arXiv subjects

Leonardo E. Silbert

Publications and source records attributed to Leonardo E. Silbert.

35 records · Page 2Linked to original sources

arXiv2016

Spatial Distributions of Local Elastic Moduli Near the Jamming Transition

Recent progress on studies of the nanoscale mechanical responses in disordered systems has highlighted a strong degree of heterogeneity in the elastic moduli. In this contribution, using computer simulations, we study the elastic heterogeneities in athermal amorphous solids, composed of isotropic, static, sphere packings, near the jamming transition. We employ techniques, based on linear response methods, that are amenable to experimentation. We find that the local elastic moduli are randomly distributed in space and are described by Gaussian probability distributions, thereby lacking any significant spatial correlations, that persists all the way down to the transition point. However, the shear modulus fluctuations grow as the jamming threshold is approached, which is characterized by a new power-law scaling. Through this diverging behavior we are able to identify a characteristic length scale, associated with shear modulus heterogeneities, that distinguishes between bulk and local elastic responses.

cond-mat.soft↗

arXiv2015

Diffusion in jammed particle packs

Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions, $ϕ$, in the vicinity of the jamming transition at $ϕ_{c}$. Various diffusion properties are computed over several orders of magnitude in both time and packing pressure. Two well-separated regimes of normal, "Fickian" diffusion, where the mean squared displacement is linear in time, are observed. The first corresponds to diffusion inside individual spheres, while the latter is the long-time bulk diffusion. The intermediate anomalous diffusion regime and the long-time value of the diffusion coefficient are both shown to be controlled by particle contacts, which in turn depend on proximity to $ϕ_{c}$. The time required to recover normal diffusion $t^*$ scales as $(ϕ-ϕ_c)^{-0.5}$ and the long-time diffusivity $D_\infty \sim (ϕ- ϕ_c)^{0.5}$, or $D_\infty \sim 1/t^*$. It is shown that the distribution of mean first passage times associated with the escape of random walkers between neighboring particles controls both $t^*$ and $D_\infty$ in the limit $ϕ\rightarrow ϕ_c$.

cond-mat.stat-mech↗

arXiv2015

Critical-like Features of Stress Response in Frictional Packings

The mechanical response of static, unconfined, overcompressed face centred cubic, granular arrays is studied using large-scale, discrete element method simulations. Specifically, the stress response due to the application of a localised force perturbation - the Green function technique - is obtained in granular packings generated over several orders of magnitude in both the particle friction coefficient and the applied forcing. We observe crossover behaviour in the mechanical state of the system characterised by the changing nature of the resulting stress response. The transition between anisotropic and isotropic stress response exhibits critical-like features through the identification of a diverging length scale that distinguishes the spatial extent of anisotropic regions from those that display isotropic behaviour. A multidimensional phase diagram is constructed that parameterises the response of the system due to changing friction and force perturbations.

cond-mat.soft↗

arXiv2011

Jamming of frictional spheres and random loose packing

The role of friction coefficient, $μ$, on the jamming properties of disordered, particle packings is studied using computer simulations. Compressed, soft-sphere packings are brought towards the jamming transition - the point where a packing loses mechanical stability - by decreasing the packing fraction. The values of the packing fraction at the jamming transition, $ϕ^μ_{c}$, gradually decrease from the random close packing point for zero friction, to a value coincident with random loose packing as the friction coefficient is increased over several orders of magnitude. This is accompanied by a decrease in the coordination number at the jamming transition, $z^μ_{c}$, which varies from approximately six to four with increasing friction. Universal power law scaling is observed in the pressure and coordination number as a function of distance from the generalised, friction-dependent jamming point. Various power laws are also reported between the $ϕ^μ_{\rm c}$, $z^μ_{\rm c}$, and $μ$. Dependence on preparation history of the packings is also investigated.

