Table of contents

The third International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Madrid, Spain, from Thursday 28 to Sunday 31 August 2014.

The Conference was attended by more than 200 participants and hosted about 350 oral, poster, and virtual presentations. More than 600 pre-registered authors were also counted. The third IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc.

The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel oral sessions and one poster session were running every day. However, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time.

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

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

Using the space-time transformations, approximate analytical solutions of the D- dimensional propagator in the presence of q-deformed Woods-Saxon potential are obtained. The analytical expression of the energy eigenvalues is given for various quantum numbers and the corresponding normalized eigenfunctions are obtained in terms of hypergeometric function. Our results are compared with those given by The Nikivorov-Uvarov method.

In the present work, we derive a family of higher order exponential variational integrators for the numerical integration of systems containing slow and fast potential forces. To increase the order of variational integrators, first the discrete Lagrangian in a time interval is defined as a weighted sum of the evaluation of the continuous Lagrangian at intermediate time nodes while expressions for configurations and velocities are obtained using interpolating functions that can depend on free parameters. Secondly, in order to choose those parameters appropriately, exponential integration techniques are embedded. When the potential can be split into a fast and a slow component, we use different quadrature rules for the approximation of the different parts in the discrete action. Finally, we study the behavior of this family of integrators in numerical tests.

In interdependent networks, failures of nodes in one constituent network lead nodes in another network to fail. This happens recursively and leads to a cascade of failures. It is known that the interdependent networks with random inter-connections have weaker robustness than the individual networks. However, if the interdependent networks have degree correlations between the networks constructing them as in the actual cases, the robustness of the interdependent networks may be changed. In this paper, we perform numerical simulations on interdependent networks and obtain the giant cluster sizes after the cascade of failures in order to evaluate the robustness. We show that when a interdependent network has a positive degree inter-correlation, it has the stronger robustness than that for the networks with no degree correlation. We show not only the numerical simulation results but theoretical ones for the robustness of the interdependent networks.

We generalize previous studies on critical phenomena in communication networks [1,2] by adding computational capabilities to the nodes. In our model, a set of tasks with random origin, destination and computational structure is distributed on a computational network, modeled as a graph. By varying the temperature of a Metropolis Montecarlo, we explore the global latency for an optimal to suboptimal resource assignment at a given time instant. By computing the two-point correlation function for the local overload, we study the behavior of the correlation distance (both for links and nodes) while approaching the congested phase: a transition from peaked to spread g(r) is seen above a critical (Montecarlo) temperature T_c. The average latency trend of the system is predicted by averaging over several network traffic realizations while maintaining a spatially detailed information for each node: a sharp decrease of performance is found over T_c independently of the workload. The globally optimized computational resource allocation and network routing defines a baseline for a future comparison of the transition behavior with respect to existing routing strategies [3,4] for different network topologies.

We model the sol-gel transition in terms of Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models and compare with experimental results. We show, numerically, that the "gel point" described as the onset of the gelation phenomena and measured experimentally, corresponds to an accumulation point of the extreme values of the derivatives of the gelation curve. We define the "critical point of a sigmoidal curve" as the limit of the points where the derivatives reach their extreme values, provided that this limit exists.

Recently, related studies on Equation Of State (EOS) have reported that generalized van der Waals (GvdW) shows poor representations in the near critical region for non-polar and non-sphere molecules. Hence, there are still remains a problem of GvdW parameters to minimize loss in describing saturated vapor densities and vice versa. This paper describes a recursive model GvdW (rGvdW) for an accurate representation of pure fluid materials in the near critical region. For the performance evaluation of rGvdW in the near critical region, other EOS models are also applied together with two pure molecule group: alkane and amine. The comparison results show rGvdW provides much more accurate and reliable predictions of pressure than the others. The calculating model of EOS through this approach gives an additional insight into the physical significance of accurate prediction of pressure in the nearcritical region.

Nonlinear optical (NLO) properties are mainly measured by the first hyperpolarizability β(0) magnitudes. Besides analyzing the NLO behaviours of monomers, dimerization of chromophores has been found of a huge interest for the application in several optical areas. In the present work, a theoretical study has been carried out on a series of dimers constituted by the azo-chromophore 4-hydroxy, 4'-cyanoazobenzene (HCAB). Combinations of vinylic and styrenic oligomers as well as of 1,3-diphenyl propnane (1,3-DPP) to HCAB have been also investigated. No influence of geometrical parameters has been detected. Indeed, after establishing a comparison with β(0) of monomeric entities, results show that the NLO response of these dimers is not guided by any additivity rule.

We investigate the effect of flow rate on the electrical current response to the applied voltage in a micro electrochemical system. To accomplish this, we considered an ion-transport model that is governed by the Nernst-Planck equation coupled to the Navier-Stokes equations for hydrodynamics. The Butler-Volmer relation provides the boundary conditions, which represent reaction kinetics at the electrode-electrolyte interface. The result shows that convection drastically affects the rate of surface kinetics. At a physically sufficient high flow rates and lower scan rates, the current response is limited by the convection due to fresh ions being brought to the electrode surface and immediately taken away before any surface reaction. However, at high flow and scan rates, the Faradaic current overrides current due to convection. The model also allows predicting the effect of varying electrolyte concentration and scan rates respectively.

Molecular dynamics computer simulations were combined with an electrodiffusion model to compute conduction of simple ion channels. The main assumptions of the model, and the consistency, efficiency and accuracy of the ion current calculations were tested and found satisfactory. The calculated current-voltage dependence for a synthetic peptide channel is in agreement with experiments and correctly captures the asymmetry of current with respect to applied field.

A numerical study was performed to give a quantitative description of a heavily sooting, non-premixed laminar flame established in a shear boundary layer in microgravity. The competition between fuel pyrolysis rate, radiation loss due to soot formation and oxygen- side diffusion creates a number of unusual phenomena. A three-dimensional, laminar diffusion flame over plate in low-speed concurrent flow was formulated and solved. The model consists of full Navier-Stokes equations for mass, momentum, energy and species. Gas radiation associated with soot formation is included. The PAH inception model, which is based on the formation of two and three-ringed aromatic species, reproduces correctly the measured soot from a laminar ethylene diffusion flame. The flame standoff distance is beyond the boundary layer thickness, while soot resides always within the boundary layer. The fraction of the total energy released by the flame to the surface increases with a rise of pyrolysis rate due to increase in the flame volume. The zone of the high heat flux increases noticeably when the flame becomes most obviously dual on the cross-stream section due to development of the counter-rotating vortex.

Both ab initio molecular dynamics simulations based on the Born-Oppenheimer approach calculations and a quantum theoretical model are used in order to study the IR spectrum of the acetic acid dimer in the gas phase. The theoretical model is taking into account the strong anharmonic coupling, Davydov coupling, multiple Fermi resonances between the first harmonics of some bending modes and the first excited state of the symmetric combination of the two vO-H modes and the quantum direct and indirect relaxation. The IR spectra obtained from DFT-based molecular dynamics is compared with our theoretical lineshape and with experiment. Note that in a previous work we have shown that our approach reproduces satisfactorily the main futures of the IR experimental lineshapes of the acetic acid dimer [Mohamed el Amine Benmalti, Paul Blaise, H. T. Flakus, Olivier Henri-Rousseau, Chem Phys, 320(2006) 267-274.].

This study focusses on the investigation of the potential binding of the fungicide difenoconazole to soil chitinases using a computational approach. Computational characterization of the substrate binding sites of Serratia marcescens and Bacillus cereus chitinases using Fpocket tool reflects the role of hydrophobic residues for the substrate binding and the high local hydrophobic density of both sites. Molecular docking study reveals that difenoconazole is able to bind to Serratia marcescens and Bacillus cereus chitinases active sites, the binding energies being comparable.

The reaction of charged aluminium clusters with water in the gas phase is investigated theoretically. To this end, the doublet potential energy surface for the Al_n⁺ + H₂O → Al_nO⁺ + H₂ reaction with n=6 is explored using density functional theory. The calculated reaction pathways include the initial adduct ion formation, the O-H bond activation and H₂ elimination steps, and are consistent with the recent experimental report (Ref.2). The results of the current quantum-chemical study are relevant to the issues of catalytic role of the main group metal clusters and H₂ generation.

In this work, we present a novel technique, based on molecular dynamics simulations, that allows the study of the lateral chain packing in a lipid bilayer. It utilizes the radial distribution function of the alkyl chains to determine the arrangement of the chains along the bilayer plane. The positions of the mass centres of the chains are projected onto the bilayer plane and a 2D radial distribution function is calculated for these projections. The proposed technique can be particularly useful for lipid bilayers in the gel (solid) phase where the chains present a limited degree of mobility. As a case study, we have examined a bilayer that consists of ceramide NS 24:0. Ceramide bilayers can be found in the lipid domain of the skin where they have a significant role in its barrier function. The specific bilayer was found (at 300 K) to adopt a strictly hexagonal chain packing with a separation distance between the chains of 0.466 nm, in good agreement with the available experimental data.

By using first-principles simulations, we investigate the interaction of silicene and germanene with various non-metallic substrates. We first consider weak van der Waals interactions between the 2D layers and dichalcogenide substrates, like MoX₂ (X=S, Se, Te). The buckling of the silicene or germanene layer is correlated to the lattice mismatch between the 2D material and the MoX₂ template. The electronic properties of silicene or germanene on these different templates then largely depend on the buckling of the 2D material layer: highly buckled silicene or germanene on MoS₂ are predicted to be metallic, while low buckled silicene on MoTe₂ is predicted to be semi-metallic, with preserved Dirac cones at the K points. We next study the covalent bonding of silicene and germanene on (0001) ZnS and ZnSe surfaces. On these substrates, silicene or germanene are found to be semiconducting. Remarkably, the nature and magnitude of their energy band gap can be controlled by an out-of-plane electric field.

Kinematic analysis and simulation of hybrid drive system are addressed in this study. A seven link mechanism with two degrees of freedom is selected as the configuration of the system. Kinematic analysis is performed by loop closure equations and required inputs of servo motor are given to get desired ram motion scenario. MATLAB/SimMechanics platform is used to model the hybrid driven mechanical system mechanism characteristics. The simulation results are presented herein.

The proposed method of the free energy calculation is based on the approximation of the energy distribution in the microcanonical ensemble by the Gaussian distribution. We hope that our approach will be effective for the systems with long-range interaction, where large coordination number q ensures the correctness of the central limit theorem application. However, the method provides good results also for systems with short-range interaction when the number q is not so large.

The log-concavity of the expected refund rate for an item with a nonrenewing pro-rata rebate warranty policy, and of the expected total reserve to service the warranty over the item life cycle under the same policy are proved. Upper bounds of warranty reserves are derived. The results are extended to other measures for spares and repairs under other warranty policies. Applications are given to ranking items' prices and production and inventory control.

Space and ground level electronic equipment with semiconductor devices are subjected to the deleterious effects by radiation. This paper is attempted to present the transient and post-irradiation response of optoelectronic devices to gamma (γ) rays utilizing cobalt-60. In situ measurements were made on the devices under test (DUTs) up to a total dose of 60 krad followed by a post-irradiation not in-flux test for eight hours. Current transfer ratio (CTR) with is the vital merit of the optoelectronic system is found to decrease remarkably with the absorbed dose. This degradation is induced by the interaction of the energetic photons from gamma rays via two main mechanisms. The dominant effect is the mechanism by ionization while the secondary is by displacement. This radiation effect is found to arouse either a permanent or temporarily damage in the DUTs depending on their current drives and also the Total Ionizing Dose (TID) absorbed. The TID effects by gamma rays are cumulative and gradually take place throughout the lifecycle of the devices exposed to radiation. The full damage cascade phenomenon in the DUTs is calculated via the simulation.

In this paper we study the dynamics of a semiconductor laser with optical injection. The time behaviour of solutions of a system of three coupled nonlinear rate equations, describing the electric field amplitude and the carrier concentration and the phase difference within the resonator, is discussed both qualitatively and numerically. We then concentrate on the periodic orbits that emanate from Hopf bifurcations. Depending on the injection strength and the phase difference two types of oscillations can be found, such as relaxation and periodic oscillations

We evaluate the dependence among large values of a spatial process of maxima trough a coefficient that can be applied in natural, technical and societal extreme phenomena. Its main properties are: a) k locations can be taken into account; b) it takes values in [0,1] and higher values indicate stronger dependence; c) it is independent of the univariate marginal distributions of the random field; d) it can be related with other coefficients in the literature such as the tail dependence and the extremal coefficients; e) it agrees with the concordance property for multivariate distributions; f) it has as a particular case the variogram from geostatistics; g) it can be easily estimated. We illustrate the application of the introduced coefficient with the estimation of the degree of dependence among large values of the amount of tritium in drinking water for tree cities.

The bound state solutions of the Feynman propagator with the rotating Deng- Fan molecular potential are presented approximately. An approximation of the centrifugal potential is used and nonlinear space-time transformations are applied. A relation between the original path integral and the Green function of a new quantum soluble system is derived. The energy spectrum and the normalized eigenfunctions are both obtained for the application of this technique to the Deng-Fan molecular potential. Our results are in very good agreement with those found by using numerical and other methods.

We introduce a model in which the grating is absent in a finite-width stripe in the waveguide, thus creating a gapless channel in the gapped medium. Two semi-infinite grating separated by the plain stripe may have a relative phase shift. This system modifies the Bragg bandgap, creating intra-gap defect modes (DFs) which are pinned to the gapless channel. A DF solution in the linear system is found analytically. Further, numerical analysis of the full nonlinear system demonstrates that the shape and stability of Bragg solitons are also strongly affected by the presence of the gapless channel, and by the possible phase shift between the two semi-infinite gratings. In particular, asymmetric and flat-top solitons appear.

