Exponential and power law distribution of mass clusters in a (magnetic-like) deposition model of elongated grains in 2D piles

TL;DR

This study explores how the probability of grain rotation affects cluster formation in a 2D granular pile model, revealing exponential or power-law distributions of cluster sizes based on nip flip likelihood.

Contribution

It introduces a generalized magnetic-like deposition model with a scalar 'nip' degree of freedom, analyzing the impact of grain rotation probability on cluster size distributions.

Findings

Cluster-mass distribution can be exponential or power law.

Nip flip probability influences cluster formation.

Analytical exponents relate to Hamiltonian parameters.

Abstract

A generalized so called magnetically controlled ballistic rain-like deposition (MBD) model of granular piles has been numerically investigated in 2D. The grains are taken to be elongated disks whence characterized by a two-state scalar degree of freedom, called ''nip'', their interaction being described through a Hamiltonian. Results are discussed in order to search for the effect of nip flip (or grain rotation from vertical to horizontal and conversely) probability in building a granular pile. The characteristics of creation of + (or $-$) nip's clusters and clusters of holes (missing nips) are analyzed. Two different cluster-mass regimes have been identified, through the cluster-mass distribution function which can be exponential or have a power law form depending on whether the nip flip (or grain rotation) probability is large or small. Analytical forms of the exponent are empirically found in terms of the Hamiltonian parameters.