Table of contents

The first International Conference on Mathematical Modelling in Physical Sciences (IC-MSQUARE) took place in Budapest, Hungary, from Monday 3 to Friday 7 September 2012. The conference was attended by more than 130 participants, and hosted about 290 oral, poster and virtual papers by more than 460 pre-registered authors. The first IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields in which mathematical modelling is used, such as theoretical/mathematical physics, neutrino physics, non-integrable systems, dynamical systems, computational nanoscience, biological physics, computational biomechanics, complex networks, stochastic modelling, fractional statistics, DNA dynamics, and macroeconomics. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, two parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time.

The mounting question is whether this occurred accidentally, or whether IC-MSQUARE is a necessity in the field of physical and mathematical modelling. For all of us working in the field, the existing and established conferences in this particular field suffer from two distinguished and recognized drawbacks: the first is the increasing orientation, while the second refers to the extreme specialization of the meetings. Therefore, a conference which aims to promote the knowledge and development of high-quality research in mathematical fields concerned with applications of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology, environmental sciences etc., appears to be a necessity. This is the key role that IC-MSQUARE will play.

We would like to thank the Keynote Speaker and the Invited Speakers for their significant contributions to IC-MSQUARE. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee.

Conference Chairmen

Theocharis Kosmas Department of Physics, University of Ioannina

Elias Vagenas RCAAM, Academy of Athens

Dimitrios Vlachos Department of Computer Science and Technology, University of Peloponnese

The PDF also contains a list of members of the International Scientific Committes and details of the Keynote and Invited Speakers.

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.

Vascular diseases of the human brain are one of the reasons of deaths and people's incapacitation not only in Russia, but also in the world. The danger of an arteriovenous malformation (AVM) is in premature rupture of pathological vessels of an AVM which may cause haemorrhage. Long-term prognosis without surgical treatment is unfavorable. The reduced impact method of AVM treatment is embolization of a malformation which often results in complete obliteration of an AVM. Pre-surgical mathematical modeling of an arteriovenous malformation can help surgeons with an optimal sequence of the operation. During investigations, the simple mathematical model of arteriovenous malformation is developed and calculated, and stationary and non-stationary processes of its embolization are considered. Various sequences of embolization of a malformation are also considered. Calculations were done with approximate steady flow on the basis of balanced equations derived from conservation laws. Depending on pressure difference, a fistula-type AVM should be embolized at first, and then small racemose AVMs are embolized. Obtained results are in good correspondence with neurosurgical AVM practice.

A PD+PI type fuzzy logic controller with sliding surface is presented in this study. This controller consists of two parts which are PD type and PI type fuzzy logic units. Inputs to those fuzzy logic units are the sliding surface functions and their derivatives. The integrated controller is applied to two degrees of freedom vehicle active suspension model. Both time and frequency domain analysis are evaluated. Numerical results demonstrate that the proposed controller improves the vibration isolation of the vehicle body, without causing a suspension degeneration problem and without degrading road holding very much.

An approach to (normalized) infinite dimensional integrals, including normalized oscillatory integrals, through a sequence of evaluations in the spirit of the Monte Carlo method for probability measures is proposed. in this approach the normalization through the partition function is included in the definition. For suitable sequences of evaluations, the ("classical") expectation values of cylinder functions are recovered.

We present a new approach for the clustering of high dimensional data without prior assumptions about the structure of the underlying distribution. The proposed algorithm is based on a concept adapted from nuclear physics. To partition the data, we model the dynamic behaviour of nucleons interacting in an N-dimensional space. An adaptive nuclear potential, comprised of a short-range attractive (strong interaction) and a long-range repulsive term (Coulomb force) is assigned to each data point. By modelling the dynamics, nucleons that are densely distributed in space fuse to build nuclei (clusters) whereas single point clusters repel each other. The formation of clusters is completed when the system reaches the state of minimal potential energy. The data are then grouped according to the particles' final effective potential energy level. The performance of the algorithm is tested with several synthetic datasets showing that the proposed method can robustly identify clusters even when complex configurations are present. Furthermore, quantitative MRI data from 43 multiple sclerosis patients were analyzed, showing a reasonable splitting into subgroups according to the individual patients' disease grade. The good performance of the algorithm on such highly correlated non-spherical datasets, which are typical for MRI derived image features, shows that Nuclear Potential Clustering is a valuable tool for automated data analysis, not only in the MRI domain.

Ray tracing technique is an important tool not only for forward but also for inverse problems in Geophysics, which most of the seismic processing steps depends on. However, implementing ray tracing codes can be very time consuming. This article presents a computer library to trace rays in 2.5D media composed by stack of layers. The velocity profile inside each layer is such that the eikonal equation can be analitically solved. Therefore, the ray tracing within such profile is made fast and accurately. The great advantage of an analytical ray tracing library is the numerical precision of the quantities computed and the fast execution of the implemented codes. Although ray tracing programs already exist for a long time, for example the seis package by Červený, with a numerical approach to compute the ray. Regardless of the fact that numerical methods can solve more general problems, the analytical ones could be part of a more sofisticated simulation process, where the ray tracing time is completely relevant. We demonstrate the feasibility of our codes using numerical examples.

In this study an active controller is presented for vibration suppression of a full-bus suspension model that use air spring. Since the air spring on the full-bus model may face different working conditions, auxiliary chambers have been designed. The vibrations, caused by the irregularities of the road surfaces, are tried to be suppressed via a multi input-single output fuzzy logic controller. The effect of changes in the number of auxiliary chambers on the vehicle vibrations is also investigated. The numerical results demonstrate that the presented fuzzy logic controller improves both ride comfort and road holding.

Computer simulations of chemical systems can be used to reliably predict physical properties. Accurate molecular models, which are indispensable, are mathematically described by force fields, which have to be parameterized. Recently, an automated gradient-based parametrization procedure was published by the authors based on the minimization of a loss function between simulated and experimental physical properties. The applicability of the utilized algorithms is not trivial at all because of two reasons: First, simulation data is affected by statistical noise and second, the molecular simulations required for the loss function evaluations (involving finite differences approximations of gradients and Hessians) are extremely time-consuming. In this work, a more efficient approach to compute gradients and Hessians is presented. The method developed here is based on directional instead of partial derivatives. It is shown that up to 75% of the simulations can be avoided using this method.

The time dependent GinzburgLandau equations (TDGLE) are used to study the superconducting properties of a disk by taking into account the influence of internal defects. The Link variable algorithm is applied to a circular geometry surrounded by an insulator and immersed in an external magnetic field applied perpendicular to its plane. The TDGLE are used upon taking the magnetic field and the order parameter invariant along z-direction. We show that the magnetic response is substantially modified by the competition between the confinement geometry and the geometric position of the defects leads to vortex configurations which are not compatible with the symmetry of the sample geometry.

In recent years, algorithms and computer simulation methodologies have developed to the stage where simulation can now play a complementary role with experiment, aiding in interpretation of experimental data. Several different approaches to the study of superconductor samples have been developed and their use demonstrated. In this work, we solve numerically the nonlinear time dependent Ginzburg Landau equations to study the vortex dynamics in a mesoscopic type II cylinder superconductor containing one rectangular hole in the presence of an external field applied perpendicular to the surfaces. We calculate the spatial distribution of the superconducting electron density and the phase of the superconducting order parameter using the numerical method based on the technique of gauge invariant variables. It is assumed that the inner hole edge is in contact with a metallic material while the outer edge is in contact with vacuum. The vortex dynamics and the magnetization curves are studied as a function of the external magnetic field.

The Green's function contains much information about physical systems. Mathematically, the fractional moment method (FMM) developed by Aizenman and Molchanov connects the Green's function and the transport of electrons in the Anderson model. Recently, it has been discovered that the Green's function on a graph can be represented using self-avoiding walks on a graph, which allows us to connect localization properties in the system and graph properties. We discuss FMM in terms of the self-avoiding walks on a general graph with a small number of assumptions.

Quantum mechanical many-body systems described by an arbitrary Hamiltonian () are analyzed. It is shown how positive semidefinite operator () properties are able to lead in this case to exact results related to the ground state and the low lying part of the excitation spectrum. This is done independent on dimensionality and integrability. The technique first casts the Hamiltonian in a positive semidefinite form in exact terms ( = + C, where C is a scalar). Second, the ground state is deduced by constructing the most general Hilbert space vector, on which applying , one obtains zero as a result. It is underlined, that the procedure, if applied for variable total number of particles N, allows to obtain information also related to the low lying part of the excitation spectrum. The uniqueness of the ground states can be demonstrated via the study of the kernel of ' = − C. The physical properties of the obtained phases are deduced based on ground state expectation values calculated in terms of the constructed ground states. Since for a fixed structure of , usually the transformation = + C is exact only in a restricted parameter space domain (), the deduced ground states are present only in . A global view on the phase diagram is obtained by different transformations of in positive semidefinite form.

The minimum-phase requirement restricts that filter has all its zeros on or inside the unit circle. As a result the filter does not have a linear phase. It is well known that the sharpening technique can be used to simultaneous improvements of both the pass-band and stop-band of a linear-phase FIR filters and cannot be used for other types of filters. In this paper we demonstrate that the sharpening technique can also be applied to minimum-phase filters, after small modification. The method is illustrated with one practical examples of design.

Recent advances in computer fluid dynamics (CFD) and rapid increase of computational power of current computers have led to the development of CFD models capable to describe fire in complex geometries incorporating a wide variety of physical phenomena related to fire. In this paper, we demonstrate the use of Fire Dynamics Simulator (FDS) for cinema fire modelling. FDS is an advanced CFD system intended for simulation of the fire and smoke spread and prediction of thermal flows, toxic substances concentrations and other relevant parameters of fire. The course of fire in a cinema hall is described focusing on related safety risks. Fire properties of flammable materials used in the simulation were determined by laboratory measurements and validated by fire tests and computer simulations

This paper considers the analysis and design of OQPSK digital modulation. We first establish the discrete time formulation, which allows us to find the equivalent redundant filter banks. It is well known that redundant filter banks are related with redundant transformation of the Frame theory. According to the Frame theory, the redundant transformations and corresponding representations are not unique. In this way, we show that the solution to the pulse shaping problem is not unique. Then we use this property to minimize the effect of the channel noise in the reconstructed symbol stream. We evaluate the performance of the digital communication using numerical examples.

In this paper we suggest the method of 3D vector tomography problem solving. The problem consists in determination of potential part of 3D vector field by its known the normal Radon transform. The singular value decomposition of the normal Radon transform operator is obtained. Based on obtained decomposition inversion formula is derived. The decomposition can be the basis for numerical solution of given problem.

We know that the quantum system evolves to different physical phenomena according to initial states. However, the situation is very different in the open system. We consider the system and the environment governed by the Markovian process. The density matrix (the reduced density matrix) of the system satisfies the Kossakowski-Lindblad equation. We calculate the expectation value of the z-direction-magnetization in the system for various types of 1) initial states and 2) interactions between the system and the environment. In all the cases, the values of the magnetization approached asymptotically to the same point even though the different initial states and different interaction types between the system and the environment are applied. The paths to asymptotically approach the final values are different according to the initial states and the interactions. These facts show that the physical results of expectation value are independent of the initial states.

We propose a method for modeling the magnetic properties of nanomaterials with different structures. The method is based on the Ising model and the approximation of the random field interaction. It is shown that in this approximation, the magnetization of the nanocrystal depends only on the number of nearest neighbors of the lattice atoms and the values of exchange integrals between them. This gives a good algorithmic problem of calculating the magnetization of any nano-object, whether it is ultrathin film or nanoparticle of any shape and structure, managing only a rule of selection of nearest neighbors. By setting different values of exchange integrals, it is easy to describe ferromagnets, antiferromagnets, and ferrimagnets in a unified formalism. Having obtained the magnetization curve of the sample it is possible to find the Curie temperature as a function of, for example, the thickness of ultrathin film. Afterwards one can obtain the numerical values for critical exponents of the phase transition "ferromagnet – paramagnet". Good agreement between the results of calculations and the experimental data proves the correctness of the method.

Imaging of perfectly conducting crack(s) in a 2-D homogeneous medium using boundary data is studied. Based on the singular structure of the Multi-Static Response (MSR) matrix whose elements are normalized by an adequate test function at several frequencies, an imaging functional is introduced and analyzed. A non-iterative imaging procedure is proposed. Numerical experiments from noisy synthetic data show that acceptable images of single and multiple cracks are obtained.

Structural model of silicate melts and glasses obtained by rapid cooling of the melt is far from complete at present. Modern models suggest the existence of the five different types of silicon-oxygen tetrahedra which are distinguish by the ratio of bridging and terminal oxygen atoms per silicon atom (the so-called basic structural blocks or units) in the structure of silicate glasses and melts and also assume that the several types of such units can exist in the glass and melt structures simultaneously. The knowledge of the concentrations of these units depending on the composition and temperature (the so-called Qⁿ distribution) is a necessary element for the development of an adequate model of silicate systems and to explaining their physical and chemical properties. Three-parameter statistical method to modeling of Qⁿ distribution in silicate melts and glasses is present in this paper. This method allows calculating the concentration of structural units in a wide composition range at different temperatures. The method is based on a destruction of a preassigned network as a model of depolymerization of the silicon-oxygen framework in the process its interaction with the modifier oxides. Qⁿ distribution, distribution of silicon-oxygen tetrahedra according to their next-nearest neighbours, and distribution of bridging bonds in alkali-silicate glasses and melts were obtained in frame of the developed approach.

