Related papers: Numerically Analytical Methods of Solution of the …
A general algorithm for calculating the reflection and refraction of nonuniform plane waves from an arbitrarily oriented and charged planar interface between two lossy isotropic media is proposed based on the decomposition of the complex…
This article is the second in a series of two papers concerning the mathematical study of a boundary integral equation of the second kind that describes the interaction of $N$ dielectric spherical particles undergoing mutual polarisation.…
The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at relatively small angle with respect to the…
We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm…
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media…
This paper analyzes the nonlinear correspondence between the reflectivity profile (model) and the plane wave impulse response at the boundary (data) for a three-dimensional half space consisting of a sequence of homogeneous horizontal…
Solving crystal structures from kinematical X-ray or electron diffraction patterns of single crystals requires many more diffracted beams to be recorded than there are atoms in the structure, since the phases of the structure factors can…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
This paper presents an analytical formulation for correcting the diffraction associated to the second harmonic of an acoustic wave, more compact than that usually used. This new formulation, resulting from an approximation of the correction…
Diffraction tomography is a noninvasive technique that estimates the refractive indices of unknown objects and involves an inverse-scattering problem governed by the wave equation. Recent works have shown the benefit of nonlinear models of…
A 2D problem of acoustic wave scattering by a segment bearing impedance boundary conditions is considered. In the current paper (the first part of a series of two) some preliminary steps are made, namely, the diffraction problem is reduced…
A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the…
The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are…
A method is presented to investigate diffraction of an electromagnetic plane wave by an infinitely thin infinitely conducting circular cylinder with longitudinal slots. It is based on the use of the combined boundary conditions method that…
We present two complementary models to study stationary nonlinear solutions in one-dimensional plasmonic slot waveguides made of a finite-thickness nonlinear dielectric core surrounded by metal regions. The considered nonlinearity is of…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
This paper concerns with nonuniform sampling and interpolation methods combined with variational models for the solution of a generalized image inpainting problem and the restoration of digital signals. In particular, we discuss the problem…
A great deal of theoretical and experimental efforts have been devoted in the last decades to the study of long-wavelength photodetection mechanisms in field-effect transistors hosting two-dimensional (2D) electron systems. A particularly…