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

Fahad Puthalath1,2, Apurba Biswas3,4, V V Prasad5

  • 1Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany.

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|November 18, 2023
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Summary
This summary is machine-generated.

Ballistic aggregation models show that particle shape influences exponents. Only the point-particle model exhibits universal exponents, while others depend on density, impacting velocity correlations.

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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.