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

Vacancy formation in a 1D chain of dust particles in a DC discharge

The paper presents the first experimental observation of an atypical phenomena during self-organization of dust particles into a one-dimensional chain structure levitated vertically in the plasma of a DC glow discharge. Using a laser, the third (middle) dust particle was removed from the chain of five particles so that the positions of the remaining particles did not significantly change, and a vacancy occurred in the place of the removed particle. This state of the chain turned out to be very stable, which is confirmed by the observation of the subsequent exchange of places of the fourth and the fifth particles of the chain upon the action of the laser on the forth particle. After the exchange process, vertical positions of all particles (first, second, fourth and fifth) in the chain remained almost the same as before the exchange, and the vacancy at the position of the third particle was preserved. The experimental data and the video record of the observed phenomena as well as the estimates of the plasma parameters are presented. An assumption has been made about the mechanism of the discovered phenomena that at present discharge conditions both the vacancy formation and the dust particles positions exchange are possible due to a strong ion wakes which are formed behind the upstream dust particles of the chain.

Structure formation induced by non-reciprocal cell-cell interactions in a multicellular system

Collective cellular behavior plays a crucial role in various biological processes, ranging from developmental morphogenesis to pathological processes such as cancer metastasis. Our previous research has revealed that a mutant cell of Dictyostelium discoideum exhibits collective cell migration, including chain migration and traveling band formation, driven by a unique tail-following behavior at contact sites, which we term "contact following locomotion" (CFL). Here, we uncover an imbalance of forces between the front and rear cells within cell chains, leading to an additional propulsion force in the rear cells. Drawing inspiration from this observation, we introduce a theoretical model that incorporates non-reciprocal cell-cell interactions. Our findings highlight that the non-reciprocal interaction, in conjunction with self-alignment interactions, significantly contributes to the emergence of the observed collective cell migrations. Furthermore, we present a comprehensive phase diagram, showing distinct phases at both low and intermediate cell densities. This phase diagram elucidates a specific regime that corresponds to the experimental system.

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.

Symmetries of many-body systems imply distance-dependent potentials

Considering an interatomic potential U(q), where q=[q_{1},q_{2},⋯,q_{N}]∈R^{3N} is a vector describing positions q_{i}∈R^{3}, it is shown that U can be defined as a function of the interatomic distance variables r_{ij}=|q_{i}-q_{j}| provided the potential U satisfies some symmetry assumptions. Moreover, the potential U can be defined as a function of a proper subset of the distance variables r_{ij}, provided N>5, with the number of distance variables used scaling linearly with the number of atoms N.

Structural properties of a chain of dust particles in a field of external forces

This paper presents a numerical study of the structural parameters of a one-dimensional chain of three dust particles levitating in the near-electrode layer of an rf discharge or in the stratum of a dc discharge. The model considers the motion of dust particles under the action of gravity, external electric field, the Coulomb repulsion, and the electrostatic force from the space charge surrounding the dust particles. Particular attention is paid to the effect of plasma polarization around dust particles and the wake formation under the action of the external electric field. Calculations showed that the charge of the first dust particle in the chain and the total charge of the entire chain, as well as the length of the chain, grow linearly with the external electric field strength. Obtained data are in qualitative agreement with the experimental and numerical data presented in the literature. It was shown that for a certain large value of the external electric field, the charge of the third dust particle is the smallest of all the particles in the chain. It was found that with an increase in the mean value of the external electric field, the chain of dust particles is displaced as a whole in the direction opposite to the action of the electrostatic force on them.

Active Brownian motion of strongly coupled charged grains driven by laser radiation in plasma

The systems of active Brownian grains can be considered as open systems, in which there is an exchange of energy and matter with the environment. The collective phenomena of active Brownian grains can demonstrate analogies with ordinary phase transitions. We study the active Brownian motion of light-absorbing and strongly interacting grains far from equilibrium suspended in gas discharge under laser irradiation when the nature and intensity of the active motion depend on the effect of radiation. Active Brownian motion is caused by photophoresis, i.e., absorption of laser radiation at the metal-coated surface of the grain creates radiometric force, which in turn drives the grains. We experimentally observed the active Brownian motion of charged grains in the transition of the grain monolayer from the solid to liquid state. An analysis of the character of motion, including the mean-square and linear displacement and persistence length at various values of the randomization (coupling parameter) of the grain structure, was presented.

Experimental evolution of active Brownian grains driven by quantum effects in superfluid helium

Complex structures, consisting of a large number of interacting subsystems, have the ability to self-organize and evolve, when the scattering of energy coming from the outside ensures the maintenance of stationary ordered structures with an entropy less than the equilibrium entropy. One of the fundamental problems here is the role of quantum phenomena in the evolution of macroscopic objects. We provide experimental evidence for the active Brownian motion and evolution of structures driven by quantum effects for micron-sized grains levitating in superfluid helium. The active Brownian motion of grains was induced by quantum turbulence during the absorption of laser irradiation by grains. The intensity of Brownian motion associated with quantum vortices increased by 6-7 orders of magnitude compared to the values from the Einstein formula. We observed the grain structures in a state far from thermodynamic equilibrium and their evolution to more complex organized structures with lower entropy due to the quantum mechanism of exceedingly high entropy loss in superfluid helium.

