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001 978-3-319-26883-5
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020 _a9783319268835
_9978-3-319-26883-5
024 7 _a10.1007/978-3-319-26883-5
_2doi
050 4 _aTA349-359
072 7 _aTGMD
_2bicssc
072 7 _aSCI096000
_2bisacsh
072 7 _aTGMD
_2thema
082 0 4 _a620.105
_223
245 1 0 _aMacroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity
_h[electronic resource] /
_cedited by Adrian Muntean, Jens D. M. Rademacher, Antonios Zagaris.
250 _a1st ed. 2016.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aXIII, 295 p. 15 illus., 13 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Applied Mathematics and Mechanics,
_x2197-6732 ;
_v3
505 0 _aIntroduction -- Continuum Limits of Discrete Models via G -Convergence -- On Evolutionary G -convergence for Gradient Systems -- Homoclinic Points of Principal Algebraic Actions.
520 _aThis 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.
650 0 _aMechanics, Applied.
_93253
650 0 _aSolids.
_93750
650 0 _aMathematics.
_911584
650 0 _aEngineering mathematics.
_93254
650 0 _aEngineering—Data processing.
_931556
650 0 _aDynamical systems.
_956990
650 1 4 _aSolid Mechanics.
_931612
650 2 4 _aApplications of Mathematics.
_931558
650 2 4 _aMathematical and Computational Engineering Applications.
_931559
650 2 4 _aDynamical Systems.
_956991
700 1 _aMuntean, Adrian.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
_956992
700 1 _aRademacher, Jens D. M.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
_956993
700 1 _aZagaris, Antonios.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
_956994
710 2 _aSpringerLink (Online service)
_956995
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319268828
776 0 8 _iPrinted edition:
_z9783319268842
830 0 _aLecture Notes in Applied Mathematics and Mechanics,
_x2197-6732 ;
_v3
_956996
856 4 0 _uhttps://doi.org/10.1007/978-3-319-26883-5
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c79855
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