Diffusion Equation and classical Schrödinger Equation have been derived from Brownian motion and the quantum limits have been derived, which transform the classical Schrödinger equation in to usual quantum equation without any formal analytic continuation and waveparticle duality. These quantum limits have been shown to lead to Heisenberg uncertainty relation between position and momentum of th...

The understanding of thermal conductance in both classical and quantum mechanical systems is one of the fundamental problems of non-equilibrium statistical mechanics. A particular aspect that has attracted much interest is the observation that autonomous translation invariant systems in dimensions one and two exhibit anomalously large conductivity. The canonical example here is a chain of anhar...

2 Macroscopic modeling 5 2.1 Concentration measures, mixture velocity and diffusion fluxes . . . . . . . . 5 2.2 Species transport equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Fick model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Limits of Fick model: osmotic diffusion, reverse diffusion and diffusion barrier 8 2.5 Maxwell-Stefan mo...

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.

Abstract. In earlier papers Saxena et al. (2002, 2003) derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which extended the work of Haubold and Mathai (2000). The object of the present paper is to investigate the solution of a unified form of fractional kinetic equation in which the free term contains any integrable function f(t),...

After the successful applications of the combination of the method of fundamental solutions (MFS), the method of particular solutions (MPS), and the eigenfunctions expansion method (EEM) to solve 2D homogeneous and nonhomogeneous diffusion equations by Young et al. (Young et al., Numer Meth Part Differ Equat 22 (2006), 1173), this article intends to extend the same fundamental concepts to calcu...

In this paper we study an optimal control problem for a singular diffusion equation associated with total variation energy. The singular diffusion equation is derived as an Allen-Cahn type equation, and then the observing optimal control problem corresponds to a temperature control problem in the solid-liquid phase transition. We show the existence of an optimal control for our singular diffusi...

Mass diffusion in multicomponent gas mixtures is governed by a coupled system of linear equations for the diffusive mass ̄uxes in terms of thermodynamic driving forces, known as the generalized Stefan±Maxwell equation. In computations of mass diffusion in multicomponent gas mixtures, this coupling between the different components results in considerable computational overhead. Consequently, sim...

A new modified diffusi on coefficient (MDC) technique for solv ing conve ction diffusion equation is proposed. The Galerkin finite-element discretization process is applied on the modified equation rather than the original one. For a class of one-dimensional convec-tion–diffusion equations, we derive the modi fied diffusion coefficient analytically as a function of the equation coefficients and...