Superdiffusion in two-dimensional Yukawa liquids

Universal scaling of transverse sound speed and its isomorphic property in Yukawa fluids

Molecular dynamical simulations are performed to investigate the scaling of the transverse sound speed in two-dimensional (2D) and 3D Yukawa fluids. From the calculated diagnostics of the radial distribution function, the mean-squared displacement, and the Pearson correlation coefficient, the approximate isomorphic curves for 2D and 3D liquidlike Yukawa systems are obtained. It is found that the structure and dynamics of 2D and 3D liquidlike Yukawa systems exhibit the isomorphic property under the conditions of the same relative coupling parameter Γ/Γ_{m}=const. It is demonstrated that the reduced transverse sound speed, i.e., the ratio of the transverse sound speed to the thermal speed, is an isomorph invariant, which is a quasiuniversal function of Γ/Γ_{m}. The obtained isomorph invariant of the reduced transverse sound speed can be useful to estimate the transverse sound speed, or determine the coupling strength, with applications to dusty (complex) plasma or colloidal systems.

Anomalous diffusion of E. coli under microfluidic confinement and chemical gradient

We report a two-layer microfluidic device to study the combined effect of confinement and chemical gradient on the motility of wild-type E. coli. We track individual E. coli in 50 μm and 10 μm wide microchannels, with a channel height of 2 μm, to generate quasi-2D conditions. We find that contrary to expectations, bacterial trajectories are superdiffusive even in the absence of a chemical (glucose) gradient. The superdiffusive behaviour becomes more pronounced upon introducing a chemical gradient or strengthening the lateral confinement. Run length distributions for weak lateral confinement in the absence of chemical gradients follow an exponential distribution. Both confinement and chemoattraction induce deviations from this behaviour, with the run length distributions approaching a power-law form under these conditions. Both confinement and chemoattraction suppress large-angle tumbles as well. Our results suggest that wild-type E. coli modulates both its runs and tumbles in a similar manner under physical confinement and chemical gradient. Our findings have implications for understanding how bacteria modulate their motility behaviour in natural habitats.

Determination of best particle tracking velocimetry method for two-dimensional dusty plasmas

A practical procedure of determining the best choice of particle tracking velocimetry (PTV) methods for the analysis of two-dimensional (2D) dusty plasmas is provided. Using the measured particle positions with errors, the algorithm of PTV introduces further systematic errors while calculating particle velocities. To better quantify the errors, computer simulations of 2D Yukawa liquids are performed so that the true particle positions and velocities are precisely known. Synthetic data are achieved by varying the time interval between frames and adding the uncertainty with the different magnitude to the particle position data. Various PTV methods are used to calculate the velocity data from the achieved synthetic data, and the obtained velocity data from these PTV methods are compared with the true velocity data using two diagnostics to determine the best PTV method for various conditions. The results of various PTV methods with the simulation data are further confirmed by the demonstration using the 2D dusty plasma experimental data. This practical procedure is also applicable to determine the best PTV method for dusty plasmas in different conditions, such as those in Tokamaks, and for other physical systems, including colloids, granular materials, and fluid mechanics.

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.

Fickian yet non-Gaussian diffusion in two-dimensional Yukawa liquids

We investigate Fickian diffusion in two-dimensional (2D) Yukawa liquids using molecular dynamics simulations. We compute the self-van Hove correlation function G_{s}(r,t) and the self-intermediate scattering function F_{s}(k,t), and we compare these functions with those obtained from mean-squared displacement (MSD) using the Gaussian approximation. According to this approximation, a linear MSD with time implies a Gaussian behavior for G_{s}(r,t) and F_{s}(k,t) at all times. Surprisingly, we find that these functions deviate from Gaussian at intermediate timescales, indicating the failure of the Gaussian approximation. Furthermore, we quantify these deviations by the non-Gaussian parameter, and we find that the deviations increase when the temperature of the liquid decreases. The origin of the non-Gaussian behavior may be the heterogeneous dynamics of dust particles observed in 2D Yukawa liquids.

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.

Perpendicular diffusion of a dilute beam of charged dust particles in a strongly coupled dusty plasma

The diffusion of projectiles drifting through a target of strongly coupled dusty plasma is investigated in a simulation. A projectile's drift is driven by a constant force F. We characterize the random walk of the projectiles in the direction perpendicular to their drift. The perpendicular diffusion coefficient Dp⊥ is obtained from the simulation data. The force dependence of Dp⊥ is found to be a power law in a high force regime, but a constant at low forces. A mean kinetic energy Wp for perpendicular motion is also obtained. The diffusion coefficient is found to increase with Wp with a linear trend at higher energies, but an exponential trend at lower energies.

