arXiv subjects

Sergey Leble

Publications and source records attributed to Sergey Leble.

At least 19 recordsLinked to original sources

arXiv2018

Interaction of orthogonal-polarized waves in 1D metamaterial with Kerr nonlinearity

A theoretical study of wave propagation in 1D metamaterial is presented. A system of nonlinear evolution equation for electromagnetic waves with both polarizations account is derived by means of projection operators method for general nonlinearity and dispersion. The system describes interaction of opposite directed waves with a given polarization. The particular case of Kerr nonlinearity and Drude dispersion is considered. In such approximation it results in the correspondent systems of nonlinear equations that generalizes the Schäfer-Wayne one. Particular solutions in case of slow-varying envelopes are found, plotted and analyzed in gigahertz range. Travelling wave solution for the system of equation of interaction of orthogonal-polarized waves is also obtained and the correspondent nonlinear dispersion relations are written in explicit form.

physics.optics↗

arXiv2016

1+1-dimensional Yang-Mills equations and mass via quasiclassical correction to action

Two-dimensional Yang-Mills models in a pseudo-euclidean space are considered from a point of view of a class of nonlinear Klein-Gordon-Fock equations. It is shown that the Nahm reduction does not work, another choice is proposed and investigated. A quasiclassical quantization of the models is based on Feynmann-Maslov path integral construction and its zeta function representation in terms of a Green function diagonal for an auxiliary heat equation with an elliptic potential. The natural renormalization use a freedom in vacuum state choice as well as the choice of the norm of an evolution operator eigenvectors. A nonzero mass appears via the quasiclassical correction.

hep-th↗

arXiv2016

Electrical Resistivity Model for Quasi-one-dimensional structures

In this paper electron-impurity scattering coefficient of Bloch waves for one dimensional Dirac comb potential is used for calculation of temperature dependence of resistivity within kinetic theory. We restrict ourselves by scattering on impurities that is also modeled by zero-range potential. The standard averaging is expressed by integral that is evaluated within advanced numerical procedure. The plots on base of the calculations results demonstrate strong variability as function of temperature and impurity strength.

cond-mat.mes-hall↗

arXiv2015

General equation for directed Electromagnetic Pulse Propagation in 1D metamaterial: Projecting Operators Method

We consider a boundary problem for 1D electrodynamics modeling of a pulse propagation in a metamaterial medium. We build and apply projecting operators to a Maxwell system in time domain that allows to split the linear propagation problem to directed waves for a material relations with general dispersion. Matrix elements of the projectors act as convolution integral operators. For a weak nonlinearity we generalize the linear results still for arbitrary dispersion and derive the system of interacting right/left waves with combined (hybrid) amplitudes. The result is specified for the popular metamaterial model with Drude formula for both permittivity and permeability coefficients. We also discuss and investigate stationary solutions of the system related to some boundary regimes.

math-ph↗

arXiv2015

N-fold scattering series for Kolmogorov equation

We consider a formulation of initial problem for Kolmogorov equation that corresponds a localized source of particles to be scattered by medium with given scattering amplitude density (scattering indicatrix). The multiple scattering expansion and amplitudes are introduced and the corresponding series solution of the equation is constructed. We investigate the multiple integral representation for the series terms, transform it into a form, convenient for estimations and prove convergence of the series. An application to light beam scattering and LIDAR problem solution is outlined.

cond-mat.stat-mech↗

arXiv2015

Bloch wave scattering on pseudopotential impurity in 1D Dirac comb model

This paper presents calculation of electron-impurity scattering coefficient of Bloch waves for one dimensional Dirac comb potential. The impurity is also modeled as delta function pseudopotential that allows explicit solution of Schrödinger equation and scattering problem for Bloch waves.

