String models of interfacial pattern formation

Eshel Ben-Jacob, Nigel Goldenfeld, J. S. Langer, Gerd Schön

Research output: Contribution to journalArticlepeer-review


We introduce a new approach to describe the dynamics of interfacial pattern formation. The central idea is that local properties may dominate the dynamics of the interface in many realistic situations. Here we have chosen to present a model for dendritic solidification where the basic mechanism which allows pattern formation - the Mullins-Sekerka instability - is well understood. In this and many other cases where the dynamics is driven by an additional field such as thermal or chemical diffusion, the coupling of this field to the interface may be phenomenologically described by a boundary layer with its own dynamics. With the inclusion of the non-equilibrium effect of crystalline anisotropy, our preliminary results appear to reproduce the observed dynamics of dendritic growth.

Original languageEnglish (US)
Pages (from-to)245-252
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Issue number1-3
StatePublished - Jul 1984
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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