Effect of magnetic field on the velocity autocorrelation and the caging of particles in two-dimensional Yukawa liquids

We investigate the effect of an external magnetic field on the velocity autocorrelation function and the "caging" of the particles in a two-dimensional strongly coupled Yukawa liquid, via numerical simulations. The influence of the coupling strength on the position of the dominant peak in the frequency spectrum of the velocity autocorrelation function confirms the onset of a joint effect of the magnetic field and strong correlations at high coupling. Our molecular dynamics simulations quantify the decorrelation of the particles' surroundings: the magnetic field is found to increase significantly the caging time, which reaches values well beyond the time scale of plasma oscillations. The observation of the increased caging time is in accordance with findings that the magnetic field decreases diffusion in similar systems.

From transport to disorder: thermodynamic properties of finite dust clouds

The quantities entropy and diffusion are measured for two- and three-dimensional (3D) dust clusters in the fluid state. Entropy and diffusion are predicted to be closely linked via unstable modes. The method of instantaneous normal modes is applied for various laser-heated clusters to determine these unstable modes and the corresponding diffusive properties. The configurational entropy is measured for 2D and 3D clusters from structural rearrangements. The entropy shows a threshold behavior at a critical temperature for the 2D clusters, allowing us to estimate a configurational melting temperature. Further, the entropic disorder increases for larger clusters. Finally, the predicted relation between entropy and unstable modes has been confirmed from our experiments for 2D systems, whereas 3D systems do not show such a clear correlation.

Higher harmonics of the magnetoplasmon in strongly coupled Coulomb and Yukawa systems

The generation of higher harmonics of the magnetoplasmon frequency which has recently been reported in strongly coupled two-dimensional Yukawa systems is investigated in detail and, in addition, extended to two-dimensional Coulomb systems. We observe higher harmonics over a much larger frequency range than before and compare the theoretical prediction with the simulations. The influence of the coupling, structure, and thermal energy on the excitation of these modes is examined in detail. We also report on the effect of friction on the mode spectra to make predictions about the experimental observability of this new effect.

Identifying anomalous diffusion and melting in dusty plasmas

Anomalous diffusion in liquids and the solid-liquid phase transition (melting) are studied in two-dimensional Yukawa systems. The self-intermediate scattering function (self-ISF), calculated from simulation data, exhibits a temporal decay, or relaxation, with a characteristic relaxation time. This decay is found to be useful for distinguishing normal and anomalous diffusion in a liquid, and for identifying the solid-liquid phase transition. For liquids, a scaling of the relaxation time with length scale is found. For the solid-liquid phase transition, the shape of the self-ISF curve is found to be a sensitive indicator of phase. Friction has a significant effect on the timing of relaxation, but not the melting point.

Is diffusion anomalous in two-dimensional Yukawa liquids?

There have recently been many predictions of "superdiffusion" in two-dimensional strongly coupled Yukawa systems, both by computer simulations and in dusty plasma experiments, with substantially varying diffusion exponents. Here we show that the results crucially depend on the strength of dissipation and the time instant of the measurement. For sufficiently large friction even subdiffusion is possible. However, there are strong indications that, in the long-time limit, anomalous diffusion vanishes and the system returns to normal diffusion, for dissipative as well as for frictionless systems.

Critical fluctuations and anomalous transport in soft Yukawa-Langevin systems

Simulation of a Langevin-dynamics model demonstrates emergence of critical fluctuations and anomalous grain transport which have been observed in experiments on "soft" quasi-two-dimensional dusty plasma clusters. Our model does not contain external drive or plasma interactions that serve to drive the system away from thermodynamic equilibrium. The grains are confined by an external potential, interact via static Yukawa forces, and are subject to stochastic heating and dissipation from neutrals. One remarkable feature is emergence of leptokurtic probability distributions of grain displacements xi(tau) on time scales tau < tau(Delta), where tau(Delta) is the time at which the standard deviation sigma(tau) identical with (xi(2)(tau))(1/2) approaches the mean intergrain distance Delta. Others are development of humps in the distributions on multiples of Delta , anomalous Hurst exponents, and transitions from leptokurtic toward Gaussian displacement distributions on time scales tau > tau(Delta). The latter is a signature of intermittency, here interpreted as a transition from bursty transport associated with hopping on intermediate time scales to vortical flows on longer time scales. These intermittency features are quantitatively modeled by a single-particle Itô-Langevin stochastic equation with a nonlinear drift term.

