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Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity/ edited by Adrian Muntean, Jens D. M. Rademacher, Antonios Zagaris.
other author:	Muntean, Adrian.
Description:	XIII, 295 p. 15 illus., 13 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mechanics. -
Online resource:	https://doi.org/10.1007/978-3-319-26883-5
ISBN:	9783319268835

Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity
Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity[electronic resource] /edited by Adrian Muntean, Jens D. M. Rademacher, Antonios Zagaris. - 1st ed. 2016. - XIII, 295 p. 15 illus., 13 illus. in color.online resource. - Lecture Notes in Applied Mathematics and Mechanics,32197-6724 ;. - Lecture Notes in Applied Mathematics and Mechanics,2.

Introduction -- Continuum Limits of Discrete Models via G -Convergence -- On Evolutionary G -convergence for Gradient Systems -- Homoclinic Points of Principal Algebraic Actions.

This book is the offspring of a summer school school “Macroscopic and large scale phenomena: coarse graining, mean field limits and ergodicity”, which was held in 2012 at the University of Twente, the Netherlands. The focus lies on mathematically rigorous methods for multiscale problems of physical origins. Each of the four book chapters is based on a set of lectures delivered at the school, yet all authors have expanded and refined their contributions. Francois Golse delivers a chapter on the dynamics of large particle systems in the mean field limit and surveys the most significant tools and methods to establish such limits with mathematical rigor. Golse discusses in depth a variety of examples, including Vlasov--Poisson and Vlasov--Maxwell systems. Lucia Scardia focuses on the rigorous derivation of macroscopic models using $\Gamma$-convergence, a more recent variational method, which has proved very powerful for problems in material science. Scardia illustrates this by various basic examples and a more advanced case study from dislocation theory. Alexander Mielke's contribution focuses on the multiscale modeling and rigorous analysis of generalized gradient systems through the new concept of evolutionary $\Gamma$-convergence. Numerous evocative examples are given, e.g., relating to periodic homogenization and the passage from viscous to dry friction. Martin Göll and Evgeny Verbitskiy conclude this volume, taking a dynamical systems and ergodic theory viewpoint. They review recent developments in the study of homoclinic points for certain discrete dynamical systems, relating to particle systems via ergodic properties of lattices configurations.

ISBN: 9783319268835

Standard No.: 10.1007/978-3-319-26883-5doiSubjects--Topical Terms:

527684
Mechanics.

LC Class. No.: TA349-359

Dewey Class. No.: 531

Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity
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