Active nematic ratchet in asymmetric obstacle arrays.

We numerically investigate the effect of an asymmetric periodic obstacle array in a two-dimensional active nematic. We find that activity in conjunction with the asymmetry leads to a ratchet effect or unidirectional flow of the fluid along the asymmetry direction. The directional flow is still present even in the active turbulent phase when the gap between obstacles is sufficiently small. We demonstrate that the dynamics of the topological defects transition from flow mirroring to smectic-like as the gap between obstacles is made smaller, and explain this transition in terms of the pinning of negative winding number defects between obstacles. This also leads to a nonmonotonic ratchet effect magnitude as a function of obstacle size, so that there is an optimal obstacle size for ratcheting at fixed activity.

Peak effect and dynamics of stripe- and pattern-forming systems on a periodic one-dimensional substrate.

We examine the ordering, pinning, and dynamics of two-dimensional pattern-forming systems interacting with a periodic one-dimensional substrate. In the absence of the substrate, particles with competing long-range repulsion and short-range attraction form anisotropic crystal, stripe, and bubble states. When the system is tuned across the stripe transition in the presence of a substrate, we find that there is a peak effect in the critical depinning force when the stripes align and become commensurate with the substrate. Under an applied drive, the anisotropic crystal and stripe states can exhibit soliton depinning and plastic flow. When the stripes depin plastically, they dynamically reorder into a moving stripe state that is perpendicular to the substrate trough direction. We also find that when the substrate spacing is smaller than the widths of the bubbles or stripes, the system forms pinned stripe states that are perpendicular to the substrate trough direction. The system exhibits multiple reentrant pinning effects as a function of increasing attraction, with the anisotropic crystal and large bubble states experiencing weak pinning but the stripe and smaller bubble states showing stronger pinning. We map out the different dynamic phases as a function of filling, the strength of the attractive interaction term, the substrate strength, and the drive, and demonstrate that the different phases produce identifiable features in the transport curves and particle orderings.

Phase separation, edge currents, and Hall effect for active matter with Magnus dynamics.

We examine run-and-tumble disks in two-dimensional systems where the particles also have a Magnus component to their dynamics. For increased activity, we find that the system forms a motility-induced phase-separated (MIPS) state with chiral edge flow around the clusters, where the direction of the current is correlated with the sign of the Magnus term. The stability of the MIPS state is non-monotonic as a function of increasing Magnus term amplitude, with the MIPS region first extending down to lower activities followed by a break up of MIPS at large Magnus amplitudes into a gel-like state. We examine the dynamics in the presence of quenched disorder and a uniform drive and find that the bulk flow exhibits a drive-dependent Hall angle. This is a result of the side jump effect produced by scattering from the pinning sites and is similar to the behavior found for skyrmions in chiral magnets with quenched disorder.

Reversible, irreversible, and mixed regimes for periodically driven disks in random obstacle arrays.

We examine an assembly of repulsive disks interacting with a random obstacle array under a periodic drive and find a transition from reversible to irreversible dynamics as a function of drive amplitude or disk density. At low densities and drives, the system rapidly forms a reversible state where the disks return to their exact positions at the end of each cycle. In contrast, at high amplitudes or high densities, the system enters an irreversible state where the disks exhibit normal diffusion. Between these two regimes, there can be an intermediate irreversible state where most of the system is reversible, but localized irreversible regions are present that are prevented from spreading through the system due to a screening effect from the obstacles. We also find states that we term "combinatorial reversible states" in which the disks return to their original positions after multiple driving cycles. In these states, individual disks exchange positions but form the same configurations during the subcycles of the larger reversible cycle.

Motility-induced phase separation and frustration in active matter swarmalators.

We introduce a two dimensional system of active matter swarmalators composed of elastically interacting run-and-tumble active disks with an internal parameter ϕ_{i}. The disks experience an additional attractive or repulsive force with neighboring disks depending upon their relative difference in ϕ_{i}, making them similar to swarmalators used in robotic systems. In the absence of the internal parameter, the system forms a motility-induced phase separated (MIPS) state, but when the swarmalator interactions are present, a wide variety of other active phases appear depending upon whether the interaction is attractive or repulsive and whether the particles act to synchronize or ant-synchronize their internal parameter values. These phases include a gas-free gel regime, arrested clusters, a labyrinthine state, a regular MIPS state, a frustrated MIPS state for attractive antisynchronization, and a superlattice MIPS state for attractive synchronization.

Vortex Lattices in Active Nematics with Periodic Obstacle Arrays.

