Lattice models for ballistic aggregation in one-dimension

Abstract

We propose two lattice models in one dimension, with stochastically hopping particles which aggregate on contact. The hops are guided by "velocity rates" which themselves evolve according to the rules of ballistic aggregation as in a sticky gas in continuum. Our lattice models have both velocity and density fields and an appropriate real time evolution, such that they can be compared directly with event driven molecular dynamics (MD) results for the sticky gas. We demonstrate numerically that the long time and large distance behavior of the lattice models are identical to that of the MD, and some exact results known for the sticky gas. In particular, the exactly predicted form of the non-Gaussian tail of the velocity distribution function is clearly exhibited. This correspondence of the lattice models and the sticky gas in continuum is nontrivial, as the latter has a deterministic dynamics with local kinematic constraint, in contrast with the former; yet the spatial velocity profiles (with shocks) of the lattice models and the MD have striking match.

7 pages, 5 figures

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• Energy decay in three-dimensional freely cooling granular gas
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• Velocity Distribution of Driven Inelastic One-component Maxwell gas
• A Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation
• Coarse grained dynamics of the freely cooling granular gas in one dimension
• Asymptotic behavior of the velocity distribution of driven inelastic gas with scalar velocities: analytical results
• Hydrodynamics of granular particles on a line
• Active and Passive Transport of Cargo in a Corrugated Channel: A Lattice Model Study
• Asymptotic velocity distribution of a driven one dimensional binary granular Maxwell gas