Non-Gaussian statistics and superdiffusion in a driven-dissipative dusty plasma

Particle random motion can exhibit both anomalous diffusion and non-Gaussian statistics in some physical systems. Anomalous diffusion is quantified by a deviation from alpha=1 in a power law for a particle's mean-square displacement, MSD proportional, variant(Deltat)alpha. A deviation from Gaussian statistics for a probability distribution function (PDF) is quantified by fitting to a kappa function or Tsallis distribution, with a fit parameter q. We report an experiment and simulations to test a theory that connects anomalous diffusion and non-Gaussian statistics. In the experiment, a single-layer dusty plasma, which behaved as a two-dimensional (2D) driven-dissipative system, had a non-Gaussian PDF. By adjusting an externally applied laser heating, q was varied over a wide range. A correlation between the deviations from Gaussian statistics and normal diffusion for a 2D liquid was found in the experiment. This correlation indicates a connection between anomalous diffusion and non-Gaussian statistics. However, such a connection is lacking in equilibrium 2D Yukawa liquids, as demonstrated in numerical simulations.

Rapid heating and cooling in two-dimensional Yukawa systems

Simulations are reported to investigate solid superheating and liquid supercooling of two-dimensional systems with a Yukawa interparticle potential. Motivated by experiments where a dusty plasma is heated and then cooled suddenly, we track particle motion using a simulation with Langevin dynamics. Hysteresis is observed when the temperature is varied rapidly in a heating and cooling cycle. As in the experiment, transient solid superheating, but not liquid supercooling, is observed. Solid superheating, which is characterized by solid structure above the melting point, is found to be promoted by a higher rate of temperature increase.

Solid superheating observed in two-dimensional strongly coupled dusty plasma

It is demonstrated experimentally that strongly coupled plasma exhibits solid superheating. A 2D suspension of microspheres in dusty plasma, initially self-organized in a solid lattice, was heated and then cooled rapidly by turning laser heating on and off. Particles were tracked using video microscopy, allowing atomistic-scale observation during melting and solidification. During rapid heating, the suspension remained in a solid structure at temperatures above the melting point, demonstrating solid superheating. Hysteresis diagrams did not indicate liquid supercooling in this 2D system.

Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma

Anomalous diffusion and non-Gaussian statistics are detected experimentally in a two-dimensional driven-dissipative system. A single-layer dusty plasma suspension with a Yukawa interaction and frictional dissipation is heated with laser radiation pressure to yield a structure with liquid ordering. Analyzing the time series for mean-square displacement, superdiffusion is detected at a low but statistically significant level over a wide range of temperatures. The probability distribution function fits a Tsallis distribution, yielding q, a measure of nonextensivity for non-Gaussian statistics.

Heat transport in a two-dimensional complex (dusty) plasma at melting conditions

The heat transport in a two-dimensional complex (dusty) plasma undergoing a phase transition was studied experimentally. A single layer of highly charged polymer microspheres was suspended in a plasma sheath. A part of this lattice was heated by two counterpropagating focused laser beams that moved rapidly around in the lattice and provided short intense random kicks to the particles. Above a threshold, the lattice locally melted. The spatial profiles of the particle kinetic temperature were analyzed to find a thermal conductivity, which did not depend on temperature.

Accurate particle position measurement from images

The moment method is an image analysis technique for subpixel estimation of particle positions. The total error in the calculated particle position includes effects of pixel locking and random noise in each pixel. Pixel locking, also known as peak locking, is an artifact where calculated particle positions are concentrated at certain locations relative to pixel edges. We report simulations to gain an understanding of the sources of error and their dependence on parameters the experimenter can control. We suggest an algorithm, and we find optimal parameters an experimenter can use to minimize total error and pixel locking. For a dusty plasma experiment, we find that a subpixel accuracy of 0.017 pixel or better can be attained. These results are also useful for improving particle position measurement and particle tracking velocimetry using video microscopy in fields including colloids, biology, and fluid mechanics.

