Role of collisions in erosion of regolith during a lunar landing.

The supersonic gas plume of a landing rocket entrains lunar regolith, which is the layer of loose solids covering the lunar surface. This ejection is problematic due to scouring and dust impregnation of surrounding hardware, reduction in visibility for the crew, and spoofing of the landing sensors. To date, model predictions of erosion and ejection dynamics have been based largely on single-trajectory models in which the role of interparticle collisions is ignored. In the present work, the parameters affecting the erosion rate of monodisperse solids are investigated using the discrete element method (DEM). The drag and lift forces exerted by the rocket exhaust are incorporated via one-way coupling. The results demonstrate that interparticle collisions are frequent in the region immediately above the regolith surface; as many as 20% of particles are engaged in a collision at a given time. These collisions play an important role both in the erosion dynamics and in the final trajectories of particles. In addition, a direct assessment of the influence of collisions on the erosion rate is accomplished via a comparison between a "collisionless" DEM model and the original DEM model. This comparison shows that the erosion dynamics change drastically when collisions are considered and that the erosion rate is dependent on the collision parameters (coefficient of restitution and coefficient of friction). Physical explanations for these trends are provided.

H theorem for contact forces in granular materials.

A maximum entropy theorem is developed and tested for granular contact forces. Although it is idealized, describing two-dimensional packings of round, rigid, frictionless, cohesionless disks with coordination number Z=4, it appears to describe a central part of the physics present in the more general cases. The theorem does not make the strong claims of Edwards' hypothesis, nor does it rely upon Edwards' hypothesis at any point. Instead, it begins solely from the physical assumption that closed loops of grains are unable to impose strong force correlations around the loop. This statement is shown to be a generalization of Boltzmann's assumption of molecular chaos (his stosszahlansatz), allowing for the extra symmetries of granular stress propagation compared to the more limited symmetries of momentum propagation in a thermodynamic system. The theorem that follows from this is similar to Boltzmann's H theorem and is presented as an alternative to Edwards' hypothesis for explaining some granular phenomena. It identifies a very interesting feature of granular packings: if the generalized stosszahlansatz is correct, then the bulk of homogeneous granular packings must satisfy a maximum entropy condition simply by virtue of being stable, without any exploration of phase space required. This leads to an independent derivation of the contact force statistics, and these predictions have been compared to numerical simulation data in the isotropic case. The good agreement implies that the generalized stosszahlansatz is indeed accurate at least for the isotropic state of the idealized case studied here, and that it is the reductionist explanation for contact force statistics in this case.

Elegance of disordered granular packings: a validation of Edward's hypothesis.

We have found a way to analyze Edwards' density of states for static granular packings in the special case of round, rigid, frictionless grains assuming a constant coordination number. It obtains the most entropic density of single grain states, which predicts several observables including the distribution of contact forces. We compare these results against empirical data obtained in dynamic simulations of granular packings. The agreement is quite good, helping validate the use of statistical mechanics methods in granular physics. The differences between theory and empirics are mainly related to the coordination number, and when the empirical data are sorted by that number we obtain several insights that suggest an underlying elegance in the density of states.

Granular contact force density of states and entropy in a modified Edwards ensemble.

A method has been found to analyze Edwards' granular contact force probability functional for a special case. As a result, the granular contact force probability density functions are obtained from first principles for this case. The results are in excellent agreement with the experimental and simulation data. The derivation assumes Edwards' flat measure--a density of states (DOS) that is uniform within the metastable regions of phase space. The enabling assumption, supported by physical arguments and empirical evidence, is that correlating information is not significantly recursive through loops in the packing. Maximizing a state-counting entropy results in a transport equation that can be solved numerically. For the present this has been done using the "mean-structure approximation," projecting the DOS across all angular coordinates to more clearly identify its predominant nonuniformities. These features are (1) the grain factor Psi related to grain stability and strong correlation between the contact forces on the same grain and (2) the structure factor Upsilon related to Newton's third law and strong correlation between neighboring grains.

Comment on "Mechanical analog of temperature for the description of force distribution in static granular packings".

It has been proposed by Ngan [Phys. Rev. E 68, 011301 (2003)] that the granular contact force distribution may be analytically derived by minimizing the analog of a thermodynamic free energy, in this case consisting of the total potential energy stored in the compressed contacts minus a particular form of entropy weighted by a parameter. The parameter is identified as a mechanical temperature. I argue that the particular form of entropy cannot be correct and as a result the proposed method produces increasingly errant results for increasing grain rigidity. This trend is evidenced in Ngan's published results and in other numerical simulations and experiments.