Binary Mixtures in Linear Convection Arrays.

We numerically investigated the dynamics of a mixture of finite-size active and passive disks in a linear array of two-dimensional convection rolls. The interplay of advection and steric interactions produces a number of interesting effects, like the stirring of a passive colloidal fluid by a small fraction of slow active particles, or the separation of the mixture active and passive colloidal fractions by increasing the motility of the active one, which eventually clusters in stagnation areas along the array walls. These mechanisms are quantitatively characterized by studying the dependence of the diffusion constants of the active and passive particles on the parameters of the active mixture fraction.

Autonomous ratcheting by stochastic resetting.

We propose a generalization of the stochastic resetting mechanism for a Brownian particle diffusing in a one-dimensional periodic potential: randomly in time, the particle gets reset at the bottom of the potential well it was in. Numerical simulations show that in mirror asymmetric potentials, stochastic resetting rectifies the particle's dynamics, with a maximum drift speed for an optimal average resetting time. Accordingly, an unbiased Brownian tracer diffusing on an asymmetric substrate can rectify its motion by adopting an adaptive stop-and-go strategy. Our proposed ratchet mechanism can model the directed autonomous motion of molecular motors and micro-organisms.

Narrow Pore Crossing of Active Particles under Stochastic Resetting.

We propose a two-dimensional model of biochemical activation process, whereby self-propelling particles of finite correlation times are injected at the center of a circular cavity with constant rate equal to the inverse of their lifetime; activation is triggered when one such particle hits a receptor on the cavity boundary, modeled as a narrow pore. We numerically investigated this process by computing the particle mean-first exit times through the cavity pore as a function of the correlation and injection time constants. Due to the breach of the circular symmetry associated with the positioning of the receptor, the exit times may depend on the orientation of the self-propelling velocity at injection. Stochastic resetting appears to favor activation for large particle correlation times, where most of the underlying diffusion process occurs at the cavity boundary.

Colloidal Stochastic Resonance in Confined Geometries.

We investigate the dynamical properties of a colloidal particle in a double cavity. Without external driving, the particle hops between two free-energy minima with transition mean time depending on the system's entropic and energetic barriers. We then drive the particle with a periodic force. When the forcing period is set at twice the transition mean time, a statistical synchronization between particle motion and forcing phase marks the onset of a stochastic resonance mechanism. Comparisons between experimental results and predictions from the Fick-Jacobs theory and Brownian dynamics simulation reveal significant hydrodynamic effects, which change both resonant amplification and noise level. We further show that hydrodynamic effects can be incorporated into existing theory and simulation by using an experimentally measured particle diffusivity.

Colloidal clustering and diffusion in a convection cell array.

We numerically investigated the clustering of a uniform suspension of finite-size disks in a linear array of two-dimensional convection cells. We observed that, due to steric interactions, the disks tend to form coherently rotating spatial structures at the center of each cell, as a combined effect of advection and pair collisions. Micellar, ring-like and hexatic patterns emerge in the deterministic regime, depending on the suspension density, but dissolve in the presence of thermal fluctuations. Moreover, pair collisions suffice to activate cell crossings even by noiseless disks and, therefore, cause athermal diffusion. The robustness of such collision induced effects is studied against the opposing action of thermal noise, transverse biases, and particle self-propulsion.

Diffusion of active particles in convective flows.

We numerically investigated the diffusion of an active Janus particle in periodic arrays of planar counter-rotating convection rolls at high Péclet numbers. We considered convection patterns with distinct longitudinal and transverse advection properties and characterized the dependence of the relevant diffusion constants on the particle's dynamical parameters, namely, self-propulsion speed, correlation time and chirality. Numerical results are interpreted analytically based on qualitative arguments of classical transport theory. The purpose of the present analysis is controlling active matter transport in microfluidic devices.

Active particle diffusion in convection roll arrays.

Undesired advection effects are unavoidable in most nano-technological applications involving active matter. However, it is conceivable to govern the transport of active particles at the small scales by suitably tuning the relevant advection and self-propulsion parameters. To this purpose, we numerically investigated the Brownian motion of active Janus particles in a linear array of planar counter-rotating convection rolls at high Péclet numbers. Similarly to passive particles, active microswimmers exhibit advection enhanced diffusion, but only for self-propulsion speeds up to a critical value. The diffusion of faster Janus particles is governed by advection along the array's edges, whereby distinct diffusion regimes are observed and characterized. Contrary to passive particles, the relevant spatial distributions of active Janus particles are inhomogeneous. These peculiar properties of active matter are related to the combined action of noise and self-propulsion in a confined geometry and hold regardless of the actual flow boundary conditions.

