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.
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Mục lục
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.Giới thiệu về tác giả
Errico Presutti is professor of classical mechanics at the Department of Mathematics of the University of Roma Tor Vergata.
Ngôn ngữ Anh ● định dạng PDF ● Trang 470 ● ISBN 9783540733058 ● Kích thước tập tin 4.9 MB ● Nhà xuất bản Springer Berlin ● Thành phố Heidelberg ● Quốc gia DE ● Được phát hành 2008 ● Có thể tải xuống 24 tháng ● Tiền tệ EUR ● TÔI 2163488 ● Sao chép bảo vệ DRM xã hội
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