Lecture Notes in Applied Mathematics and Mechanics

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

Editors: Muntean, Adrian, Rademacher, Jens, Zagaris, Antonios (Eds.)

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  • Latest 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
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Softcover $129.99
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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.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $99.00
price for USA in USD
  • ISBN 978-3-319-26883-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.99
price for USA in USD
  • ISBN 978-3-319-26882-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

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
Series Volume
3
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-26883-5
DOI
10.1007/978-3-319-26883-5
Softcover ISBN
978-3-319-26882-8
Series ISSN
2197-6724
Edition Number
1
Number of Pages
XIII, 295
Number of Illustrations
2 b/w illustrations, 13 illustrations in colour
Topics