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.

Small surfaces of Willmore type in Riemannian manifolds

In this paper we investigate the properties of small surfaces of Willmore type in Riemannian manifolds. By \emph{small} surfaces we mean topological spheres contained in a geodesic ball of small enough radius. In particular, we show that if there exist such surfaces with positive mean curvature in the geodesic ball $B_r(p)$ for arbitrarily small radius $r$ around a point $p$ in the Riemannian manifold, then the scalar curvature must have a critical point at $p$. As a byproduct of our estimates we obtain a strengthened version of the non-existence result of Mondino \cite{Mondino:2008} that implies the non-existence of certain critical points of the Willmore functional in regions where the scalar curvature is non-zero.Comment: 25 pages. Minor correction

Detailed L3 measurements of Bose-Einstein correlations and a region of anti-correlations in hadronic Z^0 decays at LEP

L3 preliminary data of two-particle Bose-Einstein correlations are reported for hadronic Z^0 decays in e+e- annihilation at LEP. The invariant relative momentum Q is identified as the eigenvariable of the measured correlation function. Significant anti-correlations are observed in the Bose-Einstein correlation function in a broad region of 0.5 - 1.6 GeV with a minimum at Q close to 0.8 GeV. Absence of Bose-Einstein correlations is demonstrated in the region above Q >= 1.6 GeV. The effective source size is found to decrease with increasing value of the transverse mass of the pair, similarly to hadron-hadron and heavy ion reactions. These feautes and our data are described well by the non-thermal tau-model, which is based on strong space-time momentum-correlations.Comment: 5 pages, 1 figure, invited talk at the XXXIXth International Symposium on Multiparticle Dynamics, Gomel, Belarus, September 200

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

Characterizing the Load Environment of Ferry Landings for Washington State Ferries and the Alaska Marine Highway System

INE/AUTC 13.0

Results of initial prop-fan model acoustic testing. Volume 1 - Discussion

Acoustic measurements on prop-fan model propulsion syste