Kang-Redner small-mass anomaly in cluster-cluster aggregation.

Area of Science:

• Statistical Physics
• Condensed Matter Physics
• Mathematical Physics

Background:

• Understanding particle aggregation dynamics is crucial in various physical systems.
• The asymptotic behavior of mass distributions provides insights into long-term system evolution.
• Previous studies often focused on different dimensionalities or aggregation models.

Purpose of the Study:

• To analyze the large-time, small-mass asymptotic behavior of the average mass distribution P(m,t).
• To investigate this behavior in a d-dimensional system of diffusing aggregating particles for 1 <= d <= 2.
• To provide analytical and numerical validation for the observed dynamics.

Main Methods:

• Renormalization group computation.
• Direct resummation of leading terms in the small-reaction-rate expansion.
• Numerical simulations in two dimensions.

Main Results:

• Derived an approximate formula for P(m,t) for m << t^(d/2) in d-dimensions, involving t, m, and epsilon = 2-d.
• In two dimensions (d=2), P(m,t) was found to be approximately ln(m)ln(t)/t^2 for m << t/ln(t).
• Numerical simulations corroborated the analytical findings in two dimensions.

Conclusions:

• The study elucidates the asymptotic mass distribution of diffusing aggregating particles in low dimensions.
• Analytical and numerical results confirm specific scaling behaviors.
• The findings contribute to the understanding of aggregation phenomena in statistical physics.