Depinning and collective dynamics of magnetically driven colloidal monolayers

Overcrowding induces fast colloidal solitons in a slowly rotating potential landscape

Collective particle transport across periodic energy landscapes is ubiquitously present in many condensed matter systems spanning from vortices in high-temperature superconductors, frictional atomic sliding, driven skyrmions to biological and active matter. Here we report the emergence of fast solitons propagating against a rotating optical landscape. These experimentally observed solitons are stable cluster waves that originate from a coordinated particle exchange process which occurs when the number of trapped microparticles exceeds the number of potential wells. The size and speed of individual solitons rapidly increase with the particle diameter as predicted by theory and confirmed by numerical simulations. We show that when several solitons coexist, an effective repulsive interaction can stabilize their propagation along the periodic potential. Our experiments demonstrate a generic mechanism for cluster-mediated transport with potential applications to condensed matter systems on different length scales.

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.

Kibble-Zurek Mechanism for Dynamical Ordering in a Driven Vortex System

The Kibble-Zurek mechanism describes the formation of topological defects in systems crossing a continuous symmetry-breaking phase transition at a finite quench rate. While this mechanism has been extensively studied for equilibrium transitions, its applicability to nonequilibrium transitions has not yet been fully examined. Recent simulation has shown the applicability of the Kibble-Zurek mechanism to dynamical ordering transitions in particlelike assemblies, including superconducting vortices, driven over random disorder. Here, we experimentally study the configurational order of vortices in the course of dynamical ordering with various quench rates. We verify a power-law scaling of the defect density with the quench rate and an impulse-adiabatic crossover on the ordered side of the transition, which are key predictions of the Kibble-Zurek mechanism. Our results suggest the applicability of the Kibble-Zurek mechanism to other nonequilibrium phase transitions.

Substrate induced freezing, melting and depinning transitions in two-dimensional liquid crystalline systems

We use molecular dynamics simulations to investigate the ordering phenomena in two-dimensional (2D) liquid crystals over the one-dimensional periodic substrate (1DPS). We have used Gay-Berne (GB) potential to model the interaction between a pair of liquid crystalline (LC) particles. The underlying substrate potential with which the GB particles interact varies sinusoidally in one direction only. At a given temperature and density of the GB system, we varied the substrate's periodicity (a_s) but fixed the substrate strength. We observed that with a small value of a_s, an underlying substrate helps to stabilize a disordered LC nematic phase to a 2D solid phase. However, for an intermediate range of a_s, the system melts and transitions to a modulate-smectic. Finally, with a further increase in a_s, the system undergoes a structural depinning transition and returns to an LC nematic phase like a free system with no substrate. We argue that a three-way interplay of the energies arising from orientation-dependent particle-particle and particle-substrate interaction makes it possible for the system to undergo substrate-periodicity-dependent multiple phase transitions in the GB LC system.

Dynamics and clogging of colloidal monolayers magnetically driven through a heterogeneous landscape

We combine experiments and numerical simulations to investigate the emergence of clogging in a system of interacting paramagnetic colloidal particles driven against a disordered landscape of larger obstacles. We consider a single aperture in a landscape of immobile silica particles which are irreversibly attached to the substrate. We use an external rotating magnetic field to generate a traveling wave potential which drives the magnetic particles against these obstacles at a constant and frequency tunable speed. Experimentally we find that the particles display an intermittent dynamics with power law distributions at high frequencies. We reproduce these results by using numerical simulations and show that clogging in our system arises at large frequency, when the particles desynchronize with the moving landscape. Further, we use the model to explore the hidden role of flexibility in the obstacle displacements and the effect of hydrodynamic interactions between the particles. We also consider numerically the situation of a straight wall and investigate the range of parameters where clogging emerges in such case. Our work provides a soft matter test-bed system to investigate the effect of clogging in driven microscale matter.

