Overview
- research on Macroscopic and Large
- Scale Phenomena such as Coarse
- Graining, Mean Field Limits and Ergodicity
- Offspring of the summer 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
- Focusing on the modeling, multiscale analysis and continuum limits of particle systems
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Applied Mathematics and Mechanics (LAMM, volume 3)
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Table of contents (4 chapters)
Keywords
About this book
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.
Editors and Affiliations
Bibliographic Information
Book Title: Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity
Editors: Adrian Muntean, Jens Rademacher, Antonios Zagaris
Series Title: Lecture Notes in Applied Mathematics and Mechanics
DOI: https://doi.org/10.1007/978-3-319-26883-5
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-26882-8Published: 04 February 2016
eBook ISBN: 978-3-319-26883-5Published: 28 January 2016
Series ISSN: 2197-6724
Series E-ISSN: 2197-6732
Edition Number: 1
Number of Pages: XIII, 295
Number of Illustrations: 2 b/w illustrations, 13 illustrations in colour
Topics: Solid Mechanics, Applications of Mathematics, Mathematical and Computational Engineering, Dynamical Systems and Ergodic Theory