Dissipative solitary waves in a two-dimensional complex plasma: Amorphous versus crystalline.

The propagation of a dissipative soliton was experimentally studied in a two-dimensional binary complex plasma. The crystallization was suppressed in the center of the particle suspension where two types of particles were mixed. The motions of individual particles were recorded using video microscopy, and the macroscopic properties of the solitons were measured in the amorphous binary mixture in the center and in the plasma crystal in the periphery. Although the overall shape and parameters of solitons propagating in amorphous and crystalline regions were quite similar, their velocity structures at small scales as well as the velocity distributions were profoundly distinct. Moreover, the local structure rearranged drastically in and behind the soliton, which was not observed in the plasma crystal. Langevin dynamics simulations were performed, and the results agreed with the experimental observations.

Collective self-optimization of communicating active particles.

The quest for how to collectively self-organize in order to maximize the survival chances of the members of a social group requires finding an optimal compromise between maximizing the well-being of an individual and that of the group. Here we develop a minimal model describing active individuals which consume or produce, and respond to a shared resource-such as the oxygen concentration for aerotactic bacteria or the temperature field for penguins-while urging for an optimal resource value. Notably, this model can be approximated by an attraction-repulsion model, but, in general, it features many-body interactions. While the former prevents some individuals from closely approaching the optimal value of the shared "resource field," the collective many-body interactions induce aperiodic patterns, allowing the group to collectively self-optimize. Arguably, the proposed optimal field-based collective interactions represent a generic concept at the interface of active matter physics, collective behavior, and microbiological chemotaxis. This concept might serve as a useful ingredient to optimize ensembles of synthetic active agents or to help unveil aspects of the communication rules which certain social groups use to maximize their survival chances.

Time-dependent inertia of self-propelled particles: The Langevin rocket.

Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics, which involve inertia, friction, and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation are manifold, ranging from minirockets (which are self-propelled by burning their own mass), to dust particles in plasma (which lose mass by evaporating material), to walkers with expiring activity. Here we present analytical solutions for several dynamical correlation functions, such as mean-square displacement and orientational and velocity autocorrelation functions. If the parameters exhibit a slow power law in time, we obtain anomalous superdiffusion with a nontrivial dynamical exponent. Finally, we constitute the "Langevin rocket" model by including orientational fluctuations in the traditional Tsiolkovsky rocket equation. We calculate the mean reach of the Langevin rocket and discuss different mass ejection strategies to maximize it. Our results can be tested in experiments on macroscopic robotic or living particles or in self-propelled mesoscopic objects moving in media of low viscosity, such as complex plasma.

Slow Dynamics in a Quasi-Two-Dimensional Binary Complex Plasma.

Slow dynamics in an amorphous quasi-two-dimensional complex plasma, comprised of microparticles of two different sizes, was studied experimentally. The motion of individual particles was observed using video microscopy, and the self-part of the intermediate scattering function as well as the mean-squared particle displacement was calculated. The long-time structural relaxation reveals the characteristic behavior near the glass transition. Our results suggest that binary complex plasmas can be an excellent model system to study slow dynamics in classical supercooled fluids.

Phase diagram of two-dimensional colloids with Yukawa repulsion and dipolar attraction.

We study the phase diagram of a two-dimensional (2D) system of colloidal particles, interacting via an isotropic potential with a short-ranged Yukawa repulsion and a long-ranged dipolar attraction. Such interactions in 2D colloidal suspensions can be induced by rapidly rotating in-plane magnetic (or electric) fields. Using computer simulations and liquid integral equation theory, we calculate the bulk phase diagram, which contains gas, crystalline, liquid, and supercritical fluid phases. The densities at the critical and triple points in the phase diagram are governed by the softness of Yukawa repulsion and can therefore be largely tuned. We observe that the liquid-gas binodals exhibit universal behavior when the effective temperature (given by the inverse magnitude of the dipolar attractions) is normalized by its value at the critical point and the density is normalized by the squared Barker-Henderson diameter. The results can be verified in particle-resolved experiments with colloidal suspensions.

Dissipative phase transitions in systems with nonreciprocal effective interactions.

