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.

Motion of a self-propelled particle with rotational inertia.

Overdamped active Brownian motion of self-propelled particles in a liquid has been fairly well studied. However, there are a variety of situations in which the overdamped approximation is not justified, for instance, when self-propelled particles move in a low-viscosity medium or when their rotational diffusivity is enhanced by internal active processes or external control. Examples of various origins include biofilaments driven by molecular motors, living and artificial microflyers and interfacial surfers, field-controlled and superfluid microswimmers, vibration-driven granular particles and autonomous mini-robots with sensorial delays, etc. All of them extend active Brownian motion to the underdamped case, i.e., to active Langevin motion, which takes into account inertia. Despite a rich experimental background, there is a gap in the theory in the field where rotational inertia significantly affects the random walk of active particles on all time scales. In particular, although the well-known models of active Brownian and Ornstein-Uhlenbeck particles include a memory effect of the direction of motion, they are not applicable in the underdamped case, because the rotational inertia, which they do not account for, can partially prevent "memory loss" with increasing rotational diffusion. We describe the two-dimensional motion of a self-propelled particle with both translational and rotational inertia and velocity fluctuations. The proposed generalized analytical equations for the mean kinetic energy, mean-square displacement and noise-averaged trajectory of the self-propelled particle are confirmed by numerical simulations in a wide range of self-propulsion velocities, moments of inertia, rotational diffusivities, medium viscosities and observation times.

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.

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.

Self-confined particle pairs in complex plasmas.

The liquid-crystal type of phase transition in complex plasmas has been observed repeatedly. However, more studies need to be done on the liquid-vapor transition in complex plasmas. In this paper, the phenomenon of coupling (condensation) of particles into self-confined particle pairs in an anisotropic plasma medium with ion flow is considered analytically and numerically using the Langevin molecular dynamics method. We obtain the stability conditions of the pair (bound) state depending on the interaction parameters and particle kinetic energy. It was shown that the breakup of the particle pair is very sensitive to the ratio of particle charges; for example, it is determined by the influence of the upper particle on the ion flow around the lower one. We also show that a self-confined pair of particles exists even if their total kinetic energy is much greater than the potential well depth for the pair state. This phenomenon occurs due to velocity correlation of particles, which arises with the nonreciprocity of interparticle interaction.

Viscosity of a strongly coupled dust component in a weakly ionized plasma.

An experimental study of the kinematic viscosity has been carried out for dust particles of size 0.95 and 3.92 µm, in weakly ionized plasma over a wide range of dust coupling parameters. Measurements of viscosity for weakly correlated dusty-plasma systems are presented for the first time. An approximation for the estimation of viscosity constants is proposed. The measured viscosity constants are compared with theoretical estimates and numerical data.

Numerical simulations of thermal conductivity in dissipative two-dimensional Yukawa systems.

Numerical data on the heat transfer constants in two-dimensional Yukawa systems were obtained. Numerical study of the thermal conductivity and diffusivity was carried out for the equilibrium systems with parameters close to conditions of laboratory experiments with dusty plasma. For calculations of heat transfer constants the Green-Kubo formulas were used. The influence of dissipation (friction) on the heat transfer processes in nonideal systems was investigated. The approximation of the coefficient of thermal conductivity is proposed. Comparison of the obtained results to the existing experimental and numerical data is discussed.

Thermodynamic and transport properties of nonideal systems with isotropic pair potentials.

The equations of state and the structural, thermodynamic, and transport properties of the two- and three-dimensional nonideal dissipative systems consisting of particles interacting with different isotropic pair potentials are studied in a wide range of parameters typical for laboratory dusty plasma. Simple semiempirical expression for the energy density in liquid systems is considered. Comparison of the theoretical and numerical results is presented.

Determination of pair interaction forces between particles in nonideal dissipative systems.

A new technique for analyzing the pair interaction forces between particles in nonideal dissipative systems is presented. The technique is based on a solution of the inverse problem describing the movement of dust particles by a system of Langevin equations. Numerical simulations in a wide range of the parameters typical for dusty plasma experiments were performed to verify the solutions of the inverse problem. The first approbations of the proposed technique for analysis of intergrain interactions in a plasma of rf discharge are presented.

Dusty-plasma liquid in the statistical theory of the liquid state.

Measurements in dusty plasmas were carried out to find the region of validity of approximate relation in statistical theory of liquid states. The integral equations with the Percus-Yewick and the hypernetted-chain closures as well as the superposition approximation were chosen as the objects for investigation. The range of validity of these approaches was obtained by the use of experimental methods for analysis of spatial correlation of dust particles in plasma.

Evolution of the mass-transfer processes in nonideal dissipative systems. I. Numerical simulation.

