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 \textit{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 \textit{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 \textit{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.Comment: 15 pages, 8 figures, to appear in Phys. Rev.

Estimation of Apollo lunar dust transport using optical extinction measurements

A technique to estimate mass erosion rate of surface soil during landing of the Apollo Lunar Module (LM) and total mass ejected due to the rocket plume interaction is proposed and tested. The erosion rate is proportional to the product of the second moment of the lofted particle size distribution N(D), and third moment of the normalized soil size distribution S(D), divided by the integral of S(D)D^2/v(D), where D is particle diameter and v(D) is the vertical component of particle velocity. The second moment of N(D) is estimated by optical extinction analysis of the Apollo cockpit video. Because of the similarity between mass erosion rate of soil as measured by optical extinction and rainfall rate as measured by radar reflectivity, traditional NWS radar/rainfall correlation methodology can be applied to the lunar soil case where various S(D) models are assumed corresponding to specific lunar sites.Comment: Acta Geophysica 201

Elegance of disordered granular packings: a validation of Edwards' 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 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.Comment: 4 pages, 5 figures, Changes in the reference

SPACE.com Interview: Effects of Lunar Dust Acceleration by Spacecraft Landing

No abstract availabl

Nature's Way of Making Audacious Space Projects Viable

Building a starship within the next 100 years is an audacious goal. To be successful, we need sustained funding that may be difficult to maintain in the face of economic challenges that are poised to arise during these next 100 years. Our species' civilization has only recently reached the classification as (approximately) Type-I on the Kardashev scale; that is, we have spread out from one small locality to become a global species mastering the energy and resources of an entire planet. In the process we discovered the profound truth that the two-dimensional surface of our world is not flat, but has positive curvature and is closed so that its area and resources are finite. It should come as no surprise to a Type I civilization when its planet's resources dWindle; how could they not? Yet we have gone year by year, government by government, making little investment for the time when civilization becomes violent in the unwelcome contractions that must follow, when we are forced too late into the inevitable choice: to remain and diminish on an unhappy world; or to expand into the only dimension remaining perpendicularly outward from the surface into space. Then some day we may become a Type-II civilization, mastering the resources of an entire solar system. Our species cannot continue as we have on this planet for another 100 years. Doubtless it falls on us today, the very time we intended to start building a starship, to make the late choice. We wished this century to be filled with enlightenment and adventure; it could be an age of desperation and war. What a time to begin an audacious project in space! How will we maintain consistent funding for the next 100 years? Fortunately, saving a civilization, mastering a solar system, and doing other great things like building starships amount to mostly the same set of tasks. Recognizing what we must be about during the next 100 years will make it possible to do them all

Plume Mitigation: Soil Erosion and Lunar Prospecting Sensor Project

Demonstrate feasibility of the simplest, lowest-mass method of measuring density of a cloud of lunar soil ejected by rocket exhaust, using new math techniques with a small baseline laser/camera system. Focus is on exploring the erosion process that occurs when the exhaust plume of a lunar rocket impacts the regolith. Also, predicting the behavior of the lunar soil that would be blasted from a lunar landing/launch site shall assist in better design and protection of any future lunar settlement from scouring of structures and equipment. NASA is gathering experimental data to improve soil erosion models and understand how lunar particles enter the plume flow

Granular Contact Forces: Proof of "Self-Ergodicity" by Generalizing Boltzmann's Stosszahlansatz and H Theorem

Ergodicity is proved for granular contact forces. To obtain this proof from first principles, this paper generalizes Boltzmann's stosszahlansatz (molecular chaos) so that it maintains the necessary correlations and symmetries of granular packing ensembles. Then it formally counts granular contact force states and thereby defines the proper analog of Boltzmann's H functional. This functional is used to prove that (essentially) all static granular packings must exist at maximum entropy with respect to their contact forces. Therefore, the propagation of granular contact forces through a packing is a truly ergodic process in the Boltzmannian sense, or better, it is self-ergodic. Self-ergodicity refers to the non-dynamic, internal relationships that exist between the layer-by-layer and column-by-column subspaces contained within the phase space locus of any particular granular packing microstate. The generalized H Theorem also produces a recursion equation that may be solved numerically to obtain the density of single particle states and hence the distribution of granular contact forces corresponding to the condition of self-ergodicity. The predictions of the theory are overwhelmingly validated by comparison to empirical data from discrete element modeling

Rocket Cratering in Simulated Lunar and Martian Environments

With NASA's planned return to the moon and possibly with lunar outposts being formed, repeated landings at the same site will be necessary. Understanding rocket plume interaction with lunar and Martian surfaces is of paramount importance in order to safely land and protect hardware surrounding the landing site. This work will report on results of three small experiments intended to explore plume impingement onto lunar and Martian surfaces: Handheld Observation of Scour Holes (HOOSH), Handheld Angle of Repose Measurements of Lunar Simulants (HARMLuS), and Mars Architecture Team study (MATS). The first two experiments were performed during two sorties of reduced gravity flights. HOOSH was designed to investigate crater formation as a function of gravitational level (lunar and Martian gravity). HARMLuS was designed to measure the Angle of Failure (related to the angle of repose) at lunar and Martian gravity. Both experiments have complex findings indicative of the hysteretic behavior of granular materials, especially resulting from reduced gravity. The MATS experiment was designed to investigate the effects of regolith compaction on the granular mechanics of crater formation. In general, the granular mechanics is a much stronger function of compaction than gravitation acceleration. Crater formation is greatly enhanced at reduced gravity (resulting in much larger craters). The angle of failure of the lunar simulants increases with decreasing gravitational acceleration, and occasionally becomes infinite for some compactions at lunar gravity. The angle of failure also increases with increasing compaction. While compaction does play a role in the time development of crater formation, the asymptotic behavior is largely unaffected.Comment: 9 pages, 8 figures. Presented at Earth & Space 2010 conferenc