Emergent structures in reaction-advection-diffusion systems on a sphere

Area of Science:

• Mathematical modeling
• Chemical kinetics
• Pattern formation

Background:

• Reaction-diffusion systems are fundamental to understanding pattern formation in nature.
• Turing instabilities describe how homogeneous states can spontaneously form spatial patterns.
• The spherical geometry introduces unique constraints not present in planar systems.

Purpose of the Study:

• To investigate the impact of advection on a two-species reaction-diffusion system confined to a sphere.
• To explore emergent behaviors arising from the interaction of advection, reaction-diffusion dynamics, and spherical geometry.
• To elucidate the mechanisms behind pattern generation and transport on a sphere.

Main Methods:

• Numerical simulations of a two-species reaction-diffusion model on a spherical domain.
• Analysis of Turing instabilities using local projections of the spherical system.
• Comparison of spherical advection effects with those in planar systems.

Main Results:

• Unidirectional advection induces pattern formation at one point on the sphere and destruction at the antipodal point.
• The interplay between Turing patterning and spherical geometry leads to emergent behaviors.
• Planar advection primarily results in pattern transport, unlike the spherical case.

Conclusions:

• Advection significantly alters pattern formation in reaction-diffusion systems on spheres, leading to unique phenomena.
• Spherical geometry combined with advection creates novel pattern dynamics, including generation and annihilation cycles.
• Understanding these effects is crucial for modeling spatio-temporal patterns in confined or curved environments.