Non-self-similar behavior in the LSW theory of Ostwald ripening

Дата и время публикации : 1998-08-04T14:07:22Z

Авторы публикации и институты :
Barbara Niethammer (University of Bonn)
Robert L. Pego (University of Maryland, College Park)

Ссылка на журнал-издание: Ссылка на журнал-издание не найдена
Коментарии к cтатье: 31 pages, LaTeX2e; Revised version, to appear in J. Stat. Phys
Первичная категория: cond-mat.mtrl-sci

Все категории : cond-mat.mtrl-sci, cond-mat.stat-mech

Краткий обзор статьи: The classical Lifshitz-Slyozov-Wagner theory of domain coarsening predicts asymptotically self-similar behavior for the size distribution of a dilute system of particles that evolve by diffusional mass transfer with a common mean field. Here we consider the long-time behavior of measure-valued solutions for systems in which particle size is uniformly bounded, i.e., for initial measures of compact support. We prove that the long-time behavior of the size distribution depends sensitively on the initial distribution of the largest particles in the system. Convergence to the classically predicted smooth similarity solution is impossible if the initial distribution function is comparable to any finite power of distance to the end of the support. We give a necessary criterion for convergence to other self-similar solutions, and conditional stability theorems for some such solutions. For a dense set of initial data, convergence to any self-similar solution is impossible.

Category: Physics