Towards a universal theory for natural patterns
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.
scientific article; zbMATH DE number 710203
scientific article