Disordered hyperuniformity is a state of matter which has isotropic liquid like properties while simultaneously having crystalline like properties such as little variation in the density fluctuations over long distances. Such states arise for the packing of photoreceptor cells in chicken eyes, jammed particle assemblies, and in nonequilibrium systems. An open question is what possible applications could utilize properties of hyperuniformity. One of the major issues for applications of type-II superconductors is how to achieve high critical currents by preventing the motion or depinning of vortices, so there is great interest in understanding which pinning site geometries will lead to the optimal pinning of vortices. Here, using large scale computational simulations, we show that vortices in a type-II superconductor with a hyperuniform pinning arrangement exhibit enhanced pinning compared to an equal number of pinning sites with a purely random arrangement, and that the enhancement is robust over a wide range of parameters. The stronger pinning arises in the hyperuniform arrays due to the suppression of pinning density fluctuations, permitting higher pin occupancy and the reduction of weak links that lead to easy flow channeling. We also show that in general, in amorphous vortex states in the presence of either random or hyperuniform pinning arrays, the vortices themselves exhibit disordered hyperuniformity due to the repulsive nature of the vortex-vortex interactions.
Using computer simulations, we study a two-dimensional system of sterically interacting self-mobile run-and-tumble disk-shaped particles with an underlying periodic quasi-one-dimensional asymmetric substrate, and show that a rich variety of collective active ratchet behaviors arise as a function of particle density, activity, substrate period, and the maximum force exerted by the substrate. The net dc drift, or ratchet transport flux, is nonmonotonic since it increases with increased activity but is diminished by the onset of self-clustering of the active particles. Increasing the particle density decreases the ratchet transport flux for shallow substrates but increases the ratchet transport flux for deep substrates due to collective hopping events. At the highest particle densities, the ratchet motion is destroyed by a self-jamming effect. We show that it is possible to realize reversals of the direction of the net dc drift in the deep substrate limit when multiple rows of active particles can be confined in each substrate minimum, permitting emergent particle-like excitations to appear that experience an inverted effective substrate potential. We map out a phase diagram of the forward and reverse ratchet effects as a function of the particle density, activity, and substrate properties.
We numerically examine colloidal particles driven over a muffin tin substrate. Previous studies of this model identified a variety of commensurate and incommensurate static phases in which topological defects can form domain walls, ordered stripes, superlattices, or disordered patchy regimes as a function of the filling fraction. Here, we show that the addition of an external drive to these static phases can produce distinct dynamical responses. At incommensurate fillings the flow occurs in the form of localized pulses or solitons correlated with topological defect structures. Transitions between different modes of motion can occur as a function of increasing drive. We measure the average particle velocity for specific ranges of external drive and show that changes in the velocity response correlate with changes in the topological defect arrangements. We also demonstrate that in the different dynamic phases, the particles have distinct trajectories and velocity distributions. Dynamic transitions between ordered and disordered flows exhibit hysteresis, while in strongly disordered regimes there is no hysteresis and the velocity-force curves are smooth. When stripe patterns are present, transport can occur at an angle to the driving direction.
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