Jamming, fragility and pinning phenomena in superconducting vortex systems

We examine driven superconducting vortices interacting with quenched disorder under a sequence of perpendicular drive pulses. As a function of disorder strength, we find four types of behavior distinguished by the presence or absence of memory effects. The fragile and jammed states exhibit memory, while the elastic and pinning dominated regimes do not. In the fragile regime, the system organizes into a pinned state during the first pulse, flows during the second perpendicular pulse, and then returns to a pinned state during the third pulse which is parallel to the first pulse. This behavior is the hallmark of the fragility proposed for jamming in particulate matter. For stronger disorder, we observe a robust jamming state with memory where the system reaches a pinned or reduced flow state during the perpendicular drive pulse, similar to the shear jamming of granular systems. We show signatures of the different states in the spatial vortex configurations, and find that memory effects arise from coexisting elastic and pinned components of the vortex assembly. The sequential perpendicular driving protocol we propose for distinguishing fragile, jammed, and pinned phases should be general to the broader class of driven interacting particles in the presence of quenched disorder.

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.

A structure-dynamics relationship in ratcheted colloids: resonance melting, dislocations, and defect clusters

We consider a two dimensional colloidal dispersion of soft-core particles driven by a one dimensional stochastic flashing ratchet that induces a time averaged directed particle current through the system. It undergoes a non-equilibrium melting transition as the directed current approaches a maximum associated with a resonance of the ratcheting frequency with the relaxation frequency of the system. We use extensive molecular dynamics simulations to present a detailed phase diagram in the ratcheting rate-mean density plane. With the help of a numerically calculated structure factor, solid and hexatic order parameters, and pair correlation functions, we show that the non-equilibrium melting is a continuous transition from a quasi-long range ordered solid to a hexatic phase. The transition is mediated by the unbinding of dislocations and formation of compact and string-like defect clusters.

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.

Orientational correlations in fluids with quenched disorder

Snapshots of colloidal particles moving on disordered two-dimensional substrates can be used to extract equal-time many-body correlations in their positions. To understand the systematics of these correlations, we perform Monte Carlo simulations of a two-dimensional model fluid placed in a quenched disordered background. We use configurations generated from these simulations to compute translational and orientational two-point correlations at equal time, concentrating on correlations in local orientational order as a function of density and disorder strength. We calculate both the disorder averaged version of conventional two-point correlation functions for orientational order, as well as the disorder averaged version of a novel correlation function of time-averaged disorder-induced inhomogeneities in local orientation analogous to the Edwards-Anderson correlation function in spin systems. We demonstrate that these correlations can exhibit interesting nonmonotonic behavior in proximity to the underlying fluid-solid transition and suggest that this prediction should be experimentally accessible.

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.

Disordering, clustering, and laning transitions in particle systems with dispersion in the Magnus term

We numerically examine a two-dimensional system of repulsively interacting particles with dynamics that are governed by both a damping term and a Magnus term. The magnitude of the Magnus term has one value for half of the particles and a different value for the other half of the particles. In the absence of a driving force, the particles form a triangular lattice, while when a driving force is applied, we find that there is a critical drive above which a Magnus-induced disordering transition can occur even if the difference in the Magnus term between the two particle species is as small as one percent. The transition arises due to the different Hall angles of the two species, which causes their motion to decouple at the critical drive. At higher drives, the disordered state can undergo both species and density phase separation into a density-modulated stripe that is oriented perpendicular to the driving direction. We observe several additional phases that occur as a function of drive and Magnus force disparity, including a variety of density-modulated diagonal-laned phases. In general, we find a much richer variety of states compared to systems of oppositely driven overdamped Yukawa particles. We discuss the implications of our work for skyrmion systems, where we predict that even for small skyrmion dispersities, a drive-induced disordering transition can occur along with clustering phases and pattern-forming states.

