Active matter or self-propelled systems have been attracting growing attention in biological systems such as swimming bacteria as well as artificial swimmers such as self-driven colloids. These systems exhibit interesting effects including an activity-induced self clustering that occurs even when all pairwise particle-particle interactions are repulsive. Due to the size scale of the active particles, tailored landscapes can be created for the particles by means of optical trapping. Using large scale simulations we examine an active matter system of self-propelled disks moving in confined geometries and in quasi-1D periodic and asymmetric saw-tooth landscapes. The system forms a dense cluster when the trapping sites are large, but still exhibits modes of motion along the edges of the clusters. We discuss how these effects could be related to a mechanical version of topological protection. For periodic quasi-1D traps we find that there can be a 1D ordering of the disks with motion occurring along only one dimension. For asymmetric substrates we find an active matter ratchet effect similar that observed previously; however, when strong interactions between the particles are introduced, we find that it is possible to obtain a reversal of the ratchet effect in which the net flow is in the direction opposite to the easy-flow direction of the substrate asymmetry. The ability to produce a reversal of the active ratchet effect suggests that it may be possible to set up a landscape in which different species of active matter particles move in opposite directions.
Colloids interacting with periodic substrates such as those created with optical traps are an ideal system in which to study various types of phase transitions such as commensurate to incommensurate states and melting behaviors, and they can also be used to create new types of ordering that can be mapped to spin systems. Here we numerically demonstrate how magnetic colloids interacting with an array of elongated two-state traps can be used to realize square artificial spin ice. By tuning the magnetic field, it is possible to precisely control the interaction strength between the colloids, making it possible to observe a transition from a disordered state to an ordered state that obeys the two-in/two-out ice rules. We also examine the dynamics of excitations of the ground state, including pairs of monopoles, and show that the monopoles have emergent attractive interactions. The strength of the interaction can be modified by the magnetic field, permitting the monopole velocity to be tuned.
There has been tremendous growth in the field of active matter, where the individual particles that comprise the system are self-driven. Examples of this class of system include biological systems such as swimming bacteria and crawling cells. More recently, non-biological swimmers have been created using colloidal Janus particles that undergo chemical reactions on one side to produce self-propulsion. These active matter systems exhibit a wide variety of behaviors that are absent in systems undergoing purely thermal fluctuations, such as transitions from uniform liquids to clusters or living crystals, pushing objects around, ratchet effects, and phase separation in mixtures of active and passive particles. Here we examine the collective effects of active matter disks in the presence of static or dynamic substrates. For colloids, such substrates could be created optically in the form of periodic, random, or quasiperiodic patterns. For thermal particles, increasing the temperature generally increases the diffusion or mobility of the particles when they move over a random or periodic substrates. We find that when the particles are active, increasing the activity can increase the mobility for smaller run lengths but decrease the mobility at large run lengths. Additionally we find that at large run lengths on a structured substrate, a variety of novel active crystalline states can form such as stripes, squares and triangular patterns.
With the use of optical traps it is possible to confine assemblies of colloidal particles in two-dimensional and quasi-one-dimensional arrays. Here we examine how colloidal particles rearrange in a quasi-one-dimensional trap with a time dependent confining potential. The particle motion occurs both through slow elastic uniaxial distortions as well as through abrupt large-scale two-dimensional avalanches associated with plastic rearrangements. During the avalanches the particle velocity distributions extend over a broad range and can be fit to a power law consistent with other studies of plastic events mediated by dislocations.
There are many examples of interacting particles that have both repulsive and attractive interaction terms. Assemblies of such particles can form clumps, gel type states, labyrinths and other patterns, while two-dimensional systems with purely repulsive interactions typically form hexagonal crystals. Here we examine the two-dimensional pattern formation of colloids with competing interactions in the presence of a quasi-one dimensional periodic substrate. For soft matter systems, such substrates can be created by various optical means. We show that the substrate can induce various patterns including commensurate bubble phases as well as modulated stripes aligned with the substrate. Beyond colloids, these results should also be general to other systems that can be modeled as particles with competing interactions moving over a surface with a quasi-one dimensional periodic substrate or modulation.
Colloids interacting with complex landscapes created by optical means exhibit a remarkable variety of novel orderings and equilibrium states. It is also possible to study nonequilibrium properties for colloids driven over optical traps when there is an additional external electric field or some other form of external driving. Recently a new type of colloidal system has been realized in which the colloids are self-driven or self-motile and undergo a persistent random walk. Self motile particle systems fall into the broader class of self-driven systems called active matter. For the case of externally driven colloidal particles moving over random or periodic arrangements of traps, various types of pinning or jamming effects can arise. Far less is known about the mobility of active matter particles in the presence or random or periodic substrates. For example, it is not known whether increasing the activity of the particles would reduce the jamming effects caused by effective friction between particles. Here we show by varying the activity and the density of active particles that various types of motion can arise. In some cases, increasing the self-driving leads to a reduction in the net flow of particles through the system.
