Crater depth prediction in granular collisions: A uniaxial compression model.

Impact crater experiments in granular media traditionally involve loosely packed sand targets. However, this study investigates granular impact craters on both loosely and more tightly packed sand targets. We report experiments that consistently adhere to power-law scaling laws for diameter as a function of impacting energy, similar to those reported by other groups for their experiments utilizing both solid and granular projectiles. In contrast, we observe significant deviations in the depth versus energy power law predicted by previous models. To address this discrepancy, we introduce a physical model of uniaxial compression that explains how depth saturates in granular collisions. Furthermore, we present an energy balance alongside this model that describes the energy transfer mechanisms acting during crater formation. We found a better way to transfer vertical momentum to horizontal degrees of freedom as the impact surface compacts, resulting in shallow craters on compacted sandbox targets. Our results reveal depth-to-diameter aspect ratios from approximately 0.051 to 0.094, allowing us to interpret the shallowness of planetary craters at the light of the uniaxial compression mechanism proposed in this work.

Diffusivity and weak clustering in a quasi-two-dimensional granular gas.

We present results from a detailed simulation of a quasi-two-dimensional dissipative granular gas, kept in a noncondensed steady state via vertical shaking over a rough substrate. This gas shows a weak power-law decay in the tails of its pair distribution functions, indicating clustering. This clustering depends monotonically on the dissipation coefficient and disappears when the sphere-sphere collisions are conservative. Clustering is also sensitive to the packing fraction. This gas also displays the standard nonequilibrium characteristics of similar systems, including non-Maxwellian velocity distributions. The diffusion coefficients are calculated over all the conditions of the simulations, and it is found that diluted gases are more diffusive for smaller restitution coefficients.

Effective potentials of dissipative hard spheres in granular matter.

We present an experimental study of the spatial correlations of a quasi-two-dimensional dissipative gas kept in a non-static steady state via vertical shaking. From high temporal resolution images we obtain the Pair Distribution Function (PDF) for granular species with different restitution coefficients. Effective potentials for the interparticle interaction are extracted using the Ornstein-Zernike equation with the Percus-Yevick closure. From both the PDFs and the corresponding effective potentials, we find a clear increase of the spatial correlation at contact with the decreasing values of the restitution coefficient.

Granular convection driven by shearing inertial forces.

Convection velocity measurements in vertically vibrated granular materials are presented. The convection velocity close to the walls grows quadratically with the difference between the maximum and critical, or excess, amplitude (proposed as a dynamic parameter to describe related problems) and it is shown numerically that the average bed-bottom relative velocity during the distancing between them, grows linearly with the squared as well. This is interpreted as the signature of an inertial shearing force or momentum transfer proportional to the bed-container relative velocity, acting mainly during the bed-plate distancing part of each cycle which leads to the formation of the convective flux.

Inertia in the Brazil nut problem.

The rise dynamics of a large particle, in a granular bed under vertical vibrations, is experimentally studied with an inductive device designed to track the particle while it climbs through the granulate under different conditions. A model based on energy considerations is presented to explain our experimental data, drawing the important conclusion that it is the inertia of the particle, assisted by Reynolds dilatancy, the driven force behind its ascension mechanism. The ascension reveals a friction profile within the column which remains unchanged for different accelerations.

Epitaxial growth of granular single crystals.

Compaction from a random-loose-packed to a random-close-packed phase is observed when monodisperse granular beds are shaken, but beyond this packing, the system freezes up in a jammed structure. Here we report a technique to grow large hard-sphere granular crystals, with perfect stacking and no defects by means of a "gas phase" epitaxial procedure. We study the growth mechanism and provide evidence that the observed granular crystallization is driven by gravity and energy dissipation.