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Modeling and Imaging 3-Dimensional Collective Cell Invasion
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Domain convexification: A simple model for invasion processes.

David Martin-Calle1, Olivier Pierre-Louis1

  • 1Institut Lumière Matière, Université de Lyon, Université Claude Bernard Lyon 1, CNRS UMR5306, Campus de la Doua, F-69622 Villeurbanne, France.

Physical Review. E
|November 18, 2023
PubMed
Summary
This summary is machine-generated.

We developed a new invasion model for growing domains that merge upon overlap. This model reveals a critical transition occurring via large avalanches, with properties dependent on system size and disk concentration.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Bootstrap percolation models describe discrete systems.
  • Continuum models are needed for more realistic physical phenomena.
  • Understanding domain growth and merging is crucial in various scientific fields.

Purpose of the Study:

  • To propose and investigate a continuum, isotropic invasion model.
  • To analyze the invasion transition and its characteristics.
  • To compare model predictions with experimental observations.

Main Methods:

  • Numerical simulations of randomly deposited overlapping disks on a plane.
  • Analysis of domain growth up to convex hulls and merging upon overlap.
  • Investigation of cluster size distribution and domain area distribution.

Main Results:

  • An invasion transition occurring via macroscopic avalanches was identified.
  • The transition threshold and width decrease with increasing system size, suggesting a vanishing threshold in the infinite size limit.
  • Cluster size distribution exhibits a power-law tail with an exponent varying linearly with disk concentration.
  • Domain area distribution shows oscillations and discontinuities; large domains have constant deviation from circularity.

Conclusions:

  • The proposed model offers a continuum counterpart to bootstrap percolation.
  • Results provide insights into finite-size effects and critical phenomena in invasion processes.
  • The model's findings are relevant to de-adhesion phenomena, such as nanoparticle intercalation in graphene.