7,732 research outputs found
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 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 for arbitrarily small radius around a point in
the Riemannian manifold, then the scalar curvature must have a critical point
at .
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
Results of initial prop-fan model acoustic testing. Volume 1 - Discussion
Acoustic measurements on prop-fan model propulsion syste
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