Colloidal dynamics on disordered substrates

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.

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.

Critical behavior of nonequilibrium depinning transitions for vortices driven by current and vortex density

We study the critical dynamics of vortices associated with dynamic disordering near the depinning transitions driven by dc force (dc current I) and vortex density (magnetic field B). Independent of the driving parameters, I and B, we observe the critical behavior of the depinning transitions, not only on the moving side, but also on the pinned side of the transition, which is the first convincing verification of the theoretical prediction. Relaxation times, [Formula: see text] and [Formula: see text], to reach either the moving or pinned state, plotted against I and B, respectively, exhibit a power-law divergence at the depinning thresholds. The critical exponents of both transitions are, within errors, identical to each other, which are in agreement with the values expected for an absorbing phase transition in the two-dimensional directed-percolation universality class. With an increase in B under constant I, the depinning transition at low B is replaced by the repinning transition at high B in the peak-effect regime. We find a trend that the critical exponents in the peak-effect regime are slightly smaller than those in the low-B regime and the theoretical one, which is attributed to the slight difference in the depinning mechanism in the peak-effect regime.

Clogging, dynamics, and reentrant fluid for active matter on periodic substrates

We examine the collective states of run-and-tumble active matter disks driven over a periodic obstacle array. When the drive is applied along a symmetry direction of the array, we find a clog-free uniform liquid state for low activity, while at higher activity, the density becomes increasingly heterogeneous and an active clogged state emerges in which the mobility is strongly reduced. For driving along nonsymmetry or incommensurate directions, there are two different clogging behaviors consisting of a drive-dependent clogged state in the low activity thermal limit and a drive-independent clogged state at high activity. These regimes are separated by a uniform flowing liquid at intermediate activity. There is a critical activity level above which the thermal clogged state does not occur, as well as an optimal activity level that maximizes the disk mobility. Thermal clogged states are dependent on the driving direction while active clogged states are not. In the low activity regime, diluting the obstacles produces a monotonic increase in the mobility; however, for large activities, the mobility is more robust against obstacle dilution. We also examine the velocity-force curves for driving along nonsymmetry directions and find that they are linear when the activity is low or intermediate but become nonlinear at high activity and show behavior similar to that found for the plastic depinning of solids. At higher drives, the active clustering is lost. For low activity, we also find a reentrant fluid phase, where the system transitions from a high mobility fluid at low drives to a clogged state at higher drives and then back into another fluid phase at very high drives. We map the regions in which the thermally clogged, partially clogged, active uniform fluid, clustered fluid, active clogged, and directionally locked states occur as a function of disk density, drift force, and activity.

Structured randomness: jamming of soft discs and pins

Simulations are used to find the zero temperature jamming threshold, φj, for soft, bidisperse disks in the presence of small fixed particles, or "pins", arranged in a lattice. The presence of pins leads, as one expects, to a decrease in φj. Structural properties of the system near the jamming threshold are calculated as a function of the pin density. While the correlation length exponent remains ν = 1/2 at low pin densities, the system is mechanically stable with more bonds, yet fewer contacts than the Maxwell criterion implies in the absence of pins. In addition, as pin density increases, novel bond orientational order and long-range spatial order appear, which are correlated with the square symmetry of the pin lattice.

Detecting depinning and nonequilibrium transitions with unsupervised machine learning

Using numerical simulations of a model disk system, we demonstrate that a machine learning generated order-parameter-like measure can detect depinning transitions and different dynamic flow phases in systems driven far from equilibrium. We specifically consider monodisperse passive disks with short range interactions undergoing a depinning phase transition when driven over quenched disorder. The machine learning derived order-parameter-like measure identifies the depinning transition as well as different dynamical regimes, such as the transition from a flowing liquid to a phase separated liquid-solid state that is not readily distinguished with traditional measures such as velocity-force curves or Voronoi tessellation. The order-parameter-like measure also shows markedly distinct behavior in the limit of high density where jamming effects occur. Our results should be general to the broad class of particle-based systems that exhibit depinning transitions and nonequilibrium phase transitions.

Depinning dynamics of two-dimensional dusty plasmas on a one-dimensional periodic substrate

We investigate the depinning dynamics of two-dimensional dusty plasmas driven over one-dimensional periodic substrates using Langevin dynamical simulations. We find that, for a specific range of substrate strengths, as the external driving force increases from zero, there are three different states, which are the pinned, the disordered plastic flow, and the moving ordered states, respectively. These three states are clearly observed using different diagnostics, including the collective drift velocity, static structural measures, the particle trajectories, the mean-squared displacements, and the kinetic temperature. We compare the observed depinning dynamics here with the depinning dynamics in other systems.

