701 research outputs found
Correlations between vibrational entropy and dynamics in super-cooled liquids
A relation between vibrational entropy and particles mean square displacement
is derived in super-cooled liquids, assuming that the main effect of
temperature changes is to rescale the vibrational spectrum. Deviations from
this relation, in particular due to the presence of a Boson Peak whose shape
and frequency changes with temperature, are estimated. Using observations of
the short-time dynamics in liquids of various fragility, it is argued that (i)
if the crystal entropy is significantly smaller than the liquid entropy at
, the extrapolation of the vibrational entropy leads to the correlation
, where is the Kauzmann temperature and is the
temperature extracted from the Vogel-Fulcher fit of the viscosity. (ii) The
jump in specific heat associated with vibrational entropy is very small for
strong liquids, and increases with fragility. The analysis suggests that these
correlations stem from the stiffening of the Boson Peak under cooling,
underlying the importance of this phenomenon on the dynamical arrest.Comment: Eqs.2 and 7 corrected, results unchange
On the dependence of the avalanche angle on the granular layer thickness
A layer of sand of thickness h flows down a rough surface if the inclination
is larger than some threshold value theta which decreases with h. A tentative
microscopic model for the dependence of theta with h is proposed for rigid
frictional grains, based on the following hypothesis: (i) a horizontal layer of
sand has some coordination z larger than a critical value z_c where mechanical
stability is lost (ii) as the tilt angle is increased, the configurations
visited present a growing proportion $_s of sliding contacts. Instability with
respect to flow occurs when z-z_s=z_c. This criterion leads to a prediction for
theta(h) in good agreement with empirical observations.Comment: 6 pages, 2 figure
The distribution of forces affects vibrational properties in hard sphere glasses
We study theoretically and numerically the elastic properties of hard sphere
glasses, and provide a real-space description of their mechanical stability. In
contrast to repulsive particles at zero-temperature, we argue that the presence
of certain pairs of particles interacting with a small force soften elastic
properties. This softening affects the exponents characterizing elasticity at
high pressure, leading to experimentally testable predictions. Denoting
the force distribution of such pairs and the
packing fraction at which pressure diverges, we predict that (i) the density of
states has a low-frequency peak at a scale , rising up to it as
, and decaying above as where and is the frequency,
(ii) shear modulus and mean-squared displacement are inversely proportional
with where
, and (iii) continuum elasticity breaks down on a
scale where
and , where is the
coordination and the spatial dimension. We numerically test (i) and provide
data supporting that in our bi-disperse system,
independently of system preparation in two and three dimensions, leading to
, , and . Our results for the
mean-square displacement are consistent with a recent exact replica computation
for , whereas some observations differ, as rationalized by the
present approach.Comment: 5 pages + 4 pages supplementary informatio
Geometric origin of excess low-frequency vibrational modes in amorphous solids
Glasses have a large excess of low-frequency vibrational modes in comparison
with crystalline solids. We show that such a feature is a necessary consequence
of the geometry generic to weakly connected solids. In particular, we analyze
the density of states of a recently simulated system, comprised of weakly
compressed spheres at zero temperature. We account for the observed a)
constancy of the density of modes with frequency, b) appearance of a
low-frequency cutoff, and c) power-law increase of this cutoff with
compression. We predict a length scale below which vibrations are very
different from those of a continuous elastic body.Comment: 4 pages, 2 figures. Argument rewritten, identical result
Toward a microscopic description of flow near the jamming threshold
We study the relationship between microscopic structure and viscosity in
non-Brownian suspensions. We argue that the formation and opening of contacts
between particles in flow effectively leads to a negative selection of the
contacts carrying weak forces. We show that an analytically tractable model
capturing this negative selection correctly reproduces scaling properties of
flows near the jamming transition. In particular, we predict that (i) the
viscosity {\eta} diverges with the coordination z as {\eta} ~
(z_c-z)^{-(3+{\theta})/(1+{\theta})}, (ii) the operator that governs flow
displays a low-frequency mode that controls the divergence of viscosity, at a
frequency {\omega}_min\sim(z_c-z)^{(3+{\theta})/(2+2{\theta})}, and (iii) the
distribution of forces displays a scale f* that vanishes near jamming as
f*/\sim(z_c-z)^{1/(1+{\theta})} where {\theta} characterizes the
distribution of contact forces P(f)\simf^{\theta} at jamming, and where z_c is
the Maxwell threshold for rigidity.Comment: 6 pages, 4 figure
Scaling of phononic transport with connectivity in amorphous solids