The basic process at the surface of the Si electrode is characterized by a cyclic oxidation of a thin silicon layer and the subsequent removal of the oxide by etching. Here, the oxide thickness evolves not uniformly due to cracks and nanopores. The mathematical model used to describe the phenomenon is based on a sequence of time dependent (oxide thickness) oscillator density functions that describes the passing of the (infinitesimal) oscillators through their minimum at each cycle. Two consecutive oscillator density functions are connected by a second order linear integral equation representing a Markov process. The kernel of the integral equation is a normalized Greens Function and represents the probability distribution for the periods of the oscillators during a cycle. Both, the oscillator density function and the twodimensional probability density for the periods of the oscillators, define a random walk. A relation between the oscillator density functions and solutions of the Fokker-Planck equation can be constructed. This allows a connection of the oscillations, originally considered only for the description of a photo-electrochemical observation, to the Schrodinger equation. In addition, if the trajectory of a virtual particle, located at the silicon oxide electrode surface, is considered during one oscillatory cycle, then it can be shown that the displacement of the particle measured at the electrode surface performs a Brownian motion.

We consider various echo-processes having different nature and discuss their mathematical models based on the special nonlinear transformations in the spectral domain. It is shown that the presence of a power polynomial in the spectral domain results in a delay of the external perturbation (signal). The correspondence between the degree of nonlinearity and arising delayed signals is established. The agreement between the numerical results and experimental data is demonstrated for several external signals.

A mathematical model of non-isothermal flow of a fluid film is presented. In conditions of Marangoni instability wave characteristics are calculated, identify areas of instability of a fluid film. It shows the influence of thermocapillary forces and forces of surface viscosity on the form of waves. Nonlinear development of perturbations belonging to a continuous band of wave numbers on the surface of a thin fluid layer is investigated within the framework of a nonlinear parabolic equation.

An rf superconducting quantum interference device (SQUID) consists of a superconducting ring interrupted by a Josephson junction (JJ). When driven by an alternating magnetic field, the induced supercurrents around the ring are determined by the JJ through the celebrated Josephson relations. This system exhibits rich nonlinear behavior, including chaotic effects. We study the dynamics of a pair of parametrically-driven coupled SQUIDs arranged in series. We take advantage of the weak damping that characterizes these systems to perform a multiple-scales analysis and obtain amplitude equations, describing the slow dynamics of the system. This picture allows us to expose the existence of homoclinic orbits in the dynamics of the integrable part of the slow equations of motion. Using high-dimensional Melnikov theory, we are able to obtain explicit parameter values for which these orbits persist in the full system, consisting of both Hamiltonian and non-Hamiltonian perturbations, to form so-called Silnikov orbits, indicating a loss of integrability and the existence of chaos.

Soliton propagation dynamics under the presence of a complex potential are investigated. Cases of both symmetric and non-symmetric potentials are studied in terms of their effect on soliton dynamics. The existence of an invariant of soliton propagation under specific symmetry conditions for the real and the imaginary part of the potential is shown. The rich set of dynamical features of soliton propagation include dynamical trapping, periodic and nonperiodic soliton mass variation and non-reciprocal dynamics. These features are systematically investigated with the utilization of an effective particle phase space approach which is shown in remarkable agreement with direct numerical simulations. The generality of the results enables the consideration of potential applications where the inhomogeneity of the gain and loss is appropriately engineered in order to provide desirable soliton dynamics.

It is a surprisingly common phenomenon that two objects collide with each other and emerge only mildly altered. We motivate a dynamic-independent, analytical framework to study these mild collisions through two specific examples: (1) Head-on collision between two non-integrable solitons, and (2) Gravitational self-interaction for a collapsing shell of radiation.

The real-space dynamics and the nonlinear interactions among Fourier modes in elastic wave turbulence are investigated by simulating the Foppl-von Karman equation. We find that the bundle structures of ridges appear intermittently in the time evolution of the stretching energy field. The time-evolution of the nonlinearity indicates the existence of active and moderate phases in turbulent state. Conditional sampling analysis reveals that the bundle structure, which is the embodiment of the strong nonlinear interactions among modes, induces the energy supply from an external force to the system.

The solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) are given in terms of determinants. The orders of these determinants are arbitrarily equal to 2N for any nonnegative integer N and generate a hierarchy of solutions which can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N(N + 1) in x and t. These solutions depend on 2N – 2 parameters and can be seen as deformations with 2N – 2 parameters of the Peregrine breather P_N: when all these parameters are equal to 0, we recover the P_N breather whose the maximum of the module is equal to 2N + 1. Several conjectures about the structure of the solutions are given.

Dynamics of solitons is considered in an extended nonlinear Schrodinger equation, including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term (scattering on damping low-frequency waves, nonlinear dispersion and inhomogeneity of the spatial second-order dispersion (SOD). It is shown that wave-number downshift by the pseudo-SRS may be compensated by upshift provided by spatially increasing SOD with taking into account nonlinear dispersion. The equilibrium state is stable for negative parameter of nonlinear dispersion and unstable for positive one. The analytical solutions are verified by comparison with numerical results

We introduce a supersymmetric extension for a parametric coupled Korteweg- de Vries system. The supersymmetric system has two real hamiltonian functionals and two associated basic Poisson structures. The basic Poisson structures allows the construction of a pencil of Poisson brackets and associated to them a hamiltonian functional depending on the parameter of the pencil. The two basic Poisson brackets are compatible.

We present the hamiltonian structures for a wide class of coupled Korteweg-de Vries systems, including the Gear and Grimshaw system that models the strong interaction of internal waves in a stratified liquid and the system of Lou, Tong, Hu and Tang that describes a two layer fluid model. Among the hamiltonian structures of these systems we found new Poisson brackets which define consistent algebras of observables.

In this communication, we use a compact split step Pade scheme (CSSPS) to solve the scalar higher-order nonlinear Schrodinger equation (HNLS) with higher-order linear and nonlinear effects. The second part, consisting of two sections, the first section is dedicated to the study numerically the stabilization of high-order solitons dynamic in optical fibers by compensation or by the interplay of higher order nonlinearity – especially quintic nonlinearity- and the self-steepening. In the second section we study also numerically the propagation of conventional chirped or unchirped solitons in optical fibers with to the management of the nonlinearity, dispersion and loss (gain).

We have found a solution of the optical pulses propagation equation in optical fibers in quadratures. We have derived an expanded equation of optical pulses propagation in silica optical fibers and found its localized solution. The derived solution of the extended equation of optical pulses propagation in optical fibers for arbitrary function of the nonlinear medium response to an external harmonic disturbance has been found in quadratures.

We study dynamical response of the nonlinear dimer relative to monochromatic wave injected via the waveguide. We show existence of a domain in space of frequency and injected amplitude where the stationary solutions of the time evolution equations do not exist. We present time dependent solutions which show that scattering waves carry multiple harmonics with frequencies spaced equidistantly.

In this work, similarity solutions of viscous one-dimensional Burgers' equation are attained by using Lie group theory. The symmetry generators are used for constructing Lie symmetries with commuting infinitesimal operators which lead the governing partial differential equation (PDE) to ordinary differential equation (ODE). Most of the constructed solutions are found in terms of Bessel functions which are new as far as authors are aware. Effect of various parameters in the evolutional profile of the solutions are shown graphically and discussed them physically.

When ultrashort pulses with large enough power are launched into highly nonlinear fibers, soliton fission gives origin to multiple fundamental solitons of different widths and peak powers. Two soliton related effects become then particularly important in the context of supercontinuum generation: the soliton self-frequency shift and the emission of dispersive radiation in the normal dispersion region. The dispersive characteristics of the optical fiber assume play a key role in these circumstances.

The current cold dark matter cosmological model explains the large scale cosmic web structure but is challenged by the observation of a relatively smooth distribution of matter in galactic clusters. We consider various aspects of modeling the dark matter around galaxies as distributed in smooth halos and, especially, the smoothness of the dark matter halos seen in N-body cosmological simulations. We conclude that the problems of the cold dark matter cosmology on small scales are more serious than normally admitted.

Molecular dynamics is a simulation technique that can be used to study failure in solids, provided the inter-atomic potential energy is able to account for the complex mechanisms at failure. Reactive potentials fitted on ab initio results or on experimental values have the ability to adapt to any complex atomic arrangement and, therefore, are suited to simulate failure. But the complexity of these potentials, together with the size of the systems considered, make simulations computationally expensive. In order to improve the efficiency of numerical simulations, simpler harmonic potentials can be used instead of complex reactive potentials in the regions where the system is close to its ground state and a harmonic approximation reasonably fits the actual reactive potential. However the validity and precision of such an approach has not been investigated in detail yet.

We present here a methodology for constructing a reduced potential and combining it with the reactive one. We also report some important features of crack propagation that may be affected by the coupling of reactive and reduced potentials. As an illustrative case, we model a crystalline two-dimensional material (graphene) with a reactive empirical bond-order potential (REBO) or with harmonic potentials made of bond and angle springs that are designed to reproduce the second order approximation of REBO in the ground state. We analyze the consistency of this approximation by comparing the mechanical behavior and the phonon spectra of systems modeled with these potentials. These tests reveal when the anharmonicity effects appear. As anharmonic effects originate from strain, stress or temperature, the latter quantities are the basis for establishing coupling criteria for on the fly substitution in large simulations.

We propose in this work an alternative method of easier calculation of necessary conditions for lossless propagation of short laser pulses in multilevel atomic media. Method is based on the quasienergy approach and illustrated with example of a five-level system. We also demostrated effective population transfer in this system.

We investigate nanoparticle self-assembly using a stochastic model based on cooperative sequential adsorption with evaporation mechanisms and aimed specifically at the creation of optical thin films. Applying the mean field approximation, we derive a rate equation for particle density. We solve directly for the particle density in both the steady state and time-dependent cases. The analytical results are compared to Monte Carlo simulations of the self-assembly process and to experimental data for self-assembled thin films. We relate our theoretical model to the final particle density for thin films created under varied nanoparticle suspension concentrations.

We consider a N – S box system consisting of a rectangular conductor coupled to a superconductor. The Green functions are constructed by solving the Bogoliubov-de Gennes equations at each side of the interface, with the pairing potential described by a step-like function. Taking into account the mismatch in the Fermi wave number and the effective masses of the normal metal – superconductor and the tunnel barrier at the interface, we use the quantum section method in order to find the exact energy Green function yielding accurate computed eigenvalues and the density of states. Furthermore, this procedure allow us to analyze in detail the nontrivial semiclassical limit and examine the range of applicability of the Bohr-Sommerfeld quantization method.

The formation and rupture of atomic-sized contacts is modelled by means of molecular dynamics simulations. Such nano-contacts are realized in scanning tunnelling microscope and mechanically controlled break junction experiments. These instruments routinely measure the conductance across the nano-sized electrodes as they are brought into contact and separated, permitting conductance traces to be recorded that are plots of conductance versus the distance between the electrodes. One interesting feature of the conductance traces is that for some metals and geometric configurations a jump in the value of the conductance is observed right before contact between the electrodes, a phenomenon known as jump-to-contact. This paper considers, from a computational point of view, the dynamics of contact between two gold nano-electrodes. Repeated indentation of the two surfaces on each other is performed in two crystallographic orientations of face-centred cubic gold, namely (001) and (111). Ultimately, the intention is to identify the structures at the atomic level at the moment of first contact between the surfaces, since the value of the conductance is related to the minimum cross-section in the contact region. Conductance values obtained in this way are determined using first principles electronic transport calculations, with atomic configurations taken from the molecular dynamics simulations serving as input structures.

We calculate the band structure, density of states, phonon dispersions and thermodynamic properties of wurtzite Aluminum nitride (AlN) using the local density approximation (LDA) and the generalized gradient approximation (GGA). The results show that wurtzite AlN is a direct gap semiconductor. The phonon, dielectric, and thermodynamic properties are discussed in detail. The calculated values are in agreement with available experimental data.

In this study, the diffuse pattern and path of hydrogen in transition metal rhodium are investigated by the first-principles calculations. Density functional theory is used to calculate the system energies of hydrogen atom occupying different positions in rhodium crystal lattice. The results indicate that the most stable position of hydrogen atom in rhodium crystal lattice locates at the octahedral interstice, and the tetrahedral interstice is the second stable site. The activation barrier energy for the diffusion of atomic hydrogen in transition metal rhodium is quantified by determining the most favorable path, i.e., the minimum-energy pathway for diffusion, that is the indirect octahedral-tetrahedral-octahedral (O-T-O) pathway, and the activation energy is 0.8345eV.

In this work, the electronic band structure and the effective mass of the ternary alloy Ga_xIn_1-xP are studied by the first principle calculations. The software QUANTUM ESPRESSO and the generalized gradient approximation (GGA) for the exchange correlations have been used in the calculations. We calculate the lattice parameter, band gap and effective mass of the ternary alloy Ga_xIn_1-xP for the Ga composition x varying from 0.0 to 1.0 by the step of 0.125. The effect of the Ga composition on the lattice parameter and the electronic density of states are discussed. The results show that the lattice parameter varies with the composition almost linearly following the Vegard's law. A direct-to-indirect band-gap crossover is found to occur close to x = 0.7. The effective masses are also calculated at Γ(000) high symmetry point along the [100] direction. The results show that the band gap and the electron effective mass vary nonlinearly with composition x.

