Interacting motile agents : taking a mean-field approach beyond monomers and nearest-neighbor steps
Penington, Catherine J., Hughes, Barry D., & Landman, Kerry A. (2014) Interacting motile agents : taking a mean-field approach beyond monomers and nearest-neighbor steps. Physical Review E, 89(3), 032714.
We consider a discrete agent-based model on a one-dimensional lattice, where each agent occupies L sites and attempts movements over a distance of d lattice sites. Agents obey a strict simple exclusion rule. A discrete-time master equation is derived using a mean-field approximation and careful probability arguments. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy are obtained. Averaged discrete simulation data are generated and shown to compare very well with the solution to the derived nonlinear diffusion equations. This framework allows us to approach a lattice-free result using all the advantages of lattice methods. Since different cell types have different shapes and speeds of movement, this work offers insight into population-level behavior of collective cellular motion.
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|Item Type:||Journal Article|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)|
|Divisions:||Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
|Copyright Owner:||Copyright 2014 American Physical Society|
|Deposited On:||21 Aug 2014 00:40|
|Last Modified:||21 Aug 2014 21:47|
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