Superdiffusion in two-dimensional Yukawa liquids

Superdiffusion of two-dimensional (2D) liquids was studied using an equilibrium molecular dynamics simulation. At intermediate temperatures, the mean-squared displacement, probability distribution function (PDF), and velocity autocorrelation function (VACF) all indicate superdiffusion; the VACF has a long-time tail; and the PDF indicates no Lévy flights. These effects are predicted to occur in 2D dusty plasmas and other 2D liquids that can be modeled with a long-range repulsive potential.

Cutoff wave number for shear waves in a two-dimensional Yukawa system (dusty plasma)

The cutoff wave number for shear waves in a liquid-state strongly coupled plasma was measured experimentally. The phonon spectra of random particle motion were measured at various temperatures in a monolayer dusty plasma, where microspheres interact with a Yukawa potential. In the liquid state of this particle suspension, shear waves were detected only for wavelengths smaller than 20 to 40 Wigner-Seitz radii, depending on the Coulomb coupling parameter. The temperature of the suspension was controlled using a laser-heating method.

Shear viscosity and shear thinning in two-dimensional Yukawa liquids

A two-dimensional Yukawa liquid is studied using two different nonequilibrium molecular dynamics simulation methods. Shear viscosity values in the limit of small shear rates are reported for a wide range of Coulomb coupling parameter and screening lengths. At high shear rates it is demonstrated that this liquid exhibits shear thinning; i.e., the viscosity eta diminishes with increasing shear rate. It is expected that two-dimensional dusty plasmas will exhibit this effect.

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.

Bispectral analysis of nonlinear compressional waves in a two-dimensional dusty plasma crystal

Bispectral analysis was used to study the nonlinear interaction of compressional waves in a two-dimensional strongly coupled dusty plasma. A monolayer of highly charged polymer microspheres was suspended in a plasma sheath. The microspheres interacted with a Yukawa potential and formed a triangular lattice. Two sinusoidal pump waves with different frequencies were excited in the lattice by pushing the particles with modulated Ar+ laser beams. Coherent nonlinear interaction of the pump waves was shown to be the mechanism of generating waves at the sum, difference, and other combination frequencies. However, coherent nonlinear interaction was ruled out for certain combination frequencies, in particular, for the difference frequency below an excitation-power threshold, as predicted by theory.

Shear viscosity of two-dimensional Yukawa systems in the liquid state

The shear viscosity of a two-dimensional (2D) liquid was calculated using molecular dynamics simulations with a Yukawa potential. The viscosity has a minimum at a Coulomb coupling parameter Gamma of about 17, arising from the temperature dependence of the kinetic and potential contributions. Previous calculations of 2D viscosity were less extensive as well as for a different potential. The stress autocorrelation function was found to decay rapidly, contrary to earlier work. These results are useful for 2D condensed matter systems and are compared to a dusty plasma experiment.

Phonons in a one-dimensional Yukawa chain: dusty plasma experiment and model

Phonons in a one-dimensional chain of charged microspheres suspended in a plasma were studied in an experiment. The phonons correspond to random particle motion in the chain; no external manipulation was applied to excite the phonons. Two modes were observed, longitudinal and transverse. The velocity fluctuations in the experiment are analyzed using current autocorrelation functions and a phonon spectrum. The phonon energy was found to be unequally partitioned among phonon modes in the dusty plasma experiment. The experimental phonon spectrum was characterized by a dispersion relation that was found to differ from the dispersion relation for externally excited phonons. This difference is attributed to the presence of frictional damping due to gas, which affects the propagation of externally excited phonons differently from phonons that correspond to random particle motion. A model is developed and fit to the experiment to explain the features of the autocorrelation function, phonon spectrum, and the dispersion relation.

