Mathematical Methods for Hydrodynamic Limits / by Anna De Masi, Errico Presutti.

Format:

Book

Author/Creator:

De Masi, Anna, 1953- author.

Presutti, Errico, 1942- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1501.

Lecture Notes in Mathematics, 0075-8434 ; 1501

Language:

English

Subjects (All):

Distribution (Probability theory).

Statistical physics.

Probability Theory and Stochastic Processes.

Complex Systems.

Statistical Physics and Dynamical Systems.

Local Subjects:

Probability Theory and Stochastic Processes.

Complex Systems.

Statistical Physics and Dynamical Systems.

Physical Description:

1 online resource (VIII, 196 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991.

System Details:

text file PDF

Summary:

Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models. Discrete velocity Boltzmann equations, reaction diffusion equations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomena are discussed in the context of Glauber+Kawasaki evolutions and reaction diffusion equations. Although the emphasis is onthe mathematical aspects, the physical motivations are explained through theanalysis of the single models, without attempting, however to survey the entire subject of hydrodynamical limits.

Contents:

Hydrodynamic limits for independent particles

Hydrodynamics of the zero range process

Particle models for reaction-diffusion equations

Particle models for the Carleman equation

The Glauber+Kawasaki process

Hydrodynamic limits in kinetic models

Phase separation and interface dynamics

Escape from an unstable equilibrium

Estimates on the V-functions.

Other Format:

Printed edition:

ISBN:

9783540466369

Access Restriction:

Restricted for use by site license.