The lattice and electronic structure of beryllium doped zinc oxide (Be_xZn_1-xO) ternary mixed crystal are studied by the first-principle calculations within the framework of the density functional theory (DFT). It turned out that the lattice parameter a and lattice parameter c decrease linearly as Be doping concentration increases, compliance with Vegard's law, the lattice parameters of the Be_xZn_1-xO ternary mixed crystal are consistent with experimental results. Band gap increases with increasing Be content, and the band gap values are corrected. As Be doping, Zn 4s states dominate the conduction band and the conduction band bottom position constantly moving to higher energy region. Density of states strength Zn 4s states with decreasing proportion of Zn is constantly reduced, make the band gap width of Be_xZn_1-xO increases.

The electron states of quantum wires KCl, KCl : Br, and KCl : I with an edge dislocations were investigated. The main problem was in study of dislocation influence on localized electron states connected with substitutional isoelectronic impurities Br⁻ and I⁻ in the neighborhood of edge dislocation line. The tight-binding semi-empirical band approximation, semi-empirical and non-empirical cluster approach were used. Semi-empirical calculations were carried out in framework of model [1,2]. Besides, the algorithms for electronic levels calculations of polar nanosystems with the partial self-consistency [3] were used. The computer simulation results lead to the conclusion that the substitutional isoelectronic impurity anions Br⁻ and I⁻ located near the dislocation line capture the holes more efficiently than in bulk of systems without dislocations.

The electron states of nanosystems of ionic compounds AgCl and KCl with extended defects (charged defects, edge dislocations) were under consideration. The semiempirical tight-binding approximation and different calculation methods were used. The obtained results and efficiency of calculation schemes are discussed. This work is an improvement of our early investigations.

In this study, we have analyzed the effect of electron beam accelerating voltage on the maximum temperature of a graphite target during pulsed electron beam ablation (PEBA). To this end, a two stage, one dimensional thermal model is used. The target is subjected to an electron pulse with accelerating voltages of 10, 13, 15, 17 and 18 kV. The surface temperature, vaporization front velocity, ablated depth, and ablation rate are estimated from the solution of the model. Simulation results have shown that target surface temperature is not proportional to the accelerating voltage. It has been found that the surface temperature increases with the accelerating voltage from 10 kV to 15 kV, and reaches a maximum value (7500 K) at 15 kV. After 15 kV, the temperature decreases with increasing accelerating voltage. Similar trends have been observed in the vaporization front velocity, ablated depth and ablation rate, with maximum values (75 m/s, 2.1 μm, and 4 μg/mm²) at 15 kV. The calculation results are in good agreement with relevant experimental data from the literature.

The terahertz quantum cascade lasers (THz-QCLs) are the compact and coherent terahertz light sources based on the inter-subband transition and resonant tunneling of carriers in semiconductor superlattice. In recent studies on tapered THz-QCLs, it was found that the self-focusing effect in the active region of the devices may cause the abnormal increase of the far-field divergence of the laser beam. By simulating the propagation of optical mode in QCL waveguide and considering both the nonlinearity effect and thermal accumulation in the active region, we propose that the refractive index change caused by the third-order nonlinearity of multi-quantum-wells in active region may be the key reason for the self-focusing in THz-QCLs. This result indicates that the nonlinear effect may have great impact on the beam quality of QCLs which must be carefully considered in applications of THz-QCLs, such as the TH- imaging systems.

Hysteresis loops of 3D ferromagnetic permalloy nano-half-balls (dots) with 100 nm base diameter have been examined by means of LLG micromagnetic simulations and finite element methods. Tests were carried out with two orthogonal directions of the externally applied field at 10 kA/(m.ns) field sweeping speed. The comparison of samples with different 3D modifications at the sub-10nm scale, accessible by nowadays lithographic techniques, enables conclusions about different mechanisms of competition between demagnetizing and exchange fields. Design paradigms provided here can be applied, e.g., in bit-patterned media used as novel magnetic storage systems.

The electron and nuclear dynamics of acetylene when interacting with strong short laser pulses has been simulated in the framework of real-space Time Dependent Density Functional Theory (TDDFT) and molecular dynamics. The stretching and dissociation of individual bonds are reported, and are shown to depend on the laser field intensity and orientation relative to the laser polarization. The ionization dynamics, including ionization from individual Kohn-Sham orbitals, is also reported. The orbital ionization dynamics are shown to vary with an increase in the intensity of the laser field.

Wormholes are theoretical products in general relativity, and are popular tools in science fictions. We know numerically the four-dimensional Ellis wormhole solution (the so- called Morris-Thorne's traversable wormhole) is unstable against an input of scalar-pulse from one side. We investigate this feature for higher-dimensional versions, both in n-dimensional general relativity and in Gauss-Bonnet gravity. We derived Ellis-type wormhole solution in n- dimensional general relativity, and found existence of unstable modes in its linear perturbation analysis. We also evolved it numerically in dual-null coordinate system, and confirmed its instability. The wormhole throat will change into black-hole horizon for the input of (relatively) positive energy, while it will change into inflationary expansion for (relatively) negative energy input. If we add Gauss-Bonnet terms (higher curvature correction terms in gravity), then wormhole tends to expand (or change to black-hole) if the coupling constant α is positive (negative).

The goal of this study is to design a geometry of an electron dump with Simple Geo code which is a freeware product and provides the ability of designing complex geometric systems easily. Also, Simple Geo can output the designed geometry in many different formats. Desired design of the electron dump is to stop the 40 – 42 MeV electron beams. To reach this aim, requested geometric design with the possible material was done with Simple Geo and a FLUKA output format file created to run the simulations in FLUKA code.

In this paper, Lorentzian wormholes with a phantom field and chiral matter fields have been obtained. In addition, it is shown that for different values of the gravitational coupling of the chiral fields, the wormhole geometry changes. Finally, the stability of the corresponding wormholes is studied and it is shown that are unstable (eg. Ellis's wormhole instability)

Due to the Heisenberg uncertainty principle, gravitational confinement of two- or three-rotating particle systems can lead to microscopic Planckian or sub-Planckian black holes with a size of order their Compton wavelength. Some properties of such states are discussed in terms of the Schwarzschild geodesics of general relativity and compared with properties computed via the combination of special relativity, equivalence principle, Newton's gravitational law and Compton wavelength. It is shown that the generalized uncertainty principle (GUP) provides a satisfactory fit of the Schwarzschild radius and Compton wavelength of such microscopic, particle-like, black holes.

We consider a novel kind of plot for presenting the behaviour of null geodesics in Schwarzschild spacetime. Our diagram depicts various features of the light rays as recorded by different classes of observers. The idea stems from the use of phase portraits for illustrating the null geodesics in Schwarzschild spacetime, above and below the horizon of a black hole, but they reveal unphysical characteristics. The plots we propose are free from such anomalies. Moreover they allow us to discover new under-horizon features.

It is stated in many text books that the any metric appearing in general relativity should be locally Lorentzian i.e. of the type g_μv = diag(1, -1, -1, -1) this is usually presented as an independent axiom of the theory, which cannot be deduced from other assumptions. The meaning of this assertion is that a specific coordinate (the temporal coordinate) is given a unique significance with respect to the other spatial coordinates. It was shown that the above assertion is a consequence of requirement that the metric of empty space should be linearly stable and need not be assumed. Some cosmological implications of the above result will be suggested.

In this article we present a dissipative Schrodinger-Langevin-like Hamiltonian which incorporates implicitly the deformed commutation relations which are linear in particle momenta due to a generalized uncertainty principle. This result is based on interpreting the deformation parameter as quantum gravitational friction on the configuration space.

We use the conditional symmetry approach to study the r-evolution of Reissner-Nordström black hole both at the classical and quantum level. We Dirac-quantize the Reissner-Nordstrom black hole using the quantum analogues of the classical conditional symmetries, and show that the existence of such symmetries yields solutions to the Wheeler-DeWitt equation which, as a semiclassical analysis shows, exhibit a good correlation with the classical regime. Finally, we use the resulting wave functions to investigate the possibility of removing the classical singularities.

In this paper, we propose to study four meteorological and seasonal time series coupled with a multi-layer perceptron (MLP) modeling. We chose to combine two transfer functions for the nodes of the hidden layer, and to use a temporal indicator (time index as input) in order to take into account the seasonal aspect of the studied time series. The results of the prediction concern two years of measurements and the learning step, eight independent years. We show that this methodology can improve the accuracy of meteorological data estimation compared to a classical MLP modelling with a homogenous transfer function.

Modern medicine and biology have been transformed into quantitative sciences of high complexity, with challenging objectives. The aims of medicine are related to early diagnosis, effective therapy, accurate intervention, real time monitoring, procedures/systems/instruments optimization, error reduction, and knowledge extraction. Concurrently, following the explosive production of biological data concerning DNA, RNA, and protein biomolecules, a plethora of questions has been raised in relation to their structure and function, the interactions between them, their relationships and dependencies, their regulation and expression, their location, and their thermodynamic characteristics. Furthermore, the interplay between medicine and biology gives rise to fields like molecular medicine and systems biology which are further interconnected with physics, mathematics, informatics, and engineering. Modelling and simulation is a powerful tool in the fields of Medicine and Biology. Simulating the phenomena hidden inside a diagnostic or therapeutic medical procedure, we are able to obtain control on the whole system and perform multilevel optimization. Furthermore, modelling and simulation gives insights in the various scales of biological representation, facilitating the understanding of the huge amounts of derived data and the related mechanisms behind them. Several examples, as well as the insights and the perspectives of simulations in biomedicine will be presented.

We consider the scattering of a non-relativistic particle by a symmetrical arrangement of two identical barriers in one-dimension, with the barriers given by the well-known four-parameter family of point interactions. We calculate the phase time and the stationary Salecker-Wigner-Peres clock time for the particular cases of a double δ and a double δ' barrier and investigate the off-resonance behavior of these time scales in the limit of opaque barriers, addressing the question of emergence of the generalized Hartman effect.

The generation of projected shadows in synthetic three-dimensional scenes is a complex procedure which, because of its computational cost, has yet to be perfected. In this work, we present an algorithm that simplifies this process using the basic three-dimensional geometry of three elements: a point cloud which defines the object that casts the shadow, the position of the light source, and a projection plane. Shadows are generated as irregular polygons with as many vertexes as the size of their corresponding generative point cloud. The parallelization potential of the resulting algorithm is then studied for real-time applications.

Laboratory exercises are an important part of general Physics teaching, both during the last years of high school and the first year of college education. Due to the need to acquire enough laboratory equipment for all the students, and the widespread access to computers rooms in teaching, we propose the development of computer simulated laboratory exercises. A representative exercise in general Physics is the calculation of the gravity acceleration value, through the free fall motion of a metal ball. Using a model of the real exercise, we have developed an interactive system which allows students to alter the starting height of the ball to obtain different fall times. The simulation was programmed in ActionScript 3, so that it can be freely executed in any operative system; to ensure the accuracy of the calculations, all the input parameters of the simulations were modelled using digital measurement units, and to allow a statistical management of the resulting data, measurement errors are simulated through limited randomization.

In our work, we calculate the dispersion relations for InGaAs – InAlAs based double quantum wells (narrow gap structures). We have developed an improved 4 × 4 version of the Transfer Matrix Approach, considering contributions from external fields when tunneling through central barrier exists. The transverse electric field is necessary to reach the resonance of electronic levels in asymmetric structures. The in-plane magnetic field induces the Zeeman effect and the spin splitting of the resonant levels. We have also included abrupt barrier effects due to the nature of the interfaces between the above materials.

Application of a self-diverting-acid based on viscoelastic surfactant (SDVA) is a promising technology for improving the efficacy of acid treatment in oil and gas-bearing carbonate reservoirs. In this study, we present a mathematical model for assessing SDVA flow and reaction with carbonate rock using the SDVA rheological characteristics. The model calculates the technological parameters for acidizing operations and the prediction of well productivity after acid treatment, in addition to technical and economic optimization of the acidizing process by modeling different acid treatment options with varying volumes, injection rates, process fluids stages and initial economic scenarios.

Resistive effects are investigated on the magnetorotational instability. The main modifications with respect to the approach to the problem in the ideal limit are the introduction of the diffusive term in the induction equation and of the decay time T of the velocity field perpendicular to the magnetic field in the dispersion relation. As a result, when resistive effects are strong, it is shown that the instability condition in the ideal limit is corrected by the coefficient κ²T², where κ denotes the epicyclic frequency. The proposed formulation is then applied to the description of the instability for a Keplerian disk and it is found that the characteristic frequency of the unstable modes saturates asymptotically to a finite value which does not depend on the distance from the central object and is fully determined by the resistivity of the disk.

Mammographies are X-ray images of the breast under external compressions called Craniocaudal (CC) and Mediolateral Oblique (MLO). Together they increase the chances of detecting cancer but the breast is shown in strongly deformed shapes. Cancer location is highly uncertain for the surgery and so the breast is commonly taken out entirely, a serious trauma for the patient. In this paper we present a fully virtual mammography procedure that faithfully reproduces all shapes of the breast and in its inside tracks the cancer at any step. The cancer is then precisely located for the surgery and can be removed through a small incision. So the whole structure is preserved and cured as an integral benefit to the patient.

