This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/22487
Description
Title
Pattern formation in systems far from equilibrium
Author(s)
Liu, Fong
Issue Date
1990
Doctoral Committee Chair(s)
Goldenfeld, Nigel D.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Condensed Matter
Language
eng
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.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
