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SUMMARY:Patterning of nonlocal transport models in biology: the impact of 
 spatial dimension - Thomas Jun Jewell (University of Oxford)
DTSTART:20230717T154000Z
DTEND:20230717T154500Z
UID:TALK201664@talks.cam.ac.uk
DESCRIPTION:Throughout developmental biology and ecology\, transport can b
 e driven by nonlocal interactions. Examples include cells that migrate bas
 ed on contact with pseudopodia extended from other cells\, and animals tha
 t move based on their vision of other animals. Nonlocal integro-PDE models
  have been used to investigate contact attraction and repulsion in cell po
 pulations in 1D. In this paper\, we generalise the analysis of pattern for
 mation in such a model from 1D to higher spatial dimensions. Numerical sim
 ulations in 2D demonstrate complex behaviour in the model\, including spat
 io-temporal patterns\, multi-stability\, and the selection of spots or str
 ipes heavily depending on interactions being attractive or repulsive. Thro
 ugh linear stability analysis in&nbsp\;N dimensions\, we demonstrate how\,
  unlike in local Turing reaction-diffusion models\, the capacity for patte
 rn formation fundamentally changes with dimensionality for this nonlocal m
 odel. Most notably\, pattern formation is possible only in higher than one
  spatial dimension for both the single species system with repulsive inter
 actions\, and the two species system with `run-and-chase' interactions. Th
 e latter case may be relevant to zebrafish stripe formation\, which has be
 en shown to be driven by run-and-chase dynamics between melanophore and xa
 nthophore pigment cells.&nbsp\;\narXiv preprint: https://arxiv.org/abs/230
 7.03117\nauthors: Thomas Jun Jewell\,&nbsp\;Andrew L. Krause\,&nbsp\;Phili
 p K. Maini\,&nbsp\;Eamonn A. Gaffney
LOCATION:Seminar Room 1\, Newton Institute
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