fog-2 and the evolution of self-fertile hermaphroditism in Caenorhabditis

Somatic and germline sex determination pathways have diverged significantly in animals, making comparisons between taxa difficult. To overcome this difficulty, we compared the genes in the germline sex determination pathways of Caenorhabditis elegans and C. briggsae, two Caenorhabditis species with similar reproductive systems and sequenced genomes. We demonstrate that C. briggsae has orthologs of all known C. elegans sex determination genes with one exception: fog-2. Hermaphroditic nematodes are essentially females that produce sperm early in life, which they use for self fertilization. In C. elegans, this brief period of spermatogenesis requires FOG-2 and the RNA-binding protein GLD-1, which together repress translation of the tra-2 mRNA. FOG-2 is part of a large C. elegans FOG-2-related protein family defined by the presence of an F-box and Duf38/FOG-2 homogy domain. A fog-2-related gene family is also present in C. briggsae, however, the branch containing fog-2 appears to have arisen relatively recently in C. elegans, post-speciation. The C-terminus of FOG-2 is rapidly evolving, is required for GLD-1 interaction, and is likely critical for the role of FOG-2 in sex determination. In addition, C. briggsae gld-1 appears to play the opposite role in sex determination (promoting the female fate) while maintaining conserved roles in meiotic progression during oogenesis. Our data indicate that the regulation of the hermaphrodite germline sex determination pathway at the level of FOG-2/GLD-1/tra-2 mRNA is fundamentally different between C. elegans and C. briggsae, providing functional evidence in support of the independent evolution of self-fertile hermaphroditism. We speculate on the convergent evolution of hermaphroditism in Caenorhabditis based on the plasticity of the C. elegans germline sex determination cascade, in which multiple mutant paths yield self fertility.

A comparison of sex determination genes in C. elegans and C. briggsae provides evidence in support of the convergent evolution of self-fertile hermaphroditism in the Caenorhabditis clade

Shear flows and shear viscosity in a two-dimensional Yukawa system (dusty plasma)

The shear viscosity of a two-dimensional liquid-state dusty plasma was measured experimentally. A monolayer of highly charged polymer microspheres, with a Yukawa interaction, was suspended in a plasma sheath. Two counterpropagating Ar+ laser beams pushed the particles, causing shear-induced melting of the monolayer and a shear flow in a planar Couette configuration. By fitting the particle velocity profiles in the shear flow to a Navier-Stokes model, the kinematic viscosity was calculated; it was of order 1 mm(2) s(-1), depending on the monolayer's parameters and shear stress applied.

Characterizing potentials using the structure of a one-dimensional chain demonstrated using a dusty plasma crystal

A procedure was developed to characterize the interparticle potential in a lattice that is confined by an external potential. The first of the two steps is to characterize the confining potential, which can be done using various schemes involving observations of particle motion. The second step is to characterize the interparticle potential using measurements of the equilibrium particle positions. This can be done with either of two methods developed here, a force-balance method or a simpler equation-of-state method. To demonstrate and test these methods, an experiment and a molecular dynamics simulation were performed with a one-dimensional Coulomb chain of particles confined in a parabolic potential. The experiment used a dusty plasma consisting of charged microspheres levitated in the plasma sheath above a narrow groove in a lower electrode.

Nonlinear interaction of compressional waves in a 2D dusty plasma crystal

Nonlinear mixing and harmonic generation of compressional waves were studied in a 2D Yukawa (screened Coulomb) triangular lattice. The lattice was a monolayer of highly charged polymer microspheres levitated in a plasma sheath. Two sinusoidal waves with different frequencies were excited in the lattice by pushing the particles with modulated Ar+ laser beams. Waves at the sum and difference frequencies and harmonics were observed propagating in the lattice. Phonons interacted nonlinearly only above an excitation-power threshold due to frictional damping, as predicted by theory.

Transverse optical mode in a one-dimensional Yukawa chain

A transverse optical mode was observed in a one-dimensional Yukawa chain. Charged particles, suspended in a strongly coupled dusty plasma, were arranged in a 1D periodic structure. Particle displacement in the direction perpendicular to the chain was restored by the confining potential. The dispersion relation of phonons was measured, verifying that the optical mode has negative dispersion, with phase and group velocities that are oppositely directed. A theoretical dispersion relation is presented and compared to the experiment and a molecular dynamics simulation.

