TY - JOUR
T1 - Rapid growth and critical behaviour in phase field models of solidification
AU - Glasner, Karl
PY - 2001
Y1 - 2001
N2 - Rapid solidification fronts are studied using a phase field model. Unlike slow moving solutions which approximate the Mullins-Sekerka free boundary problem, different limiting behaviour is obtained for rapidly moving fronts. A time-dependent analysis is carried out for various cases and the leading order behaviour of solidification front solutions is derived to be one of several travelling wave problems. An analysis of these problems is conducted, leading to expressions for front speeds in certain limits. The dynamics leading to these travelling wave solutions is derived, and conclusions about stability are drawn. Finally, a discussion is made of the relationship to other solidification models.
AB - Rapid solidification fronts are studied using a phase field model. Unlike slow moving solutions which approximate the Mullins-Sekerka free boundary problem, different limiting behaviour is obtained for rapidly moving fronts. A time-dependent analysis is carried out for various cases and the leading order behaviour of solidification front solutions is derived to be one of several travelling wave problems. An analysis of these problems is conducted, leading to expressions for front speeds in certain limits. The dynamics leading to these travelling wave solutions is derived, and conclusions about stability are drawn. Finally, a discussion is made of the relationship to other solidification models.
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U2 - 10.1017/S0956792501004351
DO - 10.1017/S0956792501004351
M3 - Article
AN - SCOPUS:0035608336
SN - 0956-7925
VL - 12
SP - 39
EP - 56
JO - European Journal of Applied Mathematics
JF - European Journal of Applied Mathematics
IS - 1
ER -