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Article Dans Une Revue Communications in Mathematical Physics Année : 1991

Stabilization of needle-crystals by the Gibbs-Thomson effect

Résumé

We develop a scheme based on pseudo-differential operators to analyze the propagation of excitations in inhomogeneous extended systems. This method is used in a very specific situation, however we think that it has some generality and should apply to various other problems of current interest. We study the well known two-dimensional symmetric model of solidification introduced by Langer and Turski. Assuming the existence of Ivantsov-like steady-state solutions, we calculate their excitation spectrum. We show that there are no unstable propagating modes if the Gibbs-Thomson effect is taken into account. This proves that the growth of needle-crystals is stable with respect to side-branching.
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Dates et versions

hal-00005465 , version 1 (19-06-2005)

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  • HAL Id : hal-00005465 , version 1

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Claude-Alain Pillet. Stabilization of needle-crystals by the Gibbs-Thomson effect. Communications in Mathematical Physics, 1991, 140, pp.241-274. ⟨hal-00005465⟩
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