Static and dynamic shear viscosity of a single-layer complex plasma

Shear softening and hardening of a two-dimensional Yukawa solid

Langevin dynamical simulations are performed to study the elastic behaviors of two-dimensional (2D) solid dusty plasmas under the periodic shear deformation. The frequency- and strain-dependent shear moduli G(ω,γ) of our simulated 2D Yukawa solid are calculated from the ratio of the shear stress to strain in different orientations. The shear-softening and -hardening properties in different lattice orientations are discovered from the obtained G(ω,γ). The component of the elastic constant tensor corresponding to the shear deformation is also calculated, whose variation trend exactly agrees with the discovered shear-softening and -hardening features in different shear directions. It is also found that the shear modulus of the 2D Yukawa solid always increases monotonically with the frequency.

Frequency-dependent complex viscosity obtained for a liquid two-dimensional dusty plasma experiment

Strongly coupled plasmas in a liquid phase can be characterized by a complex viscosity η(ω), which is a function of frequency. Data from a single experiment with dusty plasma were analyzed to compare η(ω) obtained by two fundamentally distinct methods. In a nonequilibrium method, a pair of counterpropagating laser beams, separated by a gap, applied a sinusoidal shear to a two-dimensional liquid, and η(ω) was determined using the constitutive relation. In an equilibrium method, there was no externally applied shear, so η(ω) could be calculated with a generalized Green-Kubo relation. The results for these two methods are compared for the real and imaginary parts of η(ω). For both parts, it is confirmed that the two methods yield results that agree qualitatively in their trends with frequency, with the real part diminishing with ω and the imaginary part increasing with ω, as expected for viscoelastic liquids. Quantitatively, the values of η(ω) obtained by the two methods differ slightly. For the experiment that we analyze, values for the real and imaginary parts of η(ω) are substantially greater than those reported in an earlier experiment, which we attribute to shear thinning effects in the earlier experiment. The experiment we analyze was designed to minimize shear thinning, unlike the earlier experiment.

Experiment and model for a Stokes layer in a strongly coupled dusty plasma

A Stokes layer, which is a flow pattern that arises in a viscous fluid adjacent to an oscillatory boundary, was observed in an experiment using a two-dimensional strongly coupled dusty plasma. Liquid conditions were maintained using laser heating, while a separate laser manipulation applied an oscillatory shear that was localized and sinusoidal. The evolution of the resulting flow was analyzed using space-time diagrams. These figures provide an intuitive visualization of a Stokes layer, including features such as the depth of penetration and wavelength. Another feature, the characteristic speed for the penetration of the oscillatory flow, also appears prominently in space-time diagrams. To model the experiment, the Maxwell-fluid model of a Stokes layer was generalized to describe a two-phase liquid. In our experiment, the phases were gas and dust, where the dust cloud was viscoelastic due to strong Coulomb coupling. The model is found to agree with the experiment, in the appearance of the space-time diagrams, and in the values of the characteristic speed, depth of penetration, and wavelength.

Structure and thermodynamics of two-dimensional Yukawa liquids

The thermodynamic and structural properties of two-dimensional dense Yukawa liquids are studied with molecular dynamics simulations. The "exact" thermodynamic properties are simultaneously employed in an advanced scheme for the determination of an equation of state that shows an unprecedented level of accuracy for the internal energy, pressure, and isothermal compressibility. The "exact" structural properties are utilized to formulate a novel empirical correction to the hypernetted-chain approach that leads to a very high accuracy level in terms of static correlations and thermodynamics.

Homoclinic chaos in strongly dissipative strongly coupled complex dusty plasmas

The transport properties of the weakly nonlinear (WNL) two-dimensional (2D) quasilongitudinal dust lattice mode is studied in an experimentally realized highly viscous, strongly coupled, weakly ionized plasma [V. E. Fortov et al., Phys. Rev. Lett. 109, 055002 (2012)10.1103/PhysRevLett.109.055002]. The WNL dynamics is found to be described by a 2D dissipative-dispersive nonlinear partial differential equation. The analytical and computational (for gas discharge plasma parameters) results predict strong viscosity induced Shilnikov homoclinic chaos, which, in turn, can cause a phase transition.