Darcy's Law for Yield Stress Fluids

Predicting the flow of non-Newtonian fluids in a porous structure is still a challenging issue due to the interplay between the microscopic disorder and the nonlinear rheology. In this Letter, we study the case of a yield stress fluid in a two-dimensional structure. Thanks to an efficient optimization algorithm, we show that the system undergoes a continuous phase transition in the behavior of the flow, controlled by the applied pressure difference. In analogy with studies of plastic depinning of vortex lattices in high-T_{c} superconductors, we characterize the nonlinearity of the flow curve and relate it to the change in the geometry of the open channels. In particular, close to the transition, a universal scale-free distribution of the channel length is observed and explained theoretically via a mapping to the Kardar-Parisi-Zhang equation.

Dynamic phases, stratification, laning, and pattern formation for driven bidisperse disk systems in the presence of quenched disorder

Using numerical simulations, we examine the dynamics of driven two-dimensional bidisperse disks flowing over quenched disorder. The system exhibits a series of distinct dynamical phases as a function of applied driving force and packing fraction, including a phase-separated state as well as a smectic state with liquid-like or polycrystalline features. At low driving forces, we find a clogged phase with an isotropic density distribution, while at intermediate driving forces the disks separate into bands of high and low densities with either liquid-like or polycrystalline structure in the high-density bands. In addition to the density phase separation, we find that in some cases there is a fractionation of the disk species, particularly when the disk size ratio is large. The species phase-separated regimes form a variety of patterns such as large disks separated by chains of smaller disks. Our results show that the formation of laning states can be enhanced by tuning the ratio of disk radius of the two species, due to the clumping of small disks in the interstitial regions between the large disks. This system could be experimentally realized using sterically interacting colloidal particles suspended in a viscous fluid driven over random pinning arrays or granular matter suspended in fluid moving over a random landscape.

Thermal creep and the skyrmion Hall angle in driven skyrmion crystals

We numerically examine thermal effects on the skyrmion Hall angle for driven skyrmions interacting with quenched disorder. We identify a creep regime in which motion occurs via intermittent jumps between pinned and flowing states. Here the skyrmion Hall angle is zero since the skyrmions have time to relax into equilibrium positions in the pinning sites, eliminating the side-jump motion induced by the Magnus force. At higher drives we find a crossover to a viscous flow regime where the skyrmion Hall angle is finite and increases with increasing drive or temperature. Our results are in agreement with recent experiments which also show a regime of finite skyrmion velocity with zero skyrmion Hall angle crossing over to a viscous flow regime with a skyrmion Hall angle that increases with drive.

Clogging and transport of driven particles in asymmetric funnel arrays

We numerically examine the flow and clogging of particles driven through asymmetric funnel arrays when the commensurability ratio of the number of particles per plaquette is varied. The particle-particle interactions are modeled with a soft repulsive potential that could represent vortex flow in type-II superconductors or driven charged colloids. The velocity-force curves for driving in the easy flow direction of the funnels exhibit a single depinning threshold; however, for driving in the hard flow direction, we find that there can be both negative mobility where the velocity decreases with increasing driving force as well as a reentrant pinning effect in which the particles flow at low drives but become pinned at intermediate drives. This reentrant pinning is associated with a transition from smooth 1D flow at low drives to a clogged state at higher drives that occurs when the particles cluster in a small number of plaquettes and block the flow. When the drive is further increased, particle rearrangements occur that cause the clog to break apart. We map out the regimes in which the pinned, flowing, and clogged states appear as a function of plaquette filling and drive. The clogged states remain robust at finite temperatures but develop intermittent bursts of flow in which a clog temporarily breaks apart but quickly reforms.

Dewetting and spreading transitions for active matter on random pinning substrates

We show that sterically interacting self-propelled disks in the presence of random pinning substrates exhibit transitions among a variety of different states. In particular, from a phase separated cluster state, the disks can spread out and homogeneously cover the substrate in what can be viewed as an example of an active matter wetting transition. We map the location of this transition as a function of activity, disk density, and substrate strength, and we also identify other phases including a cluster state, coexistence between a cluster and a labyrinth wetted phase, and a pinned liquid. Convenient measures of these phases include the cluster size, which dips at the wetting-dewetting transition, and the fraction of sixfold coordinated particles, which drops when dewetting occurs.