The effect of coordination on transport is investigated theoretically using
random networks of springs as model systems. An effective medium approximation
is made to compute the density of states of the vibrational modes, their energy
diffusivity (a spectral measure of transport) and their spatial correlations as
the network coordination is varied. Critical behaviors are obtained as
where these networks lose rigidity. A sharp cross-over from a regime
where modes are plane-wave-like toward a regime of extended but
strongly-scattered modes occurs at some frequency , which
does not correspond to the Ioffe-Regel criterion. Above both the
density of states and the diffusivity are nearly constant. These results agree
remarkably with recent numerical observations of repulsive particles near the
jamming threshold \cite{ning}. The analysis further predicts that the length
scale characterizing the correlation of displacements of the scattered modes
decays as with frequency, whereas for
Rayleigh scattering is found with a scattering length . It is argued that this description applies to silica glass
where it compares well with thermal conductivity data, and to transverse
ultrasound propagation in granular matter
Hypoconstrained Jammed Packings of Nonspherical Hard Particles: Ellipses and Ellipsoids
Continuing on recent computational and experimental work on jammed packings
of hard ellipsoids [Donev et al., Science, vol. 303, 990-993] we consider
jamming in packings of smooth strictly convex nonspherical hard particles. We
explain why the isocounting conjecture, which states that for large disordered
jammed packings the average contact number per particle is twice the number of
degrees of freedom per particle (\bar{Z}=2d_{f}), does not apply to
nonspherical particles. We develop first- and second-order conditions for
jamming, and demonstrate that packings of nonspherical particles can be jammed
even though they are hypoconstrained (\bar{Z}<2d_{f}). We apply an algorithm
using these conditions to computer-generated hypoconstrained ellipsoid and
ellipse packings and demonstrate that our algorithm does produce jammed
packings, even close to the sphere point. We also consider packings that are
nearly jammed and draw connections to packings of deformable (but stiff)
particles. Finally, we consider the jamming conditions for nearly spherical
particles and explain quantitatively the behavior we observe in the vicinity of
the sphere point.Comment: 33 pages, third revisio
Heterogeneous Dynamics, Marginal Stability and Soft Modes in Hard Sphere Glasses
In a recent publication we established an analogy between the free energy of
a hard sphere system and the energy of an elastic network [1]. This result
enables one to study the free energy landscape of hard spheres, in particular
to define normal modes. In this Letter we use these tools to analyze the
activated transitions between meta-bassins, both in the aging regime deep in
the glass phase and near the glass transition. We observe numerically that
structural relaxation occurs mostly along a very small number of
nearly-unstable extended modes. This number decays for denser packing and is
significantly lowered as the system undergoes the glass transition. This
observation supports that structural relaxation and marginal modes share common
properties. In particular theoretical results [2, 3] show that these modes
extend at least on some length scale where
corresponds to the maximum packing fraction, i.e. the jamming
transition. This prediction is consistent with very recent numerical
observations of sheared systems near the jamming threshold [4], where a similar
exponent is found, and with the commonly observed growth of the rearranging
regions with compression near the glass transition.Comment: 6 pages, improved versio
On the rigidity of a hard sphere glass near random close packing
We study theoretically and numerically the microscopic cause of the
mechanical stability of hard sphere glasses near their maximum packing. We show
that, after coarse-graining over time, the hard sphere interaction can be
described by an effective potential which is exactly logarithmic at the random
close packing . This allows to define normal modes, and to apply recent
results valid for elastic networks: mechanical stability is a non-local
property of the packing geometry, and is characterized by some length scale
which diverges at [1, 2]. We compute the scaling of the bulk and
shear moduli near , and speculate on the possible implications of these
results for the glass transition.Comment: 7 pages, 4 figures. Figure 4 had a wrong unit in abscissa, which was
correcte
Contact line motion for partially wetting fluids
We study the flow close to an advancing contact line in the limit of small
capillary number. To take into account wetting effects, both long and
short-ranged contributions to the disjoining pressure are taken into account.
In front of the contact line, there is a microscopic film corresponding to a
minimum of the interaction potential. We compute the parameters of the contact
line solution relevant to the matching to a macroscopic problem, for example a
spreading droplet. The result closely resembles previous results obtained with
a slip model
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