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|Title:||Pattern formation in systems far from equilibrium|
|Doctoral Committee Chair(s):||Goldenfeld, Nigel D.|
|Department / Program:||Physics|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|Subject(s):||Physics, Condensed Matter|
|Abstract:||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.
The second problem we study regards the dynamics of phase separation in block copolymer melts. By numerical minimization of the free energy for a block copolymer melt, we calculate the scaling exponents for the way in which the equilibrium lamellar thickness of the microdomains varies with the degree of polymerization. We propose a scaling theory of the approach to equilibrium, from which we relate the exponents in block copolymer systems to the dynamical exponents in spinodal decomposition. We also study the lamellar pattern formed by a propagating front. The selection of the unique front velocity and wavelength agrees well with the predictions of the marginal-stability hypothesis.
|Rights Information:||Copyright 1990 Liu, Fong|
|Date Available in IDEALS:||2011-05-07|
|Identifier in Online Catalog:||AAI9114324|