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Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics / by Errico Presutti; edited by W. Beiglböck, J.-P. Eckmann, H. Grosse, M. Loss, S. Smirnov, L. Takhtajan, J. Yngvason

Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Theoretical and Mathematical Physics | SpringerLink BücherPublisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Description: Online-Ressource (digital)ISBN:
  • 9783540733058
Subject(s): Additional physical formats: 9783540733041 | Buchausg. u.d.T.: Scaling limits in statistical mechanics and microstructures in continuum mechanics. Berlin : Springer, 2009. XVI, 467 S. | Erscheint auch als: Scaling limits in statistical mechanics and microstructures in continuum mechanics. Druck-Ausgabe Softcover version of orig. hardcover 1. ed. 2009. Berlin [u.a.] : Springer, 2009. XVI, 467 S.DDC classification:
  • 530.13
  • 515.39
  • 515.48
  • 530.13 531
MSC: MSC: *82-02 | 82B05 | 82B20 | 82B24 | 28D99 | 28D05 | 37A35 | 60F10 | 82B26RVK: RVK: UG 3100LOC classification:
  • QA313
  • QC174.85.S34
DOI: DOI: 10.1007/978-3-540-73305-8Online resources:
Contents:
pt. 1. Statistical mechanics of ising systems -- pt. 2. Mesoscopic theory, non-local functionals -- pt. 3. Phase transitions in systems with Kac potentials -- pt. 4. Appendices.
Summary: Statistical Mechanics of Ising systems -- Thermodynamic limit in the Ising model -- The phase diagram of Ising systems -- Mean field, Kac potentials and the Lebowitz–Penrose limit -- Stochastic Dynamics -- Mesoscopic Theory, non-local functionals -- Non-local, free energy functionals -- Surface tension, Gamma convergence, Wulff shape -- One dimensional interfaces -- Phase transitions in systems with Kac potentials -- 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.Summary: 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.PPN: PPN: 1647588618Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
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