Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userStability at Random Close Packing
297
0
0.0
(
0
)
Authors
Matthieu Wyart
Ask ChatGPT about the research
No Arabic abstract
The requirement that packings of hard particles, arguably the simplest structural glass, cannot be compressed by rearranging their network of contacts is shown to yield a new constraint on their microscopic structure. This constraint takes the form a bound between the distribution of contact forces P(f) and the pair distribution function g(r): if P(f) sim f^{theta} and g(r) sim (r-{sigma})^(-{gamma}), where {sigma} is the particle diameter, one finds that {gamma} geq 1/(2+{theta}). This bound plays a role similar to those found in some glassy materials with long-range interactions, such as the Coulomb gap in Anderson insulators or the distribution of local fields in mean-field spin glasses. There is ground to believe that this bound is saturated, offering an explanation for the presence of avalanches of rearrangements with power-law statistics observed in packings.
rate research
Read More
Assemblies of purely repulsive and frictionless particles, such as emulsions or hard spheres, display very curious properties near their jamming transition, which occurs at the random close packing for mono-disperse spheres. Although such systems do not contain the long and cross-linked polymeric chains characterizing a rubber, they behave macroscopically in a similar way: the shear modulus $G$ can become infinitely smaller than the bulk modulus $B$. After reviewing recent theoretical results on the structure of such packing (in particular their coordination) I will propose an explanation for the observed scaling of the elastic moduli, and explain why the arguments both apply to soft and hard particles.
We present a comparative numerical study of the ordered and the random two-dimensional sine-Gordon models on a lattice. We analytically compute the main features of the expected high temperature phase of both models, described by the Edwards-Wilkinson equation. We then use those results to locate the transition temperatures of both models in our Langevin dynamics simulations. We show that our results reconcile previous contradictory numerical works concerning the superroughening transition in the random sine-Gordon model. We also find evidence supporting the existence of two different low temperature phases for the disordered model. We discuss our results in view of the different analytical predictions available and comment on the nature of these two putative phases.
Using computed x-ray tomography we determine the three dimensional (3d) structure of binary hard sphere mixtures as a function of composition and size ratio of the particles, q. Using a recently introduced four-point correlation function we reveal that this 3d structure has on intermediate and large length scales a surprisingly regular order, the symmetry of which depends on q. The related structural correlation length has a minimum at the composition at which the packing fraction is highest. At this composition also the number of different local particle arrangements has a maximum, indicating that efficient packing of particles is associated with a structure that is locally maximally disordered.
We analyze recent experiments on the dilute rare-earth compound LiHo_xY_(1-x)F_4 in the context of an effective Ising dipolar model. Using a Monte Carlo method we calculate the low-temperature behavior of the specific heat and linear susceptibility, and compare our results to measurements. In our model the susceptibility follows a Curie-Weiss law at high temperature, chi ~ 1/(T-T_cw), with a Curie-Weiss temperature that scales with dilution, T_cw ~ x, consistent with early experiments. We also find that the peak in the specific heat scales linearly with dilution, C_max(T) ~ x, in disagreement with recent experiments. Experimental studies do not reach a consensus on the functional form of these quantities, and in particular we do not see reported scalings of the form chi ~ T^-0.75 and chi ~ exp(-T/T_0). Furthermore we calculate the ground state magnetization as a function of dilution, and re-examine the phase diagram around the critical dilution x_c=0.24(3). We find that the spin glass susceptibility for the Ising model does not diverge below x_c, while recent experiments give strong evidence for a stable spin-glass phase in LiHo_0.167Y_0.833F_4.
We experimentally investigate the response of a sheared granular medium in a Couette geometry. The apparatus exhibits the expected stick-slip motion and we probe it in the very intermittent regime resulting from low driving. Statistical analysis of the dynamic fluctuations reveals notable regularities. We observe a possible stability property for the torque distribution, reminiscent of the stability of Gaussian independent variables. In this case, however, the variables are correlated and the distribution is skewed. Moreover, the whole dynamical intermittent regime can be described with a simple stochastic model, finding good quantitative agreement with the experimental data. Interestingly, a similar model has been previously introduced in the study of magnetic domain wall motion, a source of Barkhausen noise. Our study suggests interesting connections between different complex phenomena and reveals some unexpected features that remain to be explained.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
