573 research outputs found
Some recent theoretical results on amorphous packings of hard spheres
The aim of this paper is to review and discuss qualitatively some results on
the properties of amorphous packings of hard spheres that were recently
obtained by means of the replica method. The theory gives predictions for the
equation of state of the glass, the complexity of the metastable states, the
scaling of the pressure close to jamming, the coordination of the packing and
the pair correlation function in any space dimension d. The predictions compare
very well with numerical simulations in d=3 and somehow also in d=2. The
asymptotic predictions for d->oo are within the rigorous bounds. The theory can
be extended to binary mixtures and to hard core potentials with an attractive
tail or square well.Comment: 7 pages, 6 figures; proceedings of the X International Workshop on
Disordered Systems, Molveno (TN), Italy, March 200
The ideal glass transition of Hard Spheres
We use the replica method to study the ideal glass transition of a liquid of
identical Hard Spheres. We obtain estimates of the configurational entropy in
the liquid phase, of the Kauzmann packing fraction, in the range 0.58--0.62,
and of the random close packing density, in the range 0.64--0.67, depending on
the approximation we use for the equation of state of the liquid. We also
compute the pair correlation function in the glassy states (i.e., dense
amorphous packings) and we find that the mean coordination number at random
close packing is equal to 6. All these results compare well with numerical
simulations and with other existing theories.Comment: 13 pages, 8 figure
Amorphous packings of hard spheres in large space dimension
In a recent paper (cond-mat/0506445) we derived an expression for the
replicated free energy of a liquid of hard spheres based on the HNC free energy
functional. An approximate equation of state for the glass and an estimate of
the random close packing density were obtained in d=3. Here we show that the
HNC approximation is not needed: the same expression can be obtained from the
full diagrammatic expansion of the replicated free energy. Then, we consider
the asymptotics of this expression when the space dimension d is very large. In
this limit, the entropy of the hard sphere liquid has been computed exactly.
Using this solution, we derive asymptotic expressions for the glass transition
density and for the random close packing density for hard spheres in large
space dimension.Comment: 11 pages, 1 figure, includes feynmf diagram
Fragility in p-spin models
We investigate the relation between fragility and phase space properties -
such as the distribution of states - in the mean field p-spin model, a solvable
model that has been frequently used in studies of the glass transition. By
direct computation of all the relevant quantities, we find that: i) the
recently observed correlation between fragility and vibrational properties at
low temperature is present in this model; ii) the total number of states is a
decreasing function of fragility, at variance of what is currently believed. We
explain these findings by taking into account the contribution to fragility
coming from the transition paths between different states. Finally, we propose
a geometric picture of the phase space that explains the correlation between
properties of the transition paths, distribution of states and their
vibrational properties. However, our analysis may not apply to strong systems
where inflection points in the configurational entropy as a function of the
temperature are found
Fluctuation Relation beyond Linear Response Theory
The Fluctuation Relation (FR) is an asymptotic result on the distribution of
certain observables averaged over time intervals T as T goes to infinity and it
is a generalization of the fluctuation--dissipation theorem to far from
equilibrium systems in a steady state which reduces to the usual Green-Kubo
(GK) relation in the limit of small external non conservative forces. FR is a
theorem for smooth uniformly hyperbolic systems, and it is assumed to be true
in all dissipative ``chaotic enough'' systems in a steady state. In this paper
we develop a theory of finite time corrections to FR, needed to compare the
asymptotic prediction of FR with numerical observations, which necessarily
involve fluctuations of observables averaged over finite time intervals T. We
perform a numerical test of FR in two cases in which non Gaussian fluctuations
are observable while GK does not apply and we get a non trivial verification of
FR that is independent of and different from linear response theory. Our
results are compatible with the theory of finite time corrections to FR, while
FR would be observably violated, well within the precision of our experiments,
if such corrections were neglected.Comment: Version accepted for publication on the Journal of Statistical
Physics; minor changes; two references adde
Fluctuation theorem for non-equilibrium relaxational systems driven by external forces
We discuss an extension of the fluctuation theorem to stochastic models that,