Optical traps have been extensively employed to create tailored colloidal crystalline structures where the crystals
can have long range order. Here we discuss how colloidal particles on periodic substrates can be used to
understand how frustration can produce partially ordered states. We demonstrate how to create artificial spin
ice systems using colloidal particles and describe variations on this system that include geometries in which a
random loop model can be realized. We also discuss how frustration effects can be used to control grain boundary
formation by creating energetic defects in the ground state ordering of these systems.
Active matter or self driven particle systems include swimming bacteria, crawling cells and artificial swimmers.
These systems often exhibit run and tumble dynamics; however, there are also examples of particles that move or
swim in circles, such as bacteria near surfaces. Circular swimmers have also been experimentally realized using
chiral colloidal particles. Here we examine how a substrate can be used to direct the motion of circle swimmers
and separate particles with different swimming chiralities. The combination of the time reversal symmetry
breaking by the circular motion as well as the breaking of detailed balance when the particles interact with the
barriers leads to the directed motion. We examine this effect for different types of substrate geometries and also
consider the effects of temperature. Such substrates could be created using various optical techniques.
Recently there has been growing interest in what is called active matter, or collections of particles that are self
driven rather than driven with an external field. Examples of such systems include swimming bacteria, flocks of
birds or fish, and pedestrian flow. There have also been recent experimental realizations of self-driven systems
using colloidal particles undergoing self-catalytic interactions. One example of this is light-induced catalysis
where the colloids become self-driven in the presence of light. Almost all of these studies have been performed in
the absence of a substrate. Here we examine how a substrate can be used to direct the motion of the particles.
We demonstrate a self-induced ratchet effect that occurs in the presence of disorder as well as the direction of
the particle along symmetry directions of the substrate. The type of substrate we consider may be created using
various optical techniques, and studies of this system could lead to insights into the nonequilibrium behavior
of active matter as well as to applications such as sorting of different active particle species or of active and
There are many examples of particle assemblies where the particles have competing repulsive and attractive interactions. In solid state systems, it has recently been proposed that exotic vortex states in type-I and type-II superconducting hybrids and type-1.5 superconductors fall into this category. In soft matter systems, competing
interactions can arise for charged colloids with short range attraction or with multiple length scale interactions. Systems with competing interactions have been shown to exhibit a wide variety of patterns including stripes, labyrinths, bubbles, and crystalline phases. Although there has been considerable work analyzing these phases for
different relative interaction strengths, there is little work on understanding what happens when such systems are driven over a periodic substrate. Such substrates for collective assemblies of particles could be created lithographically or using optical trap arrays and would introduce a new length scale into the system. Here we
examine how a system with competing interactions behaves when interacting with a square periodic substrate. We find a novel wetting-dewetting phenomena similar to that of liquids on surfaces. In the presence of a strong substrate, the pattern formation normally found for particles with competing interactions is lost and the
particles completely cover the substrate homogeneously. Under an applied drive, such a wetted system undergoes a transition to a partially dewetted state with anisotropic transport and structural features.
For collections of particles in a thermal bath interacting with an asymmetric substrate, it is possible for a
ratchet effect to occur where the particles undergo a net dc motion in response to an ac forcing. Ratchet
effects have been demonstrated in a variety of systems including colloids as well as magnetic vortices in type-II
superconductors. Here we examine the case of active matter or self-driven particles interacting with asymmetric
substrates. Active matter systems include self-motile colloidal particles undergoing catalysis, swimming bacteria,
artificial swimmers, crawling cells, and motor proteins. We show that a ratchet effect can arise in this type of
system even in the absence of ac forcing. The directed motion occurs for certain particle-substrate interaction
rules and its magnitude depends on the amount of time the particles spend swimming in one direction before
turning and swimming in a new direction. For strictly Brownian particles there is no ratchet effect. If the
particles reflect off the barriers or scatter from the barriers according to Snell's law there is no ratchet effect;
however, if the particles can align with the barriers or move along the barriers, directed motion arises. We
also find that under certain motion rules, particles accumulate along the walls of the container in agreement
with experiment. We also examine pattern formation for synchronized particle motion. We discuss possible applications of this system for self-assembly, extracting work, and sorting as well as future directions such as considering collective interactions and flocking models.
