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Turing patterns on radially growing domains: experiments and simulations.

Christopher Konow1, Noah H Somberg1, Jocelyne Chavez2

  • 1Department of Chemistry, Brandeis University, MS 015, Waltham, MA 02454, USA. dolnik@brandeis.edu.

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Summary
This summary is machine-generated.

Turing pattern formation in a growing system depends on radial growth rate. Faster growth yields concentric rings, while slower growth produces perpendicular patterns, revealing distinct growth modes.

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Area of Science:

  • Chemical kinetics
  • Pattern formation
  • Reaction-diffusion systems

Background:

  • Turing patterns are complex spatial structures arising from reaction-diffusion processes.
  • Radial growth introduces dynamic boundaries that influence pattern development.
  • Photosensitive reactions offer a method to control pattern formation.

Purpose of the Study:

  • To investigate the influence of radial growth rate on Turing pattern morphology.
  • To identify and characterize different growth modes in a photosensitive reaction-diffusion system.
  • To understand pattern formation dynamics in a growing two-dimensional system.

Main Methods:

  • Utilizing a photosensitive chlorine dioxide-iodine-malonic acid reaction under controlled illumination.
  • Experimentally varying the linear radial growth rate of a non-illuminated domain.
  • Performing numerical simulations using the Lengyel-Epstein model with modifications for photosensitivity.

Main Results:

  • Observed that faster radial growth leads to Turing patterns forming concentric rings parallel to the boundary.
  • Found that slower radial growth results in patterns forming perpendicular to the growing boundary.
  • Identified three distinct growth modes for Turing patterns, correlated with the radial growth rate.

Conclusions:

  • The radial growth rate is a critical factor determining Turing pattern morphology in this system.
  • The study provides insights into pattern formation mechanisms in dynamic, growing environments.
  • Findings may inform understanding of pattern development in biological systems with growth components.