{"product_id":"macroscopic-and-large-scale-phenomena-coarse-graining-mean-field-limits-and-ergodicity-von-undefined","title":"Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity","description":"\n                                \n                \u003cp\u003eThis book is the offspring of a summer school school “Macroscopic and\nlarge scale\u003c\/p\u003e\n                                \n                \n                \u003cp\u003ephenomena: coarse graining, mean field limits and ergodicity”, which was\nheld in 2012 at the University of Twente, the Netherlands. The focus lies on\nmathematically rigorous methods for multiscale problems of physical origins.\u003c\/p\u003e\n                                \n                \n                \u003cp\u003eEach of the four book chapters is based on a set of lectures delivered\nat the school, yet all authors have expanded and refined their contributions. \u003c\/p\u003e\n                                \n                \n                \u003cp\u003eFrancois Golse\ndelivers a chapter on the dynamics of large particle systems in the mean field\nlimit and surveys the most significant tools and methods to establish such\nlimits with mathematical rigor. Golse discusses in depth a variety of examples,\nincluding Vlasov--Poisson and Vlasov--Maxwell systems. \u003c\/p\u003e\n                                \n                \n                \u003cp\u003eLucia Scardia focuses\non the rigorous derivation of macroscopic models using $\\Gamma$-convergence, a\nmore recent variational method, which has proved very powerful for problems in\nmaterial science. Scardia illustrates this by various basic examples and a more\nadvanced case study from dislocation theory.\u003c\/p\u003e\n                                \n                \n                \u003cp\u003eAlexander Mielke's\ncontribution focuses on the multiscale modeling and rigorous analysis of\ngeneralized gradient systems through the new concept of evolutionary\n$\\Gamma$-convergence. Numerous evocative examples are given, e.g., relating to\nperiodic homogenization and the passage from viscous to dry friction.\u003c\/p\u003e\n                                \n                \n                \u003cp\u003eMartin Göll and Evgeny\nVerbitskiy conclude this volume, taking a dynamical systems and ergodic theory\nviewpoint. They review recent developments in the study of homoclinic points\nfor certain discrete dynamical systems, relating to particle systems via\nergodic properties of lattices configurations.\u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783319268828\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783319268828","offer_id":40604296380509,"sku":"9783319268828","price":109.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/cecaba36-e0d2-430a-ad91-758e6b61dfcb.jpg?v=1775624309","url":"https:\/\/shop.autorenwelt.de\/products\/macroscopic-and-large-scale-phenomena-coarse-graining-mean-field-limits-and-ergodicity-von-undefined","provider":"Autorenwelt Shop","version":"1.0","type":"link"}