Pattern formation in systems far from equilibrium

We study two representative problems related to the dynamics of pattern formation in non-linear, dissipative systems far from equilibrium. The first problem addresses the dynamical mechanism of velocity and shape selection in dendritic crystal growth. Using the boundary-layer model of solidification, we demonstrate the new solvability theory of velocity selection. We perform the linear stability analysis for the needle crystal steady states and establish the linear stability of the fastest needle crystal, which accounts for the unique dendrite selection in experiments. We then show, for the first time, that the competition between surface tension and kinetic anisotropy leads to the tip-splitting/sidebranching instability of the needle crystal. This explains the presence of a morphological transition and the dense-branching morphology. Finally, an efficient lattice model is developed to study the late stages of diffusion-controlled growth. We establish the existence of an asymptotic dense-branching morphology and relate it to the diffusion-limited aggregation. A clear morphological transition from kinetic effect dominated growth to surface tension dominated growth is observed, marked by a difference in the way growth velocity scales with undercooling. Scaling behaviour in the evolution of interfacial instability is found, in a planar geometry, indicating a non-linear selection of a unique length-scale, insensitive to short length-scale fluctuations.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Liu, Fong

Contributors dc:contributor

• Goldenfeld, Nigel D.

• Physics, Condensed Matter

Statement dc:rights

• Copyright 1990 Liu, Fong

Language dc:language

eng

Identifier

AAI9114324
(UMI)AAI9114324

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/22487