5 papers · 1 filter
Stochastic simulations of nonlinear reaction-diffusion equations using an exponential integrator
Elliot J. Carr
Stochastic simulations can be generated from deterministic reaction-diffusion equations by discretising in space and time and interpreting coefficients in the resulting system of d…
Properties of the matrix functions arising in exponential integrators with applications to stochastic simulations of PDEs
Elliot J. Carr
The matrix exponential and the closely related matrix phi-functions play a fundamental role in the solution of first-order systems of ordinary differential equations (ODEs). In par…
Modelling and analysis of laser flash experiments using the Cattaneo heat equation
Elliot J. Carr
Thermal diffusivity of solid materials is commonly measured using laser flash analysis. This technique involves applying a heat pulse to the front surface of a small sample of the…
Random walk models of anisotropic diffusion on rectangular and hexagonal lattices
Luke P. Filippini, Adrianne L. Jenner, Elliot J. Carr
The diffusive transport of particles in anisotropic media is a fundamental phenomenon in computational, medical and biological disciplines. While deterministic models (partial diff…
Stochastic models of advection-diffusion in layered media
Elliot J. Carr
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical ph…