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Preferential localization of a single spot in reaction-diffusion systems on non-spherical surfaces
Sankaran Nampoothiri1,2,3
1Department of Physics, Gandhi Institute of Technology and Management (GITAM) University, Bengaluru, India. sankaran.nampoothiri@unipd.it.
Soft Matter
|February 27, 2023
Summary
Breaking surface symmetry affects spot positioning in reaction-diffusion systems. Non-spherical surfaces like ellipsoids show preferential spot locations, offering insights into cellular geometry and symmetry breaking.
Area of Science:
- Mathematical modeling
- Chemical kinetics
- Theoretical physics
Background:
- Reaction-diffusion (RD) systems exhibit complex spatial patterns.
- Surface geometry can influence pattern formation in physical and biological systems.
- Rotational symmetry is a common assumption in simplified models.
Purpose of the Study:
- To investigate how breaking rotational symmetry impacts spot positioning in RD systems.
- To analyze spot behavior on non-spherical surfaces, specifically prolate and oblate ellipsoids.
- To understand the role of cell geometry in symmetry-breaking phenomena.
Main Methods:
- Analytical methods including perturbative techniques for linear stability analysis.
- Numerical simulations of non-linear RD equations.
- Steady-state analysis of spot positioning on ellipsoidal geometries.
Main Results:
- Preferential spot positioning is observed on non-spherical surfaces.
- Ellipsoidal geometry significantly influences the location of stable spots.
- The study quantifies the effect of asymmetry on pattern localization.
Conclusions:
- Surface geometry is a critical factor in determining spot positions in RD systems.
- Breaking rotational symmetry leads to predictable biases in spot location.
- Findings provide a foundation for studying cell geometry's influence on biological pattern formation.
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