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We investigate the dynamic evolution of jamming in granular media through fluctuations in the granular drag force. The successive collapse and formation of jammed states give a stick-slip nature to the fluctuations which is independent of the contact surface between the grains and the dragged object -- thus implying that the stress-induced collapse is nucleated in the bulk of the granular sample. We also find that while the fluctuations are periodic at small depths, they become stepped at large depths, a transition which we interpret as a consequence of the long-range nature of the force chains.
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Large-scale three dimensional molecular dynamics simulations of hopper flow are presented. The flow rate of the system is controlled by the width of the aperture at the bottom. As the steady-state flow rate is reduced, the force distribution $P(f)$ changes only slightly, while there is a large change in the impulse distribution $P(i)$. In both cases, the distributions show an increase in small forces or impulses as the systems approach jamming, the opposite of that seen in previous Lennard-Jones simulations. This occurs dynamically as well for a hopper that transitions from a flowing to a jammed state over time. The final jammed $P(f)$ is quite distinct from a poured packing $P(f)$ in the same geometry. The change in $P(i)$ is a much stronger indicator of the approach to jamming. The formation of a peak or plateau in $P(f)$ at the average force is not a general feature of the approach to jamming.
We demonstrate that a highly frustrated anisotropic Josephson junction array(JJA) on a square lattice exhibits a zero-temperature jamming transition, which shares much in common with those in granular systems. Anisotropy of the Josephson couplings along the horizontal and vertical directions plays roles similar to normal load or density in granular systems. We studied numerically static and dynamic response of the system against shear, i. e. injection of external electric current at zero temperature. Current-voltage curves at various strength of the anisotropy exhibit universal scaling features around the jamming point much as do the flow curves in granular rheology, shear-stress vs shear-rate. It turns out that at zero temperature the jamming transition occurs right at the isotropic coupling and anisotropic JJA behaves as an exotic fragile vortex matter : it behaves as superconductor (vortex glass) into one direction while normal conductor (vortex liquid) into the other direction even at zero temperature. Furthermore we find a variant of the theoretical model for the anisotropic JJA quantitatively reproduces universal master flow-curves of the granular systems. Our results suggest an unexpected common paradigm stretching over seemingly unrelated fields - the rheology of soft materials and superconductivity.
The drainage of particulate foams is studied under conditions where the particles are not trapped individually by constrictions of the interstitial pore space. The drainage velocity decreases continuously as the particle volume fraction $phi_{p}$ increases. The suspensions jam - and therefore drainage stops - for values $phi_{p}^{*}$ which reveal a strong effect of the particle size. In accounting for the particular geometry of the foam, we show that $phi_{p}^{*}$ accounts for unusual confinement effects when the particles pack into the foam network. We model quantitatively the overall behavior of the suspension - from flow to jamming - by taking into account explicitly the divergence of its effective viscosity at $phi_{p}^{*}$. Beyond the scope of drainage, the reported jamming transition is expected to have a deep significance for all aspects related to particulate foams, from aging to mechanical properties.
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.
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
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