In this paper, long range surface plasmon devices using metallic subwavelength gratings are experimentally
demonstrated. Subwavelength gold gratings are fabricated with deep UV interference lithography. Long range surface
plasmon device using these subwavelength gold gratings is characterized by measuring the surface plasmon resonance
reflectance curve in an attenuated total reflection setup. Surface plasmon resonance curve with approximately ten times
narrower angular width than that from long range surface plasmon propagating along metallic thin films has been observed experimentally.
We examine the statics and dynamics of charged colloids interacting with periodic optical trap arrays. In
particular we study the regime where more than one colloid is confined in each trap, creating effective dimer,
trimer, and higher order states called colloidal molecular crystals. The n-mer states have an effective orientational
degree of freedom which can be controlled with an external driving field. In general, the external field causes
a polarization effect where the orientation of the n-mers aligns with the external field, similar to liquid crystal
systems. Additionally, under a rotating external drive the n-mers can rotate with the drive. In some cases a
series of structural transitions in the colloidal crystal states occur in the rotating field due to a competition
between the ordering of the colloidal molecular crystals and the polarization effect which orients the n-mers in
the direction of the drive. We also show that for some parameters, the n-mers continuously rotate with the drive
without switching, that depinning transitions can occur where the colloids jump from well to well, and that there
are a number of distinct dynamical transitions between the phases. Finally, we illustrate colloidal orderings at
fillings of more than four colloids per trap, indicating that it is possible to create higher order colloidal crystal
We numerically examine noise fluctuations and hysteresis phenomena in charged systems that form stripe,
labyrinth or clump patterns. It is believed that charge inhomogeneities of this type arise in two-dimensional
(2D) quantum hall systems and in electron crystal structures in high temperature superconductors, while related
patterns appear in manganites and type-I superconductors. Recent noise and transport experiments in two-dimensional
electron gases and high temperature superconducting samples revealed both 1/fα noise signatures
and hysteretic phenomena. Using numerical simulations we show that 1/fα noise fluctuations and hysteresis are
generic features that occur in charge systems which undergo a type of phase separation that results in stripes,
clumps, checkerboards, or other inhomogeneous patterns. We find that these systems exhibit 1/fα fluctuations
with 1.2 < α < 1.8, rather than simple 1/f or 1/fα fluctuations. We also propose that the 2D metal insulator
transition may be associated with a clump electron glass phase rather than a Wigner glass phase.
We show with computer simulations that a rich variety of static and dynamical colloidal phases can be realized for colloids interacting with two-dimensional periodic substrates. For the static case a new type of colloidal state that we term colloidal molecular crystals occurs when there is an integer number of colloids per substrate minima. Here there is a novel orientational ordering in addition to the positional ordering of the colloids. The colloidal molecular crystals exhibit a multi-step melting in which the orientational ordering is lost first, followed by the positional ordering. This multi-step melting phenomenon agrees well with recent experiments. Additionally we show that at fillings where the number of colloids is an incommensurate fraction of the number of substrate minima, as a function of temperature there is a transition to a state in which local incommensurations become thermally activated. With an applied drive we find that a remarkable number of distinct dynamical phases can be realized, including ordered and disordered flows. We also illustrate flow phases in which the colloidal motion locks to a symmetry direction of the underlying lattice.
We analyze the noise fluctuations near charge ordering transitions in disordered materials. In particular we consider a two-dimensional (2D) system at finite temperature with a fixed number of defect sites and increase the number of mobile charges. We find that for a high density of charges the system forms a high mobility liquid with low spectral power and a white noise characteristic. As the density of charges is lowered we find a coexistence of liquid regions with locally frozen regions. In this regime the noise power is high and has a 1/fα form with α ~ 0.5 to 1.5. For the low charge density regime we find a disordered frozen regime where all the charges are localized. We also find that for increasing temperature the noise power drops. We compare our results to recent noise experiments on the 2D metal-insulator transition and the vortex-liquid to vortex glass transition found in superconductors.
We use particle dynamics simulations to probe the correlations between
noise and dynamics in a variety of disordered systems, including
superconducting vortices, 2D electron liquid crystals, colloids,
domain walls, and granular media. The noise measurements offer an
experimentally accessible link to the microscopic dynamics, such
as plastic versus elastic flow during transport, and can provide
a signature of dynamical reordering transitions in the system.
We consider broad and narrow band noise in transport systems, as
well as the fluctuations of dislocation density in a system near
the melting transition.