The reciprocity of effective interparticle forces can be violated in various open and nonequilibrium systems, in particular, in colloidal suspensions and complex (dusty) plasmas. Here, we obtain a criterion under which a nonreciprocal system can be strictly reduced to a pseudo-Hamiltonian system with a detailed dynamic equilibrium. In particular, the criterion is satisfied for catalytically active colloids interacting via nonreciprocal diffusiophoretic forces. However, in the general case, when this criterion is not satisfied, the steady state is determined by the interplay between dissipation and the energy source due to the nonreciprocity of interactions. The results indicate the realization of bistability and dissipative spinodal decomposition in a broad class of systems with nonreciprocal effective interactions.

Tunable two-dimensional assembly of colloidal particles in rotating electric fields.

Tunable interparticle interactions in colloidal suspensions are of great interest because of their fundamental and practical significance. In this paper we present a new experimental setup for self-assembly of colloidal particles in two-dimensional systems, where the interactions are controlled by external rotating electric fields. The maximal magnitude of the field in a suspension is 25 V/mm, the field homogeneity is better than 1% over the horizontal distance of 250 µm, and the rotation frequency is in the range of 40 Hz to 30 kHz. Based on numerical electrostatic calculations for the developed setup with eight planar electrodes, we found optimal experimental conditions and performed demonstration experiments with a suspension of 2.12 µm silica particles in water. Thanks to its technological flexibility, the setup is well suited for particle-resolved studies of fundamental generic phenomena occurring in classical liquids and solids, and therefore it should be of interest for a broad community of soft matter, photonics, and material science.

Wakes in complex plasmas: A self-consistent kinetic theory.

In ground-based experiments with complex (dusty) plasmas, charged microparticles are levitated against gravity by an electric field, which also drives ion flow in the parent gas. Existing analytical approaches to describe the electrostatic interaction between microparticles in such conditions generally ignore the field and ion-neutral collisions, assuming free ion flow with a certain approximation for the ion velocity distribution function (usually a shifted Maxwellian). We provide a comprehensive analysis of our previously proposed self-consistent kinetic theory including the field, ion-neutral collisions, and the corresponding ion velocity distribution. We focus on various limiting cases and demonstrate how the interplay of these factors results in different forms of the shielding potential.

Emerging activity in bilayered dispersions with wake-mediated interactions.

In a bilayered system of particles with wake-mediated interactions, the action-reaction symmetry for the effective forces between particles of different layers is broken. Under quite general conditions we show that, if the interaction nonreciprocity exceeds a certain threshold, this creates an active dispersion of self-propelled clusters of Brownian particles. The emerging activity promotes unusual melting scenarios and an enormous diffusivity in the dense fluid. Our results are obtained by computer simulation and analytical theory and can be verified in experiments with colloidal dispersions and complex plasmas.

Interpolation method for pair correlations in classical crystals.

Effects of anharmonicity on the pair correlation function of classical crystals are studied. The recently proposed shortest-graph approach using the Gaussian representation of the individual correlation peaks (the peak width is determined by the length of the shortest graph connecting a given pair of particles) is further improved, to account for anharmonic corrections due to finite temperatures and hard-sphere-like interactions. Two major effects are identified, leading to a modification of the correlation peaks at large or short distances: (i) the peaks at large distances, well described by Gaussians, should be calculated from the finite-temperature phonon spectra; (ii) at short distances, the correlation peaks deviate significantly from the Gaussian form due to the lattice discreteness. We propose the analytical interpolation method, based on the shortest-graph approach, which includes both effects. By employing the molecular dynamics simulations, the accuracy of the method is verified for three- and two-dimensional crystals with the Yukawa, inverse-power-law, and pseudo-hard-sphere pair interactions. The capabilities of the method are demonstrated by calculating the phase diagram of a three-dimensional Yukawa system.

Interparticle Attraction in 2D Complex Plasmas.

Complex (dusty) plasmas allow experimental studies of various physical processes occurring in classical liquids and solids by directly observing individual microparticles. A major problem is that the interaction between microparticles is generally not molecularlike. In this Letter, we propose how to achieve a molecularlike interaction potential in laboratory 2D complex plasmas. We argue that this principal aim can be achieved by using relatively small microparticles and properly adjusting discharge parameters. If experimentally confirmed, this will make it possible to employ complex plasmas as a model system with an interaction potential resembling that of conventional liquids.

Structural correlations in diffusiophoretic colloidal mixtures with nonreciprocal interactions.