Anisotropic Diffusion in Driven Convection Arrays.

We numerically investigate the transport of a Brownian colloidal particle in a square array of planar counter-rotating convection rolls at high Péclet numbers. We show that an external force produces huge excess peaks of the particle's diffusion constant with a height that depends on the force orientation and intensity. In sharp contrast, the particle's mobility is isotropic and force independent. We relate such a nonlinear response of the system to the advection properties of the laminar flow in the suspension fluid.

Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels.

In the absence of advection, confined diffusion characterizes transport in many natural and artificial devices, such as ionic channels, zeolites, and nanopores. While extensive theoretical and numerical studies on this subject have produced many important predictions, experimental verifications of the predictions are rare. Here, we experimentally measure colloidal diffusion times in microchannels with periodically varying width and contrast results with predictions from the Fick-Jacobs theory and Brownian dynamics simulation. While the theory and simulation correctly predict the entropic effect of the varying channel width, they fail to account for hydrodynamic effects, which include both an overall decrease and a spatial variation of diffusivity in channels. Neglecting such hydrodynamic effects, the theory and simulation underestimate the mean and standard deviation of first passage times by 40% in channels with a neck width twice the particle diameter. We further show that the validity of the Fick-Jacobs theory can be restored by reformulating it in terms of the experimentally measured diffusivity. Our work thus shows that hydrodynamic effects play a key role in diffusive transport through narrow channels and should be included in theoretical and numerical models.

Active diffusion limited reactions.

We investigate the one- and two-dimensional diffusion limited reactions A + A → 0 and A + B → 0 with A active Janus particles and B passive particles in thermal equilibrium. We show that by increasing the self-propulsion time of the A particles, the reactant densities decay faster, at least for time transients of potential interest for chemical applications, e.g., to develop smart drug delivery protocols. Asymptotic and transient density decays obey power laws with exponents that depend on the actual annihilation reaction and its dimensionality.

Active microswimmers in a finite two dimensional trap: The role of hydrodynamic interaction.

We investigate the dynamics of two identical artificial active particles suspended in a free-standing fluid film with a trap of finite radius in an acoustic tweezer. In the two dimensional Oseen approximation, their hydrodynamic coupling is long ranged, which naturally raises the question as under what conditions they can simultaneously reside in the trap. We determine a critical value of the hydrodynamic coupling below which that happens and study the ensuing active pair dynamics inside the trap. For larger couplings, only one particle sits in the trap, while the other diffuses freely until it eventually replaces the particle in the trap. Such a mechanism repeats itself with a characteristic noise-dependent mean residence-retrapping time.

Single file dynamics in soft materials.

The term single file (SF) dynamics refers to the motion of an assembly of particles through a channel with cross-sections comparable to the particles' diameter. Single file diffusion (SFD) is then the diffusion of a tagged particle in a single file, i.e., under the condition that particle passing is not allowed. SFD accounts for a large variety of processes in nature, including diffusion of colloids in synthetic and natural channels, biological motors along molecular chains, electrons in proteins and liquid helium, ions through membranes, just to mention a few examples. Albeit introduced in 1965s, over the last decade the classical notion of SF dynamics has been generalised to account for a more realistic modelling of the particle properties, file geometry, particle-particle and channel-particle interactions, which paves the way to remarkable applications of the SF model, for instance, in the technology of bio-integrated nanodevices. We provide here a comprehensive review of the recent advances in the theory of SF dynamics with the purpose of spurring further experimental work.

Diffusion of active dimers in a Couette flow.

We study the 3D dynamics of an elastic dimer consisting of an active swimmer bound to a passive cargo, both suspended in a Couette flow. Using numerical simulations, we determine the diffusivity of such an active dimer in the presence of long-range hydrodynamic interactions for different values of its self-propulsion speed and the Couette flow. We observe that the effect of hydrodynamic interactions is greatly enhanced under the condition that self-propulsion is strong enough to contrast the shear flow. The magnitude of the effect grows with the size of the dimer's constituents relative to their distance, which makes it appreciable under experimental conditions.

Nonlocality of relaxation rates in disordered landscapes.

