Showing papers by "David A. Kessler published in 1985"
TL;DR: In this paper, the authors construct a theory of velocity selection and tip stability for dendritic growth in the local evolution model, and they show that the growth rate of Dendritic patterns is determined by a nonlinear solvability condition for a translating finger.
Abstract: We construct a theory of velocity selection and tip stability for dendritic growth in the local evolution model. We show that the growth rate of dendritic patterns is determined by a nonlinear solvability condition for a translating finger. The sidebranching instability is related to a single discrete oscillatory mode about the selected velocity solution, and the existence of a critical anisotropy is shown to be due to the zero crossing of its growth rate. The marginal-stability hypothesis cannot predict the correct dynamics of this model system. We give heuristic arguments that the same ideas will apply to dendritic growth in the full diffusion system.
62 citations
TL;DR: This work presents a new stability analysis which demonstrates stability and resolves the aforementioned conflict, and describes how this lends support to a new paradigm governing interfacial pattern-forming systems, that of ``microscopic solvability.
Abstract: The finger of fluid formed during the displacement of a more viscous fluid is a well-known example of nonequilibrium pattern formation. Previous efforts claimed that the steady-state solution discovered by Saffman and Taylor was linearly unstable, in contradiction with experimental observations. In this work, we present a new stability analysis which demonstrates stability and resolves the aforementioned conflict. We describe how this lends support to a new paradigm governing interfacial pattern-forming systems, that of ``microscopic solvability.''
47 citations
TL;DR: In this article, a study of various types of critical behavior and continuum limits of ( π 2 ) 3 3 at N = ∞ is presented with special emphasis on the BMB phenomenon.
38 citations
TL;DR: In this article, it was shown that the N = ∞ phase diagram of latticized (ϕ2)33 with only nearest-neighbor interactions has the same structure as the N 2 3 + ϵ 3 phase diagram with a sharp momentum cutoff.
14 citations