Dynamic phases, clustering, and chain formation for driven disk systems in the presence of quenched disorder

We numerically examine the dynamic phases and pattern formation of two-dimensional monodisperse repulsive disks driven over random quenched disorder. We show that there is a series of distinct dynamic regimes as a function of increasing drive, including a clogged or pile-up phase near depinning, a homogeneous disordered flow state, and a dynamically phase separated regime consisting of high-density crystalline regions surrounded by a low density of disordered disks. At the highest drives the disks arrange into one-dimensional moving chains. The phase separated regime has parallels with the phase separation observed in active matter systems, but arises from a distinct mechanism consisting of the combination of nonequilibrium fluctuations with density-dependent mobility. We discuss the pronounced differences between this system and previous studies of driven particles with longer-range repulsive interactions moving over random substrates, such as superconducting vortices or electron crystals, where dynamical phase separation and distinct one-dimensional moving chains are not observed. Our results should be generic to a broad class of systems in which the particle-particle interactions are short ranged, such as sterically interacting colloids or Yukawa particles with strong screening driven over random pinning arrays, superconducting vortices in the limit of small penetration depths, or quasi-two-dimensional granular matter flowing over rough landscapes.

Dynamic phases of active matter systems with quenched disorder

Depinning and nonequilibrium transitions within sliding states in systems driven over quenched disorder arise across a wide spectrum of size scales ranging from atomic friction at the nanoscale, flux motion in type II superconductors at the mesoscale, colloidal motion in disordered media at the microscale, and plate tectonics at geological length scales. Here we show that active matter or self-propelled particles interacting with quenched disorder under an external drive represents a class of system that can also exhibit pinning-depinning phenomena, plastic flow phases, and nonequilibrium sliding transitions that are correlated with distinct morphologies and velocity-force curve signatures. When interactions with the substrate are strong, a homogeneous pinned liquid phase forms that depins plastically into a uniform disordered phase and then dynamically transitions first into a moving stripe coexisting with a pinned liquid and then into a moving phase-separated state at higher drives. We numerically map the resulting dynamical phase diagrams as a function of external drive, substrate interaction strength, and self-propulsion correlation length. These phases can be observed for active matter moving through random disorder. Our results indicate that intrinsically nonequilibrium systems can exhibit additional nonequilibrium transitions when subjected to an external drive.

Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review

We review the depinning and nonequilibrium phases of collectively interacting particle systems driven over random or periodic substrates. This type of system is relevant to vortices in type-II superconductors, sliding charge density waves, electron crystals, colloids, stripe and pattern forming systems, and skyrmions, and could also have connections to jamming, glassy behaviors, and active matter. These systems are also ideal for exploring the broader issues of characterizing transient and steady state nonequilibrium flow phases as well as nonequilibrium phase transitions between distinct dynamical phases, analogous to phase transitions between different equilibrium states. We discuss the differences between elastic and plastic depinning on random substrates and the different types of nonequilibrium phases which are associated with specific features in the velocity-force curves, fluctuation spectra, scaling relations, and local or global particle ordering. We describe how these quantities can change depending on the dimension, anisotropy, disorder strength, and the presence of hysteresis. Within the moving phase we discuss how there can be a transition from a liquid-like state to dynamically ordered moving crystal, smectic, or nematic states. Systems with periodic or quasiperiodic substrates can have multiple nonequilibrium second or first order transitions in the moving state between chaotic and coherent phases, and can exhibit hysteresis. We also discuss systems with competing repulsive and attractive interactions, which undergo dynamical transitions into stripes and other complex morphologies when driven over random substrates. Throughout this work we highlight open issues and future directions such as absorbing phase transitions, nonequilibrium work relations, inertia, the role of non-dissipative dynamics such as Magnus effects, and how these results could be extended to the broader issues of plasticity in crystals, amorphous solids, and jamming phenomena.