We investigate both analytically and by numerical simulation the relaxation of an overdamped Brownian particle in a 1D multiwell potential. We show that the mean relaxation time from an injection point inside the well down to its bottom is dominated by statistically rare trajectories that sample the potential profile outside the well. As a consequence, also the hopping time between two degenerate wells can depend on the detailed multiwell structure of the entire potential. The nonlocal nature of the transitions between two states of a disordered landscape is important for the correct interpretation of the relaxation rates in complex chemical-physical systems, measured either through numerical simulations or experimental techniques.

Confined Catalytic Janus Swimmers in a Crowded Channel: Geometry-Driven Rectification Transients and Directional Locking.

Self-propelled Janus particles, acting as microscopic vehicles, have the potential to perform complex tasks on a microscopic scale, suitable, e.g., for environmental applications, on-chip chemical information processing, or in vivo drug delivery. Development of these smart nanodevices requires a better understanding of how synthetic swimmers move in crowded and confined environments that mimic actual biosystems, e.g., network of blood vessels. Here, the dynamics of self-propelled Janus particles interacting with catalytically passive silica beads in a narrow channel is studied both experimentally and through numerical simulations. Upon varying the area density of the silica beads and the width of the channel, active transport reveals a number of intriguing properties, which range from distinct bulk and boundary-free diffusivity at low densities, to directional "locking" and channel "unclogging" at higher densities, whereby a Janus swimmer is capable of transporting large clusters of passive particles.

Diffusion of eccentric microswimmers.

We model the two-dimensional diffusive dynamics of an eccentric artificial microswimmer in a highly viscous medium. We assume that the swimmer's propulsion results from an effective force applied to a center distinct from its center of mass, both centers resting on a body's axis parallel to its average self-propulsion velocity. Moreover, we allow for angular fluctuations of the velocity about the body's axis. We prove, both analytically and numerically, that the ensuing active diffusion of the swimmer is suppressed to an extent that strongly depends on the model parameters. In particular, the active diffusion constant undergoes a transition from a quadratic to a linear dependence on the self-propulsion speed, with practical consequences on the interpretation of the experimental data. Finally, we extend our model to describe the diffusion of chiral eccentric swimmers.

Communication: Cargo towing by artificial swimmers.

An active swimmer can tow a passive cargo by binding it to form a self-propelling dimer. The orientation of the cargo relative to the axis of the active dimer's head is determined by the hydrodynamic interactions associated with the propulsion mechanism of the latter. We show how the tower-cargo angular configuration greatly influences the dimer's diffusivity and, therefore, the efficiency of the active swimmer as a micro-towing motor.

Driven microswimmers on a 2D substrate: A stochastic towed sled model.

We investigate, both numerically and analytically, the diffusion properties of a stochastic sled sliding on a substrate, subject to a constant towing force. The problem is motivated by the growing interest in controlling transport of artificial microswimmers in 2D geometries at low Reynolds numbers. We simulated both symmetric and asymmetric towed sleds. Remarkable properties of their mobilities and diffusion constants include sidewise drifts and excess diffusion peaks. We interpret our numerical findings by making use of stochastic approximation techniques.

Communication: Memory effects and active Brownian diffusion.

A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer's diffusivity. To this purpose, we propose and solve two alternative models. In the first one, we simply assume that the environmental fluctuations governing the swimmer's propulsion are exponentially correlated in time, whereas in the second one, we account for possible damped fluctuations of the propulsion velocity around the swimmer's axis. The corresponding swimmer's diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed.

Diffusion of noiseless active particles in a planar convection array.

We investigated, both analytically and numerically, the dynamics of a noiseless overdamped active particle in a square lattice of planar counter-rotating convection rolls. Below a first threshold of the self-propulsion speed, a fraction of the simulated particle's trajectories spatially diffuse around the convection rolls, whereas the remaining trajectories remain trapped inside the injection roll. We detected two chaotic diffusion regimes: (i) below a second, higher threshold of the self-propulsion speed, the particle performs a random motion characterized by asymptotic normal diffusion. Long superdiffusive transients were observed for vanishing small self-propulsion speeds. (ii) above that threshold, the particle follows chaotic running trajectories with speed and orientation close to those of the self-propulsion vector at injection and its dynamics is superdiffusive. Chaotic diffusion disappears in the ballistic limit of extremely large self-propulsion speeds.