An homogeneous reactive azeotrope is a thermodynamic coexistence condition of two phases under chemical and phase equilibrium, where compositions of both phases (in the Ung-Doherty sense) are equal. This kind of nonlinear phenomenon arises from real world situations and has applications in chemical and petrochemical industries. The modeling of reactive azeotrope calculation is represented by a nonlinear algebraic system with phase equilibrium, chemical equilibrium and azeotropy equations. This nonlinear system can exhibit more than one solution, corresponding to a double reactive azeotrope. The robust calculation of reactive azeotropes can be conducted by several approaches, such as interval-Newton/generalized bisection algorithms and hybrid stochastic-deterministic frameworks. In this paper, we investigate the numerical aspects of the calculation of reactive azeotropes using two metaheuristics: the Luus-Jaakola adaptive random search and the Firefly algorithm. Moreover, we present results for a system (with industrial interest) with more than one azeotrope, the system isobutene/methanol/methyl-tert-butyl-ether (MTBE). We present convergence patterns for both algorithms, illustrating – in a bidimensional subdomain – the identification of reactive azeotropes. A strategy for calculation of multiple roots in nonlinear systems is also applied. The results indicate that both algorithms are suitable and robust when applied to reactive azeotrope calculations for this "challenging" nonlinear system.

The design of nuclear reactors gives rises to a series of optimization problems because of the need for high efficiency, availability and maintenance of security levels. Gradient-based techniques and linear programming have been applied, as well as genetic algorithms and particle swarm optimization. The nonlinearity, multimodality and lack of knowledge about the problem domain makes de choice of suitable meta-heuristic models particularly challenging. In this work we solve the optimization problem of a nuclear reactor core design through the application of an optimal sequence of meta-heuritics created automatically. This combinatorial optimization model is known as hyper-heuristic.

This work proposes the combination of multiscale transform with fractal descriptors employed in the classification of gray-level texture images. We apply the space-scale transform (derivative + Gaussian filter) over the Bouligand-Minkowski fractal descriptors, followed by a threshold over the filter response, aiming at attenuating noise effects caused by the final part of this response. The method is tested in the classification of a well-known data set (Brodatz) and compared with other classical texture descriptor techniques. The results demonstrate the advantage of the proposed approach, achieving a higher success rate with a reduced amount of descriptors.

In this paper we give the main ideas about the numerical temporal resolution of second order in time partial differential equations with high order symmetric multistep cosine methods. These methods are efficient numerical solvers when integrating second-order in time partial differential problems subject to periodic boundary conditions, like the nonlinear wave or the beam equations.

Every molecular structure can be regarded as a graph, and each graph can be transformed into characteristic scalar – topological index. There are many, over 1000 topological indices used by chemists, but they are not equally successful in solving specific problems. For the prediction of stability of coordination compounds valence molecular connectivity index of the 3rd order (³χ^v) proved best. Stability of these compounds was expressed as log K (K stays for stability constant), which is proportional to the Gibbs free energy of reaction between metal (or metal complex) and ligand. Various molecular graphs were checked, from a simple graph of ligand, to the graphs of various metal-ligand complexes (aqua complex, complex with additional bonds etc.) leading to conclusion that chemically sounder graphs generally yield better models. The best results were obtained for the systems of one metal, mesured at the same experimental conditions. However, our graph-theoretical approach enables development of models for the simulateneous prediction of stability constants of few metals.

The variational principle is one of important guiding principles in physics. Classical equations of motion of particle can be formulated so as to give the optimized path of an action. However, when there exist uncontrollable degrees of freedom such as noise, the optimized path is affected and the original classical equations of motion may not correspond to the optimized path. The stochastic variational method (SVM) is a framework to calculate the modified optimized path by the effect of noise. This method has been developed to show that the Schrödinger equation can be derived from the classical action which leads to Newton's equation of motion by taking into account the modification of the optimized path due to noise. In this work, we will extend this idea to the case of the continuum media and show that the Euler equation of the ideal fluid is converted to the Navier-Stokes equation or the Gross-Pitaevskii equation in SVM.

We propose a hierarchical logistic equation as a model to describe the dynamical behaviour of a penetration rate of a prevalent stuff. In this model, a memory, how many people who already possess it a person who does not process it yet met, is considered, which does not exist in the logistic model. As an application, we apply this model to iPod sales data, and find that this model can approximate the data much better than the logistic equation.

The work deals with numerical solutions of 2D inviscid and laminar compressible flows in the GAMM channel and DCA 8% cascade, and of 3D inviscid compressible flows in a 3D modification of the GAMM channel (Swept Wing). The FVM multistage Runge-Kutta method and the Lax-Wendroff scheme (Richtmyer's form) with Jameson's artificial dissipation were applied to obtain the numerical solutions. The results are discussed and compared to other similar results and experiments.

Background properties in experimental particle physics are typically estimated using large data sets. However, different events can exhibit different features both because of the quantum mechanical nature of the underlying physics and due to statistical fluctuations. While signal and background fractions in a given data set can be evaluated using a maximum likelihood estimator, the shapes of the corresponding distributions are traditionally obtained using high-statistics control samples, which normally neglects the effect of fluctuations. On the other hand, if it was possible to subtract background using templates that take fluctuations into account, this would be expected to improve the resolution of observables of interest, and to reduce systematics depending on the analysis. This study is an initial step in this direction. We propose a novel algorithm inspired by the Gibbs sampler that estimates the shapes of signal and background probability density functions from a given collection of particles, using control sample templates as initial conditions and refining them to include the effect of fluctuations. Results on Monte Carlo data are presented, and the prospects for future development are discussed.

The purpose of this study is to calculate the relationship between the circular shape of a corrugated waveguide and its electrical transfer characteristics by the finite-difference time-domain (FDTD) method. To improve the waveguide to transport with a lower loss of energy than the previous design, we optimize the waveguide structure by the time evolution of the electromagnetic fields in the waveguide. However, the calculation in a 3D model is difficult because of the large data size and the long calculation run time. Therefore, we used a cylindrical symmetry model. As a result of this simulation, a correlation of the electromagnetic field in the input source position and the output position has been calculated.

Differential Evolution (DE) algorithm is powerful in optimization problems over several real parameters. DE depends on strategies to generate new trial solutions and the associated parameter values for searching performance. In self-adaptive DE, the automatic learning about previous evolution was used to determine the best mutation strategy and its parameter settings. By combining the self-adaptive DE and Hooke Jeeves local search, we developed a new docking method named SADock (Strategy Adaptation Dock) with the help of AutoDock4 scoring function. As the accuracy and performance of SADock was evaluated in self-docking using the Astex diverse set, the introduced SADock showed better success ratio (89%) than the success ratio (60%) of the Lamarckian genetic algorithm (LGA) of AutoDock4. The self-adapting scheme enabled our new docking method to converge fast and to be robust through the various docking problems.

The purpose of this report is to give a brief overview of some unpublished results about the geometry of closed critical curves of a conformally invariant functional for space curves.

This work demonstrates that simulations of advanced burning plasma operation scenarios can be successfully parallelized in time using the parareal algorithm. CORSICA -an advanced operation scenario code for tokamak plasmas is used as a test case. This is a unique application since the parareal algorithm has so far been applied to relatively much simpler systems except for the case of turbulence. In the present application, a computational gain of an order of magnitude has been achieved which is extremely promising. A successful implementation of the Parareal algorithm to codes like CORSICA ushers in the possibility of time efficient simulations of ITER plasmas.

Some mixtures, such as colloids like milk, blood, and gelatin, have homogeneous appearance when viewed with the naked eye, however, to observe them at the nanoscale is possible to understand the heterogeneity of its components. The same phenomenon can occur in pattern recognition in which it is possible to see heterogeneous patterns in texture images. However, current methods of texture analysis can not adequately describe such heterogeneous patterns. Common methods used by researchers analyse the image information in a global way, taking all its features in an integrated manner. Furthermore, multi-scale analysis verifies the patterns at different scales, but still preserving the homogeneous analysis. On the other hand various methods use textons to represent the texture, breaking texture down into its smallest unit. To tackle this problem, we propose a method to identify texture patterns not small as textons at distinct scales enhancing the separability among different types of texture. We find sub patterns of texture according to the scale and then group similar patterns for a more refined analysis. Tests were performed in four static texture databases and one dynamical one. Results show that our method provide better classification rate compared with conventional approaches both in static and in dynamic texture.

We study the phase diagram of the Blume-Emery-Griffiths-Vannimenus model on a Cayley tree with competing nearest-neighbour couplings and next-nearest-neighbour couplings and show that a detailed study of its properties can be carried out with essentially exact results, using rather simple numerical methods. In addition to the expected paramagnetic and ferromagnetic phases, we find modulated phase for Blume-Emery-Griffiths model and hence for Blume-Emery-Griffiths-Vannimenus model also.

We study scattering problems for the one-dimensional nonlinear Dirac equation (∂_t + α∂_x + iβ)ϕ = λ|ϕ|^p−1ϕ. We prove that if p > 3 (resp. p > 3 + 1/6), then the wave operator (resp. the scattering operator) is well-defined on some 0-neighborhood of a weighted Sobolev space.

We discuss image formation in gravitational lensing system using wave optics. Applying the Fresnel-Kirchhoff diffraction formula to waves scattered by a gravitational potential of a lens object, we demonstrate how images of source objects are obtained directly from waves without using a lens equation for gravitational lensing.

This paper discusses the analogs of space-time five-dimensional tangent vectors for the case of internal symmetry vector spaces associated with gauge groups in elementary particle physics and their possible application in the Standard Model of quarks and leptons.

Complementary strands in DNA double helix show temporary fluctuational openings which are essential to biological functions such as transcription and replication of the genetic information. Such large amplitude fluctuations, known as the breathing of DNA, are generally localized and, microscopically, are due to the breaking of the hydrogen bonds linking the base pairs (bps). I apply imaginary time path integral techniques to a mesoscopic Hamiltonian which accounts for the helicoidal geometry of a short circular DNA molecule. The bps displacements with respect to the ground state are interpreted as time dependent paths whose amplitudes are consistent with the model potential for the hydrogen bonds. The portion of the paths configuration space contributing to the partition function is determined by selecting the ensemble of paths which fulfill the second law of thermodynamics. Computations of the thermodynamics in the denaturation range show the energetic advantage for the equilibrium helicoidal geometry peculiar of B-DNA. I discuss the interplay between twisting of the double helix and anharmonic stacking along the molecule backbone suggesting an interesting relation between intrinsic nonlinear character of the microscopic interactions and molecular topology.

The aim of the KATRIN experiment is to determine the absolute neutrino mass scale in a model independent way, by measuring the electron energy spectrum shape near the endpoint of tritium beta decay. For this purpose, the KATRIN experiment uses two spectrometers with high voltage, and many superconducting and air coils, to create the necessary electric and magnetic fields. In order to design the spectrometer electrodes and the coils, and to investigate and understand the various background processes and systematic effects, one needs various accurate electric and magnetic field, charged particle tracking and scattering computations, for which we use mainly our self-written C and C++ codes.

The sequential optimal experimental design formulated as an information-theoretic sensitivity analysis is applied to the ignition delay problem using real experimental. The optimal design is obtained by maximizing the statistical dependence between the model parameters and observables, which is quantified in this study using mutual information. This is naturally posed in the Bayesian framework. The study shows that by monitoring the information gain after each measurement update, one can design a stopping criteria for the experimental process which gives a minimal set of experiments to efficiently learn the Arrhenius parameters.

In this paper a new approach based on Least Squares Support Vector Machines (LS-SVMs) is proposed for solving delay differential equations (DDEs) with single-delay. The proposed method provides a closed form approximate model based solution without using any interpolation techniques. The result of this paper can be extended for DDE with multi-lags. The results of some numerical experiments are presented and compared with analytic solutions to confirm the validity and applicability of the proposed method.

We suggest a numerical solution of the problem by reconstruction of solenoidal part of the vector field defined in the unit ball. That is, approximation of solenoidal part of vector field is built by known ray transform, calculated along the lines parallel to one of the coordinate planes. Test calculations have shown good results of reconstruction solenoidal vector fields by using the proposed method.

