## Adiabatic Bond Charge Model of Phonons

June 2012

Improved the adiabatic bond charge model of phonons in semiconductors and investigated the geometry of the phonon dispersion relation in diamond structured crystals. Commissioned by *MIT Lincoln Laboratory* to increase the efficiency of quantum cascade lasers by building a computational model that elucidates the interaction between electrons and phonons.

*3D print of the dispersion surface of 13 THz transverse acoustic phonons in diamond.*

## Application of Group Representation Theory to Derive Hermite Interpolation Polynomials on a Triangle

April 2012

Derived a new class of polynomials for use in the finite element method of solving partial differential equations. Awarded first place for Ph.D. research in science at WPI Graduate Research Achievement Day 2012. Presented at the American Physical Society’s March Meeting 2012 and at New England Numerical Analysis Day 2012. Published in the *Journal of Computational Physics*.

*Interpolation polynomials associated with data at one vertex of an equilateral triangle related to a function’s value, first derivatives, and second derivatives in two dimensions.*

## Efficient Electromagnetic Field Calculations Using Hermite Finite Element Methods

April 2012

Mentored / coauthored an undergraduate thesis in physics at WPI. Developed a new method for modeling electromagnetic fields in arbitrary two-dimensional geometries (e.g. waveguides and photonic crystals) using the Hermite polynomials derived in the project described above. Won the Provost award for outstanding undergraduate research. Presented at the American Physical Society’s March Meeting 2012. Published by WPI.

*The electric and magnetic fields of particular symmetry in a photonic crystal comprising a lattice of cylindrical posts.*

## Quantum Scattering and Stealth Finite Elements in Nanoscale Systems

April 2012

Mentored / coauthored an undergraduate thesis in physics at WPI. Introduces a novel method for simulating quantum mechanical scattering in the near field of arbitrary two dimensional closed and open domains. Won Provost award for outstanding undergraduate research, tied with project mentioned above. Presented at the American Physical Society’s March Meeting 2012. Published by WPI.

*The probability current for the lowest energy resonant state of a quantum particle in a curved waveguide.*

## Emergent 1D Ising Behavior of an Austere CA Model

January 2009

Investigated the Ising model’s nature using cellular automata techniques. Published in the *Journal of Computational Physics*.

*Difference patterns of an Ising system showing how information percolates through the system.*