Diffusive and structural properties in a binary mixture of charged particles

Diffusive and structural properties in the binary mixture of charged particles are investigated based on the molecular dynamical simulation. It is shown that the particles with higher charge enhance or weaken the diffusion of the whole system depending on the coupling strength, and regimes of subdiffusion as well as normal diffusion are identified. The nonmonotonous diffusion, i.e., the diffusion at first is increased and then is decreased with increasing the higher charged particles, is strongest close to the phase from liquidlike state to solidlike state. Stronger coupling and lower concentration of higher charged particles are in favor of the formation of ordered shells centered at the higher charged particles.

Steady-shear-enhanced microdiffusion with multiple time scales of confined, mesoscopic, two-dimensional dusty-plasma liquids

We experimentally investigate the multitime scale diffusion and the spatiotemporal behaviors of the degrees of enhancement for the longitudinal and the transverse diffusions in a confined mesoscopic quasi-two-dimensional dusty-plasma liquid sheared by two parallel counterpropagating laser beams. The steady external drive directly enhances the longitudinal cooperative hopping, associated with the shear bands that have high shear rate near boundaries. It drastically excites the slow hopping modes to high fluctuation level in the outer band region, accompanied by the enhanced superdiffusion. Through cascaded many-body interaction, the excitation flows from the outer region toward the center region, from the longitudinal modes to the transverse mode, and from the slow hopping modes to the fast caging modes, which are in better contact with the thermal bath. It causes the weaker enhancement of fluctuation level, and diffusion for the center region and the fast modes. The boundary confinement further breaks the system symmetry and enhances anisotropy. It has much stronger effect on the suppression of the transverse hopping modes than the longitudinal hopping mode. The degrees of enhancement of the fluctuations by the shear stress are highly anisotropic for the large amplitude slow modes, especially in the outer region but are more isotropic in the inner band.

Self-diffusion in 2D dusty-plasma liquids: numerical-simulation results

We perform Brownian dynamics simulations for studying the self-diffusion in two-dimensional (2D) dusty-plasma liquids, in terms of both mean-square displacement and the velocity autocorrelation function (VAF). Superdiffusion of charged dust particles has been observed to be the most significant at an infinitely small damping rate gamma for intermediate coupling strength, where the long-time asymptotic behavior of VAF is found to be the product of t;{-1} and exp(-gammat). The former represents the prediction of early theories in 2D simple liquids and the latter the VAF of a free Brownian particle. This leads to a smooth transition from superdiffusion to normal diffusion, and then to subdiffusion with an increase of the damping rate. These results well explain the seemingly contradictory observations scattered in recent classical molecular dynamics simulations and experiments of dusty plasmas.

Time-correlation functions and transport coefficients of two-dimensional Yukawa liquids

The existence of coefficients for diffusion, viscosity, and thermal conductivity is examined for two-dimensional (2D) liquids. Equilibrium molecular dynamics simulations are performed using a Yukawa potential and the long-time behavior of autocorrelation functions is tested. Advances reported here as compared to previous 2D Yukawa liquid simulations include an assessment of the thermal conductivity, using a larger system size to allow meaningful examination of longer times, and development of improved analysis methods. We find that the transport coefficient exists for diffusion at high temperature and viscosity at low temperature, but not in the opposite limits. The thermal conductivity coefficient does not appear to exist at high temperature. Further advances in computing power could improve these assessments by allowing even larger system sizes and longer time series.

Self-assembly of complex structures in a two-dimensional system with competing interaction forces

Self-assembly of minimum-energy configurations of a two-dimensional system consisting of charged particles confined in a quadratic trap and interacting through competing repulsive and attractive interparticle forces is studied by means of molecular dynamics simulation. It is shown that complex configurations, including concentric shells separated by bandlike voids, connected shells with multiple regularly arranged voids, as well as small clusters of particles organized into crystal- or liquidlike structures, can exist. With increase of the particle number, a larger variety of structural patterns becomes possible. The results here are useful for a better understanding of pattern formation in two-dimensional systems, as well as in the design of specific structures for technological applications.

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.

Superdiffusion in quasi-two-dimensional Yukawa liquids

The emergence and vanishing of superdiffusion in quasi-two-dimensional Yukawa systems are investigated by molecular dynamics simulations. Using both the asymptotic behavior of the mean-squared displacement of the particles and the long-time tail of the velocity autocorrelation function as indicators of superdiffusion, we confirm the existence of a transition from normal diffusion to superdiffusion in systems changing from a three-dimensional to a two-dimensional character. A connection between superdiffusion and dimensionality is established by the behavior of the projected pair distribution function.

Superdiffusion in a model for diffusion in a molecularly crowded environment

We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in a percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times but anomalous diffusion at intermediate times. The effective exponents for square distance vs time usually are below one at these intermediate times, but they can also be larger than one for high barrier concentrations. Thus, we observe sub- and superdiffusion in a crowded environment.

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.