Effect of bias in a reaction-diffusion system in two dimensions

Area of Science:

• Statistical Physics
• Chemical Kinetics
• Computational Modeling

Background:

• Reaction diffusion systems are fundamental to understanding pattern formation and dynamics in various scientific fields.
• Particle interactions and movement rules, such as bias and annihilation, critically influence system behavior.
• Simulations often employ updating schemes that can introduce unique phenomena, like dimer formation.

Purpose of the Study:

• To investigate the impact of directional bias on a single-species reaction diffusion system on a 2D lattice.
• To compare the system's behavior under unbiased (diffusive) versus biased (positive and negative) conditions.
• To analyze the emergence of novel structures like dimers and their dependence on simulation parameters.

Main Methods:

• Simulating a single-species reaction diffusion model on a two-dimensional lattice.
• Introducing parametric bias in particle movement towards nearest neighbors.
• Implementing a parallel updating scheme to observe system dynamics.
• Analyzing particle density, dimer formation, and persistence behavior.

Main Results:

• Nonzero bias drastically alters system behavior compared to the unbiased diffusive case.
• Positive bias leads to a finite number of dimers, while negative bias results in a finite surviving particle density.
• Both dimer count and surviving density vanish with power-law dependence near the diffusive limit, exhibiting different exponents.
• Dimers are an artifact of the parallel updating scheme, indicating a continuous phase transition at the diffusive point.

Conclusions:

• Particle bias is a critical parameter in reaction diffusion systems, leading to distinct emergent behaviors.
• The simulation's updating scheme plays a crucial role in phenomena such as dimer formation.
• The study reveals a continuous phase transition at the diffusive point and a discontinuity at full positive bias, highlighting complex system dynamics.