Determination of viscosity in shear-induced melting two-dimensional dusty plasmas using Green-Kubo relation

Langevin dynamical simulations of shear-induced melting two-dimensional (2D) dusty plasmas are performed to study the determination of the shear viscosity of this system. It is found that the viscosity calculated from the Green-Kubo relation, after removing the drift motion, well agrees with the viscosity definition, i.e., the ratio of the shear stress to the shear rate in the sheared region, even the shear rate is magnified ten times higher than that in experiments. The behaviors of shear stress and its autocorrelation function of shear-induced melting 2D dusty plasmas are compared with those of uniform liquids at the same temperatures, leading to the conclusion that the Green-Kubo relation is still applicable to determine the viscosity for shear-induced melting dusty plasmas.

Strange attractors induced by melting in systems with nonreciprocal effective interactions

Newton's third law-the action-reaction symmetry-can be violated for effective interbody forces in open and nonequilibrium systems that are ubiquitous in areas as diverse as complex plasmas, colloidal suspensions, active and living soft matter, and social behavior. While studying monolayer complex plasma (confined charged particles in an ionized gas) with nonreciprocal interactions mediated by plasma flows, in silico we found that an interplay between melting and thermal activation drastically transforms the collective dynamics: the order-disorder transition modifies the system's thermal steady state so that the crystal tends to melt, whereas the fluid tends to freeze, jumping chaotically between the two states. We identified this collective chaotic behavior as strange attractors formed in a monolayer complex plasma and link the strange attractor behavior to the specifics of interparticle interactions.

Shear modulus of two-dimensional Yukawa or dusty-plasma solids obtained from the viscoelasticity in the liquid state

Langevin dynamical simulations of two-dimensional (2D) Yukawa liquids are performed to investigate the shear modulus of 2D solid dusty plasmas. Using the known transverse sound speeds, we obtain a theoretical expression of the shear modulus of 2D Yukawa crystals as a function of the screening parameter κ, which can be used as the candidate of their shear modulus. The shear relaxation modulus G(t) of 2D Yukawa liquids is calculated from the shear stress autocorrelation function, consisting of the kinetic, potential, and cross portions. Due to their viscoelasticity, 2D Yukawa liquids exhibit the typical elastic property when the time duration is much less than the Maxwell relaxation time. As a result, the infinite frequency shear modulus G_{∞}, i.e., the shear relaxation modulus G(t) when t=0, of a 2D Yukawa liquid should be related to the shear modulus of the corresponding quenched 2D Yukawa solid (with the same κ value), with all particles suddenly frozen at their locations of the liquid state. It is found that the potential portion of the infinite frequency shear modulus for 2D Yukawa liquids at any temperature well agrees with the shear modulus of 2D Yukawa crystals with the same κ obtained from the transverse sound speeds. Thus, we find that the shear modulus of 2D Yukawa solids can be obtained from the motion of individual particles of the corresponding Yukawa liquids using their viscoelastic property.

Dynamics of spinning particle pairs in a single-layer complex plasma crystal

Spontaneous formation of spinning pairs of particles, or torsions, is studied in a single-layer complex plasma crystal by reducing the discharge power at constant neutral gas pressure. At higher gas pressures, torsions spontaneously form below a certain power threshold. Further reduction of the discharge power leads to the formation of multiple torsions. However, at lower gas pressures the torsion formation is preceded by mode-coupling instability (MCI). The crystal dynamics are studied with the help of the fluctuation spectra of crystal particles' in-plane velocities. Surprisingly, the spectra of the crystal with torsions and MCI are rather similar and contain hot spots at similar locations on the (k,ω) plane, despite very different appearances of the respective particle trajectories. The torsion rotation speed is close (slightly below) to the maximum frequency of the in-plane compressional mode. When multiple torsions form, their rotation speeds are distributed in a narrow range slightly below the maximum frequency.