Scale-free channeling patterns near the onset of erosion of sheared granular beds

Erosion shapes our landscape and occurs when a sufficient shear stress is exerted by a fluid on a sedimented layer. What controls erosion at a microscopic level remains debated, especially near the threshold forcing where it stops. Here we study, experimentally, the collective dynamics of the moving particles, using a setup where the system spontaneously evolves toward the erosion onset. We find that the spatial organization of the erosion flux is heterogeneous in space and occurs along channels of local flux σ whose distribution displays scaling near threshold and follows [Formula: see text], where J is the mean erosion flux. Channels are strongly correlated in the direction of forcing but not in the transverse direction. We show that these results quantitatively agree with a model where the dynamics is governed by the competition of disorder (which channels mobile particles) and particle interactions (which reduces channeling). These observations support that, for laminar flows, erosion is a dynamical phase transition that shares similarity with the plastic depinning transition occurring in dirty superconductors. The methodology we introduce here could be applied to probe these systems as well.

Model for the erosion onset of a granular bed sheared by a viscous fluid

We study theoretically the erosion threshold of a granular bed forced by a viscous fluid. We first introduce a model of interacting particles driven on a rough substrate. It predicts a continuous transition at some threshold forcing θ_{c}, beyond which the particle current grows linearly J∼θ-θ_{c}. The stationary state is reached after a transient time t_{conv} which diverges near the transition as t_{conv}∼|θ-θ_{c}|^{-z} with z≈2.5. Both features are consistent with experiments. The model also makes quantitative testable predictions for the drainage pattern: The distribution P(σ) of local current is found to be extremely broad with P(σ)∼J/σ, and spatial correlations for the current are negligible in the direction transverse to forcing, but long-range parallel to it. We explain some of these features using a scaling argument and a mean-field approximation that builds an analogy with q models. We discuss the relationship between our erosion model and models for the plastic depinning transition of vortex lattices in dirty superconductors, where our results may also apply.

Collective transport properties of driven Skyrmions with random disorder

We use particle-based simulations to examine the static and driven collective phases of Skyrmions interacting with random quenched disorder. We show that nondissipative effects due to the Magnus term reduce the depinning threshold and strongly affect the Skyrmion motion and the nature of the dynamic phases. The quenched disorder causes the Hall angle to become drive dependent in the moving Skyrmion phase, while different flow regimes produce distinct signatures in the transport curves. For weak disorder, the Skyrmions form a pinned crystal and depin elastically, while for strong disorder the system forms a pinned amorphous state that depins plastically. At high drives the Skyrmions can dynamically reorder into a moving crystal, with the onset of reordering determined by the strength of the Magnus term.

Anisotropic particle in viscous shear flow: Navier slip, reciprocal symmetry, and Jeffery orbit

The hydrodynamic reciprocal theorem for Stokes flows is generalized to incorporate the Navier slip boundary condition, which can be derived from Onsager's variational principle of least energy dissipation. The hydrodynamic reciprocal relations and the Jeffery orbit, both of which arise from the motion of a slippery anisotropic particle in a simple viscous shear flow, are investigated theoretically and numerically using the fluid particle dynamics method [Phys. Rev. Lett. 85, 1338 (2000)]. For a slippery elliptical particle in a linear shear flow, the hydrodynamic reciprocal relations between the rotational torque and the shear stress are studied and related to the Jeffery orbit, showing that the boundary slip can effectively enhance the anisotropy of the particle. Physically, by replacing the no-slip boundary condition with the Navier slip condition at the particle surface, the cross coupling between the rotational torque and the shear stress is enhanced, as manifested through a dimensionless parameter in both of the hydrodynamic reciprocal relations and the Jeffery orbit. In addition, simulations for a circular particle patterned with portions of no-slip and Navier slip are carried out, showing that the particle possesses an effective anisotropy and follows the Jeffery orbit as well. This effective anisotropy can be tuned by changing the ratio of no-slip portion to slip potion. The connection of the present work to nematic liquid crystals' constitutive relations is discussed.

Active matter transport and jamming on disordered landscapes

We numerically examine the transport of active run-and-tumble particles with steric particle-particle interactions driven with a drift force over random disordered landscapes composed of fixed obstacles. For increasing run lengths, the net particle transport initially increases before reaching a maximum and decreasing at larger run lengths. The transport reduction is associated with the formation of cluster or living crystal states that become locally jammed or clogged by the obstacles. We also find that the system dynamically jams at lower particle densities when the run length is increased. Our results indicate that there is an optimal activity level for transport of run-and-tumble type active matter through quenched disorder and could be important for understanding biological transport in complex environments or for applications of active matter particles in random media.

