Velocity-jump models with crowding effects
Velocity jump processes are discrete random walk models that have many applications including the study of biological and ecological collective motion. In particular, velocity jump models are often used to represent a type of persistent motion, known as a “run and tumble”, which is exhibited by some isolated bacteria cells. All previous velocity jump processes are non-interacting, which means that crowding effects and agent-to-agent interactions are neglected. By neglecting these agent-to-agent interactions, traditional velocity jump models are only applicable to very dilute systems. Our work is motivated by the fact that many applications in cell biology, such as wound healing, cancer invasion and development, often involve tissues that are densely packed with cells where cell-to-cell contact and crowding effects can be important. To describe these kinds of high cell density problems using a velocity jump process we introduce three different classes of crowding interactions into a one-dimensional model. Simulation data and averaging arguments lead to a suite of continuum descriptions of the interacting velocity jump processes. We show that the resulting systems of hyperbolic partial differential equations predict the mean behavior of the stochastic simulations very well.
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|Item Type:||Journal Article|
|Keywords:||velocity jump, crowding effects, exclusion process, position jump|
|Subjects:||Australian and New Zealand Standard Research Classification > PHYSICAL SCIENCES (020000) > ATOMIC MOLECULAR NUCLEAR PARTICLE AND PLASMA PHYSICS (020200)|
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology
Current > Institutes > Institute of Health and Biomedical Innovation
Past > Schools > Mathematical Sciences
|Copyright Owner:||Copyright 2012 American Physical Society|
|Deposited On:||23 Nov 2011 22:39|
|Last Modified:||12 Apr 2012 10:57|
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