We introduce a fully written programmed code with a supervised method for generating weighted Steiner trees. Our choice of the programming language, and the use of well- known theorems from Geometry and Complex Analysis, allowed this method to be implemented with only 764 lines of effective source code. This eases the understanding and the handling of this beta version for future developments.

Zinc-bromine flow battery using aqueous electrolyte has advantages of cost effective and high energy density, but there still remains a problem improving stability and durability of electrolyte materials during long-time cell operation. This paper focuses on providing a homogeneous aqueous solution for durability and stability of zinc bromide electrolyte. For performance experiments of conventional and proposed electrolyte solutions, detailed cyclic voltammetry (CV) measurements (at a scan rate of 20 mV s⁻¹ in the range of −1.5 V~1.5 V) are carried out for 40 cycles and five kinds of electrolytes containing which has one of additives, such as (conventionally) zinc chloride, potassium chloride, (newly) lithium perchlorate, sodium perchlorate and zeolite-Y are compared with the 2.0 M ZnBr₂ electrolyte, respectively. Experimental results show that using the proposed three additives provides higher anodic and cathodic peak current density of electrolytes than using other two conventional additives, and can lead to improved chemical reversibility of zinc bromide electrolyte. Especially, the solution of which the zeolite-Y added, shows enhanced electrochemical stability of zinc bromide electrolyte. Consequently, proposed electrolytes have a significant advantage in comparison with conventional electrolytes on higher stability and durability.

Dual Energy imaging is a promising method for visualizing masses and microcalcifications in digital mammography. The advent of two X-ray energies (low and high) requires a suitable detector. The scope of this work is to determine optimum detector parameters for dual energy applications. The detector was modeled through the linear cascaded (LCS) theory. It was assumed that a phosphor material was coupled to a CMOS photodetector (indirect detection). The pixel size was 22.5 μm. The phosphor thickness was allowed to vary between 20mg/cm² and 160mg/cm² The phosphor materials examined where Gd₂O₂S:Tb and Gd₂O₂S:Eu. Two Tungsten (W) anode X-ray spectra at 35 kV (filtered with 100 μm Palladium (Pd)) and 70 kV (filtered with 800 pm Ytterbium (Yb)), corresponding to low and high energy respectively, were considered to be incident on the detector. For each combination the contrast- to-noise ratio (CNR) and the detector optical gain (DOG), showing the sensitivity of the detector, were calculated. The 40 mg/cm² and 70 mg/cm² Gd₂O₂S:Tb exhibited the higher DOG values for the low and high energy correspondingly. Higher CNR between microcalcification and mammary gland exhibited the 70mg/cm² and the 100mg/cm² Gd₂O₂S:Tb for the low and the high energy correspondingly.

Dual energy mammography has the ability to improve the detection of microcalcifications leading to early diagnosis of breast cancer. In this simulation study, a prototype dual energy mammography system, using a CMOS based imaging detector with different X-ray spectra, was modeled. The device consists of a 33.91 mg/cm² Gd₂O₂S:Tb scintillator screen, placed in direct contact with the sensor, with a pixel size of 22.5 μm. Various filter materials and tube voltages of a Tungsten (W) anode for both the low and high energy were examined. The selection of the filters applied to W spectra was based on their K- edges (K-edge filtering). Hydroxyapatite (HAp) was used to simulate microcalcifications. Calcification signal-to-noise ratio (SNR_tc) was calculated for entrance surface dose within the acceptable levels of conventional mammography. Optimization was based on the maximization of SNR_tc while minimizing the entrance dose. The best compromise between SNR_tc value and dose was provided by a 35kVp X-ray spectrum with added beam filtration of 100μm Pd and a 70kVp Yb filtered spectrum of 800 μm for the low and high energy, respectively. Computer simulation results show that a SNR_tc value of 3.6 can be achieved for a calcification size of 200 μm. Compared with previous studies, this method can improve detectability of microcalcifications.

In this work, we show the resolution of the rate equations in powder random lasers by using the Crank-Nicholson finite difference method. Light propagation in our powders is described by the model of light diffusion. The generalized time-dependent random laser equations describing our system are formed by three differential coupled equations: two diffusion equations for the pump and emitted light and a rate equation for the density of the dopant molecules in the excited state. The system has been solved for two pumping schemes (one-photon and two-photon excitation) and for a wide range of temporal incident pulses (from femtoseconds to nanoseconds).

We present the newly developed stochastic model of the galactic cosmic ray (GCR) particles transport in the heliosphere. Mathematically Parker transport equation (PTE) describing non-stationary transport of charged particles in the turbulent medium is the Fokker-Planck type. It is the second order parabolic time-dependent 4-dimensional (3 spatial coordinates and particles energy/rigidity) partial differential equation. It is worth to mention that, if we assume the stationary case it remains as the 3-D parabolic type problem with respect to the particles rigidity R. If we fix the energy/rigidity it still remains as the 3-D parabolic type problem with respect to time. The proposed method of numerical solution is based on the solution of the system of stochastic differential equations (SDEs) being equivalent to the Parker's transport equation. We present the method of deriving from PTE the equivalent SDEs in the heliocentric spherical coordinate system for the backward approach. The advantages and disadvantages of the forward and the backward solution of the PTE are discussed. The obtained stochastic model of the Forbush decrease of the GCR intensity is in an agreement with the experimental data.

We developed a particle-based fluid simulation method with obstacles defined in implicit form. Our fluid simulation is based on the Moving Particle Semi-implicit (MPS) method, a typical particle-based algorithm achieving incompressible flow. In general, the particle-based fluid simulation is performed with obstacles that are defined as a set of particles located along the boundaries. We employ the implicit representation for the geometric information of obstacles which requires a new formulation of particle motion at the vicinity of boundaries. The main difficulty of MPS-based simulation with implicit obstacles is the lack of boundary particles that are required for the computation of two quantities: particle number density and particle force determined by pressure field. In our formulation, new definitions of the two quantities giving good estimation of the original ones is developed and incorporated in the MPS algorithm. In addition, we provide a modified algorithm for the construction of discrete linear system specific to the implicit representation for the computation of particle pressure. Our numerical tests show that the proposed approximation techniques provide adequate particle motion at the vicinity of the implicitly defined obstacles.

A systematic theoretical study of the binding energy of the ground state of a hydrogenic off-axis donor in a cylindrical quantum wire containing two quantum wells in a section of the tube layer is calculated in the presence of a uniform magnetic field applied parallel. We express the wave function as a product of free electron wave functions and an envelope function that depends only on the electronion separation. By using the variational principle we derive a differential equation for the envelope function, which we solve numerically.

Simultaneous effects of quantum well thickness and radius on exciton energy and density exciton states on a semiconductor nanoribbon with a finite and rectangular confining potential are studied theoretically. We show that in the structural adiabatic limit, when the width of the pattern of the particles pathways within the ribbon is much smaller than its radius, the wave equations for exciton are separable and their solutions can be found numerically. We present results of calculation of the density exciton states as functions of the wavelength and energy for different values of ribbon radius and quantum well thickness, with potential profiles rectangular and parabolic.

In this work we study the effects of barrier height and position on symmetric Al_xGa_1-xAs/GaAs/Al_xGa_1-xAs quantum wells in absence of external influences. We use a variational method within the effective mass approximation to observe the effects on the structure. The donor trial function is taken as a product of the ground state wave function, with an arbitrary correlation function that depends only on ion-electron separation. It has been observed two peaks in the curves for the dependence of the ground-state binding energies versus the donor distance from the axis and it is shown that the impurity binding energy depends strongly on the impurity position, potential shape on both quantum wells.

In this work is presented a new method for sensor deployment on 3D surfaces. The method was structured on different steps. The first one aimed discretizes the relief of interest with Delaunay algorithm. The tetrahedra and relative values (spatial coordinates of each vertex and faces) were input to construction of 3D Voronoi diagram. Each circumcenter was calculated as a candidate position for a sensor node: the corresponding circular coverage area was calculated based on a radius r. The r value can be adjusted to simulate different kinds of sensors. The Dijkstra algorithm and a selection method were applied to eliminate candidate positions with overlapped coverage areas or beyond of surface of interest. Performance evaluations measures were defined using coverage area and communication as criteria. The results were relevant, once the mean coverage rate achieved on three different surfaces were among 91% and 100%.

A nonlinear model of the economic system of "a firm" is offered. It is shown that this model has several chaotic attractors, including the Lorentz attractor and a new attractor that, in our opinion, has not yet been described in the scientific literature. The chaotic nature of the attractors that were found was confirmed by computing the Lyapunov indicators. The functioning of our economic model is demonstrated with examples of firm behaviour that change the control parameters; these are well known in practice. In particular, it is shown that changes in the specific control parameters may change the system and avoid bankruptcy for the firm.

We show that a low dimensional system can evolve toward an infinite dimensional ergodic system. We also show the existence of the reverse process, that is, a large-dimensional ergodic system that evolves toward a low-dimensional ordered system.

Nanomedicine is an emerging area of medical research that uses innovative nanotechnologies to improve the delivery of therapeutic and diagnostic agents with maximum clinical benefit. We present a versatile stochastic model that can be used to capture the basic features of drug encapsulation of nanoparticles on tree-like synthetic polymers called dendrimers. The geometry of a dendrimer is described mathematically as a Cayley tree. We use our stochastic model to study the dynamics of deposition and release of monomers (simulating the drug molecules) on Cayley trees (simulating dendrimers). We present analytical and Monte Carlo simulation results for the particle density on Cayley trees of coordination number three and four.

We present a stochastic model for adsorption and evaporation of monomers with applications to optical coatings. We consider a general case of attachment and detachment rates dependent on the overall number of particles in the system. The model is applicable to all dimensions and topologies, and can describe a variety of two-state physical systems. We report analytical results for the time-dependent particle density. We compare our analytical results with experimental data and Monte Carlo simulations.

It is argued that any possible definition of a realistic physics theory – i.e., a mathematical model representing the real world – cannot be considered comprehensive unless it is supplemented with requirement of being computationally realistic. That is, the mathematical structure of a realistic model of a physical system must allow the collection of all the system's physical quantities to compute all possible measurement outcomes on some computational device not only in an unambiguous way but also in a reasonable amount of time.

In the paper, it is shown that a deterministic quantum model of a microscopic system evolving in isolation should be regarded as realistic since the NP-hard problem of finding the exact solution to the Schrödinger equation for an arbitrary physical system can be surely solved in a reasonable amount of time in the case, in which the system has just a small number of degrees of freedom. In contrast to this, the deterministic quantum model of a truly macroscopic object ought to be considered as non-realistic since in a world of limited computational resources the intractable problem possessing that enormous amount of degrees of freedom would be the same as mere unsolvable.

By using an exactly-solvable multiparameter exponential-type potential, the bound-state solutions of the D-dimensional Eckart + Hylleraas potential are directly derived as a particular case. Althought our proposal accepts different approximations to the centrifugal term, its usefulness is exemplified in the frame of the Taskin and Kocak approach. This fact enable us to compare our results with specific potentials found in literature which are obtained here as particular cases from our proposal. That is, instead of solving an specific exponential-type potential, by resorting each time to a specialized method, the energy spectra and wavefunctions are found straightforwardly by means of the simple choice of the involved parameters. Furthermore, our proposal can be used as alternative way in the search of bound-state solutions to new exponential-type potentials besides that one can study different approximations to the term 1/r².

The new generalized quantum continuous time world line Monte Carlo algorithm was developed to calculate pair correlation functions for two-dimensional FeAs-clusters modeling of iron-based superconductors within the framework of the two-orbital model. The analysis of pair correlations depending on the cluster size, temperature, interaction, and the type of symmetry of the order parameter is carried out. The data obtained for clusters with sizes up to 1 0x1 0 FeAs-cells favor the possibility of an effective charge carrier's attraction that is corresponding the A_1g-symmetry, at some parameters of interaction.

The refraction's law of sheared region near the boundary of two kinds of sand with the different stickiness is investigated by a simulation method. Our experimental apparatus for sand system is one of the simplest sets in order to obtain shear pattern, called linear split- bottom cell. In this paper we give an analysis based on a classical numerical calculation 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 parallel pipe which is split into two halves. One of the halves can be moved along the split quasi-statically. We obtain a refraction pattern like an equipotential surface across the interface of different dielectric constants shown in the textbook. Various quantities obtained from our calculation were compared with experiments in the preceding conference. In this conference, we will show the refraction's law at the shear zone boundary crossing over two different sand systems with unequal stickiness.

Solvation of bio-molecules in water is severely affected by the presence of co-solvent within the hydration shell of the solute structure. Furthermore, since solute molecules can range from small molecules, such as methane, to very large protein structures, it is imperative to understand the detailed structure-function relationship on the microscopic level. For example, it is useful know the conformational transitions that occur in protein structures. Although such an understanding can be obtained through large-scale molecular dynamic simulations, it is often the case that such simulations would require excessively large simulation times. In this context, Kirkwood-Buff theory, which connects the microscopic pair-wise molecular distributions to global thermodynamic properties, together with the recently developed technique, called finite size scaling, may provide a better method to reduce system sizes, and hence also the computational times. In this paper, we present molecular dynamics trial simulations of biologically relevant low-concentration solvents, solvated by aqueous co-solvent solutions. In particular we compare two different methods of calculating the relevant Kirkwood-Buff integrals. The first (traditional) method computes running integrals over the radial distribution functions, which must be obtained from large system-size NVT or NpT simulations. The second, newer method, employs finite size scaling to obtain the Kirkwood-Buff integrals directly by counting the particle number fluctuations in small, open sub-volumes embedded within a larger reservoir that can be well approximated by a much smaller simulation cell. In agreement with previous studies, which made a similar comparison for aqueous co-solvent solutions, without the additional solvent, we conclude that the finite size scaling method is also applicable to the present case, since it can produce computationally more efficient results which are equivalent to the more costly radial distribution function method.