cond-mat.soft↗

arXiv2011

Stress Response in Confined Arrays of Frictional and Frictionless Particles

Stress transmission inside three dimensional granular packings is investigated using computer simulations. Localized force perturbation techniques are implemented for frictionless and frictional shallow, ordered, granular arrays confined by solid boundaries for a range of system sizes. Stress response profiles for frictional packings agree well with the predictions for the semi-infinite half plane of classical isotropic elasticity theory down to boxes of linear dimensions of approximately forty particle diameters and over several orders of magnitude in the applied force. The response profiles for frictionless packings exhibit a transitional regime to strongly anisotropic features with increasing box size. The differences between the nature of the stress response are shown to be characterized by very different particle displacement fields.

cond-mat.soft↗

arXiv2010

Tuning Jammed Frictionless Disk Packings from Isostatic to Hyperstatic

We perform extensive computational studies of two-dimensional static bidisperse disk packings using two distinct packing-generation protocols. The first involves thermally quenching equilibrated liquid configurations to zero temperature over a range of thermal quench rates $r$ and initial packing fractions followed by compression and decompression in small steps to reach packing fractions $ϕ_J$ at jamming onset. For the second, we seed the system with initial configurations that promote micro- and macrophase-separated packings followed by compression and decompression to $ϕ_J$. We find that amorphous, isostatic packings exist over a finite range of packing fractions from $ϕ_{\rm min} \le ϕ_J \le ϕ_{\rm max}$ in the large-system limit, with $ϕ_{\rm max} \approx 0.853$. In agreement with previous calculations, we obtain $ϕ_{\rm min} \approx 0.84$ for $r > r^*$, where $r^*$ is the rate above which $ϕ_J$ is insensitive to rate. We further compare the structural and mechanical properties of isostatic versus hyperstatic packings. The structural characterizations include the contact number, bond orientational order, and mixing ratios of the large and small particles. We find that the isostatic packings are positionally and compositionally disordered, whereas bond-orientational and compositional order increase with contact number for hyperstatic packings. In addition, we calculate the static shear modulus and normal mode frequencies of the static packings to understand the extent to which the mechanical properties of amorphous, isostatic packings are different from partially ordered packings. We find that the mechanical properties of the packings change continuously as the contact number increases from isostatic to hyperstatic.

cond-mat.soft↗

arXiv2009

Stress response inside perturbed particle assemblies

The effect of structural disorder on the stress response inside three dimensional particle assemblies is studied using computer simulations of frictionless sphere packings. Upon applying a localised, perturbative force within the packings, the resulting {\it Green's} function response is mapped inside the different assemblies, thus providing an explicit view as to how the imposed perturbation is transmitted through the packing. In weakly disordered arrays, the resulting transmission of forces is of the double-peak variety, but with peak widths scaling linearly with distance from the source of the perturbation. This behaviour is consistent with an anisotropic elasticity response profile. Increasing the disorder distorts the response function until a single-peak response is obtained for fully disordered packings consistent with an isotropic description.

cond-mat.soft↗

arXiv2009

Long wavelength structural anomalies in jammed systems

The structural properties of static, jammed packings of monodisperse spheres in the vicinity of the jamming transition are investigated using large-scale computer simulations. At small wavenumber $k$, we argue that the anomalous behavior in the static structure factor, $S(k) \sim k$, is consequential of an excess of low-frequency, collective excitations seen in the vibrational spectrum. This anomalous feature becomes more pronounced closest to the jamming transition, such that $S(0) \to 0$ at the transition point. We introduce an appropriate dispersion relation that accounts for these phenomena that leads us to relate these structural features to characteristic length scales associated with the low-frequency vibrational modes of these systems. When the particles are frictional, this anomalous behavior is suppressed providing yet more evidence that jamming transitions of frictional spheres lie at lower packing fractions that that for frictionless spheres. These results suggest that the mechanical properties of jammed and glassy media may therefore be inferred from measurements of both the static and dynamical structure factors.

cond-mat.soft↗

arXiv2008

Normal Modes in Model Jammed Systems in Three Dimensions

Vibrational spectra and normal modes of mechanically stable particle packings in three dimensions are analyzed over a range of compressions, from near the jamming transition, where the packings lose their rigidity, to far above it. At high frequency, the normal modes are localized at all compressions. At low frequency, the nature of the modes depends somewhat on compression. At large compressions, far from the transition, the lowest-frequency normal modes have some plane-wave character, though less than one would expect for a crystalline or isotropic solid. At low compressions near the jamming transition, the lowest-frequency modes are neither plane-wave-like nor localized. We characterize these differences, highlighting the unusual dispersion behavior that emerges for marginally jammed solids.

cond-mat.stat-mech↗

arXiv2007

Rheology and Contact Lifetime Distribution in Dense Granular Flows

We study the rheology and distribution of interparticle contact lifetimes for gravity-driven, dense granular flows of non-cohesive particles down an inclined plane using large-scale, three dimensional, granular dynamics simulations. Rather than observing a large number of long-lived contacts as might be expected for dense flows, brief binary collisions predominate. In the hard particle limit, the rheology conforms to Bagnold scaling, where the shear stress is quadratic in the strain rate. As the particles are made softer, however, we find significant deviations from Bagnold rheology; the material flows more like a viscous fluid. We attribute this change in the collective rheology of the material to subtle changes in the contact lifetime distribution involving the increasing lifetime and number of the long-lived contacts in the softer particle systems.

cond-mat.soft↗

arXiv2006

Force heterogeneities in particle assemblies: From order to disorder

The effect of increasing structural disorder on the distribution of contact forces P(f), inside three dimensional particle assemblies is systematically studied using computer simulations of model granular packings. Starting from a face-centred cubic array, where all contact forces are identical, an increasing number of defects is introduced into the assembly, after which the system is then allowed to relax into a new mechanically stable state. Three distinct protocols for imposing disorder are compared. A quantitative measure of the disorder is obtained from distributions of the coordination number and three-particle contact angle. The distribution of normal contact forces show dramatic qualitative changes with increasing disorder. In the regime where the disorder is relatively weak, the pressure and the lowest normal mode frequency scale approximately linearly in the coordination number, with distance from the crystalline state. These results for P(f) are discussed in the context of jamming phenomena in glassy and granular materials.

cond-mat.soft↗

arXiv2006

Structural signatures of the unjamming transition at zero temperature

We study the pair correlation function $g(r)$ for zero-temperature, disordered, soft-sphere packings just above the onset of jamming. We find distinct signatures of the transition in both the first and split second peaks of this function. As the transition is approached from the jammed side (at higher packing fraction) the first peak diverges and narrows on the small-$r$ side to a delta-function. On the high-$r$ side of this peak, $g(r)$ decays as a power-law. In the split second peak, the two subpeaks are both singular at the transition, with power-law behavior on their low-$r$ sides and step-function drop-offs on their high-$r$ sides. These singularities at the transition are reminiscent of empirical criteria that have previously been used to distinguish glassy structures from liquid ones.

cond-mat.stat-mech↗

arXiv2005

Effects of compression on the vibrational modes of marginally jammed solids

Glasses have a large excess of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature is a necessary consequence of the weak connectivity of the solid, and that the frequency of modes in excess is very sensitive to the pressure. We analyze in particular two systems whose density D(w) of vibrational modes of angular frequency w display scaling behaviors with the packing fraction: (i) simulations of jammed packings of particles interacting through finite-range, purely repulsive potentials, comprised of weakly compressed spheres at zero temperature and (ii) a system with the same network of contacts, but where the force between any particles in contact (and therefore the total pressure) is set to zero. We account in the two cases for the observed a) convergence of D(w) toward a non-zero constant as w goes to 0, b) appearance of a low-frequency cutoff w*, and c) power-law increase of w* with compression. Differences between these two systems occur at lower frequency. The density of states of the modified system displays an abrupt plateau that appears at w*, below which we expect the system to behave as a normal, continuous, elastic body. In the unmodified system, the pressure lowers the frequency of the modes in excess. The requirement of stability despite the destabilizing effect of pressure yields a lower bound on the number of extra contact per particle dz: dz > p^(1/2), which generalizes the Maxwell criterion for rigidity when pressure is present. This scaling behavior is observed in the simulations. We finally discuss how the cooling procedure can affect the microscopic structure and the density of normal modes.

cond-mat.dis-nn↗

arXiv2002

Statistics of the contact network in frictional and frictionless granular packings

Simulated granular packings with different particle friction coefficient mu are examined. The distribution of the particle-particle and particle-wall normal and tangential contact forces P(f) are computed and compared with existing experimental data. Here f equivalent to F/F-bar is the contact force F normalized by the average value F-bar. P(f) exhibits exponential-like decay at large forces, a plateau/peak near f = 1, with additional features at forces smaller than the average that depend on mu. Computations of the force-force spatial distribution function and the contact point radial distribution function indicate that correlations between forces are only weakly dependent on friction and decay rapidly beyond approximately three particle diameters. Distributions of the particle-particle contact angles show that the contact network is not isotropic and only weakly dependent on friction. High force-bearing structures, or force chains, do not play a dominant role in these three dimensional, unloaded packings.

cond-mat.stat-mech↗

arXiv2002

Granular flow down a rough inclined plane: transition between thin and thick piles

The rheology of granular particles in an inclined plane geometry is studied using molecular dynamics simulations. The flow--no-flow boundary is determined for piles of varying heights over a range of inclination angles $θ$. Three angles determine the phase diagram: $θ_{r}$, the angle of repose, is the angle at which a flowing system comes to rest; $θ_{m}$, the maximum angle of stability, is the inclination required to induce flow in a static system; and $θ_{max}$ is the maximum angle for which stable, steady state flow is observed. In the stable flow region $θ_{r}<θ<θ_{max}$, three flow regimes can be distinguished that depend on how close $θ$ is to $θ_{r}$: i) $θ>>θ_{r}$: Bagnold rheology, characterized by a mean particle velocity $v_{x}$ in the direction of flow that scales as $v_{x}\propto h^{3/2}$, for a pile of height $h$, ii) $θ\gtrsimθ_{r}$: the slow flow regime, characterized by a linear velocity profile with depth, and iii) $θ\approxθ_{r}$: avalanche flow characterized by a slow underlying creep motion combined with occasional free surface events and large energy fluctuations. We also probe the physics of the initiation and cessation of flow. The results are compared to several recent experimental studies on chute flows and suggest that differences between measured velocity profiles in these experiments may simply be a consequence of how far the system is from jamming.

cond-mat.soft↗

arXiv2001

Geometry of Frictionless and Frictional Sphere Packings

We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although frictionless packings of hard-spheres are always isostatic (with six contacts) regardless of construction history and restitution coefficient, frictional packings achieve a multitude of hyperstatic packings that depend on system parameters and construction history. Instead of immediately dropping to four, the coordination number reduces smoothly from $z=6$ as the friction coefficient $μ$ between two particles is increased.

cond-mat.soft↗

arXiv2000

Gravity-driven Dense Granular Flows

We report and analyze the results of numerical studies of dense granular flows in two and three dimensions, using both linear damped springs and Hertzian force laws between particles. Chute flow generically produces a constant density profile that satisfies scaling relations suggestive of a Bagnold grain inertia regime. The type of force law has little impact on the behavior of the system. Bulk and surface flows differ in their failure criteria and flow rheology, as evidenced by the change in principal stress directions near the surface. Surface-only flows are not observed in this geometry.

cond-mat.soft↗