Aspects of jamming in two-dimensional athermal frictionless systems

In this work we provide an overview of jamming transitions in two dimensional systems focusing on the limit of frictionless particle interactions in the absence of thermal fluctuations. We first discuss jamming in systems with short range repulsive interactions, where the onset of jamming occurs at a critical packing density and where certain quantities show a divergence indicative of critical behavior. We describe how aspects of the dynamics change as the jamming density is approached and how these dynamics can be explored using externally driven probes. Different particle shapes can produce jamming densities much lower than those observed for disk-shaped particles, and we show how jamming exhibits fragility for some shapes while for other shapes this is absent. Next we describe the effects of long range interactions and jamming behavior in systems such as charged colloids, vortices in type-II superconductors, and dislocations. We consider the effect of adding obstacles to frictionless jamming systems and discuss connections between this type of jamming and systems that exhibit depinning transitions. Finally, we discuss open questions such as whether the jamming transition in all these different systems can be described by the same or a small subset of universal behaviors, as well as future directions for studies of jamming transitions in two dimensional systems, such as jamming in self-driven or active matter systems.

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

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.

Dynamics of self-organized driven particles with competing range interaction

Nonequilibrium self-organized patterns formed by particles interacting through competing range interaction are driven over a substrate by an external force. We show that, with increasing driving force, the preexisted static patterns evolve into dynamic patterns either via disordered phase or depinned patterns or via the formation of nonequilibrium stripes. Strikingly, the stripes are formed either in the direction of the driving force or in the transverse direction, depending on the pinning strength. The revealed dynamical patterns are summarized in a dynamical phase diagram.

Colloidal lattice shearing and rupturing with a driven line of particles

We examine the dynamics of two-dimensional colloidal systems using numerical simulations of a system with a drive applied to a thin region in the middle of the sample to produce a local shear. For a monodisperse colloidal assembly, we find a well-defined decoupling transition separating a regime of elastic motion from a plastic phase where the driven particles break away or decouple from the bulk particles and produce a shear band. For a bidisperse assembly, the onset of a bulk disordering transition coincides with the broadening of the shear band. We identify several distinct dynamical regimes that are correlated with features in the velocity-force curves. As a function of bidispersity, the decoupling force shows a nonmonotonic behavior associated with features in the noise fluctuations, power spectra, and bulk velocity profiles. When pinning is added in the bulk, we find that the shear band regions can become more localized, causing a decoupling of the driven particles from the bulk particles. For a system with thermal noise and no pinning, the shear band region becomes more extended and the average velocity of the driven particles drops at the thermal disordering transition of the bulk system.

Sliding elastic lattice: an explanation of the motion of superconducting vortices

We introduce a system where an elastic lattice of particles is moved slowly at a constant velocity under the influence of a local external potential, construct a rigid-body model through simplification processes, and show that the two systems produce similar results. Then, we apply our model to a superconducting vortex system and produce path patterns similar to the ones reported in Lee et al. [Phys. Rev. B 84, 060515(R) (2011)], suggesting that the reasoning of the simplification processes in this paper is a possible explanation of the experimentally observed phenomenon.

Jamming in systems with quenched disorder

We numerically study the effect of adding quenched disorder in the form of randomly placed pinning sites on jamming transitions in a disk packing that jams at a well-defined point J in the clean limit. Quenched disorder decreases the jamming density and introduces a depinning threshold. The onset of a finite threshold coincides with point J at the lowest pinning densities, but for higher pinning densities there is always a finite depinning threshold even well below jamming. We find that proximity to point J strongly affects the transport curves and noise fluctuations, and we observe a change from plastic behavior below jamming, where the system is highly heterogeneous, to elastic depinning above jamming. Many of the general features we find are related to other systems containing quenched disorder, including the peak effect observed in vortex systems.

Characterizing plastic depinning dynamics with the fluctuation theorem

We demonstrate that the fluctuation theorem can be used to characterize plastic flow phases in collectively interacting particle assemblies driven over quenched disorder when strong fluctuations and crackling noise with 1/f(α) character occur. By measuring the frequency of entropy-destroying trajectories and the diffusivity near the threshold for motion, we map out the different dynamic phases and demonstrate that the fluctuation theorem holds in the strongly fluctuating plastic flow regime which was previously shown to be chaotic. For different driving rates and disorder strength, we find that it is possible to define an effective temperature which decreases with increasing drive, as expected for this type of system. When the size of the pinning sites is large, we identify specific regimes where the fluctuation theorem holds only at long times due to an excess of negative entropy events that occur when particles undergo circular motions within the traps. We discuss how the fluctuation theorem could be applied to plastic flow in other driven nonthermal systems with quenched disorder such as superconducting vortices, magnetic domain walls, Coulomb glasses, and earthquake models.