Experimental small-angle scattering (SAS) data characterized, on a double logarithmic scale, by a succession of power-law decays with decreasing values of scattering exponents, can be described in terms of fractal structures with positive Lebesgue measure (fat fractals). Here we present a theoretical model for fat fractals and show how one can extract structural information about the underlying fractal using SAS method, for the well known fractals existing in the literature: Vicsek and Menger sponge. We calculate analytically the fractal structure factor and study its properties in momentum space. The models allow us to obtain the fractal dimension at each structural level inside the fractal, the number of particles inside the fractal and about the most common distances between the center of mass of the particles.

The thermodynamical stability of DNA minicircles is investigated by means of path integral techniques. Hydrogen bonds between base pairs on complementary strands can be broken by thermal fluctuations and temporary fluctuational openings along the double helix are essential to biological functions such as transcription and replication of the genetic information. Helix unwinding and bubble formation patterns are computed in circular sequences with variable radius in order to analyze the interplay between molecule size and appearance of helical disruptions. The latter are found in minicircles with < 100 base pairs and appear as a strategy to soften the stress due to the bending and torsion of the helix.

It has been shown that the eddy current method is one of the most effective techniques for the detection and characterization of surface and near-surface defects in conductive mediums especially in aluminum alloy. It is one of the most applied methods in industries which require a maximum of reliability and security (aerospace, aeronautics, nuclear, Etc).

In this study, a code to solve electromagnetic problems by employing the finite element method is developed.

The suggested model can simulate the probe response to the presence of a defect hidden in a multi-layered structure or a riveted structure on aluminum alloy. The developed code is based on the discretization in three dimensions of the Maxwell's equations in harmonic mode by the finite element method based on the combined potential formulations. That will enable us to interpret the results, to present them in graphical form and to carry out simulations for various applications

The class of quantum codes called stabilizer codes is increasingly well-understood. The premise of the stabilizer formalism is that a quantum code can be efficiently described by a subgroup of its error group, and, interestingly, the stabilizer formalism permits correspondences with classical linear codes. In this paper, we examine one such correspondence, and we shall use this to establish the number of distinct stabilizer codes that exist for a fixed parametrisation.

The Fibonacci sequence is a famously well-known integer sequence from the thirteenth century which has transcended its original motivation. It possesses many interested and varied applications within architecture, engineering and science. Less well known is the Narayana sequence which itself has interesting and wide-ranging Fibonacci-type connections. In this paper, we shall recall Narayana's original motivation that gives rise to the sequence bearing his name. We also provide an interesting application of this sequence to the construction to quantum gate circuitry used in quantum computation.

In our previous works we described a statistical method to interpret the results of extensive air shower simulations. For an isotropically distributed flux of cosmic rays, we used this method to deduce diagrams of mean values of shower maxima versus energy decades. To have a more realistic result, we considered the effect of a non-isotropic flux of cosmic rays at different energy ranges. This effect was considered as a weight factor deduced from a set of observed data. We discussed about the effect of this weight factor on our final resulted diagrams of mean shower maxima and for different interaction models compared the resulted distributions of very high energy cosmic ray's mass composition.

The representation analysis of Bertaut is used to enumerate all possible magnetic structures in rare earth iron garnets (RE₃Fe₅O₁₂) for the RE and Fe ions on the 6e, 6e' and 12f, 2b, 6d Wyckoff positions respectively in the highest rhombohedral subgroup Rc of the cubic space group Iad. The basis vectors of the one-dimensional irreducible representation A_2g lead to noncollinear magnetic structures of the RE moments which produce a better description than those based on the models of Wolf et al. Some results of the "double umbrella" structure found in our recent neutron powder diffraction studies of terbium iron garnet are reported.

An approximate analytical channel potential model of polycrystalline silicon thin film transistors operated in the strong inversion region under the high gate and low drain biases is proposed. Thus, the linear relationship between the channel potential and the drain voltage is derived in the strong inversion region under the above bias condition when the polysilicon layer is ultrathin. This model agrees with the two-dimensional-device simulation results under different gate voltages, different drain voltages and different channel lengths. By comparing the relative errors between the model and the simulation results, it presents that this model is more suitable under the higher gate voltage V_g or the lower drain voltage V_d, regardless of the channel length. And this approximate analytical model is helpful in solving the two- dimensional-device problem by one-dimensional Poisson's equation since the drain bias is taken into account in the channel potential.

The surface tension γ and the pressure difference Δp for spherical membranes are calculated using Monte Carlo simulation technique. We study the so-called tethered and uid surface discrete models that are defined on the fixed-connectivity (tethered) and dynamically triangulated (uid) lattices respectively. Hamiltonians of the models include a self-avoiding potential, which makes the enclosed volume well defined. We find that there is reasonable accuracy in the technique for the calculation of γ using the real area A if the bending rigidity κ or A/N is sufficiently large. We also find that γ becomes constant in the limit of A/N → ∞ both in the tethered and uid surfaces. The property lim_A/N→∞ γ = const corresponds to certain experimental results in cell biology.

Nematic liquid crystals confined in asymmetric π-cells and subjected to intense electrical and mechanical stresses undergo strong distortions which can be relaxed by means of the order reconstruction, a fast switching mechanism connecting topologically different textures, assuming bulk and/or surface characteristics depending on both amplitude of the applied electric fields and anchoring angles of the nematic molecules on the confining surfaces. In the frame of the Landau-de Gennes order tensor theory, we provide a numerical model implemented with a moving mesh finite element method appropriate to describe the nematic order dynamics, allowing to map the switching properties of the nematic texture.

Porous materials such as zeolites and metal organic frameworks have been of growing importance as materials for energy-related applications such as CO₂ capture, hydrogen and methane storage, and catalysis. The current state-of-the-art molecular simulations allow for accurate in silico prediction of materials' properties but the computational cost of such calculations prohibits their application in the characterisation of very large sets of structures, which would be required to perform brute-force screening. Our work focuses on the development of novel methodologies to efficiently characterize and explore this complex materials space. In particular, we have been developing algorithms and tools for enumeration and characterisation of porous material databases as well as efficient screening approaches. Our methodology represents a ensemble of mathematical methods. We have used Voronoi tessellation-based techniques to enable high-throughput structure characterisation, statistical techniques to perform comparison and screening, and continuous optimisation to design materials. This article outlines our developments in material design.

The sequence alignment is one of the most important tasks in Bioinformatics, playing an important role in the sequences analysis. There are many strategies to perform sequence alignment, since those use deterministic algorithms, as dynamic programming, until those ones, which use heuristic algorithms, as Progressive, Ant Colony (ACO), Genetic Algorithms (GA), Simulated Annealing (SA), among others. In this work, we have implemented the objective function COFFEE in the MSA-GA tool, in substitution of Weighted Sum-of-Pairs (WSP), to improve the final results. In the tests, we were able to verify the approach using COFFEE function achieved better results in 81% of the lower similarity alignments when compared with WSP approach. Moreover, even in the tests with more similar sets, the approach using COFFEE was better in 43% of the times.

Analytic energy eigenvalues approximations have been found for the 2-D quadratic Zeeman effect in hydrogenlike atoms. Here a new technique has been used, the so called multipoint quasirational technique (MPQA), which is an extension of the two-point quasirational approximation (TPQA) technique, previously used for the same problem. In our previous calculations, two expansions were used, one for small values of the magnetic field and other for large values, that is, expansions around zero and the infinity were determined. Later a bridge between both expansions was built using simple auxiliary functions as well as rational ones. In the present paper expansions around intermediate points were also determined, and used. In this way, the corresponding analytic bridge function is determined, taken care also of these new expansions, so the technique is a multiple point quasirational approximation (MPQA). The calculations are carried out for the ground state 1s and the excited states 2p⁻ and 3d⁻, respectively. These results are now much better than those obtained in previous works.

High performance computing of Meshless Time Domain Method (MTDM) on multi-GPU using the supercomputer HA-PACS (Highly Accelerated Parallel Advanced system for Computational Sciences) at University of Tsukuba is investigated. Generally, the finite difference time domain (FDTD) method is adopted for the numerical simulation of the electromagnetic wave propagation phenomena. However, the numerical domain must be divided into rectangle meshes, and it is difficult to adopt the problem in a complexed domain to the method. On the other hand, MTDM can be easily adept to the problem because MTDM does not requires meshes. In the present study, we implement MTDM on multi-GPU cluster to speedup the method, and numerically investigate the performance of the method on multi-GPU cluster. To reduce the computation time, the communication time between the decomposed domain is hided below the perfect matched layer (PML) calculation procedure. The results of computation show that speedup of MTDM on 128 GPUs is 173 times faster than that of single CPU calculation.

The Poisson equation for the plasma sheath potential near a wall, leads to a nonlinear differential equation, whose analytic solution is not known. The usual approximation taking only the first non-null term does not give good accuracy. Other approximations taken two additional terms are better, but they fail to give good accuracy in the intermediate region. Here a new analytic approximated solution is presented with much higher accuracy, and more precise results, not only near and far away of the wall, but also in the transition region. Two figures showing these new analytic solutions as a function of the relevant parameters are presented. The advantages of the present solution compared with those of pervious works are shown.

The exactly-solvable position-dependent mass Schrodinger equation (PDMSE) for the Thomas-Fermi potential is presented. The PDMSE is transformed into a standard Schrodinger equation (SSE) with constant mass by means of a point canonical transformation scheme. By proposing an exponential type potential of the SSE it is possible to determine a PDMSE with the Thomas-Fermi potential. The resulting PDMSE is carried to the Sturm- Liouville form and the corresponding theory is developed for the particular resulting problem in order to obtain closed solutions in terms of Bessel functions of the first kind. Beyond the case considered in this work, the approach is general and can be useful in the study of electronic properties of non-uniform materials in which the carrier effective mass depends on the position as well as in the search of new solvable potentials suitable for quantum systems.

The purpose of this study is to detect finger movement using a singular spectrum transformation method. Human gesture recognition is essential for realizing natural user interfaces. However, constructing a robust, easily installable interface is extremely difficult. Our proposed method uses singular spectrum transformation to classify finger movements. This method robustly classifies gestures and behavior.

The problem of microwave (MW) electromagnetic radiation impact on a single water-in-oil droplet is considered. The system of heat equations within the droplet and in the surrounding liquid, incompressible Navier-Stokes equations within the droplet and in the surrounding liquid, and equation of state are considered. The formulated problem is solved numerically using TDMA (Tri-diagonal-matrix algorithm), SIMPLE algorithm and VOF method (volume of fluid method for the dynamics of free boundaries) in Euler coordinates. The results in the form of the dependence of the temperature within the droplet and in the surrounding liquid on the time of microwave impact and streamlines thermal convection are represented; dependence of the velocity of droplet's moving on the power of the of the microwave impact is shown. The obtained results can help to establish criteria for the efficient applicable of the microwave method for the water-in-oil emulsions destruction.

The Wnt/β-catenin pathway is a signal transduction pathway made of proteins, which plays an important role in oncogenesis. Ethan Lee and and co-workers introduced in 2003 a detailed mathematical model of this pathway, incorporating the kinetics of protein-protein interactions, protein synthesis/degradation and phosphorylation/dephosphorylation. The fast/slow dynamics of Lee's system are examined here, by employing the Computational Singular Perturbation (CSP) algorithm. CSP reproduces the results of the classical singular perturbation analysis in an algorithmic fashion, producing an approximation of (i) the low dimensional Slow Invariant Manifold (SIM), where the solution evolves and (ii) the reduced model that governs the flow there. The temporal variation of the dimensions of the SIM will be presented and the components of the pathway that are responsible (i) for the generation of the SIM and (ii) for driving the system on it will be identified.

A reactive system will be considered, the slow dynamics of which is characterized by time scales that are of explosive character; i.e., the components of the system that generate them tend to lead the system away from equilibrium. In particular, the initiation of a methane/air mixture autoignition will be considered for various initial temperatures and pressures. The species that relate to the explosive time scales and reactions that are responsible for the generation of these time scales will be identified. The analysis will be based on the Computational Singular Perturbation (CSP) algorithm, which is employed for the construction of the the reduced system that governs the long range (slow) evolution of the system. It will be demonstrated that an excellent agreement with the existing literature is obtained.

The present work deals with the study of the entropy generation in the natural convection process in both square cavities and square cavities with hot wavy walls through numerical simulations for different undulations and Rayleigh numbers, while keeping the Prandtl number constant. The results show that the heat transfer rate is notably affected by the shape of the hot wall geometry compared with the square one. It has been found in this investigation that the mean Nusselt number in the case of heat transfer in a cavity with wavy walls is lower, as compared to heat transfer in a cavity without undulations. Based on the obtained dimensionless velocity and temperature values, the distributions of the local entropy generation due to heat transfer and fluid friction, the local Bejan number, and the local entropy generation are determined and plotted for different undulations and Rayleigh number. The study is performed for Rayleigh number 10⁵ <Ra<10⁷ irreversibility coefficients 10⁻⁴< ϕ <10⁻². The total entropy generation is found to increase with increasing undulation number

This paper addresses the Line Pack Management of the "GZ1 Hassi R'mell-Arzew" gas pipeline. For a gas pipeline system, the decision-making on the gas line pack management scenarios usually involves a delicate balance between minimization of the fuel consumption in the compression stations and maximizing gas line pack. In order to select an acceptable Line Pack Management of Gas Pipeline scenario from these two angles for "GZ1 Hassi R'mell- Arzew" gas pipeline, the idea of multi-objective decision-making has been introduced. The first step in developing this approach is the derivation of a numerical method to analyze the flow through the pipeline under transient isothermal conditions. In this paper, the solver NSGA-II of the modeFRONTIER, coupled with a matlab program was used for solving the multi-objective problem.

