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Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics (Theoretical and Mathematical Physics)

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Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics (Theoretical and Mathematical Physics) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

Focusing on the links connecting statistical and continuum mechanics, this book introduces both theories before leading on to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.

About the Author

Errico Presutti is professor of classical mechanics at the Department of Mathematics of the University of Roma Tor Vergata.

Table of Contents

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.

Product Details

ISBN:
9783642092367
Author:
Presutti, Errico
Publisher:
Springer
Subject:
Differential Equations
Subject:
Gamma convergence
Subject:
Ising models
Subject:
Kac potentials
Subject:
LMP model
Subject:
MSC (2000): 82B26, 49Q20, 74A15
Subject:
Statistical mechanics
Subject:
generalized Pirogov-Sinai theory
Subject:
non local free energy functionals
Subject:
phase transitions in the continuum
Subject:
probabilistic methods
Subject:
Dynamical Systems and Ergodic Theory
Subject:
mathematical methods in physics
Subject:
Mathematics-Differential Equations
Subject:
Mathematical Analysis
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2009
Series:
Theoretical and Mathematical Physics
Publication Date:
20101119
Binding:
TRADE PAPER
Language:
English
Pages:
486
Dimensions:
235 x 155 mm 731 gr

Related Subjects

Reference » Science Reference » Technology
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Physics » Math

Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics (Theoretical and Mathematical Physics) New Trade Paper
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Product details 486 pages Springer - English 9783642092367 Reviews:
"Synopsis" by , Focusing on the links connecting statistical and continuum mechanics, this book introduces both theories before leading on to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.
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