Anisotropic sliding dynamics, peak effect, and metastability in stripe systems

A variety of soft and hard condensed matter systems are known to form stripe patterns. Here we use numerical simulations to analyze how such stripe states depin and slide when interacting with a random substrate and with driving in different directions with respect to the orientation of the stripes. Depending on the strength and density of the substrate disorder, we find that there can be pronounced anisotropy in the transport produced by different dynamical flow phases. We also find a disorder-induced "peak effect" similar to that observed for superconducting vortex systems, which is marked by a transition from elastic depinning to a state where the stripe structure fragments or partially disorders at depinning. Under the sudden application of a driving force, we observe pronounced metastability effects similar to those found near the order-disorder transition associated with the peak effect regime for three-dimensional superconducting vortices. The characteristic transient time required for the system to reach a steady state diverges in the region where the flow changes from elastic to disordered. We also find that anisotropy of the flow persists in the presence of thermal disorder when thermally induced particle hopping along the stripes dominates. The thermal effects can wash out the effects of the quenched disorder, leading to a thermally induced stripe state. We map out the dynamical phase diagram for this system, and discuss how our results could be explored in electron liquid crystal systems, type-1.5 superconductors, and pattern-forming colloidal assemblies.

Fluctuations, jamming, and yielding for a driven probe particle in disordered disk assemblies

Using numerical simulations we examine the velocity fluctuations and velocity-force curve characteristics of a probe particle driven with constant force through a two-dimensional disordered assembly of disks which has a well-defined jamming point J at a density of ϕJ=0.843. As ϕ increases toward ϕJ, the average velocity of the probe particle decreases and the velocity fluctuations show an increasingly intermittent or avalanchelike behavior. When ϕ is within a few percent of the jamming density, the velocity distributions are exponential, while when ϕ is less than 1% away from jamming, the velocity distributions have a power-law character with exponents in agreement with recent experiments. The velocity power spectra exhibit a crossover from a Lorentzian form to a 1/f shape near jamming. We extract a correlation length exponent ν which is in good agreement with recent shear simulations. For ϕ>ϕJ, there is a critical threshold force F(c) that must be applied for the probe particle to move through the sample which increases with increasing ϕ. The velocity-force curves are linear below jamming, while at jamming they have a power-law form. The onset of the probe motion above ϕJ occurs via a local yielding of the particles around the probe particle which we term a local shear banding effect.

Depinning dynamics of two-dimensional magnetized colloids on a random substrate

We perform Langevin simulations on the depinning dynamics of two-dimensional magnetized colloids on a random substrate. On increasing the magnetic field strength, we find for the first time a crossover from plastic to smectic flows as well as a crossover from smectic to elastic crystal flows above depinning. For both the smectic and elastic crystal flows, a power-law scaling relationship could be obtained between the average velocity and applied driving force. The scaling exponent is found to be larger than 1 for smectic flow. But, for the elastic crystal flow, the scaling exponent is found to be less than 1. For the plastic flow, no power-law scaling relationship between the average velocity and applied driving force can be derived and history dependence of the depinning occurs. Within the crossover from plastic to smectic flows, a sudden decrease in the critical driving force is observed, and a sudden increase is found in the critical driving force across the crossover from smectic to elastic crystal flows, accompanied by a crossing of the curves of average velocity versus driving force.

Random organization and plastic depinning

We provide evidence that the general phenomenon of plastic depinning can be described as an absorbing phase transition, and shows the same features as the random organization which was recently studied in periodically driven particle systems [L. Corte, Nature Phys. 4, 420 (2008)]. In the plastic flow system, the pinned regime corresponds to the absorbing state and the moving state corresponds to the fluctuating state. When an external force is suddenly applied, the system eventually organizes into one of these two states with a time scale that diverges as a power law at a nonequilibrium transition. We propose a simple experiment to test for this transition in systems with random disorder.

Diffusion in two-dimensional colloidal systems on periodic substrates

We study the diffusive behavior of two-dimensional charged colloidal suspensions subjected to a sinusoidal substrate by means of Brownian dynamics simulations. We mainly focus on the dependence of the mean-square displacement on the substrate strength. Our findings show a variation in the particle diffusion due to a substrate-induced distortion of the dynamic cage of nearest-neighbor colloids. This mechanism leads to a transition from normal diffusion at short times to subdiffusion on intermediate time scales. However, at long times normal diffusion is recovered. We also show that the variation in the long-time self-diffusion coefficient may be associated with the freezing and re-entrant melting transitions.