When the number of events associated with a signal process is estimated in particle physics, it is common practice to extrapolate background distributions from control regions to a predefined signal window. This allows accurate estimation of the expected, or average, number of background events under the signal. However, in general, the actual number of background events can deviate from the average due to fluctuations in the data. Such a difference can be sizable when compared to the number of signal events in the early stages of data analysis following the observation of a new particle, as well as in the analysis of rare decay channels. We report on the development of a data-driven technique that aims to estimate the actual, as opposed to the expected, number of background events in a predefined signal window. We discuss results on toy Monte Carlo data and provide a preliminary estimate of systematic uncertainty.

Digital image segmentation is the process of assigning distinct labels to different objects in a digital image, and clustering techniques can be used to achieve such segmentations. However, many traditional segmentation algorithm fail to segment objects that are characterized by textures whose patterns cannot be successfully described by simple statistics computed over a very restricted area. In this paper we present a fuzzy clustering algorithm that achieves the segmentation of images with color textures by employing a distance function based on the Skew Divergence, that is based on the well-known Kullback-Leibler Divergence. In order for such a distance to produce good results when applied to color images, we reduced the dimensionality of the image's histogram, thus eliminating the sparsity of the color histogram and speeding up the execution of the algorithm. We performed experiments on thin rock sections and compared our results to the segmentations obtained by the Fuzzy C-Means and by another fuzzy segmentation technique, showing the superiority of our approach.

This paper are presented novel algorithms for exact limits of a broad class of infinite alternating series. Many of these series are found in physics and other branches of science and their exact values found for us are in complete agreement with the values obtained by other authors. Finally, these simple methods are very powerful in calculating the limits of many series as shown by the examples.

The structural and electronic properties of CdTe(001), CdSe(001), and ZnSe(001) C(2 x 2) reconstructed surfaces have been investigated through the use of first-principles calculations. To simulate the surface, we employed the slab model. Using the experimentally determined lattice parameters as inputs, we relaxed the internal atomic positions of the outer atomic layers. We demonstrate that our model appropriately reproduces both the surface structural parameters and the known electronic properties found for these semiconductor compounds in bulk. Finally, we discuss our results of the projected bulk bands and the surface and resonance states found for these surfaces.

We have formulated the transmission probability of an electron in a Corbino quantum disk by taking into account charging effect. The geometrical potential of the Corbino disk has a singularity at the centre of the disk. In order to avoid this singularity problem, we have to reformulate the Schrödinger equation in the Riemannian manifold. The Schrödinger equation describing the motion of the electron in the Corbino disk must be expressed by introducing a momentum operator reformed by the metric tensor. In order to obtain a Hermitian momentum operator, we must deform the Hilbert space by introducing a new wave function. This deformation leads to the extra potential term in the Schroodinger equation, which depends on the metric, i.e., the geometry of the disk. It should be noted that the charging energy of confining electrons in the Corbino disk should depend on the geometry of the disk. We discuss the quantum tunneling of an electron confined in the Corbino disk in order to investigate the effect of both geometrical potential and charging energy of confining electrons in the Corbino disk by using the Wentzel-Kramers-Brillouin (WKB) method. It is expected that the charging energy, which depends on the effective confining potential, plays an important role in the transmission probability. This suggests that the formulated transmission probability is applicable to the analysis of the single-electron transistor.

This paper describes the analysis and modelling of word usage frequency time series. During one of previous studies, an assumption was put forward that all word usage frequencies have uniform dynamics approaching the shape of a Gaussian function. This assumption can be checked using the frequency dictionaries of the Google Books Ngram database. This database includes 5.2 million books published between 1500 and 2008. The corpus contains over 500 billion words in American English, British English, French, German, Spanish, Russian, Hebrew, and Chinese. We clustered time series of word usage frequencies using a Kohonen neural network. The similarity between input vectors was estimated using several algorithms. As a result of the neural network training procedure, more than ten different forms of time series were found. They describe the dynamics of word usage frequencies from birth to death of individual words. Different groups of word forms were found to have different dynamics of word usage frequency variations.

Pre-processing is an important stage in the analysis of magnetic resonance images (MRI), because the effect of specific image artefacts, such as intensity inhomogeneity, noise and low contrast can adversely affect the quantitative image analysis. The image histogram is a useful tool in the analysis of MR images given that it allows a close relationship with important image features such as contrast and noise. The noise and variable contrast are elements that locally modify the quality of images. The key issue of this study derives from the fact that the spatial histogram can contain outliers indicating corrupted image information through the disorder of the bins. These aberrant errors should be excluded from the studied data sets. Here, the outliers are evaluated by using rigorous methods based on the probability theory and Chauvenet (CC), Grubbs (GC) and Peirce's (PC) criteria. In order to check the quality of the MR images, the Minkowsky (MD), Euclidean (ED) and cosine (CD) distance functions were used. They act as similarity scores between the histogram of the acquired MRI and the processed image. This analysis is necessary because, sometimes, the distance function exceeds the co-domain because of the outliers. In this paper, 32 MRIs are tested and the outliers are removed so that the distance functions generate uncorrupted and real values.

Lymphoma is a type of cancer that affects the immune system, and is classified as Hodgkin or non-Hodgkin. It is one of the ten types of cancer that are the most common on earth. Among all malignant neoplasms diagnosed in the world, lymphoma ranges from three to four percent of them. Our work presents a study of some filters devoted to enhancing images of lymphoma at the pre-processing step. Here the enhancement is useful for removing noise from the digital images. We have analysed the noise caused by different sources like room vibration, scraps and defocusing, and in the following classes of lymphoma: follicular, mantle cell and B-cell chronic lymphocytic leukemia. The filters Gaussian, Median and Mean-Shift were applied to different colour models (RGB, Lab and HSV). Afterwards, we performed a quantitative analysis of the images by means of the Structural Similarity Index. This was done in order to evaluate the similarity between the images. In all cases we have obtained a certainty of at least 75%, which rises to 99% if one considers only HSV. Namely, we have concluded that HSV is an important choice of colour model at pre-processing histological images of lymphoma, because in this case the resulting image will get the best enhancement.

The current study aims to carry out a CFD-exergy based analysis to assess the main areas of loss in a supersonic steam ejector encountered in ejector refrigeration systems. The governing equations for a compressible flow are solved using finite volume approach based on SST k-ω model to handle turbulence effects. Flow rates and the computed mean temperatures and pressures have been used to calculate the exergy losses within the different regions of the ejector as well as its overall exergy efficiency. The primary mass flow rate, the secondary mass flow rate and the entrainment ratio predicted by the model have been compared with the experimental data from the literature.

The aim of this work is to develop analytical models for the thermodynamic equilibrium at the interfaces (gas mixture / Quarz Micro Balance sensor arrays based on conducting polymers). Differential equations, which describe the change in the partial sensitivities of the sensor array elements depending on the gas mixture components concentrations, and the sensor array parameters, have been developed. Moreover, the responses of the sensor array as a function of the concentrations of the gas mixture components have been modeled.

MR technology is one of the best and most reliable ways of studying the brain. Its main drawback is the so-called intensity inhomogeneity or bias field which impairs the visual inspection and the medical proceedings for diagnosis and strongly affects the quantitative image analysis. Noise is yet another artifact in medical images. In order to accurately and effectively restore the original signal, reference is hereof made to filtering, bias correction and quantitative analysis of correction. In this report, two denoising algorithms are used; (i) Basis rotation fields of experts (BRFoE) and (ii) Anisotropic Diffusion (when Gaussian noise, the Perona-Malik and Tukey's biweight functions and the standard deviation of the noise of the input image are considered).

The Bondi-Metzner-Sachs (BMS) group B is the common asymptotic group of all asymptotically flat (lorentzian) space-times, and is the best candidate for the universal symmetry group of General Relativity (G.R.). B admits generalizations to real space-times of any signature, to complex space-times, and supersymmetric generalizations for any space- time dimension. With this motivation McCarthy constructed the strongly continuous unitary irreducible representations (IRs) of B some time ago, and he identified B(2,2) as the generalization of B appropriate to the to the 'ultrahyperbolic signature' (+,+,−,−) and asymptotic flatness in null directions. We continue this programme by introducing a new group UHB(2, 2) in the group theoretical study of ultrahyperbolic G.R. which happens to be a proper subgroup of B(2, 2). In this short paper we report on the first general results on the representation theory of UHB(2, 2). In particular the main general results are that the all little groups of UHB(2, 2) are compact and that the Wigner-Mackey's inducing construction is exhaustive despite the fact that UHB(2, 2) is not locally compact in the employed Hilbert topology. At the end of the paper we comment on the significance of these results.

Nowadays, a dynamic progress in computational techniques allows for development of various methods, which offer significant speed-up of computations, especially those related to the problems of quantum optics and quantum computing. In this work, we propose computational solutions which re-implement the quantum trajectory method (QTM) algorithm in modern parallel computation environments in which multi-core CPUs and modern many-core GPUs can be used. In consequence, new computational routines are developed in more effective way than those applied in other commonly used packages, such as Quantum Optics Toolbox (QOT) for Matlab or QuTIP for Python.

Most of the processes taking place in the auroral region of Earth's ionosphere are reflected in a variety of dynamic forms of the aurora borealis. In order to study these processes it is necessary to consider temporary and spatial variations of the characteristics of ionospheric plasma. Most traditional methods of classical physics are applicable mainly for stationary or quasi-stationary phenomena, but dynamic regimes, transients, fluctuations, selfsimilar scaling could be considered using the methods of nonlinear dynamics. Special interest is the development of the methods for describing the spatial structure and the temporal dynamics of auroral ionosphere based on the ideas of percolation theory and fractal geometry. The fractal characteristics (the Hausdorff fractal dimension and the index of connectivity) of Hall and Pedersen conductivities are used to the description of fractal patterns in the ionosphere. To obtain the self-consistent estimates of the parameters the Hausdorff fractal dimension and the index of connectivity in the auroral zone, an additional relation describing universal behavior of the fractal geometry of percolation at the critical threshold is applied. Also, it is shown that Tsallis statistics can be used to study auroral ionosphere

The Monte-Carlo method was used for study of magnetization processes in 2D layered high temperature superconductors (HTSC) with internal ferromagnetic defects. The magnetization was treated under application of transport current and external dc magnetic field. The voltage-current characteristics (I-V curve) were calculated in presence of external dc magnetic field. A novel S-type I-V curve of the superconductor/ferromagnet system in external magnetic field was demonstrated. It was shown that the S-type nonlinearity is due to the local reversal magnetization of magnetic particles by the field of vortices. The H-T phase diagram which demonstrates the region of existence I-V curve nonlinearity was obtained. The conditions for electromagnetic generation at the region of nonlinearity were found and the frequency of such a generation was estimated.

The decimation filter is necessary to prevent aliasing during the process of decreasing sampling rate, which is called decimation. Due its simplicity, the most popular decimation filter is the comb filter. However, this filter exhibits a high passband droop in the passband magnitude characteristic, which must be avoided to prevent the distortion of the decimated signal. In this paper we present the sharpening technique to improve comb passband characteristic. In order to decrease complexity introduced by sharpening, we also consider two-stage structure where the sharpening is applied only at the second stage. Different examples are included to illustrate the benefits of the proposed method.

In this article, two reliable techniques, Haar wavelet method and optimal homotopy asymptotic method (OHAM) are presented. Haar wavelet method is an efficient numerical method for the numerical solution of fractional order partial differential equation like Fisher type. The approximate solutions of the fractional Fisher type equation are compared with the optimal homotopy asymptotic method as well as with the exact solutions. Comparisons between the obtained solutions with the exact solutions exhibit that both the featured methods are effective and efficient in solving nonlinear problems. However, the results indicate that OHAM provides more accurate value than Haar wavelet method.

The data required to build geological models of the subsurface are often unavailable from direct measurements or well logs. In order to image the subsurface geological structures several geophysical methods have been developed. The magnetotelluric (MT) method uses natural, time-varying electromagnetic (EM) fields as its source to measure the EM impedance of the subsurface. The interpretation of these data is routinely undertaken by solving inverse problems to produce 1D, 2D or 3D electrical conductivity models of the subsurface. In classical MT inverse problems the investigated models are parametrized using a fixed number of unknowns (i.e. fixed number of layers in a 1D model, or a fixed number of cells in a 2D model), and the non-uniqueness of the solution is handled by a regularization term added to the objective function. This study presents a different approach to the 1D MT inverse problem, by using a trans-dimensional Monte Carlo sampling algorithm, where trans-dimensionality implies that the number of unknown parameters is a parameter itself. This construction has been shown to have a built-in Occam razor, so that the regularization term is not required to produce a simple model. The influences of subjective choices in the interpretation process can therefore be sensibly reduced. The inverse problem is solved within a Bayesian framework, where posterior probability distribution of the investigated parameters are sought, rather than a single best-fit model, and uncertainties on the model parameters, and their correlation, can be easily measured.

