Persistence of zero velocity fronts in reaction diffusion systems.

Area of Science:

• Chemical Engineering
• Physical Chemistry
• Nonlinear Dynamics

Background:

• Steady fronts in reaction-diffusion systems typically have zero velocity only at specific parameter values.
• Experimental observations of fronts with zero velocity over a parameter range appear paradoxical under standard theory.

Purpose of the Study:

• To explain the experimental observation of fronts with near-zero velocity over a finite parameter interval.
• To identify the conditions in reaction-diffusion systems that lead to this phenomenon.

Main Methods:

• Theoretical analysis of two-component reaction-diffusion systems.
• Investigating systems with disparate diffusion coefficients.
• Examining systems where the slowly diffusing component has two stable states.

Main Results:

• Demonstrated that velocity dependence on control parameters can result in very small velocities over a finite interval.
• Showed this effect occurs in systems with two components, differing diffusion coefficients, and bistable slow variables.
• The velocity scale ratio approaches zero as the smaller diffusion coefficient tends to zero.

Conclusions:

• The apparent paradox of zero-velocity fronts over a parameter range is resolved by considering specific system properties.
• This behavior is characteristic of reaction-diffusion systems with significant differences in diffusion rates and bistability in one component.