Compressional and shear wakes in a two-dimensional dusty plasma crystal

Wakes composed of compressional and shear waves were studied experimentally in a two-dimensional screened-Coulomb crystal. Highly charged microspheres suspended in a plasma settled in a horizontal monolayer and arranged in a triangular lattice with a repulsive interparticle potential. Wakes were excited by a moving spot of Ar+ laser light. Depending on the laser spot speed, compressional waves formed a Mach cone and multiple lateral or transverse wakes, similar to ship wakes on the water surface, due to a combination of acoustic and dispersive properties. Shear waves, however, formed only a Mach cone, due to their nearly acoustic, i.e., dispersionless character. The experimental results show agreement with a recently developed theory and with molecular dynamics simulations, which assume a binary Yukawa interparticle potential. A generally useful method is presented for calculating the real part of the dispersion relation of the compressional waves based on the analysis of the spatial structure of a phonon wake. Fitting the resulting dispersion relation provides an independent measure of the interparticle potential, parametrized by the screening parameter kappa and particle charge Q.

Nonlinear compressional waves in a two-dimensional Yukawa lattice

A modified Korteweg-de Vries (KdV) equation is obtained for studying the propagation of nonlinear compressional waves and pulses in a chain of particles including the effect of damping. Suitably altering the linear phase velocity makes this equation useful also for the problem of phonon propagation in a two-dimensional (2D) lattice. Assuming a Yukawa potential, we use this method to model compressional wave propagation in a 2D plasma crystal, as in a recent experiment. By integrating the modified KdV equation the pulse is allowed to evolve, and good agreement with the experiment is found. It is shown that the speed of a compressional pulse increases with its amplitude, while the speed of a rarefactive pulse decreases. It is further discussed how the drag due to the background gas has a crucial role in weakening nonlinear effects and preventing the emergence of a soliton.

Nonlinear longitudinal waves in a two-dimensional screened Coulomb crystal

Nonlinear interactions of longitudinal waves were observed in a two-dimensional plasma crystal, i.e., a lattice composed of highly charged microspheres immersed in a plasma. The waves were launched by radiation pressure of a laser, and wave spectra in omega-k space were analyzed at various amplitudes of waves. At a sufficiently large amplitude of wave, the second and third wave harmonics satisfying a dispersion relation were observed. As the second harmonic propagates from the excitation region, it was amplified for a small distance, and then damped. The experimental results were compared to a nonlinear wave theory and to a molecular dynamic simulation.

Decharging of complex plasmas: first kinetic observations

The first experiment on the decharging of a complex plasma in microgravity conditions was conducted. After switching off the rf power, in the afterglow plasma, ions and electrons rapidly recombine and leave a cloud of charged microparticles. Because of microgravity, the particles remain suspended in the experimental chamber for a sufficiently long time, allowing precise measurements of the rest particle charge. A simple theoretical model for the decharging is proposed which agrees quite well with the experiment results and predicts the rest charge at lower gas pressures.

Experiments and molecular-dynamics simulation of elastic waves in a plasma crystal radiated from a small dipole source

The radiation of elastic waves from a localized source is observed experimentally in a two-dimensional plasma crystal. An initial shear stress applied by a laser forms a small dipole source. The emerging complex wave pattern is shown to consist of outgoing compressional and shear wave pulses. Subsequent structures are identified as inward-going waves due to the finite size of the source region, which reappear on the opposite side. The compressional wave forms a trailing wave train due to strong dispersion, while the nondispersive shear wave evolves into a vortex-antivortex pair on either side. The experiments are compared with a molecular-dynamics simulation.

Phonon spectrum in a plasma crystal

The Fourier spectra of longitudinal and transverse waves corresponding to random particle motion were measured in a two-dimensional plasma crystal. The crystal was composed of negatively charged microspheres immersed in a plasma at a low gas pressure. The phonons were found to obey a dispersion relation that assumes a Yukawa interparticle potential. The crystal was in a nonthermal equilibrium, nevertheless phonon energies were almost equally distributed with respect to wave number over the entire first Brillouin zone.

Dispersion relations of longitudinal and transverse waves in two-dimensional screened Coulomb crystals

Dispersion relations of longitudinal and transverse waves in two-dimensional (2D) screened-Coulomb crystals were investigated. The waves were excited in 2D crystals made from complex plasmas, i.e., dusty plasmas, by applying radiation pressure of laser light. The dependencies of the dispersion relation on the shielding parameter, the damping rate, and the wave propagation direction were experimentally measured. The measured dispersion relations agree reasonably with a recently developed theory, and the comparison yields the shielding parameter and the charge on particles.