37,518 research outputs found
Inter-dependence of the volume and stress ensembles and equipartition in statistical mechanics of granular systems
We discuss the statistical mechanics of granular matter and derive several
significant results. First, we show that, contrary to common belief, the volume
and stress ensembles are inter-dependent, necessitating the use of both. We use
the combined ensemble to calculate explicitly expectation values of structural
and stress-related quantities for two-dimensional systems. We thence
demonstrate that structural properties may depend on the angoricity tensor and
that stress-based quantities may depend on the compactivity. This calls into
question previous statistical mechanical analyses of static granular systems
and related derivations of expectation values. Second, we establish the
existence of an intriguing equipartition principle - the total volume is shared
equally amongst both structural and stress-related degrees of freedom. Third,
we derive an expression for the compactivity that makes it possible to quantify
it from macroscopic measurements.Comment: 5 pages, including 2 figures, To appear in Phys. Rev. Let
Statistical Mechanics of Vibration-Induced Compaction of Powders
We propose a theory which describes the density relaxation of loosely packed,
cohesionless granular material under mechanical tapping. Using the compactivity
concept we develope a formalism of statistical mechanics which allows us to
calculate the density of a powder as a function of time and compactivity. A
simple fluctuation-dissipation relation which relates compactivity to the
amplitude and frequency of a tapping is proposed. Experimental data of
E.R.Nowak et al. [{\it Powder Technology} 94, 79 (1997) ] show how density of
initially deposited in a fluffy state powder evolves under carefully controlled
tapping towards a random close packing (RCP) density. Ramping the vibration
amplitude repeatedly up and back down again reveals the existence of reversible
and irreversible branches in the response. In the framework of our approach the
reversible branch (along which the RCP density is obtained) corresponds to the
steady state solution of the Fokker-Planck equation whereas the irreversible
one is represented by a superposition of "excited states" eigenfunctions. These
two regimes of response are analyzed theoretically and a qualitative
explanation of the hysteresis curve is offered.Comment: 11 pages, 2 figures, Latex. Revised tex
A deductive statistical mechanics approach for granular matter
We introduce a deductive statistical mechanics approach for granular
materials which is formally built from few realistic physical assumptions. The
main finding is an universal behavior for the distribution of the density
fluctuations. Such a distribution is the equivalent of the Maxwell-Boltzmann's
distribution in the kinetic theory of gasses. The comparison with a very
extensive set of experimental and simulation data for packings of monosized
spherical grains, reveals a remarkably good quantitative agreement with the
theoretical predictions for the density fluctuations both at the grain level
and at the global system level. Such agreement is robust over a broad range of
packing fractions and it is observed in several distinct systems prepared by
using different methods. The equilibrium distributions are characterized by
only one parameter () which is a quantity very sensitive to changes in the
structural organization. The thermodynamical equivalent of and its relation
with the `granular temperature' are also discussed.Comment: 15 pages, 6 figure
Effect of weightlessness and radiation on the growth of the wheat coleoptile for the purpose of defining and verifying an experiment suitable for use in a biosatellite
Effects of temperature, X-ray irradiation, and elevated gravity on wheat seedling growt
Mechanism for the failure of the Edwards hypothesis in the SK spin glass
The dynamics of the SK model at T=0 starting from random spin configurations
is considered. The metastable states reached by such dynamics are atypical of
such states as a whole, in that the probability density of site energies,
, is small at . Since virtually all metastable states
have a much larger , this behavior demonstrates a qualitative failure of
the Edwards hypothesis. We look for its origins by modelling the changes in the
site energies during the dynamics as a Markov process. We show how the small
arises from features of the Markov process that have a clear physical
basis in the spin-glass, and hence explain the failure of the Edwards
hypothesis.Comment: 5 pages, new title, modified text, additional reference
Fluctuation-dissipation relation and the Edwards entropy for a glassy granular compaction model
We analytically study a one dimensional compaction model in the glassy
regime. Both correlation and response functions are calculated exactly in the
evolving dense and low tapping strength limit, where the density relaxes in a
fashion. The response and correlation functions turn out to be
connected through a non-equilibrium generalisation of the
fluctuation-dissipation theorem. The initial response in the average density to
an increase in the tapping strength is shown to be negative, while on longer
timescales it is shown to be positive. On short time scales the
fluctuation-dissipation theorem governs the relation between correlation and
response, and we show that such a relationship also exists for the slow degrees
of freedom, albeit with a different temperature. The model is further studied
within the statistical theory proposed by Edwards and co-workers, and the
Edwards entropy is calculated in the large system limit. The fluctuations
described by this approach turn out to match the fluctuations as calculated
through the dynamical consideration. We believe this to be the first time these
ideas have been analytically confirmed in a non-mean-field model.Comment: 4 pages, 3 figure
- …