ABSTRACT
We numerically study the local stress distribution within athermal, isotropically stressed, mechanically stable, packings of bidisperse frictionless disks above the jamming transition in two dimensions. Considering the Fourier transform of the local stress, we find evidence for algebraically increasing fluctuations in both isotropic and anisotropic components of the stress tensor at small wave numbers, contrary to recent theoretical predictions. Such increasing fluctuations imply a lack of self-averaging of the stress on large length scales. The crossover to these increasing fluctuations defines a length scale â_{0}, however, it appears that â_{0} does not vary much with packing fraction Ï, nor does â_{0} seem to be diverging as Ï approaches the jamming Ï_{J}. We also find similar large length scale fluctuations of stress in the inherent states of a quenched Lennard-Jones liquid, leading us to speculate that such fluctuations may be a general property of amorphous solids in two dimensions.
ABSTRACT
We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction Ï(J). For configurations with a fixed isotropic global stress tensor, we investigate the fluctuations of the local packing fraction Ï(r) to test whether such configurations display the hyperuniformity that has been claimed to exist exactly at Ï(J). For our configurations, generated by a rapid quench protocol, we find that hyperuniformity persists only out to a finite length scale and that this length scale appears to remain finite as the system stress decreases towards zero, i.e., towards the jamming transition. Our result suggests that the presence of hyperuniformity at jamming may be sensitive to the specific protocol used to construct the jammed configurations.
ABSTRACT
We show that the maximum entropy hypothesis can successfully explain the distribution of stresses on compact clusters of particles within disordered mechanically stable packings of soft, isotropically stressed, frictionless disks above the jamming transition. We show that, in our two-dimensional case, it becomes necessary to consider not only the stress but also the Maxwell-Cremona force-tile area as a constraining variable that determines the stress distribution. The importance of the force-tile area had been suggested by earlier computations on an idealized force-network ensemble.
ABSTRACT
We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction Ï(J). For configurations with a fixed isotropic global stress tensor, we compute the averages, variances, and correlations of conserved quantities (stress Γ(C), force-tile area A(C), Voronoi volume V(C), number of particles N(C), and number of small particles N(sC)) on compact subclusters of particles C, as a function of the cluster size and the global system stress. We find several significant differences depending on whether the cluster C is defined by a fixed radius R or a fixed number of particles M. We comment on the implications of our findings for maximum entropy models of jammed packings.
ABSTRACT
We numerically study the distributions of global pressure that are found in ensembles of statically jammed and quasistatically sheared systems of bidisperse, frictionless disks at fixed packing fraction Ï in two dimensions. We use these distributions to address the question of how pressure increases as Ï increases above the jamming point Ï(J), p â¼ |Ï-Ï(J)(y). For statically jammed ensembles, our results are consistent with the exponent y being simply related to the power law of the interparticle soft-core interaction. For sheared systems, however, the value of y is consistent with a nontrivial value, as found previously in rheological simulations.