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

  • Adrian Muntean
  • Jens Rademacher
  • Antonios Zagaris

Part of the Lecture Notes in Applied Mathematics and Mechanics book series (LAMM, volume 3)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Martin Göll, Evgeny Verbitskiy
    Pages 251-292
  3. Back Matter
    Pages 293-295

About this book

Introduction

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.

Keywords

Macroscopic and Large Scale Phenomena Coarse Graining Mean Field Limits Ergodicity Particle Systems Multiscale Analysis

Editors and affiliations

  • Adrian Muntean
    • 1
  • Jens Rademacher
    • 2
  • Antonios Zagaris
    • 3
  1. 1.Eindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Fachbereich Mathematik und InformatikUniversitat BremenBremenGermany
  3. 3.Faculteit Elektrotech, Wiskunde en InfoUniversiteit TwenteENSCHEDEThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-26883-5
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-26882-8
  • Online ISBN 978-3-319-26883-5
  • Series Print ISSN 2197-6724
  • Series Online ISSN 2197-6732
  • Buy this book on publisher's site
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