623 research outputs found
Friction law and hysteresis in granular materials
The macroscopic friction of particulate materials often weakens as the flow
rate is increased, leading to potentially disastrous intermittent phenomena
including earthquakes and landslides. We theoretically and numerically study
this phenomenon in simple granular materials. We show that velocity-weakening,
corresponding to a non-monotonic behavior in the friction law , is
present even if the dynamic and static microscopic friction coefficients are
identical, but disappears for softer particles. We argue that this instability
is induced by endogenous acoustic noise, which tends to make contacts slide,
leading to faster flow and increased noise. We show that soft spots, or
excitable regions in the materials, correspond to rolling contacts that are
about to slide, whose density is described by a nontrivial exponent .
We build a microscopic theory for the non-monotonicity of , which also
predicts the scaling behavior of acoustic noise, the fraction of sliding
contacts and the sliding velocity, in terms of . Surprisingly,
these quantities have no limit when particles become infinitely hard, as
confirmed numerically. Our analysis rationalizes previously unexplained
observations and makes new experimentally testable predictions.Comment: 6 pages + 3 pages S
Effect of Friction on Dense Suspension Flows of Hard Particles
We use numerical simulations to study the effect of particle friction on
suspension flows of non-Brownian hard particles. By systematically varying the
microscopic friction coefficient and the viscous number , we build a
phase diagram that identifies three regimes of flow: Frictionless, Frictional
Sliding, and Rolling. Using energy balance in flow, we predict relations
between kinetic observables, confirmed by numerical simulations. For realistic
friction coefficient and small viscous numbers (below ) we show
that the dominating dissipative mechanism is sliding of frictional contacts,
and we characterize asymptotic behaviors as jamming is approached. Outside this
regime, our observations support that flow belongs to the universality class of
frictionless particles. We discuss recent experiments in the context of our
phase diagram.Comment: 8 page
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
Theory of the Jamming Transition at Finite Temperature
A theory for the microscopic structure and the vibrational properties of soft
sphere glass at finite temperature is presented. With an effective potential,
derived here, the phase diagram and vibrational properties are worked out
around the Maxwell critical point at zero temperature and pressure .
Variational arguments and effective medium theory identically predict a
non-trivial temperature scale with
such that low-energy vibrational properties are hard-sphere like for , and zero-temperature soft-sphere like otherwise. However, due to
crossovers in the equation of state relating , , and the packing fraction
, these two regimes lead to four regions where scaling behaviors differ
when expressed in terms of and . Scaling predictions are presented
for the mean-squared displacement, characteristic frequency, shear modulus, and
characteristic elastic length in all regions of the phase diagram.Comment: 8 pages + 3 pages S
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
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
Unified Theory of Inertial Granular Flows and Non-Brownian Suspensions
Rheological properties of dense flows of hard particles are singular as one
approaches the jamming threshold where flow ceases, both for aerial granular
flows dominated by inertia, and for over-damped suspensions. Concomitantly, the
lengthscale characterizing velocity correlations appears to diverge at jamming.
Here we introduce a theoretical framework that proposes a tentative, but
potentially complete scaling description of stationary flows. Our analysis,
which focuses on frictionless particles, applies {\it both} to suspensions and
inertial flows of hard particles. We compare our predictions with the empirical
literature, as well as with novel numerical data. Overall we find a very good
agreement between theory and observations, except for frictional inertial flows
whose scaling properties clearly differ from frictionless systems. For
over-damped flows, more observations are needed to decide if friction is a
relevant perturbation or not. Our analysis makes several new predictions on
microscopic dynamical quantities that should be accessible experimentally.Comment: 13 pages + 3 pages S
Straightening of Thermal Fluctuations in Semi-Flexible Polymers by Applied Tension
We investigate the propagation of a suddenly applied tension along a
thermally excited semi-flexible polymer using analytical approximations,
scaling arguments and numerical simulation. This problem is inherently
non-linear. We find sub-diffusive propagation with a dynamical exponent of 1/4.
By generalizing the internal elasticity, we show that tense strings exhibit
qualitatively different tension profiles and propagation with an exponent of
1/2.Comment: Latex file; with three postscript figures; .ps available at
http://dept.physics.upenn.edu/~nelson/pull.p
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