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Physica D 146 (2000) 328340 Dual fronts in a phase field model

Summary: Physica D 146 (2000) 328­340
Dual fronts in a phase field model
Karl Glasnera,, Robert Almgrenb
a Department of Mathematics, University of Utah, 155 S. 1400 E., Salt Lake City, UT 84112-0090, USA
b Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA
Received 15 February 1999; received in revised form 17 July 2000; accepted 25 July 2000
Communicated by C.K.R.T. Jones
We study a dual front behavior observed in a reaction­diffusion system arising initially in the context of phase field models.
A precursor front propagates into a stable phase, generating a metastable "intermediate phase". This intermediate phase then
decays via an oscillating front, producing a periodic structure which later coarsens. Unlike previously studied models in
which dual fronts appear, the appearance of the split front is controlled not by an interchange of wave speeds, but by the
existence of the precursor wave. By means of an expansion in small thermal diffusivity, we argue that this behavior is generic.
© 2000 Elsevier Science B.V. All rights reserved.
Keywords: Dual front; Intermediate phase; Reaction­diffusion system
1. Introduction
An important element in the study of pattern formation is the propagation of fronts by means of which the system
moves from one state to another. For example, if the system is initially prepared in a uniform stationary state B
(stable or unstable), then we would write B A to denote a front advancing into the B state, leaving a (presumably
stable) state A in its wake. The speed of advance, vAB, is determined by the properties of the states A and B, and


Source: Almgren, Robert F. - Courant Institute of Mathematical Sciences, New York University
Glasner, Karl B. - Department of Mathematics, University of Arizona


Collections: Mathematics; Physics