196 citations · 214 across the 2 of their papers we have counts for
4 papers
Equilibrium solutions of the shallow water equations
Peter B. Weichman, Dean M. Petrich
A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contai…
Theoretical Model for Faraday Waves with Multiple-Frequency Forcing
Ron Lifshitz, Dean M. Petrich
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equa…
Interface Proliferation and the Growth of Labyrinths in a Reaction-Diffusion System
Raymond E. Goldstein, David J. Muraki, Dean M. Petrich
In the bistable regime of the FitzHugh-Nagumo model of reaction-diffusion systems, spatially homogeneous patterns may be nonlinearly unstable to the formation of compact ``localize…
A Nonlocal Contour Dynamics Model for Chemical Front Motion
Dean M. Petrich, Raymond E. Goldstein
Pattern formation exhibited by a two-dimensional reaction-diffusion system in the fast inhibitor limit is considered from the point of view of interface motion. A dissipative nonlo…