TY - BOOK ID - 14296036 TI - Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics PY - 2009 SN - 3540733043 3642092365 9786611871727 1281871729 3540733051 PB - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, DB - UniCat KW - Continuum mechanics. KW - Scaling laws (Statistical physics). KW - Calculus KW - Atomic Physics KW - Mathematics KW - Physics KW - Physical Sciences & Mathematics KW - Scaling laws (Statistical physics) KW - Statistical mechanics. KW - Micromechanics. KW - Mechanics of continua KW - Ratio and proportion (Statistical physics) KW - Scale invariance (Statistical physics) KW - Scaling hypothesis (Statistical physics) KW - Scaling phenomena (Statistical physics) KW - Mathematics. KW - Dynamics. KW - Ergodic theory. KW - Physics. KW - Dynamical Systems and Ergodic Theory. KW - Mathematical Methods in Physics. KW - Composite materials KW - Solid state physics KW - Microstructure KW - Elasticity KW - Mechanics, Analytic KW - Field theory (Physics) KW - Mechanics KW - Quantum statistics KW - Statistical physics KW - Thermodynamics KW - Physical laws KW - Ranking and selection (Statistics) KW - Differentiable dynamical systems. KW - Mathematical physics. KW - Physical mathematics KW - Differential dynamical systems KW - Dynamical systems, Differentiable KW - Dynamics, Differentiable KW - Differential equations KW - Global analysis (Mathematics) KW - Topological dynamics KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics KW - Ergodic transformations KW - Continuous groups KW - Mathematical physics KW - Measure theory KW - Transformations (Mathematics) KW - Dynamical systems KW - Kinetics KW - Force and energy KW - Statics UR - https://www.unicat.be/uniCat?func=search&query=sysid:14296036 AB - 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. ER -