Asymptotic expansion of the full nonlocal solidification problem

Wim Van Saarloos, John D. Weeks, Gabriel Kotliar

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We analyze the shape z(x) of two-dimensional needle crystals far away from the tip and find that in general the deviation z away from the Ivantsov solution has an asymptotic behavior of the form zx-, with a noninteger exponent. For the asymptotic behavior, the regime where the Péclet number p is less than (1/2) and the one where p is larger than (1/2) are distinct. For p>(1/2), the exponent is calculated explicitly, while for p<(1/2), we present numerical evidence for the existence of the exponent . These results differ from those used in earlier numerical and analytical studies of two-dimensional dendritic growth.

Original languageEnglish (US)
Pages (from-to)2288-2292
Number of pages5
JournalPhysical Review A
Issue number5
StatePublished - 1987

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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