Lattice models for ballistic aggregation: Cluster-shape-dependent exponents

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems

Background:

• Ballistic aggregation is a fundamental process in physics.
• Understanding particle interactions and aggregate formation is crucial for complex systems.
• Previous models often simplify aggregate shapes, limiting applicability.

Purpose of the Study:

• To investigate the impact of aggregate shape on ballistic aggregation dynamics.
• To determine universal exponents in different aggregation models.
• To analyze the dependence of velocity correlations on mass and number density.

Main Methods:

• Large-scale Monte Carlo simulations on a two-dimensional square lattice.
• Modeling three distinct aggregate shapes: point particles, fractal shapes, and spheres.
• Analysis of power-law temporal decay for particle number and energy.
• Examination of velocity correlations as a function of mass.

Main Results:

• Exponents describing temporal decay and velocity correlations were determined.
• Universality of exponents was observed exclusively in the point-particle model.
• In fractal and spherical models, exponents were density-dependent.
• Velocity correlations vanished at high number densities for non-point particle models.
• The fractal dimension for the fractal-shape model was found to be approximately 1.49.

Conclusions:

• Aggregate shape significantly influences the universality of exponents in ballistic aggregation.
• The point-particle model offers a universal description, while shape-dependent models require density considerations.
• Findings provide insights into the role of morphology in aggregation processes and complex system dynamics.