low group delay, like in communications, speech processing, and predictive coding, among others. This paper presents a novel simple method for the direct design of low-pass minimum-phase (MP) filters. Method is based on design of two compensated combs, using a multiplier-less minimum-phase compensator, and sharpening technique. The first comb defines the stop band and pass band of the MP filter, while the second comb decreases side lobes of the first comb, thus increasing attenuation of the resulting MP filter. Knowing that all zeros of comb filter are on the unit circle, the compensated comb is also a MP filter. Similarly, under the special condition, the sharpening of multiplier-less compensated comb may also result in a MP multiplier-less filter. The benefit of the proposed method is illustrated in the provided design examples.

We perform Monte-Carlo simulations of the anti-ferromagnetic (AF) spin-1 Blume- Capel (BC) model and the AF Ising model on triangular lattice. We estimate the exact critical magnetic fields for both models at zero temperature using the Wang-Landau sampling method. We also show the phase diagrams and the critical lines for the models using the joint density functions. We find that the shapes of critical lines for the models are identical, but the phase transitions across the critical lines are different.

The off-lattice AB heteropolymer model, consisting of the hydrophobic (A) and hydrophilic (B) polymers, is one of popular protein models. Its energy function includes the bending energy and the van der Waals interaction energy. The properties and the energy landscape of the C-terminal beta-hairpin of protein G are studied in the off-lattice AB heteropolymer model with conformational space annealing, a powerful global optimization method.

Mesh generation for TCAD modeling is challenging. Because densities of carriers can change by several orders of magnitude in thin areas, a significant change of the solution can be observed for two very similar meshes. The mesh must be defined at best to minimize this change. To address this issue, a criterion based on polynomial interpolation on adjacent nodes is proposed that adjusts accurately the mesh to the gradients of Degrees of Freedom. Furthermore, a dynamic mesh that follows changes of DF in DC and transient mode is a powerful tool for TCAD users. But, in transient modeling, adding nodes to a mesh induces oscillations in the solution that appears as spikes at the current collected at the contacts. This paper proposes two schemes that solve this problem. Examples show that using these techniques, the dynamic mesh generator of the TCAD tool ECORCE handle semiconductors devices in DC and transient mode.

Current HPC clusters are capable to reduce execution time of parallelized tasks significantly. The paper discusses the use of two selected strategies of cluster computational resources allocation and their impact on parallel efficiency of fire simulation. Simulation of a simple corridor fire scenario by Fire Dynamics Simulator parallelized by the MPI programming model is tested on the HPC cluster at the Institute of Informatics of Slovak Academy of Sciences in Bratislava (Slovakia). The tests confirm that parallelization has a great potential to reduce execution times achieving promising values of parallel efficiency of the simulation, however, the results also show that the use of increasing numbers of computational meshes resulting in increasing numbers of used computational cores does not necessarily decrease the execution time nor the parallel efficiency of simulation. The results obtained indicate that the simulation achieves different values of the execution time and the parallel efficiency in regard of the used strategy for cluster computational resources allocation.

In recent years significant progress have been made in the development of nonlinear data processing techniques. Such techniques are widely used in digital data filtering and image enhancement. Many of the most effective nonlinear filters based on order statistics. The widely used median filter is the best known order statistic filter. Generalized form of these filters could be presented based on Lloyd's statistics. Filters based on order statistics have excellent robustness properties in the presence of impulsive noise. In this paper, we present special approach for synthesis of order statistics filters using artificial neural networks. Optimal Lloyd's statistics are used for selecting of initial weights for the neural network. Adaptive properties of neural networks provide opportunities to optimize order statistics filters for data with asymmetric distribution function. Different examples demonstrate the properties and performance of presented approach.

In this paper, we provide an approximate analysis of an M/M/s queue using the operator method (strong stability method). Indeed, we use this approach to study the stability of the M/M/∞ system (ideal system), when it is subject to a small perturbation in its structure (M/M/s is the resulting perturbed system). In other words, we are interested in the approximation of the characteristics of an M/M/s system by those of an M/M/∞ one. For this purpose, we first determine the approximation conditions of the characteristics of the perturbed system, and under these conditions we obtain the stability inequalities for the stationary distribution of the queue size. To evaluate the performance of the proposed method, we develop an algorithm which allows us to compute the various obtained theoretical results and which is executed on the considered systems in order to compare its output results with those of simulation.

In this paper we consider the coupled Kadomtsev-Petviashvili system. From compatibility conditions we obtain the form of matrix operators. After using a gauge transformation, obtained a new type of Lax representation for the hierarchy of Heisenberg ferromagnet equation, which is equivalent to the gauge coupled Kadomtsev-Petviashvili system.

The use of space-time geodesic approach of classical mechanics is investigated, in order to derive time adaptive high order phase fitted variational integrators. The proposed technique is employed for systems of which the Lagrangian is of separable form. To this end, first the unfolding of the standard Euler-Lagrange system to its space-time manifold is presented and then it is rewritten as a geodesic problem with zero potential energy. Preliminary simulation results (without optimizing the choice of step sizing) show that one can use the spacetime geodesic formulation to generate an adaptive scheme that still preserves some underlying geometric structure.

In this Invited paper, we begin by a historical introduction to provide a motivation for the classical problems of interatomic force computation and associated challenges. This analysis will lead us from early theoretical and experimental accomplishments to the integration of these fascinating interactions into the operation of realistic, next-generation micro- and nanodevices both for the advanced metrology of fundamental physical processes and in breakthrough industrial applications. Among several powerful strategies enabling vastly enhanced performance and entirely novel technological capabilities, we shall specifically consider Casimir force time-modulation and the adoption of non-trivial geometries. As to the former, the ability to alter the magnitude and sign of the Casimir force will be recognized as a crucial principle to implement thermodynamical nano-engines. As to the latter, we shall first briefly review various reported computational approaches. We shall then discuss the game-changing discovery, in the last decade, that standard methods of numerical classical electromagnetism can be retooled to formulate the problem of Casimir force computation in arbitrary geometries. This remarkable development will be practically illustrated by showing that such an apparently elementary method as standard finite-differencing can be successfully employed to numerically recover results known from the Lifshitz theory of dispersion forces in the case of interacting parallel-plane slabs. Other geometries will be also be explored and consideration given to the potential of non-standard finite-difference methods. Finally, we shall introduce problems at the computational frontier, such as those including membranes deformed by Casimir forces and the effects of anisotropic materials. Conclusions will highlight the dramatic transition from the enduring perception of this field as an exotic application of quantum electrodynamics to the recent demonstration of a human climbing vertically on smooth glass.