164 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
Emergence of order in random languages
We consider languages generated by weighted context-free grammars. It is
shown that the behaviour of large texts is controlled by saddle-point equations
for an appropriate generating function. We then consider ensembles of grammars,
in particular the Random Language Model of E. DeGiuli, Phys. Rev. Lett., 122,
128301, 2019. This model is solved in the replica-symmetric ansatz, which is
valid in the high-temperature, disordered phase. It is shown that in the phase
in which languages carry information, the replica symmetry must be broken.Comment: 16 pages + 1 appendix; v2: references added and some explanations
expanded. J. Phys. A: Math. Theor 201
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
Comment on âWhat Determines the Static Force Chains in Stressed Granular Media?â
Comment on O. Gendelman, Y. G. Pollack, I. Procaccia, S. Sengupta, and J.
Zylberg, Physical Review Letters 116, 078001 (2016).Comment: 1 pag
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
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