Reversible to irreversible flow transition in periodically driven vortices

We show that periodically driven superconducting vortices in the presence of quenched disorder exhibit a transition from reversible to irreversible flow under increasing vortex density or cycle period. This type of behavior has recently been observed for periodically sheared colloidal suspensions and we demonstrate that driven vortex systems exhibit remarkably similar behavior. We also provide evidence that the onset of irreversible behavior is a dynamical phase transition.

Disordering transitions and peak effect in polydisperse particle systems

We show numerically that in a binary system of Yukawa particles, a dispersity-driven disordering transition occurs. In the presence of quenched disorder this disordering transition coincides with a marked increase in the depinning threshold, known as a peak effect. We find that the addition of poorly pinned particles can increase the overall pinning in the sample by increasing the amount of topological disorder present. If the quenched disorder is strong enough to create a significant amount of topological disorder in the monodisperse system, addition of a poorly pinned species generates further disorder but does not produce a peak in the depinning force. Our results indicate that for binary mixtures, optimal pinning occurs for topological defect fraction densities from 0.2 to 0.25. For defect densities below this range, the system retains orientational order. We determine the effect of the pinning density, strength, and radius on the depinning peak and find that the peak effect is more pronounced in weakly pinning systems.

Superparamagnetic colloids confined in narrow corrugated substrates

We report a Brownian dynamics simulation study of the structure and dynamics of superparamagnetic colloids subject to external substrate potentials and confined in narrow channels. Our study is motivated by the importance of phenomena like commensurable-incommensurable phase transitions, anomalous diffusion, and stochastic activation processes that are closely related to the system under investigation. We focus mainly on the role of the substrate in the order-disorder mechanisms that lead to a rich variety of commensurate and incommensurate phases, as well as its effect on the single-file diffusion in interacting systems and the depinning transition in one dimension.

Statics and dynamics of 2D colloidal crystals in a random pinning potential

We report the first experimental study of a model system of a two-dimensional colloidal crystal in a random pinning potential. The colloidal crystal consists of monodispersed charged polystyrene microspheres suspended in deionized aqueous media and confined near a rough charged surface. It is found that the static orientational correlation function g6(r) decays exponentially for intermediate and strong pinning, in agreement with theories. The driven depinning is dominated by thermally activated creep motion along 1D-like channels between regions with short-range order. A coexistence model is proposed for describing the observations.

Coarsening of topological defects in oscillating systems with quenched disorder

We use large scale simulations to study interacting particles in two dimensions in the presence of both an ac drive and quenched disorder. As a function of ac amplitude, there is a crossover from a low drive regime where the colloid positions are highly disordered to a higher ac drive regime where the system dynamically reorders. We examine the coarsening of topological defects formed when the system is quenched from a disordered low ac amplitude state to a high ac amplitude state. When the quench is performed close to the disorder-order crossover, the defect density decays with time as a power law with alpha = 1/4 to 1/3. For deep quenches, in which the ac drive is increased to high values such that the dynamical shaking temperature is strongly reduced, we observe a logarithmic decay of the defect density into a grain boundary dominated state. We find a similar logarithmic decay of defect density in systems containing no pinning. We specifically demonstrate these effects for vortices in thin film superconductors, and discuss implications for dynamical reordering transition studies in these systems.

Crossover from intermittent to continuum dynamics for locally driven colloids

We simulate a colloid with charge q(d) driven through a disordered assembly of interacting colloids with charge q and show that, for q(d) approximately q, the velocity-force relation is nonlinear and the velocity fluctuations of the driven particle are highly intermittent with a 1/f characteristic. When g(d) >>q , the average velocity drops, the velocity-force relation becomes linear, and the velocity fluctuations are Gaussian. We discuss the results in terms of a crossover from strongly intermittent heterogeneous dynamics to continuum dynamics. We also make several predictions for the transient response in the different regimes.