Enhancing Nanoparticle Diffusion on a Unidirectional Domain Wall Magnetic Ratchet

The performance of nanoscale magnetic devices is often limited by the presence of thermal fluctuations, whereas in micro- and nanofluidic applications the same fluctuations may be used to spread reactants or drugs. Here, we demonstrate the controlled motion and the enhancement of diffusion of magnetic nanoparticles that are manipulated and driven across a series of Bloch walls within an epitaxially grown ferrite garnet film. We use a rotating magnetic field to generate a traveling wave potential that unidirectionally transports the nanoparticles at a frequency tunable speed. Strikingly, we find an enhancement of diffusion along the propulsion direction and a frequency-dependent diffusion coefficient that can be precisely controlled by varying the system parameters. To explain the reported phenomena, we develop a theoretical approach that shows a fair agreement with the experimental data enabling an exact analytical expression for the enhanced diffusivity above the magnetically modulated periodic landscape. Our technique to control thermal fluctuations of driven magnetic nanoparticles represents a versatile and powerful way to programmably transport magnetic colloidal matter in a fluid, opening the doors to different fluidic applications based on exploiting magnetic domain wall ratchets.

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.

Manipulation of emergent vortices in swarms of magnetic rollers

Active colloids are an emergent class of out-of-equilibrium materials demonstrating complex collective phases and tunable functionalities. Microscopic particles energized by external fields exhibit a plethora of fascinating collective phenomena, yet mechanisms of control and manipulation of active phases often remains lacking. Here we report the emergence of unconfined macroscopic vortices in a system of ferromagnetic rollers energized by a vertical alternating magnetic field and elucidate the complex nature of a magnetic roller-vortex interactions with inert scatterers. We demonstrate that active self-organized vortices have an ability to spontaneously switch the direction of rotation and move across the surface. We reveal the capability of certain non-active particles to pin the vortex and manipulate its dynamics. Building on our findings, we demonstrate the potential of magnetic roller vortices to effectively capture and transport inert particles at the microscale.

Clogging and depinning of ballistic active matter systems in disordered media

We numerically examine ballistic active disks driven through a random obstacle array. Formation of a pinned or clogged state occurs at much lower obstacle densities for the active disks than for passive disks. As a function of obstacle density, we identify several distinct phases including a depinned fluctuating cluster state, a pinned single-cluster or jammed state, a pinned multicluster state, a pinned gel state, and a pinned disordered state. At lower active disk densities, a drifting uniform liquid forms in the absence of obstacles, but when even a small number of obstacles are introduced, the disks organize into a pinned phase-separated cluster state in which clusters nucleate around the obstacles, similar to a wetting phenomenon. We examine how the depinning threshold changes as a function of disk or obstacle density and find a crossover from a collectively pinned cluster state to a disordered plastic depinning transition as a function of increasing obstacle density. We compare this to the behavior of nonballistic active particles and show that as we vary the activity from completely passive to completely ballistic, a clogged phase-separated state appears in both the active and passive limits, while for intermediate activity, a readily flowing liquid state appears and there is an optimal activity level that maximizes the flux through the sample.

Velocity force curves, laning, and jamming for oppositely driven disk systems

Using simulations we examine a two-dimensional disk system in which two disk species are driven in opposite directions. We measure the average velocity of one of the species versus the applied driving force and identify four phases as function of drive and disk density: a jammed state, a completely phase separated state, a continuously mixing phase, and a laning phase. The transitions between these phases are correlated with jumps in the velocity-force curves that are similar to the behavior observed at dynamical phase transitions in driven particle systems with quenched disorder such as vortices in type-II superconductors. In some cases the transitions between phases are associated with negative differential mobility in which the average absolute velocity of either species decreases with increasing drive. We also consider the situation where the drive is applied to only one species as well as systems in which both species are driven in the same direction with different drive amplitudes. We show that the phases are robust against the addition of thermal fluctuations. Finally, we discuss how the transitions we observe could be related to absorbing phase transitions where a system in a phase separated or laning regime organizes to a state in which contacts between the disks no longer occur and dynamical fluctuations are lost.

