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Register a new userJamming as a random first-order percolation transition
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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$.
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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 kinetically constrained models of glassy transitions, and determine which model characteristics are crucial in allowing a rigorous proof that such models have discontinuous transitions with faster than power law diverging length and time scales. The models we investigate have constraints similar to that of the knights model, introduced by Toninelli, Biroli, and Fisher (TBF), but differing neighbor relations. We find that such knights-like models, otherwise known as models of jamming percolation, need a ``No Parallel Crossing rule for the TBF proof of a glassy transition to be valid. Furthermore, most knight-like models fail a ``No Perpendicular Crossing requirement, and thus need modification to be made rigorous. We also show how the ``No Parallel Crossing requirement can be used to evaluate the provable glassiness of other correlated percolation models, by looking at models with more stable directions than the knights model. Finally, we show that the TBF proof does not generalize in any straightforward fashion for three-dimensiona
We investigate universal features of the jamming transition in granular materials, colloids and glasses. We show that the jamming transition in these systems has common features: slowing of response to external perturbation, and the onset of structural heterogeneities.
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.
This work studies the jamming and percolation of parallel squares in a single-cluster growth model. The Leath-Alexandrowicz method was used to grow a cluster from an active seed site. The sites of a square lattice were occupied by addition of the equal size $k times k$ squares (E-problem) or a mixture of $k times k$ and $m times m$ ($m leqslant k$) squares (M-problem). The larger $k times k$ squares were assumed to be active (conductive) and the smaller $m times m$ squares were assumed to be blocked (non-conductive). For equal size $k times k$ squares (E-problem) the value of $p_j = 0.638 pm 0.001$ was obtained for the jamming concentration in the limit of $krightarrowinfty$. This value was noticeably larger than that previously reported for a random sequential adsorption model, $p_j = 0.564 pm 0.002$. It was observed that the value of percolation threshold $p_{mathrm{c}}$ (i.e., the ratio of the area of active $k times k$ squares and the total area of $k times k$ squares in the percolation point) increased with an increase of $k$. For mixture of $k times k$ and $m times m$ squares (M-problem), the value of $p_{mathrm{c}}$ noticeably increased with an increase of $k$ at a fixed value of $m$ and approached 1 at $kgeqslant 10m$. This reflects that percolation of larger active squares in M-problem can be effectively suppressed in the presence of smaller blocked squares.
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