cond-mat.mes-hall↗

arXiv2014

On inverse problem of waves identification by measurements at one point vicinity

A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and electromagnetic problems are discussed within the restrictions outlined. The projecting operator technique is used to split the solution space and analyze input of a wave monitoring in vicinity of an observation point. The solution space is supplied by $L_2$ norm via the problem conservation law; its finite-dimensional analog is used as a measure of a given mode presence and information about form. The algorithm of the problem solution is presented in terms of appropriate regularization to reconstruct an incoming pulses origin. The dissipation and entropy mode account in the problem of acoustic waves extraction is also discussed in terms of correspondent projecting technique.

math-ph↗

arXiv2014

Modeling of X-ray attenuation via photon statistics evolution

We consider a formulation of Cauchy problem for Kolmogorov equation which corresponds a localized source of particles to be scattered by medium with given scattering amplitude density. The multiple scattering amplitudes are introduced and the corresponding series solution of the equation is constructed. We investigate the one-fold integral representation for the series terms, its estimations and values of photon number of a finite and point receivers. An application to X-ray beam scattering for orthogonal and inclined to a layer is considered.

cond-mat.stat-mech↗

arXiv2014

A Mathematica Program for heat source function of 1D heat equation reconstruction by three types of data

We solve an inverse problem for the one-dimensional heat diffusion equation. We reconstruct the heat source function for the three types of data: 1) single position point and different times, 2) constant time and uniformly distributed positions, 3) random position points and different times. First we demonstrate reconstruction using simple inversion of discretized Kernel matrix. Then we apply Tikhonov regularization for two types of the parameter of regularization estimation. The first one, which is in fact exemplary simulation, is based on minimization of the distance in C space of reconstructed function to the initial source function. Second rule is known as Discrepancy principle. We generate the data from the chosen source function. In order to get some measure of accuracy of reconstruction we compare the result with the function from which data was generated. We also deliver corresponding application in symbolic computation environment of Mathematica. The program has a lot of flexibility, it can perform reconstruction for much more general input then one considered in the paper.

math.NA↗

arXiv2014

The method of dynamic projection operators in the theory of hyperbolic systems of partial differential equations with variable coefficients

We consider a generalization of the projecting operators method for the case of Cauchy problem for systems of 1D evolution differential equations of first order with variable coefficients. It is supposed that the coefficients dependence on the only variable x is weak, that is described by a small parameter introduction. Such problem corresponds, for example, to the case of wave propagation in a weakly inhomogeneous medium. As an example, we specify the problem to adiabatic acoustics. For the Cauchy problem, to fix unidirectional modes, the projection operators are constructed. The method of successive approximations (perturbation theory) is developed and based on pseudodifferential operators theory. The application of these projection operators allows to obtain approximate evolution equations corresponding to the separated directed waves.

math-ph↗

arXiv2013

Diffraction of light by a nanowire

A general scattering problem of a plane electromagnetic wave on an infinite cylindrical rod is formulated and solved in a form of Bessel functions series expansion. The conductivity account via Ohm law directly in Maxwell equation leads to complex wavenumber and hence the complex arguments of Bessel functions inside the cylinder. The general formula for averaged by period Pointing vector is derived. For numerical calculations asymptotics of Bessel functions are used. Dependence of scattered wave intensity as function of angle and frequency is presented for different values of the rod radius.

physics.class-ph↗

arXiv2013

An approximate analytical solution of free convection problem for vertical isothermal plate via transverse coordinate Taylor expansion

The model under consideration is based on approximate analytical solution of two dimensional stationary Navier-Stokes and Fourier-Kirchhoff equations. Approximations are based on the typical for natural convection assumptions: the fluid noncompressibility and Bousinesq approximation. We also assume that ortogonal to the plate component (x) of velocity is neglectible small. The solution of the boundary problem is represented as a Taylor Series in $x$ coordinate for velocity and temperature which introduces functions of vertical coordinate (y), as coefficients of the expansion. The correspondent boundary problem formulation depends on parameters specific for the problem: Grashoff number, the plate height (L) and gravity constant. The main result of the paper is the set of equations for the coefficient functions for example choice of expansion terms number. The nonzero velocity at the starting point of a flow appears in such approach as a development of convecntional boundary layer theory formulation.