Active turbulence in a gas of self-assembled spinners

Colloidal particles subject to an external periodic forcing exhibit complex collective behavior and self-assembled patterns. A dispersion of magnetic microparticles confined at the air-liquid interface and energized by a uniform uniaxial alternating magnetic field exhibits dynamic arrays of self-assembled spinners rotating in either direction. Here, we report on experimental and simulation studies of active turbulence and transport in a gas of self-assembled spinners. We show that the spinners, emerging as a result of spontaneous symmetry breaking of clock/counterclockwise rotation of self-assembled particle chains, generate vigorous vortical flows at the interface. An ensemble of spinners exhibits chaotic dynamics due to self-generated advection flows. The same-chirality spinners (clockwise or counterclockwise) show a tendency to aggregate and form dynamic clusters. Emergent self-induced interface currents promote active diffusion that could be tuned by the parameters of the external excitation field. Furthermore, the erratic motion of spinners at the interface generates chaotic fluid flow reminiscent of 2D turbulence. Our work provides insight into fundamental aspects of collective transport in active spinner materials and yields rules for particle manipulation at the microscale.

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.

Structural transitions and hysteresis in clump- and stripe-forming systems under dynamic compression

Using numerical simulations, we study the dynamical evolution of particles interacting via competing long-range repulsion and short-range attraction in two dimensions. The particles are compressed using a time-dependent quasi-one dimensional trough potential that controls the local density, causing the system to undergo a series of structural phase transitions from a low density clump lattice to stripes, voids, and a high density uniform state. The compression proceeds via slow elastic motion that is interrupted with avalanche-like bursts of activity as the system collapses to progressively higher densities via plastic rearrangements. The plastic events vary in magnitude from small rearrangements of particles, including the formation of quadrupole-like defects, to large-scale vorticity and structural phase transitions. In the dense uniform phase, the system compresses through row reduction transitions mediated by a disorder-order process. We characterize the rearrangement events by measuring changes in the potential energy, the fraction of sixfold coordinated particles, the local density, and the velocity distribution. At high confinements, we find power law scaling of the velocity distribution during row reduction transitions. We observe hysteresis under a reversal of the compression when relatively few plastic rearrangements occur. The decompressing system exhibits distinct phase morphologies, and the phase transitions occur at lower compression forces as the system expands compared to when it is compressed.

Micromagnet arrays enable precise manipulation of individual biological analyte-superparamagnetic bead complexes for separation and sensing

In this article, we review lab on a chip (LOC) devices that have been developed for processing magnetically labelled biological analytes, e.g., proteins, nucleic acids, viruses and cells, based on micromagnetic structures and a time-varying magnetic field. We describe the methods that have been developed for fabricating micromagnetic arrays and the bioprocessing operations that have been demonstrated using superparamagnetic (SPM) beads, i.e., programmed transport, switching, separation of specific analytes, and pumping and mixing of fluids in microchannels. The primary advantage of micromagnet devices is that they make it possible to develop systems that control individual SPM beads, enabling high-efficiency separation and analysis. These devices do not require hydrodynamic control and lend themselves to parallel processing of large arrays of SPM beads with modest levels of power consumption. Micromagnet devices are well suited for bioanalytical applications that require high-resolution separation, e.g., detection of rare cell types such as circulating tumour cells, or biosensor applications that require multiple magnetic bioprocessing operations on a single chip.

Dynamic Assembly of Magnetic Colloidal Vortices

Magnetic colloids in external time-dependent fields are subject to complex induced many-body interactions governing their self-assembly into a variety of equilibrium and out-of-equilibrium structures such as chains, networks, suspended membranes, and colloidal foams. Here, we report experiments, simulations, and theory probing the dynamic assembly of superparamagnetic colloids in precessing external magnetic fields. Within a range of field frequencies, we observe dynamic large-scale structures such as ordered phases composed of precessing chains, ribbons, and rotating fluidic vortices. We show that the structure formation is inherently coupled to the buildup of torque, which originates from internal relaxation of induced dipoles and from transient correlations among the particles as a result of short-lived chain formation. We discuss in detail the physical properties of the vortex phase and demonstrate its potential in particle-coating applications.

