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Effect of obstructions on growing Turing patterns.

Milos Dolnik1, Christopher Konow1, Noah H Somberg1

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Summary
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Obstructions in growing domains alter Turing pattern formation, creating new shapes and disrupting growth. This research offers a flexible simulation framework for studying pattern development in complex environments.

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Area of Science:

  • Mathematical Biology
  • Chemical Physics
  • Pattern Formation

Background:

  • Turing pattern formation is crucial for biological development.
  • Growing domains present unique challenges for pattern stability.
  • Discrete domain discontinuities can significantly influence pattern dynamics.

Purpose of the Study:

  • To investigate the impact of domain discontinuities on Turing pattern formation.
  • To explore how various obstruction geometries affect pattern morphology and growth.
  • To develop a customizable simulation framework for heterogeneous growing domains.

Main Methods:

  • Numerical simulations using the Lengyel-Epstein reaction-diffusion model.
  • Simulating pattern formation on radially expanding circular domains.
  • Incorporating diverse obstruction geometries (walls, slits, blocks).

Main Results:

  • Obstructions significantly alter Turing pattern formation, leading to novel morphologies.
  • Obstructions can induce growth mode switching and disrupt local pattern formation.
  • The effects of obstructions depend on their shape, placement, and domain growth rate.

Conclusions:

  • Domain discontinuities are critical factors in Turing pattern formation on growing substrates.
  • The findings provide insights into biological pattern formation in non-idealized environments.
  • The developed framework facilitates further numerical and experimental investigations.