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Stopping a reaction-diffusion front.

Jean-Guy Caputo1, Gustavo Cruz-Pacheco2, Benoît Sarels3

  • 1Laboratoire de Mathématiques, INSA Rouen Normandie - B.P. 8, Avenue de l'Université, 76801 Saint-Etienne du Rouvray, France.

Physical Review. E
|April 17, 2021
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Summary
This summary is machine-generated.

Reaction-diffusion fronts behave differently when encountering defects. Bistable fronts can be pinned, while monostable fronts cannot, forming a secondary pulse instead. This impacts biological modeling, such as tumor growth studies.

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Area of Science:

  • Physics
  • Applied Mathematics
  • Computational Biology

Background:

  • Reaction-diffusion systems are fundamental to modeling phenomena like pattern formation and biological pattern development.
  • Defects in reaction-diffusion systems can significantly alter front propagation dynamics.
  • Understanding front-defect interactions is crucial for applications in biology and materials science.

Purpose of the Study:

  • To investigate and compare the pinning dynamics of bistable and monostable reaction-diffusion fronts interacting with a defect (reaction-free region).
  • To elucidate the distinct behaviors of bistable versus monostable fronts when encountering such defects.
  • To provide insights relevant to biological modeling, particularly in contexts like tumor growth.

Main Methods:

  • Utilized collective variables to describe the reaction-diffusion front.
  • Employed numerical simulations to observe and analyze front behavior.
  • Performed analysis of the time-independent problem to establish pinning criteria.

Main Results:

  • Confirmed that bistable fronts can be pinned by the reaction-free defect, supported by theoretical criteria and simulations.
  • Demonstrated that monostable fronts cannot be pinned and instead generate a secondary pulse past the defect.
  • Quantified the time required for the appearance of this secondary pulse for monostable fronts.

Conclusions:

  • Bistable and monostable fronts exhibit fundamentally different responses to pinning defects.
  • The pinning behavior is critically dependent on the front's bistability or monostability.
  • These findings have significant implications for accurately modeling biological processes involving front propagation and defects.