Viscosity of two-dimensional strongly coupled dusty plasma modified by a perpendicular magnetic field

Transport properties of two-dimensional (2D) strongly coupled dusty plasmas have been investigated in detail, but never for viscosity with a strong perpendicular magnetic field; here, we examine this scenario using Langevin dynamics simulations of 2D liquids with a binary Yukawa interparticle interaction. The shear viscosity η of 2D liquid dusty plasma is estimated from the simulation data using the Green-Kubo relation, which is the integration of the shear stress autocorrelation function. It is found that, when a perpendicular magnetic field is applied, the shear viscosity of 2D liquid dusty plasma is modified substantially. When the magnetic field is increased, its viscosity increases at low temperatures, while at high temperatures its viscosity diminishes. It is determined that these different variational trends of η arise from the different behaviors of the kinetic and potential parts of the shear stress under external magnetic fields.

Overestimation of Viscosity by the Green-Kubo Method in a Dusty Plasma Experiment

The Green-Kubo (GK) method is widely used in simulations of strongly coupled plasmas to obtain the viscosity coefficient. However, the method's applicability, which is often taken for granted, has not been tested experimentally. We report an experimental test using a two-dimensional strongly coupled dusty plasma. We find that the GK viscosity is ≈60% larger than the result of a benchmark hydrodynamic method, obtained in the same experiment with the same conditions except for the presence of shear.

Plasma crystal dynamics measured with a three-dimensional plenoptic camera

Three-dimensional (3D) imaging of a single-layer plasma crystal was performed using a commercial plenoptic camera. To enhance the out-of-plane oscillations of particles in the crystal, the mode-coupling instability (MCI) was triggered in it by lowering the discharge power below a threshold. 3D coordinates of all particles in the crystal were extracted from the recorded videos. All three fundamental wave modes of the plasma crystal were calculated from these data. In the out-of-plane spectrum, only the MCI-induced hot spots (corresponding to the unstable hybrid mode) were resolved. The results are in agreement with theory and show that plenoptic cameras can be used to measure the 3D dynamics of plasma crystals.

Slow plastic creep of 2D dusty plasma solids

We report complex plasma experiments, assisted by numerical simulations, providing an alternative qualitative link between the macroscopic response of polycrystalline solid matter to small shearing forces and the possible underlying microscopic processes. In the stationary creep regime we have determined the exponents of the shear rate dependence of the shear stress and defect density, being α=1.15±0.1 and β=2.4±0.4, respectively. We show that the formation and rapid glide motion of dislocation pairs in the lattice are dominant processes.

Superdiffusion of two-dimensional Yukawa liquids due to a perpendicular magnetic field

Stochastic transport of a two-dimensional (2D) dusty plasma liquid with a perpendicular magnetic field is studied. Superdiffusion is found to occur especially at higher magnetic fields with β of order unity. Here, β = ω(c)/ω(pd) is the ratio of the cyclotron and plasma frequencies for dust particles. The mean-square displacement MSD = 4D(α)t(α) is found to have an exponent α > 1, indicating superdiffusion, with α increasing monotonically to 1.1 as β increases to unity. The 2D Langevin molecular dynamics simulation used here also reveals that another indicator of random particle motion, the velocity autocorrelation function, has a dominant peak frequency ω(peak) that empirically obeys ω(peak)(2) = ω(c)(2) + ω(pd)(2)/4.

Channeling of particles and associated anomalous transport in a two-dimensional complex plasma crystal

Implications of the recently discovered effect of channeling of upstream extra particles for transport phenomena in a two-dimensional plasma crystal are discussed. Upstream particles levitated above the lattice layer and tended to move between the rows of lattice particles. An example of heat transport is considered, where upstream particles act as moving heat sources, which may lead to anomalous heat transport. The average channeling length observed was 15-20 interparticle distances. Other features of the channeling process are also reported.

