Stabilization of needle-crystals by the Gibbs-Thomson effect
Pillet, Claude-Alain
HAL, hal-00005465 / Harvested from HAL
Text on HAL
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.
Publié le : 1991-07-05
Classification:  pattern formation,  dentritic growth,  sidebranching,  needle crystal,  Gibbs-Thomson,  [PHYS.PHYS.PHYS-CLASS-PH]Physics [physics]/Physics [physics]/Classical Physics [physics.class-ph],  [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph],  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],  [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA],  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],  [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] 
@article{hal-00005465,
     author = {Pillet, Claude-Alain},
     title = {Stabilization of needle-crystals by the Gibbs-Thomson effect},
     journal = {HAL},
     volume = {1991},
     number = {0},
     year = {1991},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00005465}
}

Pillet, Claude-Alain. Stabilization of needle-crystals by the Gibbs-Thomson effect. HAL, Tome 1991 (1991) no. 0, . http://gdmltest.u-ga.fr/item/hal-00005465/