in the limit of zero external drive, are not able to equilibrate with their
environment, extending results presented by Sellitto (cond-mat/9809186). We
show that if the entropy production rate is suitably defined, its probability
distribution function verifies the Fluctuation Relation with the ambient
temperature replaced by a (frequency-dependent) effective temperature. We
derive modified Green-Kubo relations. We illustrate these results with the
simple example of an oscillator coupled to a nonequilibrium bath driven by an
external force. We discuss the relevance of our results for driven glasses and
the diffusion of Brownian particles in out of equilibrium media and propose a
concrete experimental strategy to measure the low frequency value of the
effective temperature using the fluctuations of the work done by an ac
conservative field. We compare our results to related ones that appeared in the
literature recently.Comment: 39 pages, 6 figure
Fluctuations of entropy production in the isokinetic ensemble
We discuss the microscopic definition of entropy production rate in a model
of a dissipative system: a sheared fluid in which the kinetic energy is kept
constant via a Gaussian thermostat. The total phase space contraction rate is
the sum of two statistically independent contributions: the first one is due to
the work of the conservative forces, is independent of the driving force and
does not vanish at zero drive, making the system non-conservative also in
equilibrium. The second is due to the work of the dissipative forces, and is
responsible for the average entropy production; the distribution of its
fluctuations is found to verify the Fluctuation Relation of Gallavotti and
Cohen. The distribution of the fluctuations of the total phase space
contraction rate also verify the Fluctuation Relation. It is compared with the
same quantity calculated in the isoenergetic ensemble: we find that the two
ensembles are equivalent, as conjectured by Gallavotti. Finally, we discuss the
implication of our results for experiments trying to verify the validity of the
FR.Comment: 8 pages, 4 figure
Fluctuations relation and external thermostats: an application to granular materials
In this note we discuss a paradigmatic example of interacting particles
subject to non conservative external forces and to the action of thermostats
consisting of external (finite) reservoirs of particles. We then consider a
model of granular materials of interest for experimental tests that had
recently attracted lot of attentions. This model can be reduced to the
previously discussed example under a number of assumptions, in particular that
inelasticity due to internal collisions can be neglected for the purpose of
measuring the large deviation functional for entropy production rate. We show
that if the restitution coefficient in the granular material model is close to
one, then the required assuptions are verified on a specific time scale and we
predict a fluctuation relation for the entropy production rate measured on the
same time scale.Comment: 7 pages; updated to take into account comments received on the first
version; to appear on J.Stat.Mech.(2006
A note on rattlers in amorphous packings of binary mixtures of hard spheres
It has been recently pointed out by Farr and Groot (arXiv:0912.0852) and by
Kyrylyuk and Philipse (Prog. Colloid Polym. Sci., 2010, in press) that our
theoretical result for the jamming density of a binary mixture of hard spheres
(arXiv:0903.5099) apparently violates an upper bound that is obtained by
considering the limit where the diameter ratio r = DA/DB goes to infinity. We
believe that this apparent contradiction is the consequence of a
misunderstanding, which we try to clarify here.Comment: 2 pages, 2 figures; final version published on J.Chem.Phy
Jamming Criticality Revealed by Removing Localized Buckling Excitations
Recent theoretical advances offer an exact, first-principle theory of jamming
criticality in infinite dimension as well as universal scaling relations
between critical exponents in all dimensions. For packings of frictionless
spheres near the jamming transition, these advances predict that nontrivial
power-law exponents characterize the critical distribution of (i) small
inter-particle gaps and (ii) weak contact forces, both of which are crucial for
mechanical stability. The scaling of the inter-particle gaps is known to be
constant in all spatial dimensions -- including the physically relevant
and 3, but the value of the weak force exponent remains the object of
debate and confusion. Here, we resolve this ambiguity by numerical simulations.
We construct isostatic jammed packings with extremely high accuracy, and
introduce a simple criterion to separate the contribution of particles that
give rise to localized buckling excitations, i.e., bucklers, from the others.
This analysis reveals the remarkable dimensional robustness of mean-field
marginality and its associated criticality.Comment: 12 pages, 4 figure
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