**Anzhela **Baghumyan

Graduate Assistant, Department of Mathematics**Advisor:** Vladislav Panferov** Project Description Summary:** Working on mathematical theory of emergent behavior, such as flocking of birds, schooling of fish or sychronization of rhythms in biological systems. She is applying techniques from analysis and differential geometry to study behavior of particle systems appearing in the studies of emergent phenomena.

# Graduate Students 2012-2013

## Baghumyan, Anzhela

## Demirdjian, Levon

**Levon **Demirdjian

Graduate Assistant, Department of Mathematics**Advisor:** Majid Mojirsheibani** Project Description Summary:** Classification and probabilistic pattern recognition with missing data; Kernel-based classification; estimation of the smoothing parameters of a kernel when there are missing covariates; classification on convex sets.

## Euler, Graig

**Graig **Euler

Graduate Assistant, Department of Mathematics**Advisor:** Alexander Alekseenko** Project Description Summary:** Development & implementation in Fortran of high order discontinuous Galerkin discretizations of model kinetic equations in velocity space. Study of numerical properties of the BGK and the ES-BGK kinetic models in one spatial and one velocity dimension and comparison to the experiment. Deterministic numerical solution of spatially homogeneous Boltzmann equation. Development and implementation of BGK model with velocity dependent collision frequency.

## Havens, Sam

**Sam **Havens

Graduate Assistant, Department of Mathematics**Advisor:** David Klein** Project Description Summary:** Study a problem in cosmology and general relativity. The goal is to determine maximal Fermi charts in a class of inflationary Robertson-Walker cosmologies and investigate the behavior of geometrically defined relative velocities of distant test particles.

## Kelkar, Asawari

**Asawari **Kelkar

Graduate Assistant, Department of Mathematics**Advisor:** Emmanuel Yomba** Project Description Summary:** The goal is to analyze the local behavior of the solutions corresponding to a class of coupled system of nonlinear Schrodinger equations, as well as a complex coupled system of nonlinear Newell-Segel-Whitehead equations. Such an analysis is performed using the so-called Modulational Instability (MI) approach.

## Khoram, Nafiseh

**Nafiseh **Khoram

Graduate Assistant, Department of Mathematics**Advisor:** Rabia Djellouli** Project Description Summary:** The main objective is to calibrate a brain response model using fMRI measurements. This requires the development of an efficient solution methodology for identifying the parameters of the so-called Balloon model. The method is a regularized iterative method equipped with a denoising procedure.

## Mametkuliyev, Muhamed

**Muhamed **Mametkuliyev

Graduate Assistant, Department of Chemistry and Biochemistry**Advisor:** Jussi Eloranta** Project Description Summary:** Study solvation dynamics in liquids. Investigate radical reactions in water (including diffusion studies) and study non-polar solvation of molecules.

## Pinchak, Julia

**Julia **Pinchak

Graduate Assistant, Department of Mathematics**Advisor:** Al Sethuraman** Project Description Summary:** The work pertains to the area of secure wireless communication, and lies at the interface of communications (i.e., electrical) engineering and mathematics. The problem concerns communication over a wireless channel in the presence of eavesdroppers. The goal is to prove a conjecture regarding lattices in high-dimensional space that will help design ways to communicate in such a way that the eavesdropper only hears noise and nothing of the message..

## Rains, Christine

**Christine **Rains

Graduate Assistant, Department of Geological Sciences**Advisor:** Dayanthie Weeraratne** Project Description Summary:** The formation of liquid-metal diapirs in the early Earth has been proposed as an important metal-silicate differentiation mechanism in Earth's formation. These diapirs, which consist of a liquid-metal “nose” and entrained melted-silicate conduit, may also have played a key role in the observed core superheat in the Earth and in the creation of the siderophile enrichment observed in the mantle today. We investigate the physical processes of metal diapir formation using three-component laboratory fluid experiments representing the Earth's solid proto-mantle, a silicate magma ocean formed by shock-induced melting due to a late-stage impactor, and a liquid iron pond created from the core of the melted impactor. We describe the conditions under which trailing conduits of metal diapirs will form and stay open and delineate conduit geometry and diapir shape under different conditions of density and viscosity in each layer.

## Wood, Shannon

**Shannon **Wood

Graduate Assistant, Department of Chemistry and Biochemistry**Advisor:** Sean Murray** Project Description Summary:** Study the synthesis and function of polyhydroxybutyrate in the aquatic bacterium Cauobacter crescents. PHB is of interest because it is one of the co-polymers used in the production of biodegradable plastics.