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The kinetic energy of a freely cooling granular gas decreases as a power law $t^{-theta}$ at large times $t$. Two theoretical conjectures exist for the exponent $theta$. One based on ballistic aggregation of compact spherical aggregates predicts $theta= 2d/(d+2)$ in $d$ dimensions. The other based on Burgers equation describing anisotropic, extended clusters predicts $theta=d/2$ when $2le d le 4$. We do extensive simulations in three dimensions to find that while $theta$ is as predicted by ballistic aggregation, the cluster statistics and velocity distribution differ from it. Thus, the freely cooling granular gas fits to neither the ballistic aggregation or a Burgers equation description.
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We study the inhomogeneous clustered regime of a freely cooling granular gas of rough particles in two dimensions using large-scale event driven simulations and scaling arguments. During collisions, rough particles dissipate energy in both the normal and tangential directions of collision. In the inhomogeneous regime, translational kinetic energy and the rotational energy decay with time $t$ as power-laws $t^{-theta_T}$ and $t^{-theta_R}$. We numerically determine $theta_T approx 1$ and $theta_R approx 1.6$, independent of the coefficients of restitution. The inhomogeneous regime of the granular gas has been argued to be describable by the ballistic aggregation problem, where particles coalesce on contact. Using scaling arguments, we predict $theta_T=1$ and $theta_R=1$ for ballistic aggregation, $theta_R$ being different from that obtained for the rough granular gas. Simulations of ballistic aggregation with rotational degrees of freedom are consistent with these exponents.
We present an experimental investigation of the probability distribution of normal contact forces, $P(F)$, at the bottom boundary of static three dimensional packings of compressible granular materials. We find that the degree of deformation of individual grains plays a large role in determining the form of this distribution. For small amounts of deformation we find a small peak in $P(F)$ below the mean force with an exponential tail for forces larger than the mean force. As the degree of deformation is increased the peak at the mean force grows in height and the slope of the exponential tail increases.
The Quantizer problem is a tessellation optimisation problem where point configurations are identified such that the Voronoi cells minimise the second moment of the volume distribution. While the ground state (optimal state) in 3D is almost certainly the body-centered cubic lattice, disordered and effectively hyperuniform states with energies very close to the ground state exist that result as stable states in an evolution through the geometric Lloyds algorithm [Klatt et al. Nat. Commun., 10, 811 (2019)]. When considered as a statistical mechanics problem at finite temperature, the same system has been termed the Voronoi Liquid by [Ruscher et al. EPL 112, 66003 (2015)]. Here we investigate the cooling behaviour of the Voronoi liquid with a particular view to the stability of the effectively hyperuniform disordered state. As a confirmation of the results by Ruscher et al., we observe, by both molecular dynamics and Monte Carlo simulations, that upon slow quasi-static equilibrium cooling, the Voronoi liquid crystallises from a disordered configuration into the body-centered cubic configuration. By contrast, upon sufficiently fast non-equilibrium cooling (and not just in the limit of a maximally fast quench) the Voronoi liquid adopts similar states as the effectively hyperuniform inherent structures identified by Klatt et al. and prevents the ordering transition into a BCC ordered structure. This result is in line with the geometric intuition that the geometric Lloyds algorithm corresponds to a type of fast quench.
In the frame of a well established lattice gas model for granular compaction, we investigate the high intensity tapping regime where a pile expands significantly during external excitation. We find that this model shows the same general trends as more sophisticated models based on molecular dynamic type simulations. In particular, a minimum in packing fraction as a function of tapping strength is observed in the reversible branch of an annealed tapping protocol.
Particle beams are important tools for probing atomic and molecular interactions. Here we demonstrate that particle beams also offer a unique opportunity to investigate interactions in macroscopic systems, such as granular media. Motivated by recent experiments on streams of grains that exhibit liquid-like breakup into droplets, we use molecular dynamics simulations to investigate the evolution of a dense stream of macroscopic spheres accelerating out of an opening at the bottom of a reservoir. We show how nanoscale details associated with energy dissipation during collisions modify the streams macroscopic behavior. We find that inelastic collisions collimate the stream, while the presence of short-range attractive interactions drives structure formation. Parameterizing the collision dynamics by the coefficient of restitution (i.e., the ratio of relative velocities before and after impact) and the strength of the cohesive interaction, we map out a spectrum of behaviors that ranges from gas-like jets in which all grains drift apart to liquid-like streams that break into large droplets containing hundreds of grains. We also find a new, intermediate regime in which small aggregates form by capture from the gas phase, similar to what can be observed in molecular beams. Our results show that nearly all aspects of stream behavior are closely related to the velocity gradient associated with vertical free fall. Led by this observation, we propose a simple energy balance model to explain the droplet formation process. The qualitative as well as many quantitative features of the simulations and the model compare well with available experimental data and provide a first quantitative measure of the role of attractions in freely cooling granular streams.
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