## Areas of Research

My research is based in numerical methods for neutral particle transport (solving the Boltzmann transport equation) with an emphasis on high performance computing. These methods are often inspired by the physics of the problem at hand, developments in computer hardware, or both.

I apply these methods to reactor design, shielding, and nuclear security and nonproliferation.

In particular, my research group works on

- Deterministic solver methods
- Hybrid methods (using deterministic results to accelerate Monte Carlo)
- Metahueristic optimization algorithms
- Applications in reactor design, shielding, and nuclear security and nonproliferation
- Monte Carlo on advanced architectures (e.g. GPUs and MICs)
- Nonclassical neutron transport
- Scientific software development

### Deterministic Solver Methods

We study methods for the deterministic solution of the transport equation (using mathematical rules and discretized phase space) such as eigenvalue acceleration methods, parallelization strategies, Lagrange Discrete Ordinates, and the finite element method.

### Hybrid Methods

We study how to use coarse deterministic solutions to speed up Monte Carlo solutions (where you use random numbers to sample continuous physics to build solutions). We are currently looking at this for problems with strong anisotropies like gaps where radiation can stream readily.

### Metaheuristic Optimization Algorithms

We have developed an algorithm that performs metaheuristic optimization to design energy tuning assemblies. The algorithm combines many optimization strategies to solve a single objective, non-linear, constrained, continuous and discrete multi-modal optimization problem.

We often want specific neutron energy spectra for various purposes such as medical treatment, nuclear data investigation, or nuclear forensics, but are limited to the energy spectra we can easily produce. Our optimization code automatically designs a material stack up, given a variety of constraints, to produce the spectrum of interest.

### Applications

We perform analysis for systems things like shielding casks, molten salt reactors, pressurized water reactors, and source detection.

### Monte Carlo

GPUs have the potential to greatly enhance calculation speeds for Monte Carlo calculations. However, the process of conducting Monte Carlo for neutral particle transport on GPUs is not straightforward. We are developing a code, WARP, to do just this and there are a variety of remaining challenges in terms of methods, implementation, and studying impact.

### Nonclassical Transport

In classical particle transport, the probability that a particle interacts with the background medium is proportional to the path length traveled by that particle, and the proportionality constant depends on the density of the medium and on the particleâ€™s energy. This typically leads to an exponential attenuation law, i.e. the particle flux decreases as an exponential function of the path length (Beer-Lambert law). In certain inhomogeneous random systems, however, a nonexponential attenuation law arises due to spatial correlations between the fuel pebbles in the core. We develop methods to study nonclassical solvers in 1, 2, and 3 dimensions.

### Scientific Software Development

PyNE is an open source Python library for Nuclear Engineering (http://pyne.io/, https://github.com/pyne/pyne). There are a variety of projects that are often changing. My group occasionally contributes things to PyNE, like a collection of spatial solvers or a Bateman Equation solver.