Abstract
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined. © 2013 Society for Mathematical Biology.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 947-982 |
| Number of pages | 36 |
| Journal | Bulletin of Mathematical Biology |
| Volume | 76 |
| Issue number | 4 |
| DOIs | |
| State | Published - May 10 2013 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). MB acknowledges financial support from EPSRC. We are grateful to the organizers of the workshop "Stochastic Modelling of Reaction-Diffusion Processes in Biology," which has led to this Special Issue.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.