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Updated: Jul 2, 2025
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
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Numerical study of anisotropic diffusion in Turing patterns based on Finsler geometry modeling.
Gildas Diguet1, Madoka Nakayama2, Sohei Tasaki3
1Micro System Integration Center, Tohoku University, Sendai, Japan.
Physical Review. E
|February 17, 2024
Summary
This study introduces Finsler geometry to model anisotropic Turing patterns in reaction-diffusion systems. A novel internal degree of freedom dynamically generates diffusion, explaining emergent biological patterns and enabling control.
Area of Science:
- Theoretical Physics
- Mathematical Biology
- Chemical Kinetics
Background:
- Turing patterns (TPs) are crucial for understanding biological pattern formation.
- Standard models often assume isotropic or manually defined anisotropic diffusion.
- The origin of spontaneously emergent anisotropic patterns in nature remains an active research area.
Purpose of the Study:
- To numerically investigate anisotropic Turing patterns using Finsler geometry (FG) modeling.
- To explore the role of a dynamically generated, direction-dependent diffusion coefficient.
- To propose a novel mechanism for the emergence and control of anisotropic biological patterns.
Main Methods:
- Reaction-diffusion (RD) equations within a Finsler geometry framework.
- A hybrid numerical technique combining Metropolis Monte Carlo for internal degree of freedom (IDOF) updates and discrete RD equations for steady-state solutions.
- Dynamical generation of diffusion coefficients influenced by an IDOF.
Main Results:
- The FG model successfully generates anisotropic Turing patterns.
- The internal degree of freedom (IDOF) and its interaction with system components are identified as a source of emergent anisotropy.
- Demonstrated that the IDOF can be linked to cell diffusion and thermal fluctuations for pattern control.
Conclusions:
- Finsler geometry provides a novel framework for modeling anisotropic diffusion in reaction-diffusion systems.
- The introduced IDOF offers a potential explanation for the spontaneous emergence of anisotropic patterns observed in organisms like zebras and fish.
- The IDOF presents a pathway for externally controlling Turing patterns in biological systems.
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