The results of numerical study of mass-transfer processes in quasi-two- and three-dimensional nonideal dissipative systems are presented. Simulations were performed for different types of model pair potentials of intergrain interaction that are various combinations of power-law and exponential functions. The calculations were performed in a wide range of parameters typical for laboratory dusty plasma experiments. It was shown that the dynamics of grains in liquidlike systems for short observation times is close to the evolution of thermal oscillations in the crystal lattice.

Evolution of the mass-transfer processes in nonideal dissipative systems II: experiments in dusty plasma.

The results of the experimental study of mass-transfer processes are presented for dust systems, forming in a laboratory plasma of a radio-frequency capacitive discharge. The validity of the Langevin and Green-Kubo equations for the description of the dynamics of dusty grains in laboratory plasma is verified. A method for simultaneous determination of dusty plasma parameters, such as the kinetic temperature of the grains, their friction coefficient, and characteristic oscillation frequency, is suggested. The coupling parameter of the system under study and the minimal values of the grain charges are estimated. The parameters of the dusty subsystem obtained (diffusion coefficients, pair correlation functions, charges, and friction coefficients of the grains) are compared with the existing theoretical and numerical data.

Experimental study of the heat transport processes in dusty plasma fluid.

The results are given of an experimental investigation of heat transport processes in fluid dusty structures in rf-discharge plasmas under different conditions: for discharge in argon, and for discharge in air under an action of electron beam. The analysis of steady-state and unsteady-state heat transfer is used to obtain the coefficients of thermal conductivity and thermal diffusivity under the assumption that the observed heat transport is associated with a thermal conduction in the dusty component of plasmas. The temperature dependence of these coefficients is obtained, which agrees qualitatively with the results of numerical simulation for simple monatomic liquids.

Two-stage melting in quasi-two-dimensional dissipative Yukawa systems.

The results of numerical study of physical characteristics (the pair and triplet correlation functions, the isothermal compressibility, the heat capacities, and the diffusion constants) are presented for quasi-2D dissipative Yukawa systems. The specific features of these characteristics (reflecting the two-stage melting scenario) are investigated.

Test of the Stokes-Einstein relation in a two-dimensional Yukawa liquid.

The Stokes-Einstein relation, relating the diffusion and viscosity coefficients D and eta, is tested in two dimensions. An equilibrium molecular-dynamics simulation was used with a Yukawa pair potential. Regimes are identified where motion is diffusive and D is meaningful. The Stokes-Einstein relation, Deta proportional k(B)T, was found to be violated near the disordering transition; under these conditions collective particle motion exhibits dynamical heterogeneity. At slightly higher temperatures, however, the Stokes-Einstein relation is valid. These results may be testable in strongly coupled dusty plasma experiments.

Three-particle correlations in nonideal dusty plasma.

Results are given of experimental investigation of three-particle correlations for liquid plasma-dust structures formed in the electrode layer of a high-frequency capacitive discharge. The obtained three-particle correlation functions for experimental and numerical data are analyzed and compared with the superposition approximation. The forming of clusters of macroparticles in plasma-dust systems being analyzed is revealed.

Transport of microparticles in weakly ionized gas-discharge plasmas under microgravity conditions.

Measurements of effective structural (pair correlation function) and transport (diffusion constant) characteristics of the system of microparticles in dc and rf gas-discharge plasmas under microgravity conditions are reported. The comparison between these measurements and numerical simulations is used for complex plasma diagnostics.

Criteria of phase transitions in a complex plasma.

New empirical rules for different phase transitions (including the melting of cubic lattices and the transitions between body-centered-cubic and face-centered-cubic structures) are proposed. The arrangements of charged macroparticles in a complex "dusty" plasma are numerically investigated for the conditions of laboratory experiments on weakly ionized gas discharges.

Diffusion in microgravity of macroparticles in a dusty plasma under solar radiation.

Diffusion of macroparticles, charged by solar radiation in microgravity, is studied by analyzing experimental data obtained on the MIR space station. Temperature, velocity distributions, friction coefficient, and diffusion constants were obtained for bronze particles. A comparison of experimental and theoretical estimates shows that the dynamic behavior of the macroparticles for short observation times can be determined by observing the ambipolar diffusion.

Positively charged particles in dusty plasmas.

The trapping of dust particles has been observed in a dc abnormal glow discharge dominated by electron attachment. A dust cloud of several tens of positively charged particles was found to form in the anode sheath region. An analysis of the experimental conditions revealed that these particles were positively charged due to emission process, in contrast to most other experiments on the levitation of dust particles in gas-discharge plasmas where negatively charged particles are found. An estimate of the particle charge, taking into account the processes of photoelectron and secondary electron emission from the particle surface, is in agreement with the experimental measured values.