Andrew G. Osborne

Propagation of a solitary fission wave

Reaction-diffusion phenomena are encountered in an astonishing array of natural systems. Under the right conditions, self stabilizing reaction waves can arise that will propagate at constant velocity. Numerical studies have shown that fission waves of this type are also possible and that they exhibit soliton like properties. Here, we derive the conditions required for a solitary fission wave to propagate at constant velocity. The results place strict conditions on the shapes of the flux, diffusive, and reactive profiles that would be required for such a phenomenon to persist, and this condition would apply to other reaction diffusion phenomena as well. Numerical simulations are used to confirm the results and show that solitary fission waves fall into a bistable class of reaction diffusion phenomena.

Comparison of Numerically Stable Methods for Implementation of a Double Porosity Model with First-Order Reaction Terms

The influence of barometric cycling on gas transport through complex media can be described using a double porosity model. Here vertical channels simulate the effect of cracks that pass through homogeneous regions of media. The cracks are coupled to the atmosphere and act as boundaries for the sections of homogeneous media. Convection–diffusion models are then used to simulate gas transport through the coupled system. This approach has been used to model soil aeration, subsurface movement of volatile compounds, and the migration of gases to the surface after below ground nuclear detonations. In the present work, we describe four stable numerical methods that can be used to implement the double porosity model when first-order reactions produce and consume the gaseous species of interest. We find that all four methods satisfy analytical crosschecks and agree to at least seven digits of precision. An iterative solver based on Newton’s method is found to be optimal as it is easily scalable to 3-D models and to multithreaded execution.

A Rapid Computational Method for Reducing the Search Space Required in Nuclear Reactor Optimization

Reactor optimization is central to increasing the efficiency of nuclear fuel cycles and critical for making meaningful comparisons between different design options. Optimization algorithms work by generating trial parameter sets which can be used as inputs to reactor physics models. Unfortunately, many reactor physics codes require substantial CPU time, making optimization of large parameter sets impractical. We have developed a method for finding optima within an N-dimensional parameter space using a fast, flexible reactor physics model that is capable of performing fuel burnup calculations on the order of once per second. Global optima found in this way can then be verified using a high fidelity reactor physics code. We demonstrate our approach by considering a simple fuel pin pitch optimization for a light-water reactor, and we find our code executes in 5 minutes. Repeating this approach using a high-fidelity Monte Carlo simulation requires approximately 15 days of runtime by contrast.Copyright