physics.flu-dyn↗

arXiv2013

Proper orthogonal decomposition of eigen modes in a gas affected by a mass force

The relations connecting perturbations in acoustic and entropy modes in a gas affected by a constant mass force, are derived. The background temperature of a gas may vary in the direction of an external mass force. The relations are independent on time. They make possible to decompose the total vector of perturbations into acoustic and non-acoustic parts uniquely at any instant. %The conclusions of distribution of the energy between sound and entropy modes may be also made at any instant. In order to do this, three quantities are required, according to the number of modes. In one dimension, the reference quantities may be total perturbations in entropy, pressure and velocity. The total energy of flow is determined. The examples of dismemberment of the total field into acoustic and entropy parts relate to the unperturbed temperature of a gas which linearly depends on the spacial co-ordinate.

math-ph↗

arXiv2012

Quantum corrections to phi^4 model solutions and applications to Heisenberg chain dynamics

The Heisenberg spin chain is considered in phi^4 model approximation. Quantum corrections to classical solutions of the one-dimensional phi^4 model within the correspondent physics are evaluated with account of rest $d-1$ dimensions of a d-dimensional theory. A quantization of the models is considered in terms of space-time functional integral. The generalized zeta-function formalism is used to renormalize and evaluate the functional integral and quantum corrections to energy in quasiclassical approximation. The results are applied to appropriate conditions of the spin chain models and its dynamics, which elementary solutions, energy and the quantum corrections are calculated.

math-ph↗

arXiv2012

On analytical solution of stationary two dimensional boundary problem of natural convection

Approximate analytical solution of two dimensional problem for stationary Navier-Stokes, continuity and Fourier-Kirchhoff equations describing free convective heat transfer from isothermal surface of half infinite vertical plate is presented. The problem formulation is based on the typical for natural convection assumptions: the fluid noncompressibility and Boussinesq approximation. We also assume that orthogonal to the plate component of velocity is small. Apart from the basic equations it includes boundary conditions: the constant temperature and zero velocity on the plate. At the starting point of the flow we fix average temperature and vertical component of velocity, as well as basic conservation laws in integral form. The solution of the boundary problem is represented as a Taylor Series in horizontal variable with coefficients depending on vertical variable.

physics.flu-dyn↗

arXiv2012

Study of internal wave breaking dependence on stratification

Mixing effect in a stratified fluid is considered and examined. Euler equations for incompressible fluid stratified by a gravity field are applied to state a mathematical problem and describe the effect. It is found out that a system of Euler equations is not enough for a formulation of correct generalized problem. Some complementary relations are suggested and justified. A numerical method is developed and applied for study of processes of vortex destruction and mixing progress in a stratified fluid. The dependence of vortex destruction on a stratification scale is investigated numerically and it is shown that the effect increases with the stratification scale. It is observed that the effect of vortex destruction is absent when the fluid density is constant. Some simple mathematical explanation of the effect is suggested.

math-ph↗

arXiv2011

Green function diagonal for a class of heat equations

A construction of the heat kernel diagonal is considered as element of generalized Zeta function, that, being meromorfic function, its gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expression in the case of finite-gap potential coefficient of the heat equation are constructed.

math-ph↗

arXiv2011

A solution of LIDAR problem in double scattering approximation

A problem of monoenergetic particles pulse reflection from half-infinite stratified medium is considered in conditions of elastic scattering with absorbtion account. The theory is based on multiple scattering series solution of Kolmogorov equation for one-particle distribution function. The analytical representation for first two terms are given in compact form for a point impulse source and cylindric symmetrical detector. Reading recent articles on the LIDAR sounding of environment (e.g. Atmospheric and Oceanic Optics (2010) 23: 389-395, Kaul, B. V.; Samokhvalov, I. V. http://www.springerlink.com/content/k3p2p3582674xt21/) one recovers standing interest to the related direct and inverse problems. A development of the result fo the case of n-fold scattering and polarization account as well as correspondent convergence series problem solution of the Kolmogorov equation will be published in nearest future.

math-ph↗