Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userUniversal relaxation dynamics of sphere packings below jamming
91
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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.
We study the vibrational modes of three-dimensional jammed packings of soft ellipsoids of revolution as a function of particle aspect ratio $epsilon$ and packing fraction. At the jamming transition for ellipsoids, as distinct from the idealized case using spheres where $epsilon = 1$, there are many unconstrained and non-trivial rotational degrees of freedom. These constitute a set of zero-frequency modes that are gradually mobilized into a new rotational band as $|epsilon - 1|$ increases. Quite surprisingly, as this new band is separated from zero frequency by a gap, and lies below the onset frequency for translational vibrations, $omega^*$, the presence of these new degrees of freedom leaves unaltered the basic scenario that the translational spectrum is determined only by the average contact number. Indeed, $omega^*$ depends solely on coordination as it does for compressed packings of spheres. We also discuss the regime of large $|epsilon - 1|$, where the two bands merge.
Self-organization, and transitions from reversible to irreversible behaviour, of interacting particle assemblies driven by externally imposed stresses or deformation is of interest in comprehending diverse phenomena in soft matter. They have been investigated in a wide range of systems, such as colloidal suspensions, glasses, and granular matter. In different density and driving regimes, such behaviour is related to yielding of amorphous solids, jamming, and memory formation, emph{etc.} How these phenomena are related to each other has not, however, been much studied. In order to obtain a unified view of the different regimes of behaviour, and transitions between them, we investigate computationally the response of soft sphere assemblies to athermal cyclic shear deformation over a wide range of densities and amplitudes of shear deformation. Cyclic shear deformation induces transitions from reversible to irreversible behaviour in both unjammed and jammed soft sphere packings. Well above isotropic jamming density ($bf{phi_J}$), this transition corresponds to yielding. In the vicinity of the jamming point, up to a higher density limit we designate ${bf phi_J^{cyc}}$, an unjammed phase emerges between a localised, emph{absorbing} phase, and a diffusive, {emph irreversible} phase. The emergence of the unjammed phase signals the shifting of the jamming point to higher densities as a result of annealing, and opens a window where shear jamming becomes possible for frictionless packings. Below $bf{phi_J}$, two distinct localised states, termed point and loop reversibile, are observed. We characterise in detail the different regimes and transitions between them, and obtain a unified density-shear amplitude phase diagram.
We present experimental and numerical results for displacement response functions in packings of rigid frictional disks under gravity. The central disk on the bottom layer is shifted upwards by a small amount, and the motions of disks above it define the displacement response. Disk motions are measured with the help of a still digital camera. The responses so measured provide information on the force-force response, that is, the excess force at the bottom produced by a small overload in the bulk. We find that, in experiments, the vertical-force response shows a Gaussian-like shape, broadening roughly as the square root of distance, as predicted by diffusive theories for stress propagation in granulates. However, the diffusion coefficient obtained from a fit of the response width is ten times larger than predicted by such theories. Moreover we notice that our data is compatible with a crossover to linear broadening at large scales. In numerical simulations on similar systems (but without friction), on the other hand, a double-peaked response is found, indicating wave-like propagation of stresses. We discuss the main reasons for the different behaviors of experimental and model systems, and compare our findings with previous works.
We describe a series of experiments involving the creation of cylindrical packings of star-shaped particles, and an exploration of the stability of these packings. The stars cover a broad range of arm sizes and frictional properties. We carried out three different kinds of experiments, all of which involve columns that are prepared by raining star particles one-by-one into hollow cylinders. As an additional part of the protocol, we sometimes vibrated the column before removing the confining cylinder. We rate stability in terms of r, the ratio of the mass of particles that fall off a pile when it collapsed, to the total particle mass. The first experiment involved the intrinsic stability of the pile when the confining cylinder was removed. The second kind of experiment involved adding a uniform load to the top of the column, and then determining the collapse properties. A third experiment involved testing stability to tipping of the piles. We find a stability diagram relating the pile height, h, vs. pile diameter, delta, where the stable and unstable regimes are separated by a boundary that is roughly a power-law in h vs. delta with an exponent that is less than one. Increasing friction and vibration both tend to stabilize piles, while increasing particle size can destabilize the system under certain conditions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
