相关论文: The Diffusion Equation on a Hypersphere

We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…

In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary…

In this paper, we investigate the geometric propagation and diffraction of singularities of solutions to the wave equation on manifolds with edge singularities.

We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…

Models of diffusion in white dwarfs universally rely on the coefficients calculated by Paquette et al. (1986). We present new calculations of diffusion coefficients based on an advanced microscopic theory of dense plasmas and a numerical…

The purpose of this paper is to provide new formulas for the effective diffusion coefficient of a generalized Fick-Jacobs equation for narrow 3-dimensional channels. The generalized Fick-Jacobs equation is obtained by projecting the…

We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…

We study the problem of particles undergoing Brownian motion in an expanding sphere whose surface is an absorbing boundary for the particles. The problem is akin to that of the diffusion of impurities in a grain of polycrystalline material…

We consider the dispersion properties of tracer particles moving in non-equilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local…

Stability of a set of travelling wave solutions to the hyperbolic generalization of the convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.

We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…

The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…

Analysis of signal fluctuations of a locally fixed probe, caused by molecules diffusing under the probe, can be used to determine diffusion coefficients. Theoretical treatments so far have been limited to point-like particles or to…

We study the heat equation on a half-space or on an exterior domain with a linear dynamical boundary condition. Our main aim is to establish the rate of convergence to solutions of the Laplace equation with the same dynamical boundary…

The diffusion problem over a saddle is studied using a multi-dimensional Langevin equation. An analytical solution is derived for a quadratic potential and the probability to pass over the barrier deduced. A very simple solution is given…

Surface-active molecules supplied from a particle fixed at the water surface create a spatial gradient of the molecule concentration, resulting in Marangoni convection. Convective flow transports the molecules far from the particle,…

One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…

A quantum kinetic equation is obtained for an inhomogeneous solid having arbitrary gradient concentration and chemical potential. We find, starting from nonequilibrium statistical operator, a new equation to describe atom migration in solid…

Diffusion rates are calculated on the basis of van Hove's formula for the dynamical structure factor (DSF) related to particle scattering at mobile adsorbates. The formula is evaluated quantum mechanically using eigenfunctions obtained from…

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion…