We conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By... Show moreWe conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between particles, we extract the vibrational properties of a corresponding "shadow" system with the same configuration and interactions, but for which the dynamics of the particles are undamped. The vibrational properties are very similar to those predicted for zero-temperature sphere packings and found in atomic and molecular glasses; there is a boson peak at low frequency that shifts to higher frequency as the system is compressed above the jamming transition. Show less
By calculating the linear response of packings of soft frictionless disks to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and... Show moreBy calculating the linear response of packings of soft frictionless disks to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and nonaffine deformations as a function of the distance to jamming. Averaged over an ensemble of similar packings, these systems are well described by elasticity, while in single packings we determine a diverging length scale ℓ∗ up to which the response of the system is dominated by the local packing disorder. This length scale, which we observe directly, diverges as 1/Δz, where Δz is the difference between contact number and its isostatic value, and appears to scale identically to the length scale which had been introduced earlier in the interpretation of the spectrum of vibrational modes. It governs the crossover from isostatic behavior at the small scale to continuum behavior at the large scale; indeed we identify this length scale with the coarse graining length needed to obtain a smooth stress field. We characterize the nonaffine displacements of the particles using the displacement angle distribution, a local measure for the amount of relative sliding, and analyze the connection between local relative displacements and the elastic moduli. Show less
Ellenbroek, W.G.; Zeravcic, Z.; Saarloos, W. van; Hecke, M.L. van 2009
We numerically study the distribution P(f) of contact forces in frictionless bead packs, by averaging over the ensemble of all possible force network configurations. We resort to umbrella sampling... Show moreWe numerically study the distribution P(f) of contact forces in frictionless bead packs, by averaging over the ensemble of all possible force network configurations. We resort to umbrella sampling to resolve the asymptotic decay of P(f) for large f, and determine P(f) down to values of order 10−45 for ordered and disordered systems in two (2D) and three dimensions (3D). Our findings unambiguously show that, in the ensemble approach, the force distributions decay much faster than exponentially: P(f)∼exp(−cfα), with α≈2.0 for 2D systems, and α≈1.7 for 3D systems. Show less
Many disordered materials display a so-called jamming transition between solid-like and fluid-like states. In this thesis, we investigate jamming in granular media by studying granular packings at... Show moreMany disordered materials display a so-called jamming transition between solid-like and fluid-like states. In this thesis, we investigate jamming in granular media by studying granular packings at various distances from the transition. In numerical model systems of spherical particles, the jamming transition has many features of a critical transition. Using the linear response of such packings to external perturbations, we shed new light on their critical behavior. We analyze various scaling relations in terms of the non-affine deformations of the packing, and identify a diverging length scale that determines beyond what scale these systems can be treated as a continuum. This length scale and various other properties are determined primarily by the number of contacts between grains in the system. In the second half of the thesis we investigate force networks in granular media using the recently developed Force Network Ensemble. We discuss the analytical properties of the ensemble, and apply it to study granular media under shear stress, identifying upper bounds on the shear stress that cohesionless granular media can sustain. Show less
Somfai, E.; Hecke, M.L. van; Ellenbroek, W.G.; Shundyak, K.; Saarloos, W. van 2007
We probe the nature of the jamming transition of frictional granular media by studying their vibrational properties as a function of the applied pressure p and friction coefficient μ. The density... Show moreWe probe the nature of the jamming transition of frictional granular media by studying their vibrational properties as a function of the applied pressure p and friction coefficient μ. The density of vibrational states exhibits a crossover from a plateau at frequencies ω≳ω∗(p,μ) to a linear growth for ω≲ω∗(p,μ). We show that ω∗ is proportional to Δz, the excess number of contacts per grain relative to the minimally allowed, isostatic value. For zero and infinitely large friction, typical packings at the jamming threshold have Δz→0, and then exhibit critical scaling. We study the nature of the soft modes in these two limits, and find that the ratio of elastic moduli is governed by the distance from isostaticity. Show less
We numerically study the distribution P(f) of contact forces in frictionless bead packs, by averaging over the ensemble of all possible force network configurations. We resort to umbrella sampling... Show moreWe numerically study the distribution P(f) of contact forces in frictionless bead packs, by averaging over the ensemble of all possible force network configurations. We resort to umbrella sampling to resolve the asymptotic decay of P(f) for large f, and determine P(f) down to values of order 10−45 for ordered and disordered systems in two (2D) and three dimensions (3D). Our findings unambiguously show that, in the ensemble approach, the force distributions decay much faster than exponentially: P(f)∼exp(−cfα), with α≈2.0 for 2D systems, and α≈1.7 for 3D systems. Show less
Saarloos, W. van; Somfai, E.; Hecke, M. van; Ellenbroek, W.G.; Shundyak, K. 2007
We study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and... Show moreWe study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and fluctuates over a length scale that diverges at the jamming transition. The response to global forcing becomes increasingly nonaffine near the jamming transition. This is due to the proximity of floppy modes, the influence of which we characterize by the local linear response. We show that the local response also governs the anomalous scaling of elastic constants and contact number. Show less
Snoeijer, J.H.; Ellenbroek, W.G.; Vlugt, T.J.H.; Hecke, M.L. van 2006
An ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a priori flat measure in the... Show moreAn ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. In this paper we will give a general formulation of this force network ensemble, and derive the general expression for the force distribution P(f). For small regular packings these probability densities are obtained in closed form, while for larger packings we present a systematic numerical analysis. Since technically the problem can be written as a noninvertible matrix problem (where the matrix is determined by the contact geometry), we study what happens if we perturb the packing matrix or replace it by a random matrix. The resulting P(f)’s differ significantly from those of normal packings, which touches upon the deep question of how network statistics is related to the underlying network structure. Overall, the ensemble formulation opens up a different perspective on force networks that is analytically accessible, and which may find applications beyond granular matter. Show less
An ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a priori flat measure in the... Show moreAn ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. In this paper we will give a general formulation of this force network ensemble, and derive the general expression for the force distribution P(f). For small regular packings these probability densities are obtained in closed form, while for larger packings we present a systematic numerical analysis. Since technically the problem can be written as a noninvertible matrix problem (where the matrix is determined by the contact geometry), we study what happens if we perturb the packing matrix or replace it by a random matrix. The resulting P(f)’s differ significantly from those of normal packings, which touches upon the deep question of how network statistics is related to the underlying network structure. Overall, the ensemble formulation opens up a different perspective on force networks that is analytically accessible, and which may find applications beyond granular matter. Show less