In the Landau-de Gennes theory, the order parameter describing a biaxial nematic liquid crystal is, at each point of the region occupied by the system, a symmetric, traceless 3 × 3 matrix with three distinct eigenvalues. In the constrained case of matrices with constant eigenvalues, the order parameter space identifies with an eightfold quotient of the 3-sphere, and a configuration of a biaxial nematic liquid crystal is described by a map into such a quotient. We express the (simplest form of the) Landau-de Gennes elastic free-energy density of biaxial nematics as a density on maps into the 3-sphere, whose functional dependence is restricted by the requirements that it is well-defined on the class of configuration maps (residual symmetry) and is independent of arbitrary superposed rigid rotations (frame indifference). This is a report on joint work with D. Mucci [18], to which we refer for more details and applications.

The problem of making a network of dynamical systems synchronize onto a common evolution is the subject of much ongoing research in several scientific disciplines. It is nowadays a well-known fact that the synchronization processes are gradually influenced by the interaction topology between the dynamically interacting units. A complex coupling configuration can significantly affect the synchronization abilities of a networked system. However, the question arises what is the optimal network topology that provides enhancement of the synchronization features under given circumstances. In order to address this issue we make use of a network model in which we can smoothly tune the topology from a highly heterogeneous and efficient scale-free network to a homogeneous and less efficient network. The network is then populated with Poincaré oscillators, a paradigmatic model for limit-cycle oscillations. This oscillator model exhibits a parameter that enables changes of the limit cycle attraction and is thus immediately related to flexibility/rigidity properties of the oscillator. Our results reveal that for weak attractions of the limit cycle, intermediate homogeneous topology ensures maximal synchronization, whereas highly heterogeneous scale-free topology ensures maximal synchronization for strong attractions of the limit cycle. We argue that the flexibility/rigidity of individual nodes of the networks defines the topology, where maximal global coherence is achieved.

Two aspects of modern economic theory have dominated the recent discussion on the state of the global economy: Crashes in financial markets and whether or not traditional notions of economic equilibrium have any validity. We have all seen the consequences of market crashes: plummeting share prices, businesses collapsing and considerable uncertainty throughout the global economy. This seems contrary to what might be expected of a system in equilibrium where growth dominates the relatively minor fluctuations in prices. Recent work from within economics as well as by physicists, psychologists and computational scientists has significantly improved our understanding of the more complex aspects of these systems. With this interdisciplinary approach in mind, a behavioural economics model of local optimisation is introduced and three general properties are proven. The first is that under very specific conditions local optimisation leads to a conventional macro-economic notion of a global equilibrium. The second is that if both global optimisation and economic growth are required then under very mild assumptions market catastrophes are an unavoidable consequence. Third, if only local optimisation and economic growth are required then there is sufficient parametric freedom for macro-economic policy makers to steer an economy around catastrophes without overtly disrupting local optimisation.

We estimate the transmission efficiency of the electromagnetic wave through the system composed of waveguide and miter bend by Finite-Difference Time-Domain (FDTD) simulation. As the fisrt approach of this estimation, we choose the case that the input wave is TE₁₁ mode. In this case, the efficiency is estimated as 99.65 % for the system without grooves and 76.48 % for the system with grooves (which is called as "corrugate"). Comparing the distributions of the input electric field with that of the output electric field, the effect of the grooves is found as follows: Because the TE₁₁ mode has an anisotropy, its shape is changed by the miter bend. This property appears in the corrugated system more strongly than the non-corrugated system.

In recent years we have developed a technique for the direct computation of Feynman loop-integrals, which are notorious for the occurrence of integrand singularities. Especially for handling singularities in the interior of the domain, we approximate the iterated integral using an adaptive algorithm in the coordinate directions. We present a novel multi-core parallelization scheme for adaptive multivariate integration, by assigning threads to the rule evaluations in the outer dimensions of the iterated integral. The method ensures a large parallel granularity as each function evaluation by itself comprises an integral over the lower dimensions, while the application of the threads is governed by the adaptive control in the outer level. We give computational results for a test set of 3- to 6-dimensional integrals, where several problems exhibit a loop integral behavior.

This work proposed a generalization of the method proposed by the authors: 'A complex network-based approach for boundary shape analysis'. Instead of modelling a contour into a graph and use complex networks rules to characterize it, here, we generalize the technique. This way, the work proposes a mathematical tool for characterization signals, curves and set of points. To evaluate the pattern description power of the proposal, an experiment of plat identification based on leaf veins image are conducted. Leaf vein is a taxon characteristic used to plant identification proposes, and one of its characteristics is that these structures are complex, and difficult to be represented as a signal or curves and this way to be analyzed in a classical pattern recognition approach. Here, we model the veins as a set of points and model as graphs. As features, we use the degree and joint degree measurements in a dynamic evolution. The results demonstrates that the technique has a good power of discrimination and can be used for plant identification, as well as other complex pattern recognition tasks.

The structural and electronic properties of osmium (Os) have studied using the full potential linearized augmented plane wave method and the generalized gradient approximation for the exchange-correlation energy. The calculations were done incluiding the spin-orbit (SO) coupling and for hydrostatic pressures up to 400 GPa. The total-energy as a function of the cell volume was computed assuming four different crystal structures, namely hcp, fcc, hcp – ω and bcc. Contrary to previous non-relativistic LDA calculations our study shows that the equilibrium phase of Os correspond to the hcp structure and that remain stable in the studied range of pressures and no structural transition to the fcc, hcp – ω or bcc phases are obtained.

The exact partition functions of the Ising model on L × L square lattices with free boundary conditions are evaluated up to L = 19 using microcanonical transfer matrix. The critical behavior of the Ising antiferromagnet is analyzed using the partition function zeros for free boundary conditions and compared with the results for periodic boundary conditions.

We describe a substitution based sparse Jacobian matrix determination method using algorithmic differentiation. Utilizing the a priori known sparsity pattern, a compression scheme is determined using graph coloring. The "compressed pattern" of the Jacobian matrix is then reordered into a form suitable for computation by substitution. We show that the column reordering of the compressed pattern matrix (so as to align the zero entries into consecutive locations in each row) can be viewed as a variant of traveling salesman problem. Preliminary computational results show that on the test problems the performance of nearest-neighbor type heuristic algorithms is highly encouraging.

Although the concept of an observing device with memory is very simple and definable in terms of algorithmic machine, it is not compatible with a predictive theory involving this concept. This is sufficient to show that Physics as a whole cannot be deterministic; moreover, using the Conway-Kochen Free Will Theorem [1] and the simple logical proof of it we gave in [2], we show, without any need of free will or observer's freedom, that neither Quantum Mechanics nor any extension of this theory can be deterministic.

Modelling on Plasma and gas nitriding of austenitic and low alloy steels have strong influence of interfacial – nanoescale phenomena. Gamma prime and epsilon nitrogen-iron phases evolution during the nitriding process wasn't found explicitly simulated on literature. On present work we simulated nitrind process on low alloy steels – with their precipitation phenomena and nitrides moving interfaces – using diffusional models plus cellular automata. Surface effects and heterogeneities and local transition phenomena considered on our models show that some experimental results considered "errors" on literature are predicted by our simulations. In present work parameters like diffusion coefficient and surface conditions and gradient of nitrogen concentrations between different phases was measured.

We present a three-dimensional computational tool for atom-field interactions such as optically locked photon echoes in a three level system for both space and time axes, where time-dependent density matrix calculations are combined with iterative methods. We provide an exact numerical simulation tool without any approximations. To the best of our knowledge, this is the first computational tool for short-pulse light interactions with an optical medium, whose space dimension along the pulse propagation direction is simultaneously cared for density matrix calculations.

The baby Skyrme model is a well-known nonlinear field theory supporting topological solitons in two space dimensions. Its action functional consist of a potential term, a kinetic term quadratic in derivatives (the "nonlinear sigma model term") and the Skyrme term quartic in first derivatives. The limiting case of vanishing sigma model term (the so-called BPS baby Skyrme model) is known to support exact soliton solutions saturating a BPS bound which exists for this model. Further, the BPS model has infinitely many symmetries and conservation laws. Recently it was found that the gauged version of the BPS baby Skyrme model with gauge group U(1) and the usual Maxwell term, too, has a BPS bound and BPS solutions saturating this bound. This BPS bound is determined by a superpotential which has to obey a superpotential equation, in close analogy to the situation in supergravity. Further, the BPS bound and the corresponding BPS solitons only may exist for potentials such that the superpotential equation has a global solution. We also briefly describe some properties of soliton solutions.

In this paper, we study a new surface model for anisotropic membranes. The model is characterized by an interaction between the surface and a three-dimensional tilt order, of which projected components on the surface are recognized as a vector filed. This vector field defines a Finsler metric on the surface, and consequently the length unit on the surface becomes dependent on the position and direction. The induced interaction dynamically alters the surface tension and the bending rigidity. We numerically find that the tilts form the Kosterlitz-Thouless and low temperature configurations, which correspond to two different anisotropic phases such as disk and tubular on both of the connection-fixed and dynamically triangulated surfaces. The internal tilt order plays an important role for those anisotropic configurations.

We concern ourselves with the family of linear recurrence relations a_j = a_j−1+a_j−d with the initial conditions a₀ = . . . = a_d−1 = 1. We discuss the periodicity evaluation of such recurrences for prime powers d, and demonstrate that a key feature of our evaluation method relates to an instance of Shor's algorithm for factoring. As an application, we discuss how efficient quantum circuit designs may be completely recast as a problem relating to linear recurrence relations.

Random graphs (RG), also called mean field percolation in the frame of mesoscopic physics, are a basic model composed solely of connected entities called nodes. The connections, called bonds, can be active of broken. When the number of broken bonds is too large, the system of entities separates into a set of fragments called a partition. The exact solution for the micro-canonical partition probabilities of finite size systems was yet unresolved, thus a series of fundamental questions about the model could not be answered. We have established the exact equations of RG partition probabilities as a function of the number of nodes and of the number of broken bonds. From these probabilities, it is also possible to deduce intrinsic properties of RG. Many actual networks, while composed of complex interactions, behave like RG. We show examples where information was deduced, using RG, from systems consisting of sets of nucleons, atoms or termite nest chambers.

Operating biomass stoves in modern buildings with tight shells often requires a room-independent air supply. One possibility to arrange this supply is to use a double-wall chimney with fresh air entering through the annular gap. For this setup, a mathematical model has been developed and checked with experimental data. It turned out that for commercially available chimneys, leakage is not negligible and inclusion of leak air in the calculation is crucial for reproduction of the experimental data. Even with inclusion of this effect, discrepancies remain which call for further investigations and a refinement of the model.

In this work we study the stability of a method for the numerical solution of initial value problems, that combines finite differences with Simpson's rule. This method is applied to a one spatial dimension, convection-dominated transport problem. To solve the same problem in two spatial dimensions, the proposed method was used in combination with Strang's operator decomposition method.

Micro canonical, canonical and grand canonical systems are special cases of completely open systems. Within the framework of non-extensive and incomplete statistics, we derive the statistical distribution for a completely open system on the basis of incomplete Shannon entropy, using the maximum entropy principle. We calculate the physical properties of a linear filament using this distribution. The results are the same as those calculated using the incomplete E-V distribution, except that average values of the thermodynamic variables replace the corresponding constant values. However, the relative fluctuations in thermodynamic variables are completely different. In the canonical and grand canonical distributions, relative fluctuations are proportional to . In the incomplete statistical distribution for a completely open system, the relative fluctuations are proportional to 1. This result can explain some phenomenon that traditional and current statistical mechanics cannot explain, such as the large fluctuations of critical, super-cooled and overheated states.

We construct a bosonization of the quantum superalgebra for an arbitrary level k. We construct the screening that commutes with the quantum superalgebra for an arbitrary level k ≠ −N + 1. We propose a bosonization of the vertex operator that gives the intertwiner among the Wakimoto realization and the typical representation.

We consider the wealth and the money flow of the world trade data. We analyze the world trade data from year 1948 to 2000 which include the total amounts of the import and export for every country per year. We apply the analyzing methods of the complex networks to the world trade network. We define the wealth as the gross domestic products (GDP) of each country. We defined the backbone network of the world trade network. We generate the backbone network keeping the link with the largest wealth flowing out each country by the import and deleting all remaining links. We observed that the wealth was transferred from the poorer countries to the wealthier countries. We found the asymmetry of the world trade flow by the disparity of the networks. From the backbone network of the world trade we can identify the regional economic connections and wealth flow among the countries.

One of the most fundamental models for the complex behaviour of damage accumulation in earth materials is the fibre bundle model. One distinguishes between models with localized load sharing (LLS) and models with equal load sharing (ELS). While ELS models can be treated by mean field theory, the behaviour of LLS models is usually more complicated. Here, we consider a fibre bundle model with LLS where, in addition, we introduce a time scale by incorporating time dependent ageing of the fibres due to the accumulation of damage driven by the locally acting stress in a chemically active environment. If the accumulated damage exceeds a random threshold, the fibres fail. The non-trivial time dependence of the cumulative damage in the system can be attributed to different mechanisms that dominate at different time scales. We include this information into an analytical description of the damage accumulation process and show that the analytical description is in agreement with numerical results.

