Structural correlations in diffusiophoretic colloidal mixtures with nonreciprocal interactions

Method of spectral response to stochastic processes for measuring the nonreciprocal effective interactions

The theoretical background of the nonperturbative method of spectral response to stochastic processes (SRSP) for measuring the nonreciprocal interparticle effective interactions in strongly coupled underdamped systems is described. Analytical expressions for vibrational spectral density of confined Brownian particles with a nonreciprocal effective interaction are presented. The changes in the vibrational spectral density with varying different parameters of the system (nonreciprocity, viscosity, ratios of particle sizes, and intensities of random processes acting on each particle) are discussed using the example of a pair of nonidentical particles in a harmonic trap. The SRSP method is compared to three other nonperturbative methods. The SRSP method demonstrates an undeniable advantage when processing particle trajectories with errors in particle tracking.

Asymmetric acoustic wave scattering by a nonreciprocal and position-dependent mass defect

We investigate the asymmetric wave scattering in a phononic one-dimensional lattice with a nonreciprocal defect and position dependent masses coupled by the defect spring. The nonreciprocal interaction is characterized by a single parameter Δ while the nonlinear contribution due to position-dependent masses are controlled by a parameterχ. The transmission and reflection coefficients are analytically computed and the effects of the nonreciprocity and nonlinearity are detailed. We show that, in opposite with the linear case, the rectification factor has a frequency dependence, which leads to a more efficient diode-like action at large wavevectors. Further, the nonlinearity leads to an asymmetry of the reflected component, absent in the linear regime. We extend our analysis to a system with frictional forces which suppresses the multistability window promoted by the nonlinear mass contribution without compromising the rectification action.

Experimental study of the nonreciprocal effective interactions between microparticles in an anisotropic plasma

There is a variety of cases in nature when the action–reaction symmetry is broken. In particular, suitable conditions for this are realized in colloidal suspensions and complex plasmas. Since the first theories and simulations of the nonreciprocal effective interactions between microparticles in complex plasmas were published in 1995–1996, there have been hundreds of studies in the theoretical development of this theme. However, despite such a rich theoretical background, one of the important unsolved problems is a direct experimental determination of the nonreciprocal interparticle interaction forces. Here, we studied experimentally in detail the forces of the nonreciprocal effective interaction between microparticles suspended a radio-frequency produced plasma sheath. For this purpose, an experimental method based on an analysis of the spectral density of random processes in an open dissipative two-particle system was developed. In contrast to previous investigations, the proposed method takes into account random and dissipative processes in the system, does not require a special design of the experimental setup and any external perturbations, pre-measurements of external fields and any assumptions about the type of interaction. We found that even small charge changes of one particle, caused by its thermal motion in a wake field of another particle, can lead to a significant change in the effective (measurable) interaction between the particles.

Active particles in noninertial frames: How to self-propel on a carousel

Typically the motion of self-propelled active particles is described in a quiescent environment establishing an inertial frame of reference. Here we assume that friction, self-propulsion, and fluctuations occur relative to a noninertial frame and thereby the active Brownian motion model is generalized to noninertial frames. First, analytical solutions are presented for the overdamped case, both for linear swimmers and for circle swimmers. For a frame rotating with constant angular velocity ("carousel"), the resulting noise-free trajectories in the static laboratory frame are trochoids if these are circles in the rotating frame. For systems governed by inertia, such as vibrated granulates or active complex plasmas, centrifugal and Coriolis forces become relevant. For both linear and circling self-propulsion, these forces lead to out-spiraling trajectories which for long times approach a spira mirabilis. This implies that a self-propelled particle will typically leave a rotating carousel. A navigation strategy is proposed to avoid this expulsion, by adjusting the self-propulsion direction at will. For a particle, initially quiescent in the rotating frame, it is shown that this strategy only works if the initial distance to the rotation center is smaller than a critical radius R_{c} which scales with the self-propulsion velocity. Possible experiments to verify the theoretical predictions are discussed.

