Mesoscopic morphology and scaling law of stationary interfacial patterns for reaction diffusion systems. (English) Zbl 0812.35009

Nishiura, Yasumasa

Tatra Mt. Math. Publ. 4, 169-173 (1994).

Summary: A scaling law for stationary interfacial patterns is considered. When there is a micro-scopic constraint in the system like block copolymer, the resulting steady states display a variety of patterns from lamellar to labyrinthine ones. The goal is to determine the characteristic domain size in terms of interfacial thickness and the nonlocal interaction length. The result is consistent with the experiments.

MSC:

35B25	Singular perturbations in context of PDEs
35B35	Stability in context of PDEs
35K57	Reaction-diffusion equations
82D60	Statistical mechanics of polymers

Keywords:

scaling law; interfacial patterns; characteristic domain size