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 $T_g$, the extrapolation of the vibrational entropy leads to the correlation $T_K\approx T_0$, where $T_K$ is the Kauzmann temperature and $T_0$ 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 $f$ soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting $P(f)\sim f^{\theta_e}$ the force distribution of such pairs and $\phi_c$ the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale $\omega^*$, rising up to it as $D(\omega) \sim \omega^{2+a}$, and decaying above $\omega^*$ as $D(\omega)\sim \omega^{-a}$ where $a=(1-\theta_e)/(3+\theta_e)$ and $\omega$ is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with $\langle \delta R^2\rangle\sim1/\mu\sim (\phi_c-\phi)^{\kappa}$ where $\kappa=2-2/(3+\theta_e)$, and (iii) continuum elasticity breaks down on a scale $\ell_c \sim1/\sqrt{\delta z}\sim (\phi_c-\phi)^{-b}$ where $b=(1+\theta_e)/(6+2\theta_e)$ and $\delta z=z-2d$, where $z$ is the coordination and $d$ the spatial dimension. We numerically test (i) and provide data supporting that $\theta_e\approx 0.41$ in our bi-disperse system, independently of system preparation in two and three dimensions, leading to $\kappa\approx1.41$, $a \approx 0.17$, and $b\approx 0.21$. Our results for the mean-square displacement are consistent with a recent exact replica computation for $d=\infty$, 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 $z$ is varied. Critical behaviors are obtained as $z\to z_c$ 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 $\omega^*\sim z-z_c$, which does not correspond to the Ioffe-Regel criterion. Above $\omega^*$ 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 $1/\sqrt{\omega}$ with frequency, whereas for $\omega<<\omega^*$ Rayleigh scattering is found with a scattering length $l_s\sim (z-z_c)^3/\omega^4$. 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 $l^*\sim (\phi_c-\phi)^{-1/2}$ where $\phi_c$ 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 $\phi_c$. 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 $l^*$ which diverges at $\phi_c$ [1, 2]. We compute the scaling of the bulk and shear moduli near $\phi_c$, 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