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Field name	Details
Dewey Class	515.39
Dewey Class	515.48
Title	Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics ([Ebook]) / by Errico Presutti.
Author	Presutti, Errico
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2009.
Physical Details	XVI, 470 pages : online resource.
Series	Theoretical and mathematical physics 1864-5879
ISBN	9783540733058
Summary Note	Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.:
Contents note	Introduction -- Thermodynamic limit in the Ising model -- The phase diagram of Ising systems -- Mean field, Kac potentials and the Lebowitz-Penrose limit -- Stochastic dynamics -- Non local, free energy functional -- Surface tension, Gamma convergence, Wulff shape -- One dimensional interfaces -- Ising systems with Kac potentials -- The LMP model and the Pirogov-Sinai strategy -- Phase transitions in the LMP model -- DLR measures and the ergodic decomposition -- Appendix A: Ising model -- Appendix B: Geometric measure theory -- References -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-540-73305-8
Links to Related Works	Subject References: Continuum Mechanics . Differentiable dynamical systems . Dynamical systems and ergodic theory . Ergodic theory . Mathematical Methods in Physics . Mathematical Physics . Scaling laws (Statistical physics) . Statistical Mechanics . Authors: Presutti, Errico . Corporate Authors: SpringerLink (Online service) . Series: Theoretical and mathematical physics . Classification: 515.39 . 515.48 . 515.39 (DDC 23) .

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Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics

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