Linear stability of directional solidification cells

David A. Kessler, Herbert Levine

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We formulate the problem of finding the stability spectrum of the cellular pattern seen in directional solidification. This leads to a nonlinear eigenvalue problem for an integro-differential operator. We solve this problem numerically and compare our results to those obtained by linearizing the eigenvalue problem by employing the quasistatic approximation. Contrary to some recent claims, we find no evidence for a Hopf bifurcation to a dendritic pattern.

Original languageEnglish
Pages (from-to)3197-3205
Number of pages9
JournalPhysical Review A
Issue number6
StatePublished - 1990
Externally publishedYes


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