102 citations · 207 across the 7 of their papers we have counts for
6 papers · 1 filter
Mean exit time for diffusion on irregular domains
Matthew J Simpson, Daniel J Vandenheuvel, Joshua M Wilson +2
Many problems in physics, biology, and economics depend upon the duration of time required for a diffusing particle to cross a boundary. As such, calculations of the distribution o…
Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media
Matthew J Simpson, Alexander P Browning, Christopher Drovandi +3
We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is mode…
Diffusion in heterogeneous discs and spheres: new closed-form expressions for exit times and homogenization formulae
Elliot J. Carr, Jacob M. Ryan, Matthew J. Simpson
Mathematical models of diffusive transport underpin our understanding of chemical, biochemical and biological transport phenomena. Analysis of such models often focusses on relativ…
Hole-closing model reveals exponents for nonlinear degenerate diffusivity functions in cell biology
Scott W McCue, Wang Jin, Timothy J Moroney +3
Continuum mathematical models for collective cell motion normally involve reaction-diffusion equations, such as the Fisher-KPP equation, with a linear diffusion term to describe ce…
New homogenization approaches for stochastic transport through heterogeneous media
Elliot J. Carr, Matthew J. Simpson
The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processe…
Rapid calculation of maximum particle lifetime for diffusion in complex geometries
Elliot J Carr, Matthew J Simpson
Diffusion of molecules within biological cells and tissues is strongly influenced by crowding. A key quantity to characterize diffusion is the particle lifetime, which is the time…