We show that nonlinear continuum elasticity can be effective in modeling plastic flows in
crystals if it is viewed as a Landau theory with an infinite number of equivalent energy wells …

Steady plastic flows have been compared to developed turbulence because the two
phenomena share the inherent complexity of particle trajectories, the scale free spatial …

We focus on mesoscopic dislocation patterning via a continuum dislocation dynamics theory
(CDD) in three dimensions (3D). We study three distinct physically motivated dynamics …

Plastic deformations in crystals produce microstructures with randomly oriented patches of
unstressed lattice forming complex textures. We use a mesoscopic Landau-type tensorial …

A simplified one dimensional rate dependent model for the evolution of plastic distortion is
obtained from a three dimensional mechanically rigorous model of mesoscale field …

The size dependence of the strength of nano-and micron-sized crystals is studied using a
new simulation approach in which the dynamics of the density functions of dislocations are …

Plastic deformations in crystals often produce textures in the form of randomly oriented
patches of the unstressed lattice. We use a novel mesoscopic Landau model of crystal …

This thesis consists of two parts. The first part explores a 2-d edge dislocation model to
demonstrate characteristics of Field Dislocation Mechanics (FDM) in modeling single and …

We explore new ways of regulating defect behavior in systems of conservation laws.
Contrary to usual regularization schemes (such as a vanishing viscosity limit), which attempt …

A novel compartmental modelling approach to investigate influx and efflux distribution of the
drug efavirenz is suggested. The models are developed for a patient who had been on 600 …