Anomalous kinetics in diffusion limited reactions linked to non-Gaussian concentration probability distribution...

Area of Science:

• Chemical Kinetics
• Statistical Mechanics
• Computational Physics

Background:

• Reaction-diffusion systems exhibit mean-field behavior at high concentrations.
• Spatial fluctuations become significant at low concentrations, leading to deviations from mean-field predictions.
• The transition from mean-field to anomalous kinetics is observed as concentration decreases.

Purpose of the Study:

• To investigate anomalous reaction kinetics in a one-dimensional reaction-diffusion system (A + B → C).
• To characterize the reaction-diffusion system using a stochastic modeling approach and the multi-point probability distribution function (PDF).
• To establish a direct relationship between anomalous reaction kinetics, incomplete mixing, and the non-Gaussian nature of the concentration PDF.

Main Methods:

• Stochastic modeling approach to characterize the reaction-diffusion system.
• Utilizing the multi-point probability distribution function (PDF) of species concentrations.
• Solving the Fokker-Planck equation with moving boundaries to describe PDF evolution.

Main Results:

• Anomalous reaction kinetics observed in the fluctuation-dominated regime.
• The average concentration scaling changes from t(-1) (mean-field) to t(-1/4) (anomalous).
• The concentration PDF transitions from a Gaussian to a non-Gaussian shape in the anomalous regime.

Conclusions:

• Anomalous reaction kinetics are directly linked to the evolution of the concentration PDF from Gaussian to non-Gaussian.
• Incomplete mixing plays a crucial role in the observed anomalous kinetics.
• The non-Gaussian nature of the concentration PDF is a key indicator of anomalous reaction kinetics in these systems.