Towards a universal theory for natural patterns
type: Item
instance of: scholarly article
title: Towards a universal theory for natural patterns
zbMATH Open document ID: 0812.45008
DOI: 10.1016/0167-2789(94)90199-6
published in: Physica D
publication date: 1995-05-22T00:00:00Z
review text: An attempt is made to find a macroscopic description of patterns that both unifies and simplifies classes of externally stressed, dissipative, pattern forming systems, such as convecting fluids, liquid crystals, wideband lasers, that are seemingly unrelated at the microscopic level. It is based on the construction of an order parameter equation which provides a controlled approximation of the original microscopic field in the limit of large aspect ratios. The equation is in a definite sense a regularization of the Cross-Newell phase diffusion equation. The order parameter is a real variable, but its equation involves a functional corresponding to its local amplitude. Numerical comparisons between solutions of the original equation and the regularized one are carried out.
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 76R50
Mathematics Subject Classification ID: 78A60
Mathematics Subject Classification ID: 82D30
Mathematics Subject Classification ID: 00A71
zbMATH DE Number: 710203
zbMATH Keywords: almost periodic patterns
zbMATH Keywords: numerical comparisons
zbMATH Keywords: pattern forming systems
zbMATH Keywords: convecting fluids
zbMATH Keywords: liquid crystals
zbMATH Keywords: wideband lasers
zbMATH Keywords: Cross-Newell phase diffusion equation
zbMATH Keywords: order parameter
author: T. Passot
author: Alan C. Newell
MaRDI profile type: Publication
full work available at URL: 0167-2789(94)90199-6
OpenAlex ID: W2098399303
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description: scientific article; zbMATH DE number 710203