M. B. Hastings

Community detection as an inference problem.

We express community detection as an inference problem of determining the most likely arrangement of communities. We then apply belief propagation and mean-field theory to this problem, and show that this leads to fast, accurate algorithms for community detection.

Ratchet cellular automata.

In this work we propose a ratchet effect which provides a general means of performing clocked logic operations on discrete particles, such as single electrons or vortices. The states are propagated through the device by the use of an applied ac drive. We numerically demonstrate that a complete logic architecture is realizable using this ratchet. We consider specific nanostructured superconducting geometries using superconducting materials under an applied magnetic field, with the positions of the individual vortices in samples acting as the logic states. These devices can be used as the building blocks for an alternative microelectronic architecture.

Depinning by fracture in a glassy background.

We force a single particle through a two-dimensional simulated glass of smaller particles. We find that the particle velocity obeys a robust power law that persists to drive wells above threshold. As the single driven particle moves, it induces cooperative distortions in the surrounding medium. We show theoretically that a fracture model for these distortions produces power-law behavior and discuss implications for experimental probes of soft matter systems.

Do Vortices Entangle

We propose an experiment for directly constructing and locally probing topologically entangled states of superconducting vortices which can be performed with present-day technology. Calculations using an elastic string vortex model indicate that as the pitch (the winding angle divided by the vertical distance) increases, the vortices approach each other. At values of the pitch higher than a maximum value the entangled state becomes unstable to collapse via a singularity of the model. We provide predicted experimental signatures for both vortex entanglement and vortex cutting. The local probe we propose can also be used to explore a wide range of other quantities.

Nonlinear dynamics, rectification, and phase locking for particles on symmetrical two-dimensional periodic substrates with dc and circular ac drives

We investigate the dynamical motion of particles on a two-dimensional symmetric periodic substrate in the presence of both a dc drive along a symmetry direction of the periodic substrate and an additional circular ac drive. For large enough ac drives, the particle orbit encircles one or more potential maxima of the periodic substrate. In this case, when an additional increasing dc drive is applied in the longitudinal direction, the longitudinal velocity increases in a series of discrete steps that are integer multiples of a omega/(2 pi), where a is the lattice constant of the substrate. Fractional steps can also occur. These integer and fractional steps correspond to distinct stable dynamical orbits. A number of these phases also show a rectification in the positive or negative transverse direction where a nonzero transverse velocity occurs in the absence of a dc transverse drive. We map out the phase diagrams of the regions of rectification as a function of ac amplitude, and find a series of tongues. Most of the features, including the steps in the longitudinal velocity and the transverse rectification, can be captured with a simple toy model and by arguments from nonlinear maps. We have also investigated the effects of thermal disorder and incommensuration on the rectification phenomena, and find that for increasing disorder, the rectification regions are gradually smeared and the longitudinal velocity steps are no longer flat but show a linearly increasing velocity.

Glassy ratchets for collectively interacting particles

We show that ratchet effects can occur in a glassy media of interacting particles where there is no quenched substrate. We consider simulations of a disordered binary assembly of colloids in which only one species responds to a drive. We apply an asymmetric ac drive that would produce no net dc drift of an isolated overdamped particle. When interacting particles are present, the asymmetric ac drive produces a ratchet effect. A simple model captures many of the results from simulations, including flux reversals as a function of density and temperature.