Non-Hodgkin lymphomas are of many distinct types, and different classification systems make it difficult to diagnose them correctly. Many of these systems classify lymphomas only based on what they look like under a microscope. In 2008 the World Health Organisation (WHO) introduced the most recent system, which also considers the chromosome features of the lymphoma cells and the presence of certain proteins on their surface. The WHO system is the one that we apply in this work. Herewith we present an automatic method to classify histological images of three types of non-Hodgkin lymphoma. Our method is based on the Stationary Wavelet Transform (SWT), and it consists of three steps: 1) extracting sub-bands from the histological image through SWT, 2) applying Analysis of Variance (ANOVA) to clean noise and select the most relevant information, 3) classifying it by the Support Vector Machine (SVM) algorithm. The kernel types Linear, RBF and Polynomial were evaluated with our method applied to 210 images of lymphoma from the National Institute on Aging. We concluded that the following combination led to the most relevant results: detail sub-band, ANOVA and SVM with Linear and RBF kernels.

This manuscript investigates some relations and properties between 2-cyclic self-mappings. In particular, a formal development is given to link some concepts and their basic related properties like those of approximate best proximity points, approximate best proximity point property and cyclic asymptotic regularity.

In this study is presented an automatic method to classify images from fractal descriptors as decision rules, such as multiscale fractal dimension and lacunarity. The proposed methodology was divided in three steps: quantification of the regions of interest with fractal dimension and lacunarity, techniques under a multiscale approach; definition of reference patterns, which are the limits of each studied group; and, classification of each group, considering the combination of the reference patterns with signals maximization (an approach commonly considered in paraconsistent logic). The proposed method was used to classify histological prostatic images, aiming the diagnostic of prostate cancer. The accuracy levels were important, overcoming those obtained with Support Vector Machine (SVM) and Best- first Decicion Tree (BFTree) classifiers. The proposed approach allows recognize and classify patterns, offering the advantage of giving comprehensive results to the specialists.

In this paper, computer simulation of smoke spread dynamics in industrial hall is investigated. A set of simulations of fire in three industrial halls with the same geometry varying in the height of ceiling is realized using the FDS fire simulator, version 6. The obtained simulation results are described focusing on the impact of the ceiling height and fire barriers on the fire course and smoke spread dynamics.

The objective is to demonstrate the use of reduced-order models (ROM) based on proper orthogonal decomposition (POD) to stabilize the flow over a vertically oscillating circular cylinder in the laminar regime (Reynolds number equal to 60). The 2D Navier-Stokes equations are first solved with a finite element method, in which the moving cylinder is introduced via an ALE method. Since in fluid-structure interaction, the POD algorithm cannot be applied directly, we implemented the fictitious domain method of Glowinski et al. [1] where the solid domain is treated as a fluid undergoing an additional constraint. The POD-ROM is classically obtained by projecting the Navier-Stokes equations onto the first POD modes. At this level, the cylinder displacement is enforced in the POD-ROM through the introduction of Lagrange multipliers. For determining the optimal vertical velocity of the cylinder, a linear quadratic regulator framework is employed. After linearization of the POD-ROM around the steady flow state, the optimal linear feedback gain is obtained as solution of a generalized algebraic Riccati equation. Finally, when the optimal feedback control is applied, it is shown that the flow converges rapidly to the steady state. In addition, a vanishing control is obtained proving the efficiency of the control approach.

In embryonic stem cells, various transcription factors (TFs) maintain pluripotency. To gain insights into the regulatory system controlling pluripotency, I inferred the regulatory relationships between the TFs expressed in ES cells. In this study, I applied a method based on structural equation modeling (SEM), combined with factor analysis, to 649 expression profiles of 19 TF genes measured in mouse Embryonic Stem Cells (ESCs). The factor analysis identified 19 TF genes that were regulated by several unmeasured factors. Since the known cell reprogramming TF genes (Pou5f1, Sox2 and Nanog) are regulated by different factors, each estimated factor is considered to be an input for signal transduction to control pluripotency in mouse ESCs. In the inferred network model, TF proteins were also arranged as unmeasured factors that control other TFs. The interpretation of the inferred network model revealed the regulatory mechanism for controlling pluripotency in ES cells.

Segmentation of abdominal organs from MRI data sets is a challenging task due to various limitations and artefacts. During the routine clinical practice, radiologists use multiple MR sequences in order to analyze different anatomical properties. These sequences have different characteristics in terms of acquisition parameters (such as contrast mechanisms and pulse sequence designs) and image properties (such as pixel spacing, slice thicknesses and dynamic range). For a complete understanding of the data, computational techniques should combine the information coming from these various MRI sequences. These sequences are not acquired in parallel but in a sequential manner (one after another). Therefore, patient movements and respiratory motions change the position and shape of the abdominal organs. In this study, the amount of these effects is measured using three different symmetric surface distance metrics performed to three dimensional data acquired from various MRI sequences. The results are compared to intra and inter observer differences and discussions on using multiple MRI sequences for segmentation and the necessities for registration are presented.

Classification of similar shaped objects from scattered electromagnetic waves is a difficult problem to solve. as it heavily depends on the aspect angle. Eliminating the effects of the aspect angle is possible by extracting distinguishable features from the scattered signals. These features should be robust to noise effects especially at SNR levels. where noise effects become dominant on the scattered signal. In this paper. we propose a target classification method. which uses a structural feature set extracted from scattered signal. Prior to feature extraction. a multi-scale approximation is performed using hierarchical radial basis function network topology to suppress the effects of noise on scattered signal. After principle component analysis. k-fold cross validation based experiments is performed. Results show that spherical targets are recognized successfully up to -10dB SNR.

The oscillations exhibited by the magnetization of superconducting nano and mesoscopics structures as a function of the applied magnetic field has attracted attention in the last few years. Nano/Mesoscopic hybrid systems in contact with ferromagnets exhibit interesting transport properties related to the influence of the exchange field on the density of states of clean ferromagnetic structures in contact with superconductor. In this work we study the vortex configurations in a superconducting disk with one central defect inside. The sample is surrounded by a ferromagnetic medium. We calculate the spatial distribution of the Cooper pairs and the phase of the superconducting order parameter and curves of magnetization and vorticity as a function of the magnetic applied field. We found that the first vortex penetration field decrease when a ferromagnetic/superconducting interface is used.

The purpose of this study is to find a self-organizing model for MWSN based on bee colonies in order to reduce the number of messages transmitted among nodes, and thus reduce the overall consumption energy while maintaining the efficiency of message delivery. The results obtained in this article are originated from simulations carried out with SINALGO software, which demonstrates the effectiveness of the proposed approach. The BeeAODV (Bee Ad-Hoc On Demand Distance Vector) proposed in this paper allows to considerably reduce message exchanges whether compared to AODV (Ad-Hoc On Demand Distance Vector).

The realized stochastic volatility (RSV) model that utilizes the realized volatility as additional information has been proposed to infer volatility of financial time series. We consider the Bayesian inference of the RSV model by the Hybrid Monte Carlo (HMC) algorithm. The HMC algorithm can be parallelized and thus performed on the GPU for speedup. The GPU code is developed with CUDA Fortran. We compare the computational time in performing the HMC algorithm on GPU (GTX 760) and CPU (Intel i7-4770 3.4GHz) and find that the GPU can be up to 17 times faster than the CPU. We also code the program with OpenACC and find that appropriate coding can achieve the similar speedup with CUDA Fortran.

We developed a mathematical model of Plasma Enhanced Chemical Vapor Deposition (PECVD) of silicon nitride thin films from SiH₄-NH₃-N₂-Ar mixture, an important application in modern materials science. Our multiphysics model describes gas dynamics, chemical physics, plasma physics and electrodynamics. The PECVD technology is inherently multiscale, from macroscale processes in the chemical reactor to atomic-scale surface chemistry. Our macroscale model is based on Navier-Stokes equations for a transient laminar flow of a compressible chemically reacting gas mixture, together with the mass transfer and energy balance equations, Poisson equation for electric potential, electrons and ions balance equations. The chemical kinetics model includes 24 species and 58 reactions: 37 in the gas phase and 21 on the surface. A deposition model consists of three stages: adsorption to the surface, diffusion along the surface and embedding of products into the substrate. A new model has been validated on experimental results obtained with the "Plasmalab System 100" reactor. We present the mathematical model and simulation results investigating the influence of flow rate and source gas proportion on silicon nitride film growth rate and chemical composition.

We developed a multiphysics mathematical model for simulation of silicon dioxide Chemical Vapor Deposition (CVD) from tetraethyl orthosilicate (TEOS) and oxygen mixture in a microreactor at atmospheric pressure. Microfluidics is a promising technology with numerous applications in chemical synthesis due to its high heat and mass transfer efficiency and well-controlled flow parameters. Experimental studies of CVD microreactor technology are slow and expensive. Analytical solution of the governing equations is impossible due to the complexity of intertwined non-linear physical and chemical processes. Computer simulation is the most effective tool for design and optimization of microreactors. Our computational fluid dynamics model employs mass, momentum and energy balance equations for a laminar transient flow of a chemically reacting gas mixture at low Reynolds number. Simulation results show the influence of microreactor configuration and process parameters on SiO₂ deposition rate and uniformity. We simulated three microreactors with the central channel diameter of 5, 10, 20 micrometers, varying gas flow rate in the range of 5-100 microliters per hour and temperature in the range of 300-800 °C. For each microchannel diameter we found an optimal set of process parameters providing the best quality of deposited material. The model will be used for optimization of the microreactor configuration and technological parameters to facilitate the experimental stage of this research.

The Landau-Lifshitz-Gilbert equations for the evolution of the magnetization, in presence of an external torque, can be cast in the form of the Lorenz equations and, thus, can describe chaotic fluctuations. To study quantum effects, we describe the magnetization by matrices, that take values in a Lie algebra. The finite dimensionality of the representation encodes the quantum fluctuations, while the non-linear nature of the equations can describe chaotic fluctuations. We identify a criterion, for the appearance of such non-linear terms. This depends on whether an invariant, symmetric tensor of the algebra can vanish or not. This proposal is studied in detail for the fundamental representation of u(2) = u(1) × su(2). We find a knotted structure for the attractor, a bimodal distribution for the largest Lyapunov exponent and that the dynamics takes place within the Cartan subalgebra, that does not contain only the identity matrix, thereby can describe the quantum fluctuations.

In this paper, the impact of vehicles in road tunnel on smoke spread in case of fire is illustrated using the FDS (Fire Dynamics Simulator) system. FDS is a CFD-based fire field model capable to simulate fire in various environments capturing a big variety of physical processes related to fire. A set of simulations of fire in a 300 m long two-lane single directional road tunnel with longitudinal ventilation is described focusing on the impact of vehicles on the smoke spread dynamics in the tunnel.

We present evidence that the best model for empirical volume-price distributions is not always the same and it strongly depends in (i) the region of the volume-price spectrum that one wants to model and (ii) the period in time that is being modelled. To show these two features we analyze stocks of the New York stock market with four different models: Γ, Γ-inverse, log-normal, and Weibull distributions. To evaluate the accuracy of each model we use standard relative deviations as well as the Kullback-Leibler distance and introduce an additional distance particularly suited to evaluate how accurate are the models for the distribution tails (large volume-price). Finally we put our findings in perspective and discuss how they can be extended to other situations in finance engineering.

In this paper we propose an Ising model which simulates multiple financial time series. Our model introduces the interaction which couples to spins of other systems. Simulations from our model show that time series exhibit the volatility clustering that is often observed in the real financial markets. Furthermore we also find non-zero cross correlations between the volatilities from our model. Thus our model can simulate stock markets where volatilities of stocks are mutually correlated.

In high energy physics, we deal with demanding task of signal separation from background. The Model Based Clustering method involves the estimation of distribution mixture parameters via the Expectation-Maximization algorithm in the training phase and application of Bayes' rule in the testing phase. Modifications of the algorithm such as weighting, missing data processing, and overtraining avoidance will be discussed. Due to the strong dependence of the algorithm on initialization, genetic optimization techniques such as mutation, elitism, parasitism, and the rank selection of individuals will be mentioned. Data pre-processing plays a significant role for the subsequent combination of final discriminants in order to improve signal separation efficiency. Moreover, the results of the top quark separation from the Tevatron collider will be compared with those of standard multivariate techniques in high energy physics. Results from this study has been used in the measurement of the inclusive top pair production cross section employing DØ Tevatron full Runll data (9.7 fb⁻¹).

We explicitly test if the reliability of credit ratings depends on the total number of admissible states. We analyse open access credit rating data and show that the effect of the number of states in the dynamical properties of ratings change with time, thus giving supportive evidence that the ideal number of admissible states changes with time. We use matrix estimation methods that explicitly assume the hypothesis needed for the process to be a valid rating process. By comparing with the likelihood maximization method of matrix estimation, we quantify the "likelihood-loss" of assuming that the process is a well grounded rating process.

In this paper we describe results of the principal components analysis of the dynamics of Total Electronic Content (TEC) data with the use of global maps presented by the Jet Propulsion Laboratory (NASA, USA) for the period of 2007-2011. We show that the result of the decomposition in principal components essentially depends on the method used for preprocessing the data, their representation (the used coordinate system), and the data centering technique (e.g., daily and seasonal components extracting). The use of momentarily co-moving frame of reference and other special techniques provide opportunity for the detailed analysis of the ionospheric equatorial anomaly. The covariance matrix of decomposition was calculated using Spearman's rank correlation coefficient that allows reducing statistical relationship between principal components.

