Unbiased on-lattice domain growth

Cameron A. Smith, Cécile Mailler, and Christian A. Yates
Phys. Rev. E 100, 063307 – Published 19 December 2019
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Abstract

Domain growth is a key process in many areas of biology, including embryonic development, the growth of tissue, and limb regeneration. As a result, mechanisms for incorporating it into traditional models for cell movement, interaction, and proliferation are of great importance. A previously well-used method to incorporate domain growth into on-lattice reaction-diffusion models causes a buildup of particles on the boundaries of the domain, which is particularly evident when diffusion is low in comparison to the rate of domain growth. Here we present an alternative method which addresses this unphysical buildup of particles at the boundaries and demonstrate that it is accurate for scenarios in which the previous method fails. Further, we discuss for which parameter regimes it is feasible to continue using the original method due to diffusion dominating the domain growth mechanism.

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  • Received 2 April 2019
  • Revised 18 July 2019

DOI:https://doi.org/10.1103/PhysRevE.100.063307

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Cameron A. Smith1,*, Cécile Mailler2, and Christian A. Yates1

  • 1Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom
  • 2Probability Laboratory, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom

  • *c.smith3@bath.ac.uk

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Issue

Vol. 100, Iss. 6 — December 2019

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