Computational Methods for Multidimensional Neutron Diffusion Problems

Supersymmetric methods in neutron diffusion

We present the Witten and the double Darboux constructions as applied to the diffusion of thermal neutrons from an infinitely long line source. Supersymmetric one-dimensional quantum mechanics has been introduced in 1981 as a toy model for symmetry-breaking phenomena in quantum field theory [1]. With great speed its status has changed to a powerful research discipline as one can contemplate in ...

Iterative Methods for Neutron Transport Eigenvalue Problems

We discuss iterative methods for computing criticality in nuclear reactors. In general this requires the solution of a generalised eigenvalue problem for an unsymmetric integro-differential operator in 6 independent variables, modelling transport, scattering and fission, where the dependent variable is the neutron angular flux. In engineering practice this problem is often solved iteratively, u...

Computational methods for diffusion-influenced biochemical reactions

MOTIVATION We compare stochastic computational methods accounting for space and discrete nature of reactants in biochemical systems. Implementations based on Brownian dynamics (BD) and the reaction-diffusion master equation are applied to a simplified gene expression model and to a signal transduction pathway in Escherichia coli. RESULTS In the regime where the number of molecules is small an...

Numerical Methods for Power-Law Diffusion Problems

Energy Methods for Reaction - Diffusion Problems

ENERGY METHODS FOR REACTION-DIFFUSION PROBLEMS by Xing Zhong Nonlinear reaction-diffusion equations arise in many areas of applied sciences such as combustion modeling, population dynamics, chemical kinetics, etc. A fundamental problem in the studies of these equations is to understand the long time behavior of solutions of the associated Cauchy problem. These kinds of questions were originally...