Transverse current fluctuations in the Yukawa one-component plasma

Using numerical simulations, we investigate the wave number and frequency dependent transverse current correlation function CT(k,ω) of a single-component fluid with Yukawa interaction potential, also known as the Yukawa one-component plasma. The transverse current correlation function is an important quantity because it contains the microscopic details of the viscoelastic behavior of the fluid. We show that, in the region of densities and temperatures in which shear waves do not propagate, the dynamics of the system are in striking agreement with a simple model of generalized hydrodynamics. As either the density is increased or the temperature decreased, the transverse current correlation function shows additional structure that the simple models fail to capture.

Magnetoplasmons in rotating dusty plasmas

A rotating dusty plasma apparatus was constructed to provide the possibility of experimental emulation of extremely high magnetic fields by means of the Coriolis force, observable in a corotating measurement frame. We present collective excitation spectra for different rotation rates with a magnetic induction equivalent of up to 3200 T. We identify the onset of magnetoplasmon-equivalent mode dispersion in the rotating macroscopic two-dimensional single-layer dusty plasma. The experimental results are supported by molecular dynamics simulations of 2D magnetized Yukawa systems.

Quantum bound of the shear viscosity of a strongly coupled plasma

String theory methods led to the hypothesis that the ratio of a shear viscosity coefficient to the volume density of entropy of any physical system has a lower bound. Systems with strong coupling have a small viscosity as compared to weakly coupled plasmas in which the viscosity is proportional to the mean free path. Here, we have estimated the fully ionized strongly coupled plasma viscosity based on the dynamic experimental data on electrical conductivity and have shown that the ratio of viscosity to entropy of the strongly coupled plasma is very close to that of the lower bound predicted by the string theory.

Geometrical defects in two-dimensional melting of many-particle Yukawa systems

We present a theoretical polygon construction analysis of two-dimensional melting and freezing transitions in many-particle Yukawa systems. Two-dimensional melting transitions can be characterized as proliferation of geometrical defects--nontriangular polygons, obtained by removing unusually long bonds in the triangulation of particle positions. A liquid state is characterized by the temperature-independent number of quadrilaterals and linearly increasing number of pentagons. We analyze specific types of vertices, classified by the type and distribution of polygons surrounding them, and determine temperature dependencies of their concentrations. Solid-liquid phase transitions are followed by the peaks in the abundances of certain types of vertices.

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.

Frequency-dependent shear viscosity of a liquid two-dimensional dusty plasma

The viscoelasticity of a two-dimensional (2D) liquid stronglycoupled dusty plasma is studied experimentally, without macroscopic shear. Positions and velocities of the dust particles, measured by video microscopy, are used as the inputs to the generalized Green-Kubo relation to obtain the complex viscosity η(ω). The real part of η(ω) (which corresponds to dissipation) diminishes gradually with frequency, while the imaginary part (which corresponds to elasticity) is peaked at a frequency below the 2D dusty plasma frequency. The viscoelastic approximation is found to accurately describe the 2D experimental results for η(ω), yielding the Maxwell relaxation time τ(M)=0.10 s. Results for η(ω) are compared to 2D molecular dynamics Yukawa simulations and to a previous experiment that was performed using an oscillating macroscopic shear.

Cutoff wave number for shear waves and Maxwell relaxation time in Yukawa liquids

Because liquids cannot resist shear except over very short distances comparable to the atomic spacing, shear sound waves (i.e., transverse phonons) propagate only for very short wavelengths. A measure of this limit is the cutoff wave number k(c), which is sometimes called the critical wave number. Previously k(c) was determined in molecular dynamics (MD) simulations by obtaining the dispersion relation. Another approach is developed in this paper by identifying the wave number at the onset of a negative peak in the transverse current correlation function. This method is demonstrated using a three-dimensional MD simulation of a Yukawa fluid, which mimics dusty plasmas. In general, k(c) is an indicator of conditions where elastic and dissipative effects are approximately balanced. Additionally, the crossover frequency for the real and imaginary terms of the complex viscosity of a dusty plasma is obtained; this crossover frequency corresponds to the Maxwell relaxation time.