Ratchet effect and nonlinear transport for particles on random substrates with crossed ac drives

We show in simulations that overdamped interacting particles in two dimensions with a randomly disordered substrate can exhibit novel nonequilibrium transport phenomena including a transverse ratchet effect, where a combined dc drive and circular ac drive produce a drift velocity in the direction transverse to the applied dc drive. The random disorder does not break any global symmetry; however, in two dimensions, symmetry breaking occurs due to the chirality of the circular drive. In addition to inducing the transverse ratchet effect, increasing the ac amplitude also strongly affects the longitudinal velocity response and can produce what we term an overshoot effect where the longitudinal dc velocity is higher in the presence of the ac drive than it would be for a dc drive alone. We also find a dynamical reordering transition upon increasing the ac amplitude. In the absence of a dc drive, it is possible to obtain a ratchet effect when the combined ac drives produce particle orbits that break a reflection symmetry. In this case, as the ac amplitude increases, current reversals can occur. These effects may be observable for vortices in type-II superconductors as well as for colloids interacting with random substrates.

Pinning and dynamics of colloids on one-dimensional periodic potentials

Using numerical simulations we study the pinning and dynamics of interacting colloids on periodic one-dimensional substrates. As a function of colloid density, temperature, and substrate strength, we find a variety of pinned and dynamic states including a locked smectic, pinned buckled, two-phase flow, and moving partially ordered structures. We show that for increasing colloid density, peaks in the depinning threshold occur at commensurate states. The scaling of the pinning threshold versus substrate strength changes when the colloids undergo a transition from one-dimensional chains to a buckled configuration.

Soft colloids driven and sheared by traveling wave fields

We study the dynamics of soft colloids interacting via a Gaussian pair potential in an external moving potential which is periodic in the spatial coordinate of the direction of motion. Both dynamical density functional theory and Brownian dynamics computer simulations are used to predict the steady-state density profiles. Two different situations are investigated: the first corresponds to a light wave that travels with a constant velocity v through the quiescent solvent containing the colloidal suspension. The second setup consists of two parallel repulsive walls with a periodic topographical substructure. One of the walls is at rest relative to the solvent while the other is in motion, inducing a shearing of the suspension. In the first case, we find that the amplitude of the steady-state density behaves nonmonotonically with the traveling speed v of the wave if the shape of the wave contains an edge: for increasing v , it first grows and then decreases. In the second setup we show that a strongly confined suspension induces a shear resistance which is a nonmonotonic function of the wall velocity. These effects are verifiable in real-space experiments on colloidal suspensions exposed to external laser-optical fields. In both situations, the dynamical density functional theory is in good agreement with the Brownian dynamics simulation data.

Directional locking effects and dynamics for particles driven through a colloidal lattice

We examine the dynamics of a single colloidal particle driven through a colloidal lattice which can distort in response to the driven particle. We find a remarkably rich variety of dynamical locking phenomena as we vary the angle of the applied drive with respect to the orientation of the colloidal lattice. When the driven colloid locks to certain lattice symmetry directions, its motion is not necessarily aligned with the drive. Applying a transverse force to the driven particle can result in either increased or decreased drag in the driving direction, depending on the angle of the drive. The dynamical locking produces anomalies in both the longitudinal and the transverse velocity vs driving force curves, including steps and regimes of negative differential resistance. As the interaction of the driven particle with the surrounding lattice increases, significant distortion or dislocations in the surrounding media occur, and as a result the directional locking is enhanced. We compare these results to those obtained for driving particles over fixed substrates, and show that a far richer variety of behaviors occurs when the underlying lattice is allowed to distort. We discuss how this system can be used for particle species segregation when the onset of different locking angles occurs at different drives for varied particle charges. We also show that the most pronounced locking phases should be observable at temperatures up to the melting transition of the colloidal lattice.

Dynamics of two-dimensional colloids on a disordered substrate

Using Langevin simulations, we numerically study the dynamics of two-dimensional colloids on a disordered substrate. With a decreasing strength of the interaction between colloids, we find a crossover from elastic to plastic depinnings, where a substantial increase in the depinning force is observed. Furthermore, we find a dynamical phase transition from the moving liquid to the moving smectic at high driving forces by decreasing the temperature. Peak effect occurs in the dynamical critical driving force across the transition, accompanied by a clear crossing of velocity-force dependence curves.

Local melting and drag for a particle driven through a colloidal crystal

We numerically investigate a colloidal particle driven through a colloidal crystal as a function of temperature. When the charge of the driven particle is larger or comparable to that of the colloids comprising the crystal, a local melting can occur, characterized by defect generation in the lattice surrounding the driven particle. The generation of the defects is accompanied by an increase in the drag force on the driven particle, as well as large noise fluctuations. We discuss the similarities of these results to the peak effect phenomena observed for vortices in superconductors.