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Register a new userMultiscaling at Point J: Jamming is a Critical Phenomenon
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We analyze the jamming transition that occurs as a function of increasing packing density in a disordered two-dimensional assembly of disks at zero temperature for ``Point J of the recently proposed jamming phase diagram. We measure the total number of moving disks and the transverse length of the moving region, and find a power law divergence as the packing density increases toward a critical jamming density. This provides evidence that the T = 0 jamming transition as a function of packing density is a {it second order} phase transition. Additionally we find evidence for multiscaling, indicating the importance of long tails in the velocity fluctuations.
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While frictionless spheres at jamming are isostatic, frictional spheres at jamming are not. As a result, frictional spheres near jamming do not necessarily exhibit an excess of soft modes. However, a generalized form of isostaticity can be introduced if fully mobilized contacts at the Coulomb friction threshold are considered as slipping contacts. We show here that, in this framework, the vibrational density of states (DOS) of frictional discs exhibits a plateau when the generalized isostaticity line is approached. The crossover frequency to elastic behavior scales linearly with the distance from this line. Moreover, we show that the frictionless limit, which appears singular when fully mobilized contacts are treated elastically, becomes smooth when fully mobilized contacts are allowed to slip.
We study incompressible systems of motile particles with alignment interactions. Unlike their compressible counterparts, in which the order-disorder (i.e., moving to static) transition, tuned by either noise or number density, is discontinuous, in incompressible systems this transition can be continuous, and belongs to a new universality class. We calculate the critical exponents to $O(epsilon)$in an $epsilon=4-d$ expansion, and derive two exact scaling relations. This is the first analytic treatment of a phase transition in a new universality class in an active system.
In this reply we discuss definition and estimation of the Fisher exponent in the no-enclaves percolation (NEP) model.
We determine the dimensional dependence of the percolative exponents of the jamming transition via numerical simulations in four and five spatial dimensions. These novel results complement literature ones, and establish jamming as a mixed first-order percolation transition, with critical exponents $beta =0$, $gamma = 2$, $alpha = 0$ and the finite size scaling exponent $ u^* = 2/d$ for values of the spatial dimension $d geq 2$. We argue that the upper critical dimension is $d_u=2$ and the connectedness length exponent is $ u =1$.
Seismicity and faulting within the Earth crust are characterized by many scaling laws that are usually interpreted as qualifying the existence of underlying physical mechanisms associated with some kind of criticality in the sense of phase transitions. Using an augmented Epidemic-Type Aftershock Sequence (ETAS) model that accounts for the spatial variability of the background rates $mu(x,y)$, we present a direct quantitative test of criticality. We calibrate the model to the ANSS catalog of the entire globe, the region around California, and the Geonet catalog for the region around New Zealand using an extended Expectation-Maximization (EM) algorithm including the determination of $mu(x,y)$. We demonstrate that the criticality reported in previous studies is spurious and can be attributed to a systematic upward bias in the calibration of the branching ratio of the ETAS model, when not accounting correctly for spatial variability. We validate the version of the ETAS model which possesses a space varying background rate $mu(x,y)$ by performing pseudo prospective forecasting tests. The non-criticality of seismicity has major implications for the prediction of large events.
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