We numerically model a two-dimensional active nematic confined by a periodic array of fixed obstacles. Even in the passive nematic, the appearance of topological defects is unavoidable due to planar anchoring by the obstacle surfaces. We show that a vortex lattice state emerges as activity is increased, and that this lattice may be tuned from "ferromagnetic" to "antiferromagnetic" by varying the gap size between obstacles. We map the rich variety of states exhibited by the system as a function of distance between obstacles and activity, including a pinned defect state, motile defects, the vortex lattice, and active turbulence. We demonstrate that the flows in the active turbulent phase can be tuned by the presence of obstacles, and explore the effects of a frustrated lattice geometry on the vortex lattice phase.

Skyrmion transport and annihilation in funnel geometries.

Using atomistic simulations, we have investigated the transport and annihilation of skyrmions interacting with a funnel array under a current applied perpendicular to the funnel axis. We find that transport without annihilation is possible at low currents, when the motion is dominated by skyrmion-skyrmion interactions and skyrmions push each other through the funnel opening. Skyrmion annihilation occurs for higher currents when skyrmions in the upper half of the sample exert pressure on skyrmions in the bottom half of the sample due to the external current. Upon interacting with the funnel wall, the skyrmions undergo a size reduction that makes it easier for them to pass through the funnel opening. We find five phases as a function of the applied current and the size of the funnel opening: (i) pinned, (ii) transport without annihilation, (iii) transport with annihilation, (iv) complete annihilation, and (v) a reentrant pinning phase that only occurs for very narrow openings. Our findings provide insight into how to control skyrmion transport using funnel arrays by delineating regimes in which transport of skyrmions is possible as well as the conditions under which annihilation occurs.

Dynamic phases and combing effects for elongated particles moving over quenched disorder.

We consider a two-dimensional system of elongated particles driven over a landscape containing randomly placed pinning sites. For varied pinning site density, external drive magnitude, and particle elongation, we find a wide variety of dynamic phases, including random structures, stripe or combed phases with nematic order, and clogged states. The different regimes can be identified by examining nematic ordering, cluster size, number of pinned particles, and transverse diffusion. In some regimes we find that the pinning can enhance the particle alignment, producing a nonmonotonic signature in the nematic ordering with a maximum at a particular combination of pinning density and drive. The optimal nematic occurs when a sufficient number of particles can be pinned, generating a local shear and leading to what we call a combing effect. At high drives, the combing effect is reduced when the number of pinned particles decreases. For stronger pinning, the particles form a heterogeneous clustered or clogged state that depins into a fluctuating state with high diffusion.

Friction-mediated phase transition in confined active nematics.

Using a minimal continuum model, we investigate the interplay between circular confinement and substrate friction in active nematics. Upon increasing the friction from low to high, we observe a dynamical phase transition from a circulating flow phase to an anisotropic flow phase in which the flow tends to align perpendicular to the nematic director at the boundary. We demonstrate that both the flow structure and dynamic correlations in the latter phase differ from those of an unconfined, active turbulent system and may be controlled by the prescribed nematic boundary conditions. Our results show that substrate friction and geometric confinement act as valuable control parameters in active nematics.

Noise and thermal depinning of Wigner crystals.

We examine changes in the depinning threshold and conduction noise fluctuations for driven Wigner crystals in the presence of quenched disorder. At low temperatures there is a well defined depinning threshold and a strong peak in the noise power with1/fnoise characteristics. At higher temperatures, the depinning threshold shifts to lower drives and the noise, which is also reduced in power, becomes more white in character. At lower temperatures, a washboard frequency appears when the system depins elastically or forms a moving smectic state; however, this washboard signal is strongly reduced for higher temperatures and completely disappears above the melting temperature of a system without quenched disorder. Our results are in good agreement with recent transport and noise studies for systems where electron crystal depinning is believed to arise, and also show how noise can be used to distinguish between crystal, glass, and liquid phases.

Transition from susceptible-infected to susceptible-infected-recovered dynamics in a susceptible-cleric-zombie-recovered active matter model.

The susceptible-infected (SI) and susceptible-infected-recovered (SIR) models provide two distinct representations of epidemic evolution, distinguished by whether or not the number of susceptibles always drops to zero at long times. Here we introduce a new active matter epidemic model, the "susceptible-cleric-zombie-recovered" (SCZR) model, in which spontaneous recovery is absent but zombies can recover with probability γ via interaction with a cleric. Upon colliding with a zombie, both susceptibles and clerics enter the zombie state with probability ß and α, respectively. By changing the initial fraction of clerics or their healing ability rate γ, we can tune the SCZR model between SI dynamics, in which no susceptibles or clerics remain at long times, and SIR dynamics, in which a finite number of clerics and susceptibles survive at long times. The model is relevant to certain real world diseases such as HIV where spontaneous recovery is impossible but where medical interventions by a limited number of caregivers can reduce or eliminate the spread of infection.

