Through a combination of asymptotic and numerical approaches we investigate bifurcation and pattern formation for a free boundary model related to a rapid crystallization of amorphous films and to the self-propagating high-temperature synthesis (solid combustion). The unifying feature of these diverse physical phenomena is the existence of a uniformly propagating wave of phase transition whose stability is controlled by the balance between the energy production at the interface and the energy dissipation into the medium. For the propagation on a two-dimensional strip with thermally insulated edges, we develop a multi-scale weakly-nonlinear analysis that results in a system of ordinary differential equations for the slowly varying amplitudes. We identify a nonlinear parameter which is responsible for the pattern selection, and utilize the amplitude system for predicting the evolving patterns. The pattern selection is confirmed by direct numerical simulations on the free boundary problem. Some numerical results on strongly nonlinear regimes are also presented.
Michael L. Frankel
1
;
Laura Kathryn Gross
2
;
Victor Roytburd
3
1
Indiana University Purdue University Indianapolis, USA
2
University of Akron, USA
3
Rensselaer Polytechnic Institute, Troy, USA
Michael L. Frankel; Laura Kathryn Gross; Victor Roytburd. Thermo-kinetically controlled pattern selection. Interfaces and free boundaries, Tome 2 (2000) no. 3, pp. 313-330. doi: 10.4171/ifb/22
@article{10_4171_ifb_22,
author = {Michael L. Frankel and Laura Kathryn Gross and Victor Roytburd},
title = {Thermo-kinetically controlled pattern selection},
journal = {Interfaces and free boundaries},
pages = {313--330},
year = {2000},
volume = {2},
number = {3},
doi = {10.4171/ifb/22},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/22/}
}
TY - JOUR
AU - Michael L. Frankel
AU - Laura Kathryn Gross
AU - Victor Roytburd
TI - Thermo-kinetically controlled pattern selection
JO - Interfaces and free boundaries
PY - 2000
SP - 313
EP - 330
VL - 2
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/22/
DO - 10.4171/ifb/22
ID - 10_4171_ifb_22
ER -
%0 Journal Article
%A Michael L. Frankel
%A Laura Kathryn Gross
%A Victor Roytburd
%T Thermo-kinetically controlled pattern selection
%J Interfaces and free boundaries
%D 2000
%P 313-330
%V 2
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/22/
%R 10.4171/ifb/22
%F 10_4171_ifb_22
