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We numerically investigate stress relaxation in soft athermal disks to reveal critical slowing down when the system approaches the jamming point. The exponents describing the divergence of the relaxation time differ dramatically depending on whether the transition is approached from the jammed or unjammed phase. This contrasts sharply with conventional dynamic critical scaling scenarios, where a single exponent characterizes both sides. We explain this surprising difference in terms of the vibrational density of states (vDOS), which is a key ingredient of linear viscoelastic theory. The vDOS exhibits an extra slow mode that emerges below jamming, which we utilize to demonstrate the anomalous exponent below jamming.
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We show that non-Brownian suspensions of repulsive spheres below jamming display a slow relaxational dynamics with a characteristic time scale that diverges at jamming. This slow time scale is fully encoded in the structure of the unjammed packing and can be readily measured via the vibrational density of states. We show that the corresponding dynamic critical exponent is the same for randomly generated and sheared packings. Our results show that a wide variety of physical situations, from suspension rheology to algorithmic studies of the jamming transition are controlled by a unique diverging timescale, with a universal critical exponent.
The morphology and the microscopic internal dynamics of a bidimensional gel formed by spontaneous aggregation of gold nanoparticles confined at the water surface are investigated by a suite of techniques, including grazing-incidence x-ray photon correlation spectroscopy (GI-XPCS). The range of concentrations studied spans across the percolation transition for the formation of the gel. The dynamical features observed by GI-XPCS are interpreted in view of the results of microscopical imaging; an intrinsic link between the mechanical modulus and internal dynamics is demonstrated for all the concentrations. Our work presents, to the best of our knowledge, the first example of a transition from stretched to compressed correlation function actively controlled by quasistatically varying the relevant thermodynamic variable. Moreover, by applying a model proposed time ago by Duri and Cipelletti [A. Duri and L. Cipelletti, Europhys. Lett. 76, 972 (2006)] we are able to build a novel master curve for the shape parameter, whose scaling factor allows us to quantify a long time displacement length. This characteristic length is shown to converge, as the concentration is increased, to the short time localization length determined by pseudo Debye-Waller analysis of the initial contrast. Finally, the intrinsic dynamics of the system are then compared with that induced by means of a delicate mechanical perturbation applied to the interface.
We perform numerical simulations of athermal repulsive frictionless disks and spheres in two and three spatial dimensions undergoing cyclic quasi-static simple shear to investigate particle-scale reversible motion. We identify three classes of steady-state dynamics as a function of packing fraction phi and maximum strain amplitude per cycle gamma_{rm max}. Point-reversible states, where particles do not collide and exactly retrace their intra-cycle trajectories, occur at low phi and gamma_{rm max}. Particles in loop-reversible states undergo numerous collisions and execute complex trajectories, but return to their initial positions at the end of each cycle. Loop-reversible dynamics represents a novel form of self-organization that enables reliable preparation of configurations with specified structural and mechanical properties over a broad range of phi from contact percolation to jamming onset at phi_J. For sufficiently large phi and gamma_{rm max}, systems display irreversible dynamics with nonzero self-diffusion.
We explain the structural origin of the jamming transition in jammed matter as the sudden appearance of k-cores at precise coordination numbers which are related not to the isostatic point, but to the sudden emergence of the 3- and 4-cores as given by k-core percolation theory. At the transition, the k-core variables freeze and the k-core dominates the appearance of rigidity. Surprisingly, the 3-D simulation results can be explained with the result of mean-field k-core percolation in the Erdos-Renyi network. That is, the finite-dimensional transition seems to be explained by the infinite-dimensional k-core, implying that the structure of the jammed pack is compatible with a fully random network.
We investigate the mechanical response of jammed packings of repulsive, frictionless spherical particles undergoing isotropic compression. Prior simulations of the soft-particle model, where the repulsive interactions scale as a power-law in the interparticle overlap with exponent $alpha$, have found that the ensemble-averaged shear modulus $langle G rangle$ increases with pressure $P$ as $sim P^{(alpha-3/2)/(alpha-1)}$ at large pressures. However, a deep theoretical understanding of this scaling behavior is lacking. We show that the shear modulus of jammed packings of frictionless, spherical particles has two key contributions: 1) continuous variations as a function of pressure along geometrical families, for which the interparticle contact network does not change, and 2) discontinuous jumps during compression that arise from changes in the contact network. We show that the shear modulus of the first geometrical family for jammed packings can be collapsed onto a master curve: $G^{(1)}/G_0 = (P/P_0)^{(alpha-2)/(alpha-1)} - P/P_0$, where $P_0 sim N^{-2(alpha-1)}$ is a characteristic pressure that separates the two power-law scaling regions and $G_0 sim N^{-2(alpha-3/2)}$. Deviations from this form can occur when there is significant non-affine particle motion near changes in the contact network. We further show that $langle G (P)rangle$ is not simply a sum of two power-laws, but $langle G rangle sim (P/P_c)^a$, where $a approx (alpha -2)/(alpha-1)$ in the $P rightarrow 0$ limit and $langle G rangle sim (P/P_c)^b$, where $b gtrsim (alpha -3/2)/(alpha-1)$ above a characteristic pressure $P_c$. In addition, the magnitudes of both contributions to $langle Grangle$ from geometrical families and changes in the contact network remain comparable in the large-system limit for $P >P_c$.
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