Characterizing different motility-induced regimes in active matter with machine learning and noise.

We examine motility-induced phase separation (MIPS) in two-dimensional run-and-tumble disk systems using both machine learning and noise fluctuation analysis. Our measures suggest that within the MIPS state there are several distinct regimes as a function of density and run time, so that systems with MIPS transitions exhibit an active fluid, an active crystal, and a critical regime. The different regimes can be detected by combining an order parameter extracted from principal component analysis with a cluster stability measurement. The principal component-derived order parameter is maximized in the critical regime, remains low in the active fluid, and has an intermediate value in the active crystal regime. We demonstrate that machine learning can better capture dynamical properties of the MIPS regimes compared to more standard structural measures such as the maximum cluster size. The different regimes can also be characterized via changes in the noise power of the fluctuations in the average speed. In the critical regime, the noise power passes through a maximum and has a broad spectrum with a 1/f^{1.6} signature, similar to the noise observed near depinning transitions or for solids undergoing plastic deformation.

Superlubric-pinned transition of a two-dimensional solid dusty plasma under a periodic triangular substrate.

The superlubric-pinned transition in the depinning dynamics of a two-dimensional (2D) solid dusty plasma modulated by 2D triangular periodic substrates is investigated using Langevin dynamical simulations. When the lattice structure of the 2D solid dusty plasma perfectly matches the triangular substrate, two distinctive pinned and moving ordered states are observed as the external uniform driving force gradually increases from zero. When there is a mismatch between the lattice structure and the triangular substrate, however, on shallow substrates, it is discovered that all of the particles can slide freely on the substrate even when the applied driving force is tiny. This is a typical example of superlubricity, which is caused by the competition between the substrate-particle and particle-particle interactions. If the substrate depth increases further, as the driving force increases from zero, there are three dynamical states consisting of the pinned state, the disordered plastic flow state, and the moving ordered state. In an underdense system, where there are fewer particles than potential well minima, it is found that the occurrence of the three different dynamical states is controlled by the depth of the substrate, which is quantitatively characterized using the average mobility.

Magnus induced diode effect for skyrmions in channels with periodic potentials.

Using a particle based model, we investigate the skyrmion dynamical behavior in a channel where the upper wall contains divots of one depth and the lower wall contains divots of a different depth. Under an applied driving force, skyrmions in the channels move with a finite skyrmion Hall angle that deflects them toward the upper wall for -xdirection driving and the lower wall for +xdirection driving. When the upper divots have zero height, the skyrmions are deflected against the flat upper wall for -xdirection driving and the skyrmion velocity depends linearly on the drive. For +xdirection driving, the skyrmions are pushed against the lower divots and become trapped, giving reduced velocities and a nonlinear velocity-force response. When there are shallow divots on the upper wall and deep divots on the lower wall, skyrmions get trapped for both driving directions; however, due to the divot depth difference, skyrmions move more easily under -xdirection driving, and become strongly trapped for +xdirection driving. The preferred -xdirection motion produces what we call a Magnus diode effect since it vanishes in the limit of zero Magnus force, unlike the diode effects observed for asymmetric sawtooth potentials. We show that the transport curves can exhibit a series of jumps or dips, negative differential conductivity, and reentrant pinning due to collective trapping events. We also discuss how our results relate to recent continuum modeling on a similar skyrmion diode system.

Directional locking in a two-dimensional Yukawa solid modulated by a two-dimensional periodic substrate.

Directional depinning dynamics of a two-dimensional (2D) dusty plasma solid modulated by a 2D square periodic substrate are investigated using Langevin dynamical simulations. We observe prominent directional locking effects when the direction of the external driving force is varied relative to the underlying square substrate. These locking steps appear when the direction of the driving force is close to the symmetry direction of the substrate, corresponding to the different dynamical flow patterns and the structures. In the conditions between the adjacent locking steps, moving ordered states are observed. Although the discontinuous transitions often occur between the locking steps and the nonlocking portion, the continuous transitions are also found around the locking step associated with the disordered plastic flow close to its termini. Our results show that directional locking also occurs for underdamped systems, which could be tested experimentally in dusty plasmas modulated by 2D substrates.

Using active matter to introduce spatial heterogeneity to the susceptible infected recovered model of epidemic spreading.