Nonreciprocal effective interaction forces can occur between mesoscopic particles in colloidal suspensions that are driven out of equilibrium. These forces violate Newton's third law actio = reactio on coarse-grained length and time scales. Here we explore the statistical mechanics of Brownian particles with nonreciprocal effective interactions. Our model system is a binary fluid mixture of spherically symmetric, diffusiophoretic mesoscopic particles, and we focus on the time-averaged particle pair- and triplet-correlation functions. Based on the many-body Smoluchowski equation we develop a microscopic statistical theory for the particle correlations and test it by computer simulations. For model systems in two and three spatial dimensions, we show that nonreciprocity induces distinct nonequilibrium pair correlations. Our predictions can be tested in experiments with chemotactic colloidal suspensions.

Pair correlations in classical crystals: The shortest-graph method.

The shortest-graph method is applied to calculate the pair correlation functions of crystals. The method is based on the representation of individual correlation peaks by the Gaussian functions, summed along the shortest graph connecting the two given points. The analytical expressions for the Gaussian parameters are derived for two- and three-dimensional crystals. The obtained results are compared with the pair correlation functions deduced from the molecular dynamics simulations of Yukawa, inverse-power law, Weeks-Chandler-Andersen, and Lennard-Jones crystals. By calculating the Helmholtz free energy, it is shown that the method is particularly accurate for soft interparticle interactions and for low temperatures, i.e., when the anharmonicity effects are insignificant. The accuracy of the method is further demonstrated by deriving the solid-solid transition line for Yukawa crystals, and the compressibility for inverse-power law crystals.

Wakes in inhomogeneous plasmas.

The Debye shielding of a charge immersed in a flowing plasma is an old classic problem. It has been given renewed attention in the last two decades in view of experiments with complex plasmas, where charged dust particles are often levitated in a region with strong ion flow. Efforts to describe the shielding of the dust particles in such conditions have been focused on the homogeneous plasma approximation, which ignores the substantial inhomogeneity of the levitation region. We address the role of the plasma inhomogeneity by rigorously calculating the point charge potential in the collisionless Bohm sheath. We demonstrate that the inhomogeneity can dramatically modify the wake, making it nonoscillatory and weaker.

Microscopic theory for anisotropic pair correlations in driven binary mixtures.

A self-consistent microscopic approach to calculate non-equilibrium pair correlations in strongly interacting driven binary mixtures is presented. The theory is derived from the many-body Smoluchowski equation for interacting Brownian particles by employing Kirkwood's superposition approximation as a closure relation. It is shown that the pair correlations can exhibit notable anisotropy and a strong tendency to laning in the driving direction. Furthermore, there are strong indications that pair correlations are characterized by a long-range decay along the drive. The theoretical results are in good quantitative agreement with the complementary Brownian dynamics computer simulations.

Instability of ion kinetic waves in a weakly ionized plasma.

The fundamental higher-order Landau plasma modes are known to be generally heavily damped. We show that these modes for the ion component in a weakly ionized plasma can be substantially modified by ion-neutral collisions and a dc electric field driving ion flow so that some of them can become unstable. This instability is expected to naturally occur in presheaths of gas discharges at sufficiently small pressures and thus affect sheaths and discharge structures.

Solid phases in electro- and magnetorheological systems.

Ensembles of particles with a spherically symmetric repulsive Yukawa interaction and additional dipole-dipole interaction induced by an external field exhibit numerous solid-solid phase transitions controlled by the magnitude of the field. Such interactions emerge most notably in electro- and magnetorheological fluids and plasmas. We propose a simple variational approach based on the Bogoliubov inequality for determining equilibrium solid phases. Phase diagrams for several regimes are calculated and compared with previously performed Monte Carlo and molecular dynamics simulations.

Highly resolved fluid flows: "liquid plasmas" at the kinetic level.

Fluid flow around an obstacle was observed at the kinetic (individual particle) level using "complex (dusty) plasmas" in their liquid state. These "liquid plasmas" have bulk properties similar to water (e.g., viscosity), and a comparison in terms of similarity parameters suggests that they can provide a unique tool to model classical fluids. This allows us to study "nanofluidics" at the most elementary-the particle-level, including the transition from fluid behavior to purely kinetic transport. In this (first) experimental investigation we describe the kinetic flow topology, discuss our observations in terms of fluid theories, and follow this up with numerical simulations.