Search results for "Diffusion equation"

A velocity–diffusion method for a Lotka–Volterra system with nonlinear cross and self-diffusion

2009

The aim of this paper is to introduce a deterministic particle method for the solution of two strongly coupled reaction-diffusion equations. In these equations the diffusion is nonlinear because we consider the cross and self-diffusion effects. The reaction terms on which we focus are of the Lotka-Volterra type. Our treatment of the diffusion terms is a generalization of the idea, introduced in [P. Degond, F.-J. Mustieles, A deterministic approximation of diffusion equations using particles, SIAM J. Sci. Stat. Comput. 11 (1990) 293-310] for the linear diffusion, of interpreting Fick's law in a deterministic way as a prescription on the particle velocity. Time discretization is based on the …

Well-posedness of the boundary layer equations

2004

We consider the mild solutions of the Prandtl equations on the half space. Requiring analyticity only with respect to the tangential variable, we prove the short time existence and the uniqueness of the solution in the proper function space. Theproof is achieved applying the abstract Cauchy--Kowalewski theorem to the boundary layer equations once the convection-diffusion operator is explicitly inverted. This improves the result of [M. Sammartino and R. E. Caflisch, Comm. Math. Phys., 192 (1998), pp. 433--461], as we do not require analyticity of the data with respect to the normal variable.

Parallel Schwarz methods for convection-dominated semilinear diffusion problems

2002

AbstractParallel two-level Schwarz methods are proposed for the numerical solution of convection-diffusion problems, with the emphasis on convection-dominated problems. Two variants of the methodology are investigated. They differ from each other by the type of boundary conditions (Dirichlet- or Neumann-type) posed on a part of the second-level subdomain interfaces. Convergence properties of the two-level Schwarz methods are experimentally compared with those of a variant of the standard multi-domain Schwarz alternating method. Numerical experiments performed on a distributed memory multiprocessor computer illustrate parallel efficiency of the methods.

Existence and uniqueness for the Prandtl equations

2001

International audience; Under the hypothesis of analyticity of the data with respect to the tangential variable we prove the existence and uniqueness of the mild solution of Prandtl boundary layer equation. This can be considered an improvement of the results of [8] as we do not require analyticity with respect to the normal variable. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

An algorithmic construction of entropies in higher-order nonlinear PDEs

2006

A new approach to the construction of entropies and entropy productions for a large class of nonlinear evolutionary PDEs of even order in one space dimension is presented. The task of proving entropy dissipation is reformulated as a decision problem for polynomial systems. The method is successfully applied to the porous medium equation, the thin film equation and the quantum drift–diffusion model. In all cases, an infinite number of entropy functionals together with the associated entropy productions is derived. Our technique can be extended to higher-order entropies, containing derivatives of the solution, and to several space dimensions. Furthermore, logarithmic Sobolev inequalities can …

An exact thermodynamical model of power-law temperature time scaling

2016

In this paper a physical model for the anomalous temperature time evolution (decay) observed in complex thermodynamical system in presence of uniform heat source is provided. Measures involving temperatures T with power-law variation in time as T(t)∝tβ with β∈R shows a different evolution of the temperature time rate T(t) with respect to the temperature time-dependence T(t). Indeed the temperature evolution is a power-law increasing function whereas the temperature time rate is a power-law decreasing function of time. Such a behavior may be captured by a physical model that allows for a fast thermal energy diffusion close to the insulated location but must offer more resistance to the therm…

A coupled map as a model of the dynamics of the magnetotail current sheet

2001

Abstract A magnetic field model of the magnetotail current sheet in the form of a coupled-map lattice (CML) is presented. It is continuously driven (“running”) and based on the MHD diffusion equation. Solar wind vBS data (solar wind speed multiplied by the southward component of IMF) are used for driving the model, and it is shown to exhibit perturbations (avalanches) with power-law scalings in their distributions of duration and size. Such distributions may indicate self-organized critical (SOC) behavior. Furthermore, it is shown that the power spectra of the model outputs are of bicolor power-law form with different slopes for high and low frequencies. Although the “running” model gives p…

Flux-limited diffusion equation

2013

A coupled-map model for the magnetotail current sheet

1999

A magnetic field model of the magnetotail current sheet in the form of a coupled-map lattice (CML) is presented. It is a continuously driven and based on the MHD diffusion equation. Solar wind vBs data (solar wind speed multiplied by the southward component of IMF) are used for driving the model, and it is shown to exhibit perturbations (avalanches) with power-law scalings in their distributions of duration and size. Such distributions may indicate self-organized critical (SOC) behavior. Furthermore, it is shown that the power spectra of the model outputs are of bicolor power-law form with different slopes for high and low frequencies. The model parameters determine the frequency of the bre…

Influence of a Magnetic Field on Liquid Metal Free Convection in an Internally Heated Cubic Enclosure

2002

The buoyancy‐driven magnetohydrodynamic flow in a cubic enclosure was investigated by three‐dimensional numerical simulation. The enclosure was volumetrically heated by a uniform power density and cooled along two opposite vertical walls, all remaining walls being adiabatic. A uniform magnetic field was applied orthogonally to the gravity vector and to the temperature gradient. The Prandtl number was 0.0321 (characteristic of Pb–17Li at 300°C), the Rayleigh number was 104, and the Hartmann number was made to vary between 0 and 2×103. The steady‐state Navier–Stokes equations, in conjunction with a scalar transport equation for the fluid's enthalpy and with the Poisson equation for the electr…