The widely used susceptible-infected-recovered (S-I-R) epidemic model assumes a uniform, well-mixed population, and incorporation of spatial heterogeneities remains a major challenge. Understanding failures of the mixing assumption is important for designing effective disease mitigation approaches. We combine a run-and-tumble self-propelled active matter system with an S-I-R model to capture the effects of spatial disorder. Working in the motility-induced phase separation regime both with and without quenched disorder, we find two epidemic regimes. For low transmissibility, quenched disorder lowers the frequency of epidemics and increases their average duration. For high transmissibility, the epidemic spreads as a front and the epidemic curves are less sensitive to quenched disorder; however, within this regime it is possible for quenched disorder to enhance the contagion by creating regions of higher particle densities. We discuss how this system could be realized using artificial swimmers with mobile optical traps operated on a feedback loop.

Reversible to irreversible transitions for cyclically driven particles on periodic obstacle arrays.

We examine the collective dynamics of disks moving through a square array of obstacles under cyclic square wave driving. Below a critical density, we find that the system organizes into a reversible state in which the disks return to the same positions at the end of every drive cycle. Above this density, the dynamics are irreversible and the disks do not return to the same positions after each cycle. The critical density depends strongly on the angle θ between the driving direction and a symmetry axis of the obstacle array, with the highest critical densities appearing at commensurate angles such as θ = 0° and θ = 45° and the lowest critical densities falling at θ = arctan (0.618), the inverse of the golden ratio, where the flow is the most degenerate. As the density increases, the number of cycles required to reach a reversible state grows as a power law with an exponent near ν = 1.36, similar to what is found in periodically driven colloidal and superconducting vortex systems.

Phonon spectra of a two-dimensional solid dusty plasma modified by two-dimensional periodic substrates.

Phonon spectra of a two-dimensional (2D) solid dusty plasma modulated by 2D square and triangular periodic substrates are investigated using Langevin dynamical simulations. The commensurability ratio, i.e., the ratio of the number of particles to the number of potential well minima, is set to 1 or 2. The resulting phonon spectra show that propagation of waves is always suppressed due to the confinement of particles by the applied 2D periodic substrates. For a commensurability ratio of 1, the spectra indicate that all particles mainly oscillate at one specific frequency, corresponding to the harmonic oscillation frequency of one single particle inside one potential well. At a commensurability ratio of 2, the substrate allows two particles to sit inside the bottom of each potential well, and the resulting longitudinal and transverse spectra exhibit four branches in total. We find that the two moderate branches come from the harmonic oscillations of one single particle and two combined particles in the potential well. The other two branches correspond to the relative motion of the two-body structure in each potential well in the radial and azimuthal directions. The difference in the spectra between the square and triangular substrates is attributed to the anisotropy of the substrates and the resulting alignment directions of the two-body structure in each potential well.

Pattern formation and flocking for particles near the jamming transition on resource gradient substrates.

We numerically examine a bidisperse system of active and passive particles coupled to a resource substrate. The active particles deplete the resource at a fixed rate and move toward regions with higher resources, while all of the particles interact sterically with each other. We show that at high densities, this system exhibits a rich variety of pattern-forming phases along with directed motion or flocking as a function of the relative rates of resource absorption and consumption as well as the active to passive particle ratio. These include partial phase separation into rivers of active particles flowing through passive clusters, strongly phase separated states where the active particles induce crystallization of the passive particles, mixed jammed states, and fluctuating mixed fluid phases. For higher resource recovery rates, we demonstrate that the active particles can undergo motility-induced phase separation, while at high densities, there can be a coherent flock containing only active particles or a solid mixture of active and passive particles. The directed flocking motion typically shows a transient in which the flow switches among different directions before settling into one direction, and there is a critical density below which flocking does not occur. We map out the different phases as function of system density, resource absorption and recovery rates, and the ratio of active to passive particles.

Active matter shepherding and clustering in inhomogeneous environments.

We consider a mixture of active and passive run-and-tumble disks in an inhomogeneous environment where only half of the sample contains quenched disorder or pinning. The disks are initialized in a fully mixed state of uniform density. We identify several distinct dynamical phases as a function of motor force and pinning density. At high pinning densities and high motor forces, there is a two-step process initiated by a rapid accumulation of both active and passive disks in the pinned region, which produces a large density gradient in the system. This is followed by a slower species phase separation process where the inactive disks are shepherded by the active disks into the pin-free region, forming a nonclustered fluid and producing a more uniform density with species phase separation. For higher pinning densities and low motor forces, the dynamics becomes very slow and the system maintains a strong density gradient. For weaker pinning and large motor forces, a floating clustered state appears, and the time-averaged density of the system is uniform. We illustrate the appearance of these phases in a dynamic phase diagram.