The increasing availability of portable computing devices and their interaction with physical systems ask for designing compact models and simulations to understand and characterize such interactions. For instance, monitoring a road's grade using accelerometer stationed inside a moving ground vehicle is an emerging trend in city administration. Typically the focus has largely been to develop algorithms to articulate meaning from that. But, the experimentation cannot provide with an exhaustive analysis of all scenarios and the characteristics of them. We propose an approach of modeling these interactions of physical systems with gadgets through first principles, in a compact manner to focus on limited number of interactions. We derive an approach to model the vehicle interaction with a pothole on a road, a specific case, but allowing for selectable car parameters like natural damped frequency, tire size etc, thus generalizing it. Different road profiles are also created to represent rough road with sharp irregularities. These act as excitation to the moving vehicle and the interaction is computed to determine the vertical/ lateral vibration of the system i.e vehicle with sensors using joint time-frequency signal analysis methods. The simulation is compared with experimental data for validation. We show some directions as to how simulation of such models can reveal different characteristics of the interaction through analysis of their frequency spectrum. It is envisioned that the proposed models will get enriched further as and when large data set of real life data is captured and appropriate sensitivity analysis is done.

Texture is an important visual attribute used to plant leaf identification. Although there are many methods of texture analysis, some of them specifically for interpreting leaf images is still a challenging task because of the huge pattern variation found in nature. In this paper, we investigate the leaf texture modeling based on the partial differential equations and fractal dimension theory. Here, we are first interested in decomposing the original texture image into two components f = u + v, such that u represents a cartoon component, while v represents the oscillatory component. We demonstrate how this procedure enhance the texture component on images. Our modeling uses the non-linear partial differential equation (PDE) of Perona-Malik. Based on the enhanced texture component, we estimated the fractal dimension by the Bouligand-Minkowski method due to its precision in quantifying structural properties of images. The feature vectors are then used as inputs to our classification system, based on linear discriminant analysis. We validate our approach on a benchmark with 8000 leaf samples. Experimental results indicate that the proposed approach improves average classification rates in comparison with traditional methods. The results suggest that the proposed approach can be a feasible step for plant leaf identification, as well as different real-world applications.

We investigate the scale-free network properties of the bipartite ecological network, in particular, the plant-pollinator network. In plant-pollinator network, the pollinators visit the plant to get the nectars. In contrast to the other complex network, the plant-pollinator network has not only the trophic relationships among the interacting partners but also the complexities of the coevolutionary effects. The interactions between the plant and pollinators are beneficial relations. The plant-pollinator network is a bipartite and weighted network. The networks have two types of the nodes: plant and pollinator. We consider the visiting frequency of a pollinator to a plant as the weighting value of the link. We defined the strength of a node as the sum of the weighting value of the links. We reported the cumulative distribution function (CDF) of the degree and the strength of the plant-pollinator network. The CDF of the plants followed stretched exponential functions for both degree and strength, but the CDF of the pollinators showed the power law for both degree and strength. The average strength of the links showed the nonlinear dependence on the degree of the networks.

Thermal instabilities can lead to a sudden drop of local plasma temperature by orders of magnitude and numerical modeling of the global plasma response to such phenomena is performed. An approach to operate with the plasma heat conduction κ, being a non-linear function both of the plasma temperature and of its gradient, if the heat flux limit is taken into account, is developed. It is demonstrated that the deviation of κ from Spitzer-Härm approximation normally assumed is essential to explain experimental findings by massive gas injection experiments carried out to mitigate plasma disruptions in tokamaks.

Shear propagation and formation of sheared region in a sand system are investigated by a simulation. Our experimental apparatus for sand system is one of the simplest sets in order to obtain shear pattern, called as linear split-bottom cell. In this paper we give an analysis based on simulation for the above-mentioned system. Although a sand particle has a variety of forms from sphere to needle in general, but here we assume an ensemble of the simplest shape such as cubes in a rectangular parallelpipe split into two halves. One of the halves is moved along the split quasi-statically. We obtain a pattern of shear region and various quantities obtained from our simulation are compared with experiments.

We define and study periodic strategies in 2-player finite strategic form games. and exploit their connection to non-Nash rationalizable strategies. The result of our findings is that, non-Nash rationalizable strategies are always periodic, but periodic strategies are not necessarily rationalizable.

Efficient sampling of protein conformations is very important in computational studies of protein folding. The search space of the protein conformations can be reduced by utilizing bioinformatics. The frament assembly is one such method, where the local structures are selected from the fragment sets prepared using bioinformatics tool. The conformational space of proteins is reduced to a finite discrete set by using fragment assembly. The search space can be further reduced by introducing a consistency condition at the junction of the fragments. An algorithm for exact enuemration of such conformations are introduced, which can be used for generating cadidates of the native structure for a relatively short protein.

When dealing with singular potentials, such as point interactions, the term V(x)ψ(x) in Schrödinger's equation is, in general, mathematically ill-defined. The traditional way of dealing with this difficulty, by employing regularization techniques, has led to some ambiguous results for the δ'(x) potential in the literature. Here we propose a mathematically consistent approach to deal with the one-dimensional version of this problem by considering from the beginning the distributional nature of the whole interaction term. We show that the interaction is univocally determined from two simple mathematical requirements on the interaction distribution, together with the physical requirement of probability flux conservation and considerations of symmetry.

We analyse the non-abelian algebra and the supersymmetric cohomology associated to the local and non-local conserved charges of N=1 SKdV under Poisson brackets. We then consider the breaking of the supersymmetry and obtain an integrable model in terms of Clifford algebra valued fields. We discuss the remaining conserved charges of the new system and the stability of the solitonic solutions.

Compared to clusters of transition metal atoms, H-H bond activation by main Group metal clusters is much less known. Here, we have examined a potential new way of obtaining a novel alane Al₆H₈ through addition of multiple H₂ molecules to the aluminium hexamer, i.e., Al₆ + nH₂ (n=1-4) reactions. To this end, systematic high level quantum chemical modeling calculations using density functional theory (DFT) and coupled-cluster singles-doubles-perturbative triples (CCSD(T)) method in conjunction with the aug-cc-pVTZ basis set were performed to identify the lowest energy barrier paths for the consecutive dissociation of several hydrogen molecules on Al₆, the smallest aluminium cluster with a three-dimensional ground-state structure. These computational results are relevant to the issues of hydrogen storage and novel stable alanes.

The efficiency of the direct simulation Monte Carlo (DSMC) method decreases considerably if gas is not rarefied. In order to extend the application range of the DSMC method towards non-rarefied gas regimes, the computational efficiency of the DSMC method should be increased further. One of the most time consuming parts of the DSMC method is to determine which DSMC molecules are in close proximity. If this information is calculated quickly, the efficiency of the DSMC method will be increased. Although some meshless methods are proposed, mostly structured or non-structured meshes are used to obtain this information. The simplest DSMC solvers are limited with the structured meshes. In these types of solvers, molecule indexing according to the positions can be handled very fast using simple arithmetic operations. But structured meshes are geometry dependent. Complicated geometries require the use of unstructured meshes. In this case, DSMC molecules are traced cell-by-cell. Different cell-by-cell tracing techniques exist. But, these techniques require complicated trigonometric operations or search algorithms. Both techniques are computationally expensive. In this study, a hybrid mesh structure is proposed. Hybrid meshes are both less dependent on the geometry like unstructured meshes and computationally efficient like structured meshes.

Searching for non-Hermitian, -symmetric Hamiltonians [1] with real spectra has been acquiring much interest for fourteen years. In this article, we have introduced a symmetric non-Hermitian Hamiltonian model which is given as where ω and α are real constants, and are first order differential operators. Because the Hamiltonian is pseudo-Hermitian, we have obtained the Hermitian equivalent of which is in Sturm- Liouville form leads to exactly solvable potential models which are effective screened and hyperbolic Rosen-Morse II potentials. Using convenient sinilarity transformations, we have obtained a physical Hamiltonian h for each case. Then, the Schrödinger equation is solved exactly using Shape Invariance method of Supersymmetric Quantum Mechanics [2].

The paper deals with a hyperreactive model of motion, which is based on a new approach to the fundamental momentum concept applied to a variable-mass point. In this model, the equations of motion differ from known Meshchersky-Tsiolkovsky's equations. The latter equations cannot be considered as satisfactory ones for analysis of many problems because of their inconsistency with some real processes. The suggested concept of hyperreactive motion allows determining the dependence of parameters of motion upon the time-dependent mass and, in particular, allows finding a solution to a basic problem of the highest absolute velocities that can be reached in space.

Evolutionary computation techniques, like genetic algorithms, have received a lot of attention as optimization techniques but, although they exhibit a very promising potential in curing the problem, they have not produced a significant breakthrough in the area of systematic treatment of constraints. There are two mainly ways of handling the constraints: the first is to produce an infeasibility measure and add it to the general cost function (the well known penalty methods) and the other is to modify the mutation and crossover operation in a way that they only produce feasible members. Both methods have their drawbacks and are strongly correlated to the problem that they are applied. In this work, we propose a different treatment of the constraints: we induce instabilities in the evolving population, in a way that infeasible solution cannot survive as they are. Preliminary results are presented in a set of well known from the literature constrained optimization problems.

We study the effect of vaccinating networks with different growing strategies, using various techniques that require the complete knowledge of the network. The goal is to restrain the epidemic before it spreads throughout the network and target the few key nodes that will help contain it. Our target networks are chosen to have relatively large modularity index and various immunization techniques are applied to them.

This paper is an analytic process of introducing the concept of roles in a complex network. Each node has a specific connectivity pattern to the rest of the nodes in the network. There are many nodes that have the same number of connections and also the same type. In this case we say that two nodes can have the same role. The work described here, shows the process of identifying the roles of all the nodes in a network and grouping them accordingly.

In recent years, researchers discovered by empirical studies that the majority of networked systems that occurring in nature and society, exhibit an emerging behavior which is caused by the statistical properties of these systems. Two of the most important factors that characterize those complex systems is the degree distribution of the underlying network and the so called small world property. In this work, we examine the application of evolutionary processes on these systems in order to derive useful results for human dynamics modeling. Simulation experiments are used to explain universal properties observed recently in the vote distribution of proportional elections. Moreover, it has been founded that the hierarchical or modular nature of complex networks accelerates the convergent of a hybrid genetic algorithm applied in a rather complex search space.

We present an asymptotic method giving a probability of presence of the iterated spots of R^d by a polynomial function f. We use the well-known Perron Frobenius operator (PF) that lets certain sets and measure invariant by f. Probabilistic solutions can exist for the deterministic iteration. If the theoretical result is already known, here we quantify these probabilities. This approach seems interesting to use for computing situations when the deterministic methods don't run. Among the examined applications, are asymptotic solutions of Lorenz, Navier-Stokes or Hamilton's equations. In this approach, linearity induces many difficult problems, all of whom we have not yet resolved.

The probability density functions (PDFs) of energy dissipation rates created from the whole of the DNS region of the size 4096³ (named whl-PDFs) for various sizes of coarse graining areas are analyzed by multifractal PDF theory (MPDFT). Furthermore, other PDFs named max-PDF and min-PDF for various sizes of coarse graining areas, created respectively from the partial DNS regions of the size 512³ with maximum and minimum enstrophy, are also analyzed by making use of the whl-PDF. It is shown that there is a whl-PDF with an appropriate size of coarse graining area, whose slope of the tail part can adjust the slope of the tail-part of a max-PDF. On the other hand, there is a whl-PDF whose center part can adjust quite accurately the center part of a min-PDF. Note that the partial DNS region with maximum (minimum) enstrophy is the region of maximally dense (rare) vortexes, and therefore contributes mainly to the tail (center) part of the whl-PDF. It is found that these adjustments are systematic with respect to the sizes of coarse graining areas.

The prediction of atomic arrangements for a nanoalloy is of critical importance in developing a novel catalyst for clean energy applications because these arrangements determine the catalytic activities of a nanoalloy. So, the development of a reliable method for predicting atomic arrangements has become increasingly important. In this study, the atomic arrangements of the Pt-Cu in a truncated octahedron (TOh) shaped nanoalloy of various Pt-Cu compositions were predicted. We developed a genetic algorithm (GA) code to predict atomic arrangements, and this code was combined with classical molecular dynamics (MD) simulations to evaluate the optimality of each atomic arrangement. The GA calculation predicted a predominantly multilayered core-shell structure for the Pt-Cu nanoalloy, regardless of the Pt-Cu composition ratio. The cause of a multilayered core-shell structure in the Pt-Cu nanoalloy can be interpreted by the interaction between the intrinsic properties of Pt and Cu, such as their surface energies and miscibility.

