Titlebook: Macroscopic and Large Scale Phenomena: Coarse Graining, Mean Field Limits and Ergodicity; Adrian Muntean,Jens Rademacher,Antonios Zagaris

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Lecture Notes in Applied Mathematics and Mechanicshttp://image.papertrans.cn/m/image/621098.jpg

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https://doi.org/10.1007/978-3-319-26883-5Macroscopic and Large Scale Phenomena; Coarse Graining; Mean Field Limits; Ergodicity; Particle Systems;

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Continuum Limits of Discrete Models via ,-Convergence,nce. The focus of this contribution is on one-dimensional chains of particles, and the starting point is the interaction energy of the system. The nature of the interaction depends on the application and we will consider the case of convex and non convex potentials and both short and long-range interactions.

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Homoclinic Points of Principal Algebraic Actions,ummable homoclinic points were successfully used in the computation of entropy and in the study of probabilistic properties of dynamical systems, e.g., Central Limit Theorems. Moreover, homoclinic points allow one to construct coding maps which link certain particle systems to algebraic dynamical systems.

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On Evolutionary ,-Convergence for Gradient Systems,tic, and rate-independent systems as well as the passage from classical gradient to rate-independent systems. Various examples, such as periodic homogenization, are used to illustrate the abstract concepts and results.