244 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.
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
Hyperstaticity and loops in frictional granular packings
The hyperstatic nature of granular packings of perfectly rigid disks is
analyzed algebraically and through numerical simulation. The elementary loops
of grains emerge as a fundamental element in addressing hyperstaticity. Loops
consisting of an odd number of grains behave differently than those with an
even number. For odd loops, the latent stresses are exterior and are
characterized by the sum of frictional forces around each loop. For even loops,
the latent stresses are interior and are characterized by the alternating sum
of frictional forces around each loop. The statistics of these two types of
loop sums are found to be Gibbsian with a "temperature" that is linear with the
friction coefficient mu when mu<1.Comment: 4 pages; Powders and Grains 2009, Golden, Colorado, US
Spatial and Temporal Extrapolation of Disdrometer Size Distributions Based on a Lagrangian Trajectory Model of Falling Rain
Methodologies to improve disdrometer processing, loosely based on
mathematical techniques common to the field of particle flow and fluid
mechanics, are examined and tested. The inclusion of advection and vertical
wind field estimates appears to produce significantly improved results in a
Lagrangian hydrometeor trajectory model, in spite of very strict assumptions of
noninteracting hydrometeors, constant vertical air velocity, and time
independent advection during a radar scan time interval. Wind field data can be
extracted from each radar elevation scan by plotting and analyzing reflectivity
contours over the disdrometer site and by collecting the radar radial velocity
data to obtain estimates of advection. Specific regions of disdrometer spectra
(drop size versus time) often exhibit strong gravitational sorting signatures,
from which estimates of vertical velocity can be extracted. These independent
wind field estimates can be used as initial conditions to the Lagrangian
trajectory simulation of falling hydrometeors.Comment: 25 pages, 15 figures, 4 tables. Submitted to The Open Atmospheric
Science Journal, http://www.bentham.org/open/toascj
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