Synthetic Chemotaxis and Collective Behavior in Active Matter

The ability to navigate in chemical gradients, called chemotaxis, is crucial for the survival of microorganisms. It allows them to find food and to escape from toxins. Many microorganisms can produce the chemicals to which they respond themselves and use chemotaxis for signaling, which can be seen as a basic form of communication, allowing ensembles of microorganisms to coordinate their behavior, for example, during embryogenesis, biofilm formation, or cellular aggregation. For example, Dictyostelium cells use signaling as a survival strategy: when starving, they produce certain chemicals toward which other cells show taxis. This leads to aggregation of the cells resulting in a multicellular aggregate that can sustain long starvation periods. Remarkably, the past decade has led to the development of synthetic microswimmers, which can self-propel through a solvent, analogously to bacteria and other microorganisms. The mechanism underlying the self-propulsion of synthetic microswimmers like camphor boats, droplet swimmers, and in particular autophoretic Janus colloids involves the production of certain chemicals. As we will discuss in this Account, the same chemicals (phoretic fields) involved in the self-propulsion of a (Janus) microswimmer also act on other ones and bias their swimming direction toward (or away from) the producing microswimmer. Synthetic microswimmers therefore provide a synthetic analogue to motile microorganisms interacting by taxis toward (or away from) self-produced chemical fields. In this Account, we review recent progress in the theoretical description of synthetic chemotaxis mainly based on simulations and field theoretical descriptions. We will begin with single motile particles leaving chemical trails behind with which they interact themselves, leading to effects like self-trapping or self-avoidance. Besides these self-interactions, in ensembles of synthetic motile particles each particle also responds to the chemicals produced by other particles, inducing chemical (or phoretic) cross-interactions. When these interactions are attractive, they commonly lead to clusters, even at low particle density. These clusters may either proceed toward macrophase separation, resembling Dictyostelium aggregation, or, as shown very recently, lead to dynamic clusters of self-limited size (dynamic clustering) as seen in experiments in autophoretic Janus colloids. Besides the classical case where chemical interactions are attractive, this Account discusses, as its main focus, repulsive chemical interactions, which can create a new and less known avenue to pattern formation in active systems leading to a variety of pattern, including clusters which are surrounded by shells of chemicals, traveling waves and more complex continuously reshaping patterns. In all these cases "synthetic signalling" can crucially determine the collective behavior of synthetic microswimmer ensembles and can be used as a design principle to create patterns in motile active particles.

Three-body correlations and conditional forces in suspensions of active hard disks

Self-propelled Brownian particles show rich out-of-equilibrium physics, for instance, the motility-induced phase separation (MIPS). While decades of studying the structure of liquids have established a deep understanding of passive systems, not much is known about correlations in active suspensions. In this work we derive an approximate analytic theory for three-body correlations and forces in systems of active Brownian disks starting from the many-body Smoluchowski equation. We use our theory to predict the conditional forces that act on a tagged particle and their dependence on the propulsion speed of self-propelled disks. We identify preferred directions of these forces in relation to the direction of propulsion and the positions of the surrounding particles. We further relate our theory to the effective swimming speed of the active disks, which is relevant for the physics of MIPS. To test and validate our theory, we additionally run particle-resolved computer simulations, for which we explicitly calculate the three-body forces. In this context, we discuss the modeling of active Brownian swimmers with nearly hard interaction potentials. We find very good agreement between our simulations and numerical solutions of our theory, especially for the nonequilibrium pair-distribution function. For our analytical results, we carefully discuss their range of validity in the context of the different levels of approximation we applied. This discussion allows us to study the individual contribution of particles to three-body forces and to the emerging structure. Thus, our work sheds light on the collective behavior, provides the basis for further studies of correlations in active suspensions, and makes a step towards an emerging liquid state theory.