A model of the neutral transport in tokamaks has been developed suitable for a one-dimensional transport code, TASK/TX. The model consists of the one-dimensional diffusion equations for slow, thermal and halo neutrals, which are simultaneously solved together with two-fluid equations and Maxwell’s equation. The behavior of the slow neutrals is easily modelled by a one-dimensional diffusion equa...

This paper offers a simple macroscopic approach to the question of the slip boundary condition to be imposed upon the tangential component of the fluid velocity at a solid boundary. Plausible reasons are advanced for believing that it is the energy equation rather than the momentum equation that determines the correct fluid-mechanical boundary condition. The scheme resulting therefrom furnishes...

The van Deemter equation and moment equations were used for analyzing the flow rate dependence of HETP experimentally measured in order to clarify chromatographic behavior from the kinetic points of view in columns packed with C18-silica monolith and C18-core-shell particles under RPLC conditions. They provided some information about molecular diffusion, eddy diffusion, and mass transfer kineti...

An integro-differential equation on a tree graph is used to model the time evolution and spatial distribution of a population of organisms in a river network. Individual organisms become mobile at a constant rate, and disperse according to an advection-diffusion process with coefficients that are constant on the edges of the graph. Appropriate boundary conditions are imposed at the outlet and u...

Self similar solutions u(x,t) = f(x//t) of the one-dimensional porousmedium equation are studied in this paper. These solutions emerge frominitial values that consist of two constant states: one non-positive forx < 0 and one non-negative for x > 0. With a diffusivity of the form|u| , we consider for m > 0 sign change solutions and for m e (-1,0]non-negative solutions. Th...

In this work we present an iterative algorithm for solving a parameter identification problem relative to a system of diffusion, convection and reaction equations. The parameters to estimate are the retardation factors, diffusivity, reaction and transport coefficients relative to a model of pollutant transport with chemical reaction. The proposed method solves the nonlinear least squares proble...

A nonlinear diffusion based image denoising technique is introduced in this paper. The proposed PDE denoising and restoration scheme is based on a novel diffusivity function that uses an automatically detected conductance parameter. A robust mathematical treatment is also provided for our anisotropic diffusion model. We demonstrate that edge-stopping function model is properly chosen, explainin...

A new method for mapping diffusivity profiles in tissue is presented. The Bloch-Torrey equation is modified to include a diffusion term with an arbitrary rank Cartesian tensor. This equation is solved to give the expression for the generalized Stejskal-Tanner formula quantifying diffusive attenuation in complicated geometries. This makes it possible to calculate the components of higher-rank te...

Exact solutions are presented for Burgers’ equation in a fmite layer connected to an underlying semi-infinite medium of different conductivity and diffusivity. A constant-flux boundary condition is assumed at the surface. This has direct application to steady rainfall on layered field soils. At large times, a travelling wave profile develops in the deep layer and the concentration in the upper ...

The drag on a cylindrical particle moving in a thin sheet of viscous fluid is calculated. It is supposed that the sheet is embedded in fluid of much lower viscosity. A finite steady drag is obtained, which depends logarithmically on the ratio of the viscosities. The Einstein relation is used to determine the diffusion coefficient for Brownian motion of the particle, with application to the move...