Carbon Dioxide (CO₂) sequestration into geologic formations is a means of mitigating greenhouse effect. In this work we present a new numerical simulation technique to model and monitor CO₂ sequestration in aquifers. For that purpose we integrate numerical simulators of CO₂-brine flow and seismic wave propagation (time-lapse seismics). The simultaneous flow of brine and CO₂ is modeled applying the Black-Oil formulation for two phase flow in porous media, which uses the Pressure-Volume-Temperature (PVT) behavior as a simplified thermodynamic model. Seismic wave propagation uses a simulator based on a space-frequency domain formulation of the viscoelastic wave equation. In this formulation, the complex and frequency dependent coefficients represent the attenuation and dispersion effect suffered by seismic waves travelling in fluid-saturated heterogeneous porous formations. The spatial discretization is achieved employing a nonconforming finite element space to represent the displacement vector. Numerical examples of CO₂ injection and time-lapse seismics in the Utsira formation at the Sleipner field are analyzed. The Utsira formation is represented using a new petrophysical model that allows a realistic inclusion of shale seals and fractures. The results of the simulations show the capability of the proposed methodology to monitor the spatial distribution of CO₂ after injection.

The mathematical modelling of the dynamics of particle suspension is based on the population balance equation (PBE). PBE is an integro-differential equation for the population density that is a function of time t, space coordinates and internal parameters. Usually, the particle is characterized by a unique parameter, e.g. the matter volume v. PBE consists of several terms: for instance, the growth rate and the aggregation rate. So, the growth rate is a function of v and t. In classical modelling, the growth and the aggregation are independently considered, i.e. they are not coupled. However, current applications occur where the growth and the aggregation are coupled, i.e. the change of the particle volume with time is depending on its initial value v₀, that in turn is related to an aggregation event. As a consequence, the dynamics of the suspension does not obey the classical Von Smoluchowski equation. This paper revisits this problem by proposing a new modelling by using a bivariate PBE (with two internal variables: v and v₀) and by solving the PBE by means of a numerical method and Monte Carlo simulations. This is applied to a physicochemical system with a simple growth law and a constant aggregation kernel.

The maximum development of an Extensive Air Shower (EAS) is an important parameter which is possible to be studied with EAS simulation programs. This parameter is also related to hadronic interaction models in high and low energy ranges. A Detailed study been considered to investigate the effects of zenith angle and interaction models as well as thinning parameters on the maximum development of an EAS and its mean values. Diagrams of Maximum shower development vs. energy being used to recognize the masses of the primary particles initiated those EASs. An empirical formula presented to remove the effects of zenith angle.

In the current research, a mathematical model for the post-damage improvement of the carbonated blast furnace slag cement (BFSC) exposed to accelerated carbonation is constructed. The study is embedded within the framework of investigating the effect of using lightweight expanded clay aggregate, which is incorporated into the impregnation of the sodium mono-fluorophosphate (Na-MFP) solution. The model of the self-healing process is built under the assumption that the position of the carbonation front changes in time where the rate of diffusion of Na-MFP into the carbonated cement matrix and the reaction rates of the free phosphate and fluorophosphate with the components of the cement are comparable to the speed of the carbonation front under accelerated carbonation conditions. The model is based on an initial-boundary value problem for a system of partial differential equations which is solved using a Galerkin finite element method. The results obtained are discussed and generalized to a three-dimensional case.

Quarter car model is a simple and widely used mathematical model to analyze the vibration and control problem of vehicles. In this study, a quarter car test rig is modeled as a lumped parameter system. Model parameters of the system are determined by measurements and experiments. Forced vibration method is used to identify the stiffness and damping parameters of the lumped model. A modal shaker is used to generate the road input in the test rig. The accelerations of the road input, sprung and unsprung masses are measured by piezoelectric accelerometers. The frequency response functions are obtained by using acceleration data. The identified parameters of the test rig are adjusted by comparing the experimental and simulation results.

Rényi entropy and generalized complexity measures are used to describe the chaotic behaviour of dynamical systems. These measures are found to be sensitive to the fine details of the Rössler and the Duffing maps. They are good descriptors of chaotic behaviour. Periodic windows and the fractal character of the chaotic dynamics are nicely detected.

This work proposes a novel technique for the extraction of descriptors of a texture image. The method consists in modeling the image through a complex network, based on the distribution of gray-level intensities. Therefore, we process the adjacency matrix as a geometrical object and compute its fractal dimension. Thus we apply a multiscale transform over the power-law fractal curve, obtaining the descriptors of the image. The method is tested in a classification task with a comparison to other classical texture descriptors.

In this work, a model for evolving networks is presented based on a Brownian particle. Each time, the Brownian particle enters the network through a randomly selected node. The random walk is terminated after having created m-links with visited nodes. Two strategies have been tested: in the first one, we used a generalized algorithm for the secretary problem in order to maximize the degree of the node with which the new node is connected, while in the second strategy, the Brownian particle creates links with nodes that meets twice. In all cases, scale free, modular, dissasortative networks are created.

We investigate in detail the mechanisms under which degree correlations evolve in complex networks. We consider the case where a vertex is entering the network at each time, carrying a predefined number of edges. We prove in this work, that the same elementary interactions which is responsible for emerging of scaling in complex networks, can give several patterns of degree corellations. As a test case, the effect of preferential attachement rule in degree correlations is studied in detail.

Preferential attachment is a standard mechanism producing power-laws in growing networks. Thanks to its simplicity this mechanism is realized in most of the models of scale-free network, but, unfortunately, it rather mimics scale-free networks and not explains them. Optimization based mechanisms have a much greater potential to explain the evolution of scale-free networks. We consider one of the simplest optimization based models generating power-law growing networks. Our model is defined as follows. At each time step, a new node is created and connected to m previous nodes in the network, which are selected to minimize the product s^αr, where s is the birth time of the node and r is a random number drawn from some distribution. In the case of complete optimization, the networks generated by this model have a power-law degree distribution with the exponent γ = 1 + 1/α for a wide range of the random number distributions. For partial optimization, including a finite fraction of nodes in a network, we observe an exponential degree distribution.

The main concern of epidemiological modeling is to implement an economical vaccine allocation to the population. Here, we investigate the optimal vaccination allocation in complex networks. We find that the optimal vaccine coverage depends not only on the relative cost of treatment to vaccination but also on the vaccine efficacy. Especially with a high cost of treatment, nodes with high degree are prioritized to vaccinate. These results may help us understand factors that may impact the optimal vaccination distribution in the control of epidemic dynamics.

We analyze emotionally annotated massive data from IRC (Internet Relay Chat) and model the dialogues between its participants by assuming that the driving force for the discussion is the entropy growth of emotional probability distribution.

Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.

The Hierarchies Consistency Analysis (HCA) is proposed by Guh in-cooperated along with some case study on a Resort to reinforce the weakness of Analytical Hierarchy Process (AHP). Although the results obtained enabled aid for the Decision Maker to make more reasonable and rational verdicts, the HCA itself is flawed. In this paper, our objective is to indicate the problems of HCA, and then propose a revised method called chaotic ordered HCA (COH in short) which can avoid problems. Since the COH is based upon Guh's method, the Decision Maker establishes decisions in a way similar to that of the original method.

The Internet is an example of a general physical problem dealing with motion near the speed of light relative to different time frames of reference. The second order differential equation (DE) takes the form of 'time diffusion' near the speed of light or alternatively, considered as a complex variable with real time and imaginary longitudinal components. Congestion waves are generated by peak global traffic from different time zones following the Earth's revolution defined by spherical harmonics and a day/night bias. The DE is essentially divided into space and time operators constrained by the speed of light c, band capacity w and a fractal dimension Z (Hausdorff dimension). This paper explores the relationship between the dynamics and the network including the addition of fractal derivatives to the DE for regional networks for 0 < Z < 1.

This work is related to the problem of community detection in dynamic scenarios, which for instance arises in the segmentation of moving objects, clustering of telephone traffic data, time-series micro-array data etc. A desirable feature of a clustering model which has to capture the evolution of communities over time is the temporal smoothness between clusters in successive time-steps. In this way the model is able to track the long-term trend and in the same time it smooths out short-term variation due to noise. We use the Kernel Spectral Clustering with Memory effect (MKSC) which allows to predict cluster memberships of new nodes via out-of-sample extension and has a proper model selection scheme. It is based on a constrained optimization formulation typical of Least Squares Support Vector Machines (LS-SVM), where the objective function is designed to explicitly incorporate temporal smoothness as a valid prior knowledge. The latter, in fact, allows the model to cluster the current data well and to be consistent with the recent history. Here we propose a generalization of the MKSC model with an arbitrary memory, not only one time-step in the past. The experiments conducted on toy problems confirm our expectations: the more memory we add to the model, the smoother over time are the clustering results. We also compare with the Evolutionary Spectral Clustering (ESC) algorithm which is a state-of-the art method, and we obtain comparable or better results.

A "Theory of Mind" is one of the most important skills we as humans have developed; It enables us to infer the mental states and intentions of others, build stable networks of relationships and it plays a central role in our psychological make-up and development. Findings published earlier this year have also shown that we as a species as well as each of us individually benefit from the enlargement of the underlying neuro-anatomical regions that support our social networks, mediated by our Theory of Mind that stabilises these networks. On the basis of such progress and that of earlier work, this paper draws together several different strands from psychology, behavioural economics and network theory in order to generate a novel theoretical representation of the development of our social-cognition and how subsequent larger social networks enables much of our cultural development but at the increased risk of mental disorders.

Based upon principal component analysis, a new measure called compressibility coefficient is proposed to evaluate structural holes in networks. This measure incorporates a new effect from identical patterns in networks. It is found that compressibility coefficient for Watts-Strogatz small-world networks increases monotonically with the rewiring probability and saturates to that for the corresponding shuffled networks. While compressibility coefficient for extended Barabasi-Albert scale-free networks decreases monotonically with the preferential effect and is significantly large compared with that for corresponding shuffled networks. This measure is helpful in diverse research fields to evaluate global efficiency of networks.

In this paper, we present a label propagation algorithm named ACD for anti-community detection. Experimental results on some real world networks show that our algorithm can obtain higher quality results than other methods.

Recent works have emphasized the importance of controlling complex networks and have provided novel analytical approaches based on the maximum matching among others. The analysis leads to the conclusion that the driver nodes tend to avoid the high-degree nodes. Therefore, it implies that apparently inhomogeneous networks are more difficult to control. Here we present an approach to control complex networks from the perspective of the minimum dominating set (MDS). We apply the definition of MDS to complex networks with scale-free structure P(k) ∝ k^−γ and assume that a node controls itself and each of its adjacent nodes through its links. Our theoretical calculations and simulations demonstrate that the more heterogeneous a network's degree distribution is, the smaller the fraction of individuals, devices or molecules required to control the entire system is. Here, we have extended our recent analytical derivations and we now provide a more accurate analysis for the case γ < 2. Moreover, we have also performed additional computer simulations to study in more detail the dependence of the MDS with the network size and the average degree below the phase transition at γ = 2.

Since communication networks such as the Internet, which is regarded as a complex network, have recently become a huge scale and a lot of data pass through them, the improvement of packet routing strategies for transport is one of the most significant themes in the study of computer networks. It is especially important to find routing strategies which can bear as many traffic as possible without congestion in complex networks. First, using neural networks, we introduce a strategy for packet routing on complex networks, where path lengths and queue lengths in nodes are taken into account within a framework of statistical physics. Secondly, instead of using shortest paths, we propose efficient paths which avoid hubs, nodes with a great many degrees, on scale-free networks with a weight of each node. We improve the heuristic algorithm proposed by Danila et. al. which optimizes step by step routing properties on congestion by using the information of betweenness, the probability of paths passing through a node in all optimal paths which are defined according to a rule, and mitigates the congestion. We confirm the new heuristic algorithm which balances traffic on networks by achieving minimization of the maximum betweenness in much smaller number of iteration steps. Finally, We model virus spreading and data transfer on peer-to-peer (P2P) networks. Using mean-field approximation, we obtain an analytical formulation and emulate virus spreading on the network and compare the results with those of simulation. Moreover, we investigate the mitigation of information traffic congestion in the P2P networks.

System could be continuously operating over an indefinitely long operation cycle, where each operation causes a random amount of damage to the system, and these damages are accumulated. We also propose a maintenance policy to optimize the expected cost rate for an infinite time span. Some useful properties and result discussions are presented, which indicate that the optimal maintenance policy is to perform preventive maintenance only depend on the level of accumulated damage, it is unnecessary to depend on the number of operation. Several special cases of such a maintenance policy are also presented and discussed.

According to institutional theorists, the forms and business models of corporation are mainly shaped by factors such as politics, regulations, social norms and cultures. This paper examines how the International Financial Reporting Standards (IFRS) and institutional environment influence the accounting quality, in response to the threat of political extraction in China. We took mainland China as an example instead in our study, following the accounting quality definition of Barth et al. [2], we found that the developments of Chinese government performance audit are conspicuously different by region; to reflect such differences, we elaborated our research by dividing mainland China into 31 categories (provinces or cities). We set 2003-2010 as the time horizon for this study. After testing the Regression model, our empirical research achieved two conclusions: 1) IFRS adoption in China should significantly improve the accounting quality, and 2) IFRS and institutional environment should synthetically influence the quality of accounting as well.

In most conventional settings, the events caused by an external shock are initiated at the moments of its occurrence. In this paper, we study a new classes of shock model, where each shock from a nonhomogeneous Poisson processes can trigger a failure of a system not immediately, as in classical extreme shock models, but with delay of some random time. We derive the corresponding survival and failure rate functions. Furthermore, we study the limiting behaviour of the failure rate function where it is applicable.

Simulation techniques have a proven track record in manufacturing industry as well as other areas such as healthcare system improvement. In this study, simulation model of a health center in Malaysia is developed through the application of WITNESS simulation software which has shown its flexibility and capability in manufacturing industry. Modelling procedure is started through process mapping and data collection and continued with model development, verification, validation and experimentation. At the end, final results and possible future improvements are demonstrated.

The pore structures (microstructures) of two metallic filters were reconstructed using the stochastic reconstruction method based on simulated annealing. The following microstructural descriptors were included in the description of the real microstructures: the two-point probability function, the lineal-path functions for the void or solid phases, i.e. simulated annealing was constrained by all low-order statistical measures that were accessible through the analysis of images of polished sections. An effect of the microstructural descriptors on the course of reconstruction was controlled by modifying two parameters of the reconstruction procedure [1]. Their values resulted from repeated reconstruction of two-dimensional microstructures in such a way that the reference (experimental) and calculated two-point cluster functions deviated negligibly. It was tacitly assumed that the parameters adjusted during two-dimensional reconstruction had the same influence on the formation of the three-dimensional microstructures. Since connectivity of phases is a critical property of the stochastically reconstructed media, clusters of pore and solid voxels were determined using the Hoshen-Kopelman algorithm. It was found that the solid phase formed one large cluster in accordance with the physical feasibility. The void phase created one large cluster and a few small clusters representing the isolated porosity. The percolation properties were further characterised using the local porosity theory [2]. Effective permeability of the replicas was estimated by solving the Stokes equation for creeping flow of an incompressible liquid in pore space. Calculated permeability values matched well their experimental counterparts.

There are no known exact formulas for the valuation of a number of exotic options, and this is particularly true for options under discrete monitoring and for American style options. Therefore, one usually recourses to a Monte Carlo Simulation approach, amongst other numerical methods, to estimate the value of these options. The problem which then arises with this method is one of variance reduction. Control variates are often used, and we present some results for the optimization of these control variables, for the valuation of Asian and lookback options. An inequality on functions of correlations useful for comparing estimators in variance reduction procedures is also provided.

We analyze the warm-standby M/M/R machine repair problem with multiple imperfect coverage which involving the service pressure condition. When an operating machine (or warm standby) fails, it may be immediately detected, located, and replaced with a coverage probability c by a standby if one is available. A recursive method is used to develop the steady-state analytic solutions. The total expected profit function per unit time is derived to determine the joint optimal values at the maximum profit. We utilize the direct search method to measure the various characteristics of the profit function followed by Quasi-Newton method to search the optimal solutions.

Extreme events have large impact throughout the span of engineering, science and economics. This is because extreme events often lead to failure and losses due to the nature unobservable of extra ordinary occurrences. In this context this paper focuses on appropriate statistical methods relating to a combination of quantile regression approach and extreme value theory to model the excesses. This plays a vital role in risk management. Locally, nonparametric quantile regression is used, a method that is flexible and best suited when one knows little about the functional forms of the object being estimated. The conditions are derived in order to estimate the extreme value distribution function. The threshold model of extreme values is used to circumvent the lack of adequate observation problem at the tail of the distribution function. The application of a selection of these techniques is demonstrated on the volatile fuel market. The results indicate that the method used can extract maximum possible reliable information from the data. The key attraction of this method is that it offers a set of ready made approaches to the most difficult problem of risk modeling.

In this paper, we study an infinite series queueing system with self-blocking phenomenon. Poisson arrivals and exponential service times are assumed. We develop the structured generator matrix to compute steady-state probabilities of the self-blocking system with infinite space by matrix-geometric method. The stability condition of the system is obtained in closed-form. We also present some performance measures including mean number in the system, and blocking probability, etc. The characteristics of the system with different service order are discussed as well.

This paper deals with an infinite-capacity multi-server queueing system with a second optional service (SOS) channel. The inter-arrival times of arriving customers, the service times of the first essential service (FES) and the SOS channel are all exponentially distributed. A customer may leave the system after the FES channel with probability (1-θ), or at the completion of the FES may immediately require a SOS with probability θ (0 ≤ θ ≤ 1). The formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is developed to determine the optimal values of the number of servers and the two service rates, simultaneously, at the minimal total expected cost per unit time. Quasi-Newton method are employed to deal with the optimization problem. Under optimal operating conditions, numerical results are provided in which several system performance measures are calculated based on assumed numerical values of the system parameters.

This study investigates the warm-standby machine repair problem which involves a controlling arrival policy and switching failure probability. It involves operating machines with S warm standbys and one single server. The failure times and repair times are assumed to follow an exponential distribution. For such system, some system performance measures are derived and a steady-state expected cost function per unit time is developed. By using Quasi-Newton method followed direct search method, we can find the joint optimal parameter values at maximum profit such that the availability constraint is satisfied.

Recently, the benefits of variational integrators have been combined with efficient high order techniques. On the other hand, a special set of high order methods are the symmetric ones, those who preserve time reversal symmetry and show improved behavior in long term integration. In the present work, we will introduce a systematic way to construct symmetric variational integrators. The idea is to apply the variational principle not in a set of intermediate points but to a set of parameters that characterize a symmetric orbit between starting and ending points. The estimated symmetric orbit may be a polynomial or a general function that sometimes is indicated by the nature of the problem to solve. The results show excellent behavior in long term integration and acceleration of the method when special functions are used.

Prediction of muscle forces using optimization based models of muscle coordination is an active research area in biomechanics. Theoretical calculation of individual muscle forces depends on solving the redundancy problem. In a musculoskeletal model, redundancy arises since the number of muscles in the model exceeds the number of degrees-of-freedom present. One of the widely used methods to solve this problem is to formulate a physiologically sound cost function and optimize this function subject to mechanical equality and inequality constraint equations. In this study, force predictions obtained from different optimization-based models were compared with those obtained from experimentally measured individual muscle forces recorded during a variety of movement conditions. Advantages and limitations of the tested models were discussed.

On the basis of the variational integrators theory, we initially examine the possibility of deriving multi-step numerical methods. Then, we propose an integration technique that approximates the action integral within one time interval by using appropriate expressions for the relevant configurations and velocities. These approximations depend on a specific number of known configurations defined at previous time nodes. Multi-step numerical methods can finally be deduced, by defining, as usually, the Lagrange function as a weighted sum over the discrete Lagrangians corresponding to each of the curve segments and using the discrete Euler-Lagrange equations.

We develop a model based on the fractional exclusion statistics to describe systems with localized states. The local distribution of the energy levels is captured in the formalism by including the positions in the definition of the species. The particle distributions on the energy axis, as well as in the real space are determined for test-case systems with a peak/dip profile in the local density of states.

I present briefly the concept of fractional exclusion statistics (FES) and I analyze two models of interacting particle systems. After I show that the models are equivalent by transforming one into the other by redefining some terms in the Hamiltonians, I calculate the heat capacity of the system and compare it with the heat capacity of an ideal Bose or Fermi gas. I show that under certain conditions the heat capacities may not be equal. I show that the interacting particle system may always be described as an ideal gas obeying FES and I show the method to construct such a gas.

Scatter processes of photons lead to blurring of images produced by CT (computed tomography) or CBCT (cone beam computed tomography). Multiple scatter is described by, at least, one Gaussian kernel. In various tasks, this approximation is crude; we need two/three Gaussian kernels to account for long-range tails (Landau tails), which appear in Molière scatter of protons, energy straggling and electron capture of charged particles passing through matter and Compton scatter. The ideal image (source function) is subjected to Gaussian convolution to yield a blurred image. The inverse problem is to obtain the source image from a detected image. Deconvolution methods of linear combinations of two/three Gaussian kernels with different parameters s₀, s₁, s₂ can be derived via an inhomogeneous Fredholm integral equation of second kind (IFIE2) and Liouville - Neumann series (LNS) to provide the source function ρ. Scatter functions s₀, s₁, s₂ are best determined by Monte-Carlo. An advantage of LNS is given, if the scatter functions s₀, s₁, s₂ depend on coordinates. The convergence criterion can always be satisfied with regard to the above mentioned cases. A generalization is given by an analysis of the Dirac equation and Fermi-Dirac statistics leading to Landau tails applied to Bethe-Bloch equation (BBE) of charged particles and electron capture.

The discovery of neutrino oscillations indicates the existence of massive neutrinos in contrast to the massless neutrinos predicted by the Standard Model. One of the simplest extensions of the SM obtained by adding a heavy right-handed neutrino singlet, N_R, per neutrino generation is the Seesaw mechanism. Within the context of this mechanism, flavour changing neutral current neutrino-nucleus reactions of the type are predicted to occur. In this contribution, motivated by the extensive studies (theoretical and experimental) of the LFV in ν⁻ → e⁻ conversion in nuclei, we investigate FCNC in neutrino-nucleus reactions. From a nuclear theory point of view, the Donnelly-Walecka model for cross sections calculations is employed. To this purpose, the single-particle transition matrix elements are evaluated from a Mathematica code developed in this work. Neutrino-nucleus reactions have important impact in Astrophysics and hence a detailed study of such exotic processes is of significant importance.

In explosive nucleosynthesis, among other reactions, prominent position posses the electron capture by nucleons and nuclei. This process plays important role in the core-collapse of massive stars by modifying the quantity Y_e. From a nuclear theory point of view, this process may be studied by using the same nuclear methods (e.g. the quasi-particle random phase approximation, QRPA, employed in the present work) with the one-body charge changing nuclear processes (β-decay modes, charged-current electron-neutrino absorption by nuclei, etc). In this work we concentrate on a detailed study of the orbital e-capture by medium-heavy nuclei (Fe region) which play fundamental role in the evolution of massive stars and in the so called explosive neutrino nucleosynthesis. We study extensively the cross sections and rates of e-capture process by "iron group peaked nuclei", isotopes that are important for investigating the neutrino nucleosynthesis and other related phenomena.

The jet in a microquasar stellar system is simulated with a relativistic hydrocode (PLUTO) and then it is imaged, in the γ-rays wave band, with a line-of-sight method, including both emission and self-absorption. A synthetic image is produced which allows to better estimate the system's physical properties. The calculation procedure in our method has been simplified by exploiting the ability to de-couple the hydrodynamical from the radiative quantities in the computations.

In supernova (SN) physics, the responses of nuclear neutrino-detectors to SN neutrino-spectra, are studied by convoluting original theoretical cross sections with well known SN (anti)neutrino-energy distributions (such distributions are the two-parameter Fermi-Dirac and Power-Law distributions). Also, the interpretation of SN neutrino signals, created at various nuclear ν-detectors, is explored by applying simulation techniques in low-energy anti-neutrino spectra of boosted β-radioactive ⁶H_e ions (beta-beam neutrinos). In the present paper, we employ simulation techniques to analyze original SN anti-neutrino signals by using synthetic beta-beam spectra (defined as linear combinations of boosted beta-beam spectra of ⁶H^e). The quality of the fits, obtained by using the MERLIN optimization package, is in general good. From a nuclear theory point of view, the resulted nuclear responses reflect the effectiveness of some detector materials as SN neutrino detectors (COBRA, CUORE, ICARUS experiments).

The goal of the present contribution is twofold: (i) To compute exact wave functions for a muon bound in the extended Coulomb potential of a muonic atom by solving the Dirac equation within the context of genetic algorithms and neural network techniques using experimental finite-size charge-densities for the attracting nucleus. (ii) To calculate partial and total rates of the ordinary muon capture in various muonic atoms. In contrast to the majority of previous realistic calculations for μ⁻-capture rates, in our present work we utilize the above mentioned exact wave functions for a muon orbiting at the Is and 2p atomic orbits. The required many-body nuclear wave functions are obtained by diagonalizing the eigenvalue problem of the quasi-particle random phase approximation (QRPA).

It was shown by Doplicher et.al. that the measurement of spacetime intervals of the order of Planck length scale is operationally impossible, as the process of measurement invariably gives rise to a black hole formation. This can be avoided by postulating non-vanishing commutation relations between the coordinates, which are now promoted to the level of operators. Formulation of quantum mechanics in these kinds of spaces through the introduction of Hilbert spaces of Hilbert-Schmidt operators is then shown to allow the construction of spectral triplets a la Connes naturally. The computation of spectral distance between pure and mixed states is then shown to exhibit a deep connection between entropy and geometry.

We investigate the properties of two- and three-dimensional non-commutative fermion gases with fixed total z-component of angular momentum, J_z, and at high density for the simplest form of non-commutativity involving constant spatial commutators. Analytic expressions for the entropy and pressure are found. The entropy exhibits non-extensive behaviour while the pressure reveals the presence of incompressibility in two, but not in three dimensions. Remarkably, for two dimensional systems close to the incompressible density, the entropy is proportional to the square root of the system size, i.e., for such systems the number of microscopic degrees of freedom is determined by the circumference, rather than the area (size) of the system. From a commutative perspective these results can also be interpreted in terms of an effective excluded volume. Possible generalizations to three dimensions, which restore rotational symmetry, are briefly discussed.

We present here how the gravothermal or Antonov's instability, which was originally formulated in the microcanonical ensemble, is modified in the presence of a cosmological constant and in the canonical ensemble. In contrast to the microcanonical ensemble, there is a minimum, and not maximum, radius for which metastable states exist. In addition this critical radius is decreasing, and not increasing, with increasing cosmological constant. The minimum temperature for which metastable states exist is decreasing with increasing cosmological constant, while above some positive value of the cosmological constant, there appears a second critical temperature. For lower temperatures than the second critical temperature value, metastable states reappear, indicating a typical reentrant phase transition. The two critical temperatures merge when the cosmological density equals one half the mean density of the system.

We review some recent results by Ambjørn et al. (1202.4435) and the authors (1202.4322,1203.5034) in which multicritical points of the CDT matrix model were found and in a particular example identified with a hard dimer model. This identification requires solving the combinatorial problem of counting configurations of dimers on CDTs.

Non-linear sigma model with target space M can be described as a single particle quantum mechanics in the corresponding free loop space LM. We first discuss a formal description of this loop space quantum mechanics (LSQM) using the general coordinates in LM. Then we consider a semi-classical limit where the string wavefunction is localized on the submanifold of vanishing loops. The semi-classical expansion is related to the tubular expansion of LSQM around this submanifold. We develop the mathematical framework required to compute the effective dynamics on the submanifold in the Born-Oppenheimer sense at leading order in α' expansion. In particular, we show that the linearized tachyon effective equation is reproduced correctly with divergent terms all proportional to the Ricci scalar of M.

The third quantization formalism of quantum cosmology adds simplicity and conceptual insight into the quantum description of the multiverse. Within such a formalism, the existence of squeezed and entangled states raises the question of whether the complementary principle of quantum mechanics has to be extended to the quantum description of the whole space-time manifold. If so, the particle description entails the consideration of a multiverse scenario and the wave description induces us to consider as well correlations and interactions among the universes of the multiverse.

We address the cosmological constant problem in the context of two-dimensional dilaton-Maxwell gravity, coupled to an arbitrary number of scalar matter fields. We are able to quantize the model non-perturbatively; we determine that the realization of the classical symmetries at the quantum level provides a mechanism that fixes the value of the cosmological constant.

Black hole dominance, assumed to be a fairly ubiquitous feature of any theory of quantum gravity, amounts to that any observer trying to perform a localized experiment on ever smaller length scales will ultimately be thwarted by the formation of a trapped surface within the spatial domain of the experiment. The argument based on Thorne's hoop conjecture, conjointly leads to a fundamental length scale in physics. Black hole dominance also suggests that ordinary field theory cannot be used to describe quantum gravity in the extreme UV, contrary to implications of asymptotic safety. We re-examine black hole dominance in an asymptotically safe scenario, in the presence of higher curvature terms an with running couplings, by modifying a proof of Thorne's hoop conjecture. We find that the proof falls apart, and along with it, so does the argument for a mandatory formation of a trapped surface inside the domain of the experiment. However, neither is there a contrary proof that local trapped surfaces do not form. Instead in this approach whether an observer can perform local measurements in arbitrary small regions of spacetime depends on the specific values of the couplings near the UV fixed point. In this sense there is no all pervasive local version of the minimal length argument. However, we argue that one trapped surface must still form outside an experiment, when the domain of this experiment is localized to scales much smaller than the Planck length. This enshrouding horizon then prevents any information from reaching observers at infinity, thus retaining a vestige of "asymptotic darkness" for them.

In general relativity, astrophysical black holes are uniquely described by the Kerr metric. Observational tests of the Kerr nature of these compact objects and, hence, of general relativity, require a metric that encompasses a broader class of black holes as possible alternatives to the usual Kerr black holes. Several such Kerr-like metrics have been constructed to date, which depend on a set of free parameters and which reduce smoothly to the Kerr metric if all deviations vanish. Many of these metrics, however, are valid only for small values of the spin or small perturbations of the Kerr metric or contain regions of space where they are unphysical hampering their ability to properly model the accretions flows of black holes. In this paper, I describe a Kerr-like black hole metric that is regular everywhere outside of the event horizon for black holes with arbitrary spins even for large deviations from the Kerr metric. This metric, therefore, provides an ideal framework for tests of the nature of black holes with observations of the emission from their accretion flows, and I give several examples of such tests across the electromagnetic spectrum with current and near-future instruments.

In this article we will find the entropy of a scalar field in the Reissner-Nordstrom black hole backgrounds using the brick wall model of t' Hooft. We will use the semi-classical WKB approximation. We will consider the modes which are globally stationary so that the WKB quantization rule used in the brick wall model remains valid. In the Schwarzschild black hole this consideration had led to a new expression of the entropy different from the conventional expression which is inversely divergent in the brick wall cut-off parameter and in terms of a proper distance cut-off parameter, is proportional to the area of the event horizon. The new expression of the scalar field entropy obtained in this article is logarithmically divergent in the brick wall cut-off parameter and is not proportional to the area of the black hole event horizon. For the extremal Reissner-Nordstrom black hole background the entropy of the scalar field is again divergent in the brick wall cut-off parameter and vanishes if the temperature of the Hawking radiation and the black hole is taken to be zero. We will next consider the entropy for a thin shell of matter field surrounding the black hole horizon. When expressed in terms of a covariant cut-off parameter, the entropy of a thin shell of matter field surrounding the horizon in the non-extreme Reissner-Nordstrom black hole background is given by an expression proportional to the area of the black hole horizon. We will briefly explain the significance of this result.

Thermodynamics unavoidably contains fluctuation theory, expressible in terms of a unique thermodynamic information metric. This metric produces an invariant thermodynamic Riemannian curvature scalar R which, in fluid and spin systems, measures interatomic interactions. Specifically, |R| measures the size of organized fluctuating microscopic structures, and the sign of R indicates whether the interactions are effectively attractive or repulsive. R has also been calculated for black hole thermodynamics for which there is no consensus about any underlying microscopic structures. It is hoped that the physical interpretation of R in fluid and spin systems might offer insight into black hole microstructures. I give a brief review of results for R in black holes, including stability, the sign of R, R = 0, diverging |R|, and various claims of "inconsistencies" in thermodynamic metric geometry.

We search for a universal property of quantum gravity. By "universal", we mean the independence from any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on). To do so, we try to put the basis of our discussion on theories established by some experiments. Thus, we focus our attention on thermodynamical and statistical-mechanical basis of the black hole thermodynamics: Let us assume that the Bekenstein-Hawking entropy is given by the Boltzmann formula applied to the underlying theory of quantum gravity. Under this assumption, the conditions justifying Boltzmann formula together with uniqueness of Bekenstein-Hawking entropy imply a reasonable universal property of quantum gravity. The universal property indicates a repulsive gravity at Planck length scale, otherwise stationary black holes can not be regarded as thermal equilibrium states of gravity. Further, in semi-classical level, we discuss a possible correction of Einstein equation which generates repulsive gravity at Planck length scale.

The discovery of the various thermodynamical aspects of classical gravity has led to a picture in which Einstein equations might be seen as an equation of state, relating the dynamics of null hypersurfaces to thermodynamic relations for a system at or close to equilibrium. The explanation of such a fact is expected to come from a complete theory of quantum gravity. In absence of it, I will use a pregeometric model of emergent gravity to discuss the role of Wheeler's boundary of a boundary principle in this specific problem. The goal is to show the relevance of the equilibration of the microscopic degrees of freedom in establishing the thermodynamical status of the semiclassical gravity limit, and how the equilibration of the system might lead to additional physical effects. The role of phase transitions (conjectured in certain combinatorial models proposed to define a quantum theory of gravity, namely tensor models and group field theories) will be also considered in this light, showing how criticality and deviations from it relate to these ideas.

Two fermionic systems that have an underlying supersymmetric structure are studied, a color superconductor model and Dirac fermion in a Reissner-Nordström-anti-de Sitter gravitational background. In the chiral limit of both systems, an N = 2 with zero central charge d = 1 quantum algebra, underlies both systems.

The symmetry algebra of asymptotically flat spacetimes at null infinity in four dimensions in the sense of Newman and Unti is revisited. As in the Bondi-Metzner-Sachs gauge, it is shown to be isomorphic to the direct sum of the abelian algebra of infinitesimal conformal rescalings with 4. The latter algebra is the semi-direct sum of infinitesimal supertranslations with the conformal Killing vectors of the Riemann sphere. Infinitesimal local conformal transformations can then consistently be included. We work out the local conformal properties of the relevant Newman-Penrose coefficients, construct the surface charges and derive their algebra.

We use the example of the much-studied κ-Minkowski noncommutative spacetime for illustrating a novel approach toward the analysis of the possible implications of spacetime noncommutativity. Our starting point is the proposal that spacetime noncommutativity is most naturally introduced within the manifestly-covariant formulation of quantum mechanics. This allows us to obtain a crisp characterization of the relativity of spacetime locality present in κ-Minkowski theories. And we also develop a novel description of how κ-Minkowski noncommutativity affects the fuzziness of worldlines.

This work presents a review of recent findings from the consideration of a non-minimal coupling between matter and geometry, namely the possibility of mimicking dark matter in clusters and the description of gravitational collapse — thus adding to the wide range of phenomena already covered by the theory.

We perform a non-perturbative analysis of the constraints of the Hořava Gravitational theory. In distinction to Einstein gravity the theory has constraints of the first class together with second class ones. We analyze the consequences of having to impose second classes constraints at any time in the quantum formulation of the theory. The second class constraints are formulated as strongly elliptic partial differential equations allowing a global analysis on the existence and uniqueness of the solution. We discuss the possibility of formulating the theory in terms of a master action with first class constraints only. In this case the Hořava theory would correspond to a gauged fixed version of the master theory. Finally we obtain, using the non-perturbative solution of the constraints, the explicit expression of the gravitational energy. It is, under some assumptions, always positive and the solution of Hořava field equations at minimal energy is the Minkowski metric.

The "NuMI Off-Axis electron-neutrino Appearance" (NOvA) is a second generation, long- baseline, neutrino oscillation, experiment. It is made of two detectors, a large Far detector (14 ktons) and a similar Near detector (222 tons), both made of mostly active scintillator and separated by 810 km. Along with the 700 kW NuMI-beam upgrade (a prelude to the Intensity Frontier), it will be the leading neutrino experiment at Fermilab. In the wake of the recent measurement of the θ₁₃ mixing angle, NOvA is positioned to see evidence of the neutrino mass hierarchy, possibly to resolve the θ₂₃ octant ambiguity, and begin the study of the CP violation at the lepton sector. The experiment is under construction. The design and potential of this experiment is presented here along with the current status.

We study neutral-current neutrino-nucleus reactions in nuclei that are relevant for supernova (SN) simulations and for terrestrial experiments aiming at neutrino astrophysics as well as ν-nucleus scattering cross sections measurements. Such studies allow us to improve estimates of nuclear responses to low energy neutrinos in light of the operation of nuclear v-detectors with very-low threshold and very high sensitivity. The adopted ν-energy range is extended to rather high energies (up to 100 MeV) so as to consider allowed and forbidden multipole contributions to cross sections. Both contributions are calculated within the quasi-particle random phase approximation by using realistic two-body forces (Bonn CD potential) for the residual interaction of the nuclear Hamiltonian. As a special application the ⁵⁶Fe isotope is chosen due to its significant role in SN physics and ν-detection.

In an attempt to understand the Tsallis entropy composition property, we construct an embedding of the reals into the set of 3 × 3 upper triangular matrices with real entries. We explore consequences of this embedding and of the geometry of the ambient 3 × 3 Heisenberg group. This approach establishes the polynomial growth of the volume of phase space of systems described by the Tsallis entropy and provides a general framework for understanding Abe's formula in terms of the Pansu derivative between Riemmanian spaces.

A topological extension of general relativity is presented. The superposition principle of quantum mechanics, as formulated by the Feynman path integral, is taken as a starting point. It is argued that the trajectories that enter this path integral are distinct and thus that space-time topology is multiply connected. Specifically, space-time at the Planck scale consists of a lattice of three-tori that facilitates many distinct paths for particles to travel along. To add gravity, mini black holes are attached to this lattice. These mini black holes represent Wheeler's quantum foam and result from the fact that GR is not conformally invariant. The number of such mini black holes in any time-slice through four-space is found to be equal to the number of macroscopic (so long-lived) black holes in the entire universe. This connection, by which macroscopic black holes induce mini black holes, is a topological expression of Mach's principle. The proposed topological extension of GR can be tested because, if correct, the dark energy density of the universe should be proportional the total number of macroscopic black holes in the universe at any time. This prediction, although strange, agrees with current astrophysical observations.

