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Statistical mechanics of transport in disordered lattices and reaction-diffusion systems


Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/9836

Statistical mechanics of transport in disordered lattices and reaction-diffusion systems

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Title: Statistical mechanics of transport in disordered lattices and reaction-diffusion systems
Author: Kalay, Ziya, 1984
Advisor(s): Kenkre, Vasudev
Committee Member(s): Dunlap, David
Thomas, James
Edwards, Jeremy
Department: University of New Mexico. Dept. of Physics & Astronomy
Subject: random walk
diffusion in cell membranes
pattern formation
disordered lattices
LC Subject(s): Statistical physics.
Transport theory.
Order-disorder models.
Reaction-diffusion equations.
System analysis.
Cells--Permeability--Mathematical models.
Degree Level: Doctoral
Abstract: This thesis is the report of a study of several different problems in statistical physics. The first two are about random walks in a disordered lattice, with applications to a biological system, the third is about reaction-diffusion systems, particularly the phenomena of front propagation and pattern formation, and the last is about a special kind of evolving complex networks, the addition-deletion network. The motivation for the first of the two random walk investigations is provided by the diffusion of molecules in cell membranes. A mathematical model is constructed in order to predict molecular diffusion phenomena relating to the so-called compartmentalized view of the cell membrane. The theoretical results are compared with experimental observations available in the literature. The second random walk part in the thesis contains contributions to the analysis of transport in disordered systems via effective medium theory. Calculation of time-dependent transport quantities are presented along with discussion of effects of finite system size, significance of long-range memory functions, and consequences of correlated disorder. The investigation of reaction-diffusion systems that deals with front propagation is concerned with providing a method of studying transient dynamics in such systems whereas the study of pattern formation focuses on determining necessary conditions for such patterns to arise in situations wherein sub- and super-diffusion are present in addition to simple diffusion. In the network study, results are reported on cluster size distribution in addition-deletion networks, on the basis of both numerical and analytic investigations.
Graduation Date: July 2009
URI: http://hdl.handle.net/1928/9836

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