Transport and selective chaining of bidisperse particles in a travelling wave potential

We combine experiments, theory and numerical simulation to investigate the dynamics of a binary suspension of paramagnetic colloidal particles dispersed in water and transported above a stripe-patterned magnetic garnet film. The substrate generates a one-dimensional periodic energy landscape above its surface. The application of an elliptically polarized rotating magnetic field causes the landscape to translate, inducing direct transport of paramagnetic particles placed above the film. The ellipticity of the applied field can be used to control and tune the interparticle interactions, from net repulsive to net attractive. When considering particles of two distinct sizes, we find that, depending on their elevation above the surface of the magnetic substrate, the particles feel effectively different potentials, resulting in different mobilities. We exploit this feature to induce selective chaining for certain values of the applied field parameters. In particular, when driving two types of particles, we force only one type to condense into travelling parallel chains. These chains confine the movement of the other non-chaining particles within narrow colloidal channels. This phenomenon is explained by considering the balance of pairwise magnetic forces between the particles and their individual coupling with the travelling landscape.

Regulating wave front dynamics from the strongly discrete to the continuum limit in magnetically driven colloidal systems

The emergence of wave fronts in dissipative driven systems is a fascinating phenomenon which can be found in a broad range of physical and biological disciplines. Here we report the direct experimental observation of discrete fronts propagating along chains of paramagnetic colloidal particles, the latter propelled above a traveling wave potential generated by a structured magnetic substrate. We develop a rigorously reduced theoretical framework and describe the dynamics of the system in terms of a generalized one-dimensional dissipative Frenkel-Kontorova model. The front dynamics is explored in a wide range of field parameters close to and far from depinning, where the discrete and continuum limits apply. We show how symmetry breaking and finite size of chains are used to control the direction of front propagation, a universal feature relevant to different systems and important for real applications.

Geometric Frustration of Colloidal Dimers on a Honeycomb Magnetic Lattice

We study the phase behavior and the collective dynamics of interacting paramagnetic colloids assembled above a honeycomb lattice of triangular shaped magnetic minima. A frustrated colloidal molecular crystal is realized when filling these potential minima with exactly two particles per pinning site. External in-plane rotating fields are used to anneal the system into different phases, including long range ordered stripes, random fully packed loops, labyrinth and disordered states. At a higher amplitude of the annealing field, the dimer lattice displays a two-step melting transition where the initially immobile dimers perform first localized rotations and later break up by exchanging particles across consecutive lattice minima.

Bidirectional particle transport and size selective sorting of Brownian particles in a flashing spatially periodic energy landscape

Precise bidirectional transport and size fractionation of microscopic colloidal particles is demonstratedviasquare-wave modulation of a magnetic landscape.

Microscopic dynamics of synchronization in driven colloids

Synchronization of coupled oscillators has been scrutinized for over three centuries, from Huygens' pendulum clocks to physiological rhythms. One such synchronization phenomenon, dynamic mode locking, occurs when naturally oscillating processes are driven by an externally imposed modulation. Typically only averaged or integrated properties are accessible, leaving underlying mechanisms unseen. Here, we visualize the microscopic dynamics underlying mode locking in a colloidal model system, by using particle trajectories to produce phase portraits. Furthermore, we use this approach to examine the enhancement of mode locking in a flexible chain of magnetically coupled particles, which we ascribe to breathing modes caused by mode-locked density waves. Finally, we demonstrate that an emergent density wave in a static colloidal chain mode locks as a quasi-particle, with microscopic dynamics analogous to those seen for a single particle. Our results indicate that understanding the intricate link between emergent behaviour and microscopic dynamics is key to controlling synchronization.

Synchronization may occur when naturally oscillating systems are driven by an external modulation, for example, in charge density waves. Here, Juniper et al. visualize the locked modes of synchronization at a microscopic level using a colloidal system.

Stochastic ratcheting of two-dimensional colloids: Directed current and dynamical transitions

We present results of molecular dynamics simulations for two-dimensional repulsively interacting colloids driven by a one-dimensional asymmetric and commensurate ratchet potential, switching on and off stochastically. This drives a time-averaged directed current of colloids, exhibiting resonance with change in ratcheting frequency, where the resonance frequency itself depends nonmonotonically on density. Using scaling arguments, we obtain analytic results that show good agreement with numerical simulations. With increasing ratcheting frequency, we find nonequilibrium reentrant transitions between solid and modulated liquid phases.

