Diffusivity and Ballistic Behavior of Random Walk in Random Environment

In this thesis, we study the diffusive and ballistic behaviors of random walk in random environment (RWRE) in an integer lattice with dimension at least 2. Our contributions are in three directions: a conditional law of large numbers and regeneration structures for RWRE in Gibbsian environments, quenched invariance principles for balanced elliptic (but non uniformly elliptic) environments, and a proof of the Einstein relation for balanced iid uniformly elliptic environments.Comment: PhD thesi

Quantitative homogenization in a balanced random environment

We consider discrete non-divergence form difference operators in an i.i.d. random environment and the corresponding process--the random walk in a balanced random environment in $\mathbb{Z}^d$. We first quantify the ergodicity of the environment viewed from the point of view of the particle. As a consequence, we quantify the quenched central limit theorem of the random walk with an algebraic rate. Furthermore, we prove algebraic rate of convergence for homogenization of the Dirichlet problems for both elliptic and parabolic non-divergence form difference operators.Comment: 36 pages, 1 figur

Modeling of mPGES-1 Three-Dimensional Structures: Applications in Drug Design and Discovery

This invention relates to representations of prostaglandin synthase three-dimensional structures. Such representations are suitable for designing agents that modulate the activity of the enzyme by binding to the substrate binding domain