Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions

A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet problem of the biharmonic equation in three dimensions. A fast numerical algorithm is developed based on the constructed SKIE. Its performance is illustrated via several numerical examples.     

Lie group theory of the bessel equation of the first kind of integral order

We discuss the Bessel differential equation of the first kind of integral order and the associated functions from a Lie-group-theoretical background. All the familiar properties of the Bessel equation and functions are obtained. The analytic methodology developed in the study can easily be adapted to the study of some other special functions of mathematical physics.     

Finite difference methods for second order in space,first order in time hyperbolic systems and the linear shifted wave equation as a model problem in numerical relativity

Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems. Particular attention is paid to the case when first order derivatives that can be identified with advection terms are approximated with non-centered finite difference operators. We first derive general properties of these discrete operators, then we extend a known result on numerical stability for such systems to general order of accuracy. As an application we analyze the shifted wave equation, including the behavior of the numerical phase and group speeds at different orders of approximations. Special attention is paid to when the use of off-centered schemes improves the accuracy over the centered schemes.     

求解DNLS方程的反散射法的基本问题

对DNLS方程, 反散射法应选取k²=p为基本谱参数, 其中k为通常谱参数. 并引入一个新的谱参数及一个规范变换, 由此得到自由Jost解的规范正交系, 这就是反散射法的基本问题. 同时还得到了基于谱参数p的Marchenko方程和Zakharov-Shabat反散射方程. 关键词： DNLS方程 反散射法 自由Jost解 规范正交系     

Derivation of the linear and nonlinear non-Markov fluctuation-dissipation relations of the first kind for a dynamical model

A dynamical system consisting of a subsystem having the variablesz=(q,p) and of another dynamical system (thermostat) is considered in the nonquantum case. Using a dynamical equation, it is shown that the linear and quadratic non-Markov fluctuation-dissipation relations (FDRs) of the first kind are valid in the first nonvanishing approximation in interaction constants. Applying these FDRs, one can determine the statistical properties of the fluctuations when the form of the nonlinear phenomenological equation is known. The non-Markov FDRs of the first kind are the direct generalization (to the inertial case) of the Markov FDRs that are the consequence of detailed balance.     

The first initial-boundary value problem for the space charge stratification equation in semiconductors

The internal and external initial-boundary value problems for 3D equation ?/?t (Δu ? u) ? u = 0 are considered. The problems are posed under the Dirichlet boundary condition on a Lyapunov surface. Using the method of dynamic potentials, the theorems of the unique existence of the solution are proved.     

A new integral equation method for direct electromagnetic scattering in homogeneous media and its numerical confirmation

In this paper, we derive a new integral equation method for direct electromagnetic scattering in homogeneous media and present a numerical confirmation of the new method via a computer simulation. The new integral equation method is based on a paper written by DeSanto [1 DeSanto, J. A. 1993. A New formulation of electromagnetic scattering from rough dielectric interfaces. Journal of Electromagnetic Waves and Applications, 7: 1293–1306. [CSA][Taylor & Francis Online], [Web of Science ®] , [Google Scholar]], originally for scattering from an infinite rough surface separating homogeneous dielectric half-spaces. Here, it is applied to a bounded scatterer, which can be an ohmic conductor or a dielectric, with some simplification of the continuity conditions for the fields. The new integral equation method is developed by choosing the electric field and its normal derivative as boundary unknowns, which are not the usual boundary unknowns. The new integral equation method may provide significant computational advantages over the standard Stratton–Chu method [2 Stratton, J. A. and Chu, L. J. 1939. Diffraction theory of electromagnetic waves. Physical Review, 56: 99–107. [CSA][CROSSREF][Crossref] , [Google Scholar]] because it leads to a 50% sparse, rather than 100% dense, impedance (collocation) matrix. Our theoretical development of the new integral equation method is exact.     

A new integral equation method for direct electromagnetic scattering in homogeneous media and its numerical confirmation

In this paper, we derive a new integral equation method for direct electromagnetic scattering in homogeneous media and present a numerical confirmation of the new method via a computer simulation. The new integral equation method is based on a paper written by DeSanto [1], originally for scattering from an infinite rough surface separating homogeneous dielectric half-spaces. Here, it is applied to a bounded scatterer, which can be an ohmic conductor or a dielectric, with some simplification of the continuity conditions for the fields. The new integral equation method is developed by choosing the electric field and its normal derivative as boundary unknowns, which are not the usual boundary unknowns. The new integral equation method may provide significant computational advantages over the standard Stratton-Chu method [2] because it leads to a 50% sparse, rather than 100% dense, impedance (collocation) matrix. Our theoretical development of the new integral equation method is exact.     

Numerical solving of the track wall equation in LR115 detectors etched in direct and reverse directions

Our equation of the track wall was solved numerically by using finite difference method and computer software MATHEMATICA. This method was applied for alpha particle tracks in LR115 detector, assuming both directions of etching, from the top and bottom of the sensitive layer. The equation of the track wall etched in reverse direction was derived, and has the same form as one for direct etching, with some difference in argument of V function. We will analyse the consequences of direct and reverse etching on the shape of alpha particles tracks with energies ranging from 2 to 4 MeV in thin LR115 NTDs.     

Some canonical forms for the metric of spacetimes admitting a rational first integral of the geodesic equation

Canonical forms are obtained for the metrics of space-times admitting a surface generating Killing pair, one member of which is hypersurface orthogonal.     

Optical dielectric waveguide analysis,based on the modified finite element and integral equation methods

Efficient versions of the finite element and integral equation methods have been developed to analyse the guided (surface) modes of an arbitrary shaped optical fibre. The first approach is based on the replacement of the open waveguide by the screen guide structure with an artificial impedance wall. The integral equation is solved by the adaptive collocation technique. The methods are used to calculate the dispersion characteristics of the elliptical fibre modes and their cut-off frequencies. The results obtained are compared with those calculated by other methods.     

Algorithm for solving the anharmonic vibratiqnal-rotational problem using curvilinear vibrational coordinates and the momentum representation for rotational wave functions

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 48, No. 1, pp. 103–110, January, 1988.     

一类基于混沌映射构造Hash函数方法的碰撞缺陷

混沌动力学系统在一定的参数范围内出现混沌运动，且它所产生的混沌序列具有良好的伪随机特性.以混沌映射为基础，已有文献提出了一些构造单向散列函数的方法.对这些方法进行分析，证明它们均存在碰撞缺陷，并总结了采用混沌映射构造单向散列函数时应注意的问题. 关键词： 混沌 单向散列函数 碰撞     

Using the Galerkin method to construct an analytical solution for the integral equation of a certain diffraction problem

Grodno State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 31, No. 11, pp. 1355–1361, November, 1988.     

Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.     

Algorithm for solving the equation of radiative transfer in the frequency domain

We present an algorithm that provides a frequency-domain solution of the equation of radiative transfer (ERT) for heterogeneous media of arbitrary shape. Although an ERT is more accurate than a diffusion equation, no ERT code for the widely employed frequency-domain case has been developed to date. In this work the ERT is discretized by a combination of discrete-ordinate and finite-volume methods. Two numerical simulations are presented.