On a certain solution of the Einstein-Maxwell equations

A connection is established between a certain exterior solution of the Einstein-Maxwell equations and an interior cylindrically symmetric stationary solution found earlier by one of the authors.     

Numerical solution of the Zakharov equations

A new algorithm for the numerical solution of the Zakharov equations is presented. This algorithm is explicit and it is second-order accurate. The convergence of the algorithm is demonstrated by numerically solving the Zakharov equations for several test cases.     

Numerical solution of fractional differential equations by using fractional B-spline

In this paper, we present fractional B-spline collocation method for the numerical solution of fractional differential equations. We consider this method for solving linear fractional differential equations which involve Caputo-type fractional derivatives. The numerical results demonstrate that the method is efficient and quite accurate and it requires relatively less computational work. For this reason one can conclude that this method has advantage on other methods and hence demonstrates the importance of this work.     

On Bose-Einstein condensation in any dimension

A general property of an ideal Bose gas as temperature tends to zero and when conditions of degeneracy are satisfied is to have an arbitrarily large population in the groud state (or in its neighborhood); thus, condensation occurs in any dimension D but for D ≤ 2 there is no critical temperature. Some astrophysical consequences, as well as the temperature-dependent mass case, are discussed.     

Theory of the double heterostructure laser: I. Numerical solution of the charge transport equations

As a first stage in self-consistent calculations of the optical and electrical properties of the double heterostructure laser, a numerical integration procedure has been developed for the solution of the charge transport equations. The procedure is capable of integrating the equations for a range of device parameters without excessive demands upon computing facilities. The calculated distributions of electrons and holes across the device reveal the inadequacies of analytical solutions to approximate forms of the equations. It is found to be essential to a proper treatment of the transport problem to include the variation of the electric field by way of Poisson's equations. The retention of Poisson's equation in the scheme of transport equations introduces difficulties in an integration routine. It is these difficulties that are successfully overcome by the procedure described in this paper.     

New approach to solution of photorefractive transport equations

In our work we propose a novel method of analysis of photorefractive transport equations. The method based on a perturbative approach can be used in the case of two wave mixing and four wave mixing geometry, i.e. for the samples illuminated by interference patterns. Presented approach can be employed for a broad range of material and experimental parameters, particularly for arbitrary depth of light modulation pattern. The approximate analytical solution is compared with results of numerical calculations and a good agreement practically in every case was found. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Šwinoujście, Poland     

Numerical solution of differential-algebraic equations in mechanical systems simulation

The numerical solution of the differential-algebraic equations of motion of mechanical systems offers many computational challenges. In this paper we describe progress which has been made in understanding the formulation of the equations of motion from the viewpoint of numerical stability, and outline some of the difficulties which must be resolved for efficient and reliable numerical methods in real-time simulation of mechanical systems.     

Higher spin gauge theories in any dimension

Some general properties of higher spin gauge theories are summarized, with the emphasize on the nonlinear theories in any dimension. To cite this article: M.A. Vasiliev, C. R. Physique 5 (2004).

Résumé

Des propriétés générales des théories de jauge de grands spins sont présentées, en insistant particulièrement sur les théories non-linéaires en dimensions diverses. Pour citer cet article : M.A. Vasiliev, C. R. Physique 5 (2004).     

Numerical solution of differential equations with colored noise

Using the general theory of numerical integration of stochastic differential equations, a constructive approach to numerical methods for a system with colored noise is proposed. Efficient methods up to the 5/2 strong order and up to the third weak order, including Runge-Kutta and implicit schemes, are presented. The algorithms are tested on the Kubo oscillator.     

A solution of the Maxwell equations for any static,axisymmetric vacuum space-time

We study Maxwell's equations in a static, axisymmetric vacuum space-time. For any such background metric a solution is found, which far from all masses goes over into a homogeneous magnetic field parallel to the axis of symmetry.     

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采用高密度等离子体电子传导模型,计算出了一整套适用于模拟强磁场下任意混合材料中局部电离和局部简并的等离子体中的输运参数,获得的参数在很宽的等离子体温度和密度范围内有合理的精度,可广泛应用于Z箍缩等离子体、激光聚变和磁约束聚变的模拟。     

Numerical solution of the radiation transport equation in disk geometry

We describe an efficient numerical method for solving the problem of radiation transport in a dusty medium with two dimensional (2-D) disk geometry. It is a generalization of the one-dimensional quasi-diffusion method in which the transport equation is cast in diffusion form and then solved as a boundary value problem. The method should be applicable to a variety of astronomical sources, the dynamics of which are angular-momentum dominated and hence not accurately treated by spherical geometry, e.g. protoplanetary nebulae, circumstellar disks, interstellar molecular clouds, accretion disks, and disk galaxies. The computational procedure and practical considerations for implementing the method are described in detail. To illustrate the effects of 2-D radiation transport, we compare some model results (dust temperature distributions and i.r. flux spectra) for externally heated, interstellar dust clouds with spherically symmetric and disk geometry.     

Application of a singular perturbation expansion to the solution of certain Fokker-Planck equations

We show that a singular perturbation expansion for the solution of a parabolic equation can be applied to some Fokker-Planck equations arising in the analysis of the effects of noise on laser operations. A generalization to the approximate solution of the Smoluchowski equation, when diffusion is a small effect, is given.     

Numerical solution of lattice Schwinger-Dyson equations in the large-N limit

In this article, I establish the general leading large-N form of the Fokker-Planck operator for lattice gauge theories. In this formalism, the lattice Schwinger-Dyson equations appear naturally as the statement of minimization of the effective-Fokker-Planck potential. A numerical procedure is proposed that consists in minimizing a suitably truncated piece of this potential, together with a constraint. For a simple model, I show that this leads to much more accurate results than to attempt to naively solve a set of truncated Schwinger-Dyson equations, which, as I point out, do not have a standard weak coupling expansion.     

任意维固体的热力学性质的研究

精确地计算了n维固体的热力学函数、热容,讨论了极端高、低温近似时的结果;并将不同维数的热力学性质统一地由一组公式表达了出来.     

Entanglement entropy of fermions in any dimension and the Widom conjecture

We show that entanglement entropy of free fermions scales faster than area law, as opposed to the scaling L(d-1) for the harmonic lattice, for example. We also suggest and provide evidence in support of an explicit formula for the entanglement entropy of free fermions in any dimension d, S approximately c(deltagamma, deltaomega)L(d-1) logL as the size of a subsystem L-->infinity, where deltagamma is the Fermi surface and is the boundary of the region in real space. The expression for the constant c(deltagamma, deltaomega) is based on a conjecture due to Widom. We prove that a similar expression holds for the particle number fluctuations and use it to prove a two sided estimate on the entropy S.