Alignments of a Microparticle Pair in a Glow Discharge

Stability of a vertically aligned microparticle pair in a stratified glow DC discharge is experimentally investigated. Using laser perturbations, it is shown that, for the same discharge parameters, a pair of microparticles can be suspended in two stable configurations: vertical and horizontal. The interparticle interaction and the electric field of the stratum in the region of particle levitation are quantitatively investigated for the first time. The decharging effect of the lower (downstream) particle by the ion flow wake is also observed for the first time in a glow discharge. The obtained experimental data made it possible to check the analytical criteria for the configurational stability of the system.

Active Ornstein-Uhlenbeck model for self-propelled particles with inertia

Self-propelled particles, which convert energy into mechanical motion, exhibit inertia if they have a macroscopic size or move inside a gaseous medium, in contrast to micron-sized overdamped particles immersed in a viscous fluid. Here we study an extension of the active Ornstein-Uhlenbeck model, in which self-propulsion is described by colored noise, to access these inertial effects. We summarize and discuss analytical solutions of the particle's mean-squared displacement and velocity autocorrelation function for several settings ranging from a free particle to various external influences, like a linear or harmonic potential and coupling to another particle via a harmonic spring. Taking into account the particular role of the initial particle velocity in a nonstationary setup, we observe all dynamical exponents between zero and four. After the typical inertial time, determined by the particle's mass, the results inherently revert to the behavior of an overdamped particle with the exception of the harmonically confined systems, in which the overall displacement is enhanced by inertia. We further consider an underdamped model for an active particle with a time-dependent mass, which critically affects the displacement in the intermediate time-regime. Most strikingly, for a sufficiently large rate of mass accumulation, the particle's motion is completely governed by inertial effects as it remains superdiffusive for all times.

Plasma Parameters around a Chain-Like Structure of Dust Particles in an External Electric Field

The formation of a 1D chain-like structure of dust particles in a low-temperature argon plasma was studied. A new numerical model for calculation of the self-consistent spatial distribution of plasma parameters around a chain of dust particles was presented. The model described the motion of positively charged ions in the electric potential of several negatively charged dust particles, taking into account the action of an external electric field. The main advantage of the model was that the charges of the dust particles and the interparticle distances were determined self-consistently. As a result of numerical simulations, the dependencies of the spatial distributions of the plasma parameters (the densities of electrons and ions and the self-consistent electric potential) near the dust particles chain on the strength of the external electric field, an external force acted on the last particle, and the mean free path of the ions was determined. The obtained results made it possible to describe the process of the formation of chain-like structures of dust particles in discharge plasma.

Possible Mechanisms of String Formation in Complex Plasmas at Elevated Pressures

Possible mechanisms of particle attraction providing formation of the field aligned microparticle strings in complex plasmas at elevated gas pressures are theoretically investigated in the light of the Plasmakristall-4 (PK-4) experiment on board the International Space Station. The particle interaction energy is addressed by two different approaches: (i) using the dynamically screened wake potential for small Mach numbers derived by Kompaneets et al., in 2016, and (ii) introducing effect of polarization of the trapped ion cloud by discharge electric fields. Is is found that both approaches yield the particle interaction energy which is independent of the operational discharge mode. In the parameter space of the performed experiments, the first approach can provide onset of the particle attraction and string formation only at gas pressures higher than 40–45 Pa, whilst the mechanism based on the trapped ion effect yields attraction in the experimentally important pressure range 20–40 Pa and may reconcile theory and observations.

Active Brownian particle in homogeneous media of different viscosities: numerical simulations

Self-propelled colloids, active polymers and membranes, driven (vibrated) granular layers and hybrid synthetic-biological systems are striking examples of systems containing synthetic active Brownian particles. Such particles autonomously convert the available energy of the environment into their own directed mechanical motion. In most studies the self-propelled Brownian particles move in overdamped media. Recently, experiments with Janus particles in a low-pressure plasma have appeared. A distinctive feature of such a medium is an extremely low viscosity at which the inertial effects play a significant role, resulting in underdamped Brownian motion. At present, there is a lack of statistical theory describing the underdamped Brownian motion of self-propelled particles at all time scales. This paper presents the numerical simulation results of active Brownian motion in homogeneous media of different viscosities. The calculations are performed using a mathematical model of a self-propelled Brownian sphere with translational and rotational inertia. The time-dependent mean square displacement and mean linear displacement (the noise-averaged trajectory) of the particle are investigated as a function of medium viscosity, self-propulsion velocity and moment of inertia. Our simulation reveals that the dynamics of a self-propelled spherical particle significantly depends on two independent dimensionless parameters of the particle: the ratio of the self-propulsion velocity to the characteristic thermal velocity and the ratio of the friction coefficient to the rotational diffusion coefficient. The obtained statistical characteristics of active Brownian motion are compared with the known theoretical models in a wide range of medium viscosities. We propose simple corrections to the basic theory of overdamped active Brownian motion, which allow one to calculate the effective diffusion coefficient and the persistence length of a self-propelled Brownian particle in a medium with any dynamic viscosity. The results obtained are discussed in relation to active particles in a colloidal plasma and superfluid helium.