In this paper we analyze the problem of fermion creation as a dynamical Casimir effect inside a three dimensional sphere. We present an appropriate wave function which satisfies the Dirac equation in this geometry with MIT bag model boundary condition. We consider the radius of the sphere to have dynamics and introduce the time evolution of the quantized field by expanding it over the instantaneous basis. We explain how we can obtain the average number of particles created. In this regard we find the Bogoliubov coefficients. We consider an oscillation and determine the coupling conditions between different modes that can be satisfied depending on the cavity's spectrum. Assuming the parametric resonance case we obtain an expression for the mean number of created fermions in each mode of an oscillation.

We study the Fock quantization of scalar fields with a time dependent mass in cosmological scenarios with flat compact spatial sections. This framework describes physically interesting situations like, e.g., cosmological perturbations in flat Friedmann-Robertson-Walker spacetimes, generally including a suitable scaling of them by a background function. We prove that the requirements of vacuum invariance under the spatial isometries and of a unitary quantum dynamics select (a) a unique canonical pair of field variables among all those related by time dependent canonical transformations which scale the field configurations, and (b) a unique Fock representation for the canonical commutation relations of this pair of variables. The proof is generalizable to any compact spatial topology in three or less dimensions, though we focus on the case of the three-torus owing to the especially relevant implications.

The mechanism of low energy physics formation in the framework of multidimensional gravity is discussed. It is shown that a wide set of parameters of a primary theory could lead to the observable Universe. Quantum fluctuations of extra space metric and its consequent classical evolution play an important role in this process.

Using complex quantum Hamilton-Jacobi formulation, a new kind of non-linear equations is proposed that have almost classical structure and extend the Schrödinger equation to describe the collapse of the wave function as a finite-time process. Experimental bounds on the collapse time are of order 0.1 ms to 0.1 ps and the areas where sensitive probes of the possible collapse dynamics can be done include Bose-Einstein condensates, ultracold neutrons or ultrafast optics.

We study the continuum limit of a "radially reduced" approximation of Causal Dynamical Triangulations (CDT), so-called multigraph ensembles, and explain why they serve as realistic toy models to study the dimensional reduction observed in numerical simulations of four-dimensional CDT. We present properties of this approximation in two, three and four dimensions comparing them with the numerical simulations and pointing out some common features with 2+1 dimensional Hořava-Lifshitz gravity.

Recently a theory of excited states of Coulomb systems (P. W. Ayers, M. Levy and Á. Nagy, Phys. Rev. A 85, 042518 (2012)) has been been put forward. The talk will present and develop this new theory. It will be shown that the Coulomb density determines the Hamiltonian and the degree of excitation. The definition of a single, universal functional which is enough to describe Coulomb systems is presented. The availability of the theory is discussed.

By using a simple random-walk model, we simulate the growth of a self-assembled monolayer (SAM) pattern generated in dip pen nanolithography (DPN). In this model, the SAM pattern grows mainly via the serial pushing of molecules deposited from the tip. We examine various SAM patterns, such as lines, crosses, and letters by changing the tip scan speed.

The thermodynamic properties of dimer adsorption on square M sites wide terraces, with first- and second-neighbor adsorbate-adsorbate interaction energies, were recently numerically obtained using an extension of the transfer matrix technique developed by the authors in 1993. The rank of the transfer matrix increases rapidly with size M, and required the development of an efficient algorithm for its construction at any temperature of the system, and for all possible values of the adsorbate-adsorbate and adsorbate-substrate interaction energies. This article presents the non-trivial generalization of this algorithm for the study of dimer adsorption problems on a square lattice nanotube surface, with M sites on its circular normal section.

We give a brief review of theoretical and computational tools developed for the description and analysis of irradiation dynamics of cluster and molecules. We illustrate the capabilities of the method on the demanding example of C₆₀ irradiated by various laser fields.

Large quantum fluctuations in the strongly correlated electron systems as well as electron-phonon coupled systems are visualized by the resonating Hartree-Fock (HF) method). We show that, in the two-dimensional Hubbard model, doped holes form topological defects called polarons. It is also shown that the quantum fluctuations drastically change the lattice structures in the Su-Schrieffer-Heeger model.

The origin of sustained current oscillations at the Si/electrolyte contact is not fully understood. Oscillatory functions are regarded which describe the oscillating oxide thickness at the silicon electrode. We consider an initially vanishing two-dimensional time dependent function which oscillates between a minimum and a maximum oxide thickness at each location of the electrode. The function is continuous except at single points of the electrode at which the oxide thickness drops deeply due to the formation of nanopores in the oxide. The oscillatory function is represented by a set of infinite (infinitesimal) oscillators. The mathematical model is based on the fact that it is sufficient to register the oscillators only one time per i-th cycle at their minimum or when the phase of the oscillator equals i 2π. In phase-space representation, the passing of the phase trough the i 2π planes leads to oscillator density functions p_i(t) which define the (differential) number of oscillators passing their minimum at the i-th time at the time t. Two consecutive oscillator density functions are connected by an integral equation representing a Markov process. Together with a local model for the oxide microstructure, a fit of the model parameter to the measured current is possible. The result is that the existence of two types of oxides (with different nanopore densities) can explain sustained current oscillations and, further, it is possible to calculate the mean nanopore distance in both types of oxide.

In this work we develop a method for inferring the underlying configurational density of states of a molecular system by combining information from several microcanonical molecular dynamics or Monte Carlo simulations at different energies. This method is based on Jaynes' Maximum Entropy formalism (MaxEnt) for Bayesian statistical inference under known expectation values. We present results of its application to measure thermodynamic entropy and free energy differences in embedded-atom models of metals.

We present a new method for the solution of linearized Ginzburg-Landau problem for mesoscopic superconducting nanostructures of arbitrary shapes in applied magnetic field. The method is based on the conformal mapping of the analytical solution for the disk and uses a specially designed superconducting gauge for the vector potential corresponding to the magnetic field. As a demonstration of the methods accuracy, we calculate the distribution of the order parameter in superconducting regular polygons and compare the obtained solutions with the available numerical results. We further consider an example of irregular polygon and show the evolution of the vortex patterns in function of the geometry of samples boundary. The obtained results will be compared with available experimental data on mesoscopic and nanoscopic superconductors.

In this paper, we propose a novel approach for texture analysis based on artificial crawler model. Our method assumes that each agent can interact with the environment and each other. The evolution process converges to an equilibrium state according to the set of rules. For each textured image, the feature vector is composed by signatures of the live agents curve at each time. Experimental results revealed that combining the minimum and maximum signatures into one increase the classification rate. In addition, we pioneer the use of autonomous agents for characterizing silk fibroin scaffolds. The results strongly suggest that our approach can be successfully employed for texture analysis.

Several works on nonclassical fullerenes with heptagons have mainly considered the case with just one heptagon. In this context the isolated pentagon rule is not satisfied. The study of nonclassical fullerenes is important because some of them are more stable than the corresponding classical isomers with the same number of pentagonal bonds. We present several nonclassical fullerenes with pentagons, hexagons and two, three, or more heptagons.

Casimir forces arise from vacuum fluctuations. They are fully understood only for simple models, and are important in nano- and microtechnologies. We report our experience of computer algebra calculations towards the Casimir force for models involving inhomogeneous dielectrics. We describe a methodology that greatly increases confidence in any results obtained, and use this methodology to demonstrate that the analytic derivation of scalar Green's functions is at the boundary of current computer algebra technology. We further demonstrate that Lifshitz theory of electromagnetic vacuum energy can not be directly applied to calculate the Casimir stress for models of this type, and produce results that have led to alternative regularisations. Using a combination of our new computational framework and the new theory based on our results, we provide specific calculations of Casimir forces for planar dielectrics having permittivity that declines exponentially. We discuss the relative strengths and weaknesses of computer algebra systems when applied to this type of problem, and describe a combined numerical and symbolic computational framework for calculating Casimir forces for arbitrary planar models.

Fluorescence computed tomography is a synchrotron imaging technique aiming at reconstructing the fluorescence emission within a sample object. For a polychromatic source hitting the object, the amount of fluorescence detected is defined by a linear equation. For the monochromatic case, the operator is a Generalized Attenuated Radon Transform (GART). The main goal is to reconstruct the density function, given the sinogram data and the weight function. An eficient iterative algorithm for the inversion of the GART was presented recently by the authors. This inversion can only be performed if the weight function is previously known, which means that μ = μ(·, ) and λ are also known. For monochromatic XFCT (acronym for x-rays fluorescence computed tomography), the determination of λ is a dificult task, and we have considered the approximation λ ≈ μ, which is valid for low energies ranging from 3Kev to 10Kev. So, for solving our problem, the first step is to find μ given the polychromatic sinogram. There are different approaches for this in the literature. Recently, an elegant and efficient method for solving this problem was introduced, using a fixed point algorithm. Opposite to this, where μ(·, ) needs to be computed for all ∊ E, we claim that the integral of μ(·, ) for all has a physical meaning and provides a good aproximation for the solution. Also we present fast algorithm for computations.

Fluorescence computed tomography is a synchrotron imaging technique that reconstructs the fluorescence emission within a sample object. For a monochromatic source hitting the object, the amount of fluorescence detected is given as a linear equation. Iterative methods based on the inversion of the Radon transform were introduced. These methods were compared with the Expectation Maximization algorithm, implemented in a continuous setting. This implementation provided better quality results, but with higher computational cost. Recently, a faster OS-EM algorithm was applied in XFCT, in a discrete setting. In this manuscript we further improve on previous results by considering a relaxed version of OS-EM, in a continuous setting (faster implementation per iteration).

Scratch wounding of a urothelial cell monolayer triggers a number of events including the release of soluble, diffusible signalling factors and mechanical stimulation of cells at the wound edge. These events cause a sustained elevation in cytosolic calcium concentration in the cells surrounding the wound and a transient rise in those further away. The precise form of this calcium transient is believed to play a central role in determining the subsequent response of individual cells and ultimately leads to a co-ordinated, population-level response that rapidly closes the wound. Here we present a framework for modelling the initial phases of this process. We combine a PDE model of diffusion in the extracellular medium and an ODE model of calcium signalling that has been tailored to represent urothelial cells. The ODE model is capable of generating a wide range of calcium transients, including spikes, bursts, oscillations and sustained elevations in the cytosolic calcium concentration. In multi-cell simulations of scratch wounding in a perfusion flow we find that the spatial position of the cells relative to the wound site leads to distinct classes of calcium response, with cells proximal to the wound exhibiting a sustained elevation and cells distal to the wound exhibiting a more transient elevation. We compare these results to existing experimental data and generate a number of novel predictions that could be used to test the model experimentally.

This paper describes strategies and techniques to perform modeling and automatic mesh generation of the aorta artery and its tunics (adventitia, media and intima walls), using open source codes. The models were constructed in the Blender package and Python scripts were used to export the data necessary for the mesh generation in TetGen. The strategies proposed are able to provide meshes of complicated and irregular volumes, with a large number of mesh elements involved (12,000,000 tetrahedrons approximately). These meshes can be used to perform computational simulations by Finite Element Method (FEM).

This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with ubroken rays and for specular reflection. Our numerical method using Lambertian reflection improves the solution's accuracy by an order of magnitude compared to classical tomography with ubroken rays and for tomography in the presence of a specularly reflecting obstacle the numerical method improves the solution's accuracy approximately by a factor of three times. We present efficient new algorithms for the solution's software implementation and analyze the solution's performance and effectiveness.

We present new parallel algorithms for shape and trajectory reconstruction of moving obstacles using reflected rays. In contrast to tomography where the focus of the reconstruction method is to recover the velocity structure of the domain, the shape and trajectory reconstruction procedure directly finds the shape and trajectory of the obstacle. The rays are curves determined by the variable speed of sound and initial conditions and we develop ultrasonic ray models based on a system of differential equations. The method can achieve high-resolution and computational efficiency.

Thermal effects on the neutral-current inelastic neutrino-nucleus scattering in a supernova environment are examined by using the thermal quasi-particle random phase approximation (TQRPA). We concentrate on the total cross section of neutrino scattering on the nucleus ⁵⁶Fe, which plays a significant role in core collapse supernova dynamics. The calculations are performed for several nuclear temperatures relevant for supernova physics and for incoming neutrino energies up to 60 MeV. Our results show that finite temperature effects cause a significant enhancement in the cross section for low-energy neutrinos. These findings are in agreement with previous large-scale shell-model calculations where such an increase is closely related to Gamow-Teller transitions stemming from thermally populated nuclear states.

S Basu acknowledges that this paper was submitted to the IC-MSQUARE 2012 proceedings without the knowledge of, or consultation with, the co-author and apologises accordingly.

In addition, this paper has been found to have substantial overlap with a previously published paper, [1], and has therefore been retracted.

Reference [1] Basu S and Mattingly D 2010 Asymptotic safety, asymptotic darkness, and the hoop conjencture in the extreme UVPhysical Review D 82 124017

Retraction published: 14 June 2013