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

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