We present the results of a careful numerical analysis of the stability problem for stationary needle-crystal solutions of the symmetric model of dentritic solidification. The major outcome is that such needle crystals are stable, at least on a time scale relevant to side-branching phenomena. Our study also indicates that the tip of the needle-crystal is very sensitive to external noises, thus supporting the selective amplification mecanism advocated by Langer, Barbieri and Barber on the basis of a WKB analysis.
@article{hal-00129117,
author = {Pillet, Claude-Alain},
title = {Stabilization of needle-crystals in the symmetric model of solidification},
journal = {HAL},
volume = {1992},
number = {0},
year = {1992},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00129117}
}
Pillet, Claude-Alain. Stabilization of needle-crystals in the symmetric model of solidification. HAL, Tome 1992 (1992) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129117/