Functional colloidal micro-sieves assembled and guided above a channel-free magnetic striped film

Colloidal inclusions in lab-on-a-chip devices can be used to perform analytic operations in a non-invasive fashion. We demonstrate here a novel approach to realize fast and reversible micro-sieving operations by manipulating and transporting colloidal chains via mobile domain walls in a magnetic structured substrate. We show that this technique allows one to precisely move and sieve non-magnetic particles, to tweeze microscopic cargos or to mechanically compress highly dense colloidal monolayers.

Fully alternating, triaxial electric or magnetic fields offer new routes to fluid vorticity

Noncontact methods of generating strong fluid vorticity are important to problems involving heat and mass transfer, fluid mixing, active wetting, and droplet transport. Furthermore, because zero or even negative shear viscosities can be induced, vorticity can greatly extend the control range of the smart fluids used in magnetorheological devices. In recent work we have shown that a particular class of ac/ac/dc triaxial fields (symmetry-breaking rational fields) can create strong vorticity in magnetic particle suspensions and have presented a theory of the vorticity that is based on the symmetry of the 2-d Lissajous trajectories of the field and its converse. In this paper we demonstrate that there are three countably infinite sets of fully alternating ac/ac/ac triaxial fields whose frequencies form rational triads that have the symmetry required to drive fluid vorticity. The symmetry of the 3-d Lissajous trajectories of the field and its converse can be derived and from this the direction of the vorticity axis can be predicted, as can the dependence of the sign of the vorticity on the phase relations between the three field components. Experimental results are presented that validate the symmetry theory. These discoveries significantly broaden the class of triaxial fields that can be exploited to produce strong noncontact flow.

Stripe systems with competing interactions on quasi-one dimensional periodic substrates

We numerically examine the two-dimensional ordering of a stripe forming system of particles with competing long-range repulsion and short-range attraction in the presence of a quasi-one-dimensional corrugated substrate. As a function of increasing substrate strength or period we show that a remarkable variety of distinct orderings can be realized, including modulated stripes, prolate clump phases, two dimensional ordered kink structures, crystalline void phases, and smectic phases. Additionally in some cases the stripes align perpendicular to the substrate troughs. Our results suggest that a new route to self assembly for systems with competing interactions can be achieved through the addition of a simple periodic modulated substrate.

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.

Tunable interactions between paramagnetic colloidal particles driven in a modulated ratchet potential

We study experimentally and theoretically the interactions between paramagnetic particles dispersed in water and driven above the surface of a stripe patterned magnetic garnet film. An external rotating magnetic field modulates the stray field of the garnet film and generates a translating potential landscape which induces directed particle motion. By varying the ellipticity of the rotating field, we tune the inter-particle interactions from net repulsive to net attractive. For attractive interactions, we show that pairs of particles can approach each other and form stable doublets which afterwards travel along the modulated landscape at a constant mean speed. We measure the strength of the attractive force between the moving particles and propose an analytically tractable model that explains the observations and is in quantitative agreement with experiment.

Single-file and normal diffusion of magnetic colloids in modulated channels

Diffusive properties of interacting magnetic dipoles confined in a parabolic narrow channel and in the presence of a periodic modulated (corrugated) potential along the unconfined direction are studied using Brownian dynamics simulations. We compare our simulation results with the analytical result for the effective diffusion coefficient of a single particle by Festa and d'Agliano [Physica A 90, 229 (1978)] and show the importance of interparticle interaction on the diffusion process. We present results for the diffusion of magnetic dipoles as a function of linear density, strength of the periodic modulation and commensurability factor.

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.

Unconventional dynamic hysteresis in a periodic assembly of paramagnetic colloids

Dynamic hysteresis phenomena are widespread in physical sciences and describe the complex behavior of systems driven out of equilibrium by a periodic forcing. We use here paramagnetic colloids above a stripe-patterned garnet film as the model system to study dynamic hysteresis, the latter induced when the particles are periodically translated by an oscillating magnetic field. In contrast to the expected behavior for a bistable system, we observe that the area of the hysteresis loop decreases by increasing the driving frequency and reduces to zero for frequencies higher than 5-7s(-1). To explain the experimental results, we develop a simple model based on an overdamped Brownian particle driven by a periodic potential with an oscillating amplitude.