Precision Spray is a technique to increase performance of Precision Agriculture. This spray technique may be aided by a Wireless Sensor Network, however, for such approach, the communication between the agricultural input applicator vehicle and network is critical due to its proper functioning. Thus, this work analyzes how the number of nodes in a wireless sensor network, its type of distribution and different areas of scenario affects the performance of communication. We performed simulations to observe system's behavior changing to find the most fitted non-controlled mobility model to the system.

We study a universality of self-gravitating systems in the quasi-equilibrium state. It is shown numerically that the two dimensional self-gravitating system in the quasi-equilibrium state has the same kind of density profile as the three dimensional one. We develop a model to describe this universal quasi-equilibrium state by using a special Langevin equation with a distinctive random noise to self-gravitating systems. We find that the density profile derived theoretically is consistent well with results of observations and simulations.

A detailed comparison between two methods to calculate the shear viscosity coefficient of a hot hadronic gas is presented. We choose two systems in this comparison which are massless particles with current algebra cross section and a mixture comprised of pions with rho resonances. The two methods involved are the Green-Kubo method, applied using the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model to simulate the hadronic medium, and the Chapman-Enskog method. In addition, the effect of the resonance lifetime on the shear viscosity coefficient is investigated.

The steady laminar two-dimensional Joule heating natural convection is investigated using asymptotical analysis, the fluid is in a rectangular cavity, the direct current contributes heat for heating the process medium by a pair of plate electrodes, the top wall is cooled with atmosphere and all the other walls are kept thermally insulated. The asymptotic solution is obtained in the core region in the limit as the aspect ratio, which is defined as the ratio of the vertical dimension of cavity to the horizontal dimension of cavity, goes to zero. The numerical experiments are also carried out to compare with the asymptotic solution of the steady twodimensional Joule heating convection. The asymptotic results indicate that the expressions of velocity and temperature fields in the core region are valid in the limit of the small aspect ratio.

The notion of gravitational radiation as a radiation of the same level as the electromagnetic radiation is based on theoretically proved and experimentally confirmed fact of existence of stationary states of an electron in its gravitational field characterized by the gravitational constant K = 10⁴²G (G is the Newtonian gravitational constant) and unrecoverable space-time curvature A. This paper gives an overview of the authors' works [1, 2, 3, 4], which set out the relevant results. Additionally, data is provided on the broadening of the spectra characteristic radiation. The data show that this broadening can be explained only by the presence of excited states of electrons in their gravitational field. What is more, the interpretation of the new line of X-ray emission spectrum according to the results of observation of MOS-camera of XMM-Newton observatory is of interest. The given work contributes into further elaboration of the findings considering their application to dense high- temperature plasma of multiple-charge ions. This is due to quantitative character of electron gravitational radiation spectrum such that amplification of gravitational radiation may take place only in multiple-charge ion high-temperature plasma.

Hysteresis loops occur in many scientific and technical problems, especially as field dependent magnetization of ferromagnetic materials, but also as stress-strain-curves of materials measured by tensile tests including thermal effects, liquid-solid phase transitions, in cell biology or economics. While several mathematical models exist which aim to calculate hysteresis energies and other parameters, here we offer a simple model for a general hysteretic system, showing different hysteresis loops depending on the defined parameters. The calculation which is based on basic spreadsheet analysis plus an easy macro code can be used by students to understand how these systems work and how the parameters influence the reactions of the system on an external field. Importantly, in the step-by-step mode, each change of the system state, compared to the last step, becomes visible. The simple program can be developed further by several changes and additions, enabling the building of a tool which is capable of answering real physical questions in the broad field of magnetism as well as in other scientific areas, in which similar hysteresis loops occur.

We investigate numerically the flux quantum configurations and some thermodynamic properties of a superconducting Technetium film by using the link variables technique for one shape of circular geometry. The Technetium exhibits superconductivity properties indicated by to an extrapolated critical magnetic field value of H_c(T = 0) = 1410 Oe, a Ginzburg-Landau parameter of κ = 0.92, and a critical temperature T_c = 7.86K, being the magnetic behavior of this material characteristic of a type-II superconductor with a weak-coupling superconductor of the BCS type. The studied sample is a circular sector with angular width θ = 7π/4 surrounded by a dielectric material and submitted to external magnetic field applied perpendicular to its plane. We evaluate the magnetic moment density, Shubnikov state and free Gibbs energy as a function of the external magnetic field.

A kinetic nonlinear model of mass transfer, grain coarsening and coalescence with potential applications in sintering processes is studied. The model involves nonlinear differential equations that determine the transport of mass between grains. The rate of mass transfer is controlled by the activation energy (an Arrhenius factor) leading to a nonlinear model of mass transfer and grain coarsening. The resulting dynamical system of coupled nonlinear differential equations with random initial conditions (i.e., initial grain mass configuration) is solved by means of the Runge-Kutta method. An analysis of the fixed points of the two-grain system is carried out, and the solution of the multi-grain system is studied. We incorporate coalescence of smaller grains with larger neighbors using a cellular automaton step in the evolution of the system.

A horizontal layer between two transversely isotropic half-spaces forms a trimaterial full-space, involved in this paper. A mathematical formulation is presented to determine the response of a rigid circular membrane, which is laid down at an interface of the tri-material transversely isotropic full-space and is considered to be under a prescribed horizontal displacement. The governing equations are expressed in the cylindrical coordinate system. With the aid of a system of two scalar potential functions, the governing equations of motion can be uncoupled into two separated partial differential equations, which may be transformed to some ordinary differential equations by applying the Hankel integral transforms in the radial direction and Fourier series along the angular coordinate. After determining the unknown functions by imposing the relaxed boundary conditions, they are transformed to a set of four coupled integral equations, which are reduced to two coupled Fredholm-Volterra integral equations of the second kind, from which both displacement and the stress fields are computed. To confirm the accuracy of the numerical evaluation of the integrals involved, the numerical results are compared with the solutions exists for a transversely isotropic half-space. In order to investigate the degree of material anisotropy, some numerical evaluations are given for different combinations of transversely isotropic region.

In the frame in the quantum electrodynamics exist four basic operators; the electron self-energy, vacuum polarization, vertex correction, and the Compton operator. The first three operators are very important by its relation with renormalized and Ward identity. However, the Compton operator has equal importance, but without divergence, and little attention has been given it. We have calculated the Compton operator and obtained the closed expression for it in the frame of dimensionally continuous integration and hypergeometric functions.

We present fully resolved Direct Numerical Simulations of 2D flow over a moving airfoil, using an in-house code that solves the Navier-Stokes equations of the incompressible flow with an Immersed Boundary Method. A combination of sinusoidal plunging and pitching motions is imposed to the airfoil. Starting from a thrust producing case (Reynolds number, Re = 1000, reduced frequency, k = 1.41, plunging amplitude h₀/c = 1, pitching amplitude θ₀ = 30°, phase shift ϕ = 90°), we increase the mean pitching angle (in order to produce lift) and vary the phase shift between pitching and plunging (to optimize the direction and magnitude of the net force on the airfoil). These cases are discussed in terms of their lift coefficient, thrust coefficient and propulsive efficiency.

Non-coding RNA molecules are able to regulate gene expression and play an essential role in cells. On the other hand, bistability is an important behaviour of genetic networks. Here, we propose and study an ODE model in order to show how non-coding RNA can produce bistability in a simple way. The model comprises a single gene with positive feedback that is repressed by non-coding RNA molecules. We show how the values of all the reaction rates involved in the model are able to control the transitions between the high and low states. This new model can be interesting to clarify the role of non-coding RNA molecules in genetic networks. As well, these results can be interesting in synthetic biology for developing new genetic memories and biomolecular devices based on non-coding RNAs.

A novel efficient implicit direct forcing immersed boundary method for incompressible flows with complex boundaries is presented. In the previous work [1], the calculation is performed on the Cartesian grid regardless of the immersed object, with a fictitious force evaluated on the Lagrangian points to mimic the presence of the physical boundaries. However the explicit direct forcing method [1] fails to accurately impose the non-slip boundary condition on the immersed interface. In the present work, the calculation is based on the implicit treatment of the artificial force while in an effective way of system iteration. The accuracy is also improved by solving the Navier-Stokes equation with the rotational incremental pressure- correction projection method of Guermond and Shen [2]. Numerical simulations performed with the proposed method are in good agreement with those in the literature.

We investigate the polaron dynamics on the nonlinear lattice with the cubic nonlinearity. The electron-phonon interaction is accounted in the Su-Schrieffer-Heeger approximation. An exact analytical solution is obtained in the continuum approximation at certain relation of parameters. The numerical simulation agrees with analytics very well. Moreover, colliding polarons recover their shapes and velocities after the elastic collision suggesting that the solution belongs to the exactly integrable system. When the continuum approximation is invalid (parameters of nonlinearity and electron-phonon interaction are not small), a new family of stable multipeaked polarons is found. These polarons are formed by the coupled solitons hold together by the electron-phonon interaction.

We apply the convolution (folding) method in neutrino physics studies. We focus on its use to explore the response of some nuclear detectors to the energy spectra of laboratory neutrinos. After calculating the neutrino-nucleus cross sections (within the context of a nuclear model) for a neutrino detector, the obtained cross section values must be folded with a specific neutrino- energy distribution. In the present work we use the v-distribution of pion-muon decay at rest neutrino beams created in muon factories like the Fermilab, J-PARC, and other laboratories. Due to the fact that neutrino-nucleus interactions are very weak, the evaluated cross sections are small (~ 10⁻⁴²cm²). Thus, one needs a very fine convolution tool to obtain accurate description of the v-signals (laboratory, supernova neutrinos, etc.) recorded at some nuclear detectors.

In many physical problems, the computation of exact wave functions for muons (particles about two hundred times heavier than electrons), bound in the extended Coulomb field created by the atomic nucleus, is required. Even though the problem is trivial under the assumption of point-like nuclear systems, the consideration of the nuclear finite-size necessitates the use of advantageous numerical techniques. In the case of non-relativistic bound muons, the solution of the Schrödinger equation is reliable, but for a relativistic description the solution of the Dirac equations for the bound muon is needed. In the present contribution, as a first step, we attempt to derive a method for solving the Schrödinger equation on the basis of simulated annealing algorithms. To this end, one may optimize appropriate parametric expressions for the wave function of a muon orbiting around complex nuclei by employing the simulated annealing method recently constructed to minimize multi parametric expressions in several physical applications.

First-principles calculations have been carried out to investigate the structural and electronic properties of Mg_xZn_1-xO ternary alloys. The calculations are performed using the full potential linearized augmented plane wave (FP-LAPW) method within the density functional theory(DFT). We conclude that the structural properties of these materials, in particular the composition dependence on the lattice constant and the band gap is found to be linear. The a-axis length in the lattice gradually increases, while the c-axis length decreases with the increase in Mg doping concentration, and be corresponded with the Vegard's law linear rule. The lattice parameters of the Mg_xZn_1-xO ternary alloys are consistent with experimental data and other theoretical results. We found in the conduction band portion, the Mg 2p 2s states are moved to high energy region as the Mg content increases, so the band gap increases.

The specific heat amplitude ratios for generic anisotropic as well as isotropic Lifshitz critical behaviors for the N-vector model are computed at one-loop level using the ε_L- expansion. In the anisotropic case, we show that the universal result obtained reduces very easily to that from the simpler m-axial universality class result. In the isotropic case, if n is the number of neighbors coupled via competing interactions, we demonstrate that the ratio vanishes close to n = 4 and, becomes negative for n > 4 when it is calculated exactly, which is rather odd. The evaluation using the orthogonal approximation is shown to yield positive results for arbitrary n. Explicit computations for the case n = 2, d = 3, N = 1 yield an exact amplitude ratio equal to 0.06, with the approximate amplitude ratio being 1.17.We discuss two physical mechanisms to pick out one of the amplitude ratio values. We propose an experiment in homopolymer-diblock copolymer blends in order to determine the amplitude ratio.

In this paper, we propose a transmission type electro-absorption modulator (EAM) operating at 850 nm having low operating voltage and high absorption change with low insertion loss using a novel three step asymmetric coupled quantum well (3 ACQW) structure which can be used as an optical image shutter for high-definition (HD) three dimensional (3D) imaging. Theoretical calculations show that the exciton red shift of 3 ACQW structure is more than two times larger than that of rectangular quantum well (RQW) structure while maintaining high absorption change. The EAM having coupled cavities with 3 ACQW structure shows a wide spectral bandwidth and high amplitude modulation at a bias voltage of only -8V, which is 41% lower in operating voltage than that of RQW, making the proposed EAM highly attractive as an optical image shutter for HD 3D imaging applications.

Core/shell nanoparticles can be used in industry, medicine and biophysics, due to their unique properties. Theoretical studies of core/shell nanoparticles are mainly based on the Stoner-Wohlfarth model, and the Monte-Carlo simulation is mostly used the Metropolis algorithm. This method is an extension of one-phase nanoparticle model and not entirely correct for solving the magnetic states of core/shell nanoparticles, which represents a magnetic core covered with a magnetic or nonmagnetic shell. We developed a model of core/shell nanoparticles based on the analysis of total energy consisting of anisotropy energy E_a, magnetostatic interaction energy E_m, exchange interaction energy E_ex and energy of magnetic moment of the grain in external magnetic field E_h: E=E_a+E_m+E_ex+E_H.