Equilibrium properties and phase diagram of two-dimensional Yukawa systems

Shapiro steps observed in a two-dimensional Yukawa solid modulated by a one-dimensional vibrational periodic substrate

Depinning dynamics of a two-dimensional (2D) solid dusty plasma modulated by a one-dimensional (1D) vibrational periodic substrate are investigated using Langevin dynamical simulations. As the uniform driving force increases gradually, from the overall drift velocity varying with the driving force, four significant Shapiro steps are discovered. The data analysis results indicate that, when the ratio of the frequency from the drift motion over potential wells to the external frequency from the modulation substrate is close to integers, dynamic mode locking occurs, corresponding to the discovered Shapiro steps. Around both termini of the first and fourth Shapiro steps, the transitions are found to be always continuous, however, the transition between the second and third Shapiro steps is discontinuous, probably due to the different arrangements of particles.

A first principles study of convection cells to shear flow instability in 2D Yukawa liquids driven by Reynolds stress

The stability of kinetic-level convection cells (wherein the magnitude of macroscopic and microscopic velocities are of same order) is studied in a two-dimensional Yukawa liquid under the effect of microscopic velocity perturbations. Our numerical experiments demonstrate that for a given system aspect ratio β viz., the ratio of system length [Formula: see text] to its height [Formula: see text] and number of convective rolls initiated [Formula: see text], the fate of the convective cells is decided by [Formula: see text]. For [Formula: see text], Reynolds stress is found to be self-consistently generated and sustained, which results in tilting of convection cells, eventually leading to shear flow generation, whereas for [Formula: see text], parallel shear flow is found to be untenable. An unambiguous quantitative connection between Reynolds stress and the onset of shear flow using particle-level data is established without free parameters. The growth rate of the instability, the role of frictional forces, generalization of our findings and the possibility of realizing the same in experiments are also discussed.

Observation of the hexatic phase in a two-dimensional complex plasma using machine learning

Complex plasmas consist of ionized gas and charged solid microparticles, representing the plasma state of soft matter. We apply machine learning methods to investigate a melting transition in a two-dimensional complex plasma. A convolutional neural network is constructed and trained with the numerical simulation. The hexatic phase is successfully identified and the evolution of topological defects is studied during melting transition in both simulations and experiments.

Melting curve of two-dimensional Yukawa systems predicted by isomorph theory

The analytical expression for the conditions of the solid-fluid phase transition, i.e., the melting curve, for two-dimensional (2D) Yukawa systems is derived theoretically from the isomorph theory. To demonstrate that the isomorph theory is applicable to 2D Yukawa systems, molecular dynamical simulations are performed under various conditions. Based on the isomorph theory, the analytical isomorphic curves of 2D Yukawa systems are derived using the local effective power-law exponent of the Yukawa potential. From the obtained analytical isomorphic curves, the melting curve of 2D Yukawa systems is directly determined using only two known melting points. The determined melting curve of 2D Yukawa systems well agrees with the previous obtained melting results using completely different approaches.

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.

Finite-size effects in the static structure factor S(k) and S(0) for a two-dimensional Yukawa liquid

Finite-size effects in the static structure factor S(k) are analyzed for an amorphous substance. As the number of particles is reduced, S(0) increases greatly, up to an order of magnitude. Meanwhile, there is a decrease in the height of the first peak S_{peak}. These finite-size effects are modeled accurately by the Binder formula for S(0) and our empirical formula for S_{peak}. Procedures are suggested to correct for finite-size effects in S(k) data and in the hyperuniformity index H≡S(0)/S_{peak}. These principles generally apply to S(k) obtained from particle positions in noncrystalline substances. The amorphous substance we simulate is a two-dimensional liquid, with a soft Yukawa interaction modeling a dusty plasma experiment.

Observation of fast sound in two-dimensional dusty plasma liquids

Equilibrium molecular dynamics simulations are performed to study two-dimensional (2D) dusty plasma liquids. Based on the stochastic thermal motion of simulated particles, the longitudinal and transverse phonon spectra are calculated, and used to determine the corresponding dispersion relations. From there, the longitudinal and transverse sound speeds of 2D dusty plasma liquids are obtained. It is discovered that, for wavenumbers beyond the hydrodynamic regime, the longitudinal sound speed of a 2D dusty plasma liquid exceeds its adiabatic value, i.e., the so-called fast sound. This phenomenon appears at roughly the same length scale of the cutoff wavenumber for transverse waves, confirming its relation to the emergent solidity of liquids in the nonhydrodynamic regime. Using the thermodynamic and transport coefficients extracted from the previous studies, and relying on the Frenkel theory, the ratio of the longitudinal to the adiabatic sound speeds is derived analytically, providing the optimal conditions for fast sound, which are in quantitative agreement with the current simulation results.

Comparison of the static structure factor at long wavelengths for a dusty plasma liquid and other liquids

Especially small values of the static structure factor S(k) at long wavelengths, i.e., small k, were obtained in an analysis of experimental data, for a two-dimensional dusty plasma in its liquid state. For comparison, an analysis of S(k) data was carried out for many previously published experiments with other liquids. The latter analysis indicates that the magnitude of S(k) at small k is typically in a range 0.02-0.13. In contrast, the corresponding value for a dusty plasma liquid was found to be as small as 0.0139. Another basic finding for the dusty plasma liquid is that S(k) at small k generally increases with temperature, with its lowest value, noted above, occurring near the melting point. Simulations were carried out for the dusty plasma liquid, and their results are generally consistent with the experiment. Since a dusty plasma has a soft interparticle interaction, our findings support earlier theoretical suggestions that a useful design strategy for creating materials having exceptionally low values of S(0), so-called hyperuniform materials, is the use of a condensed material composed of particles that interact softly at their periphery.

Superlubric-pinned transition of a two-dimensional solid dusty plasma under a periodic triangular substrate

The superlubric-pinned transition in the depinning dynamics of a two-dimensional (2D) solid dusty plasma modulated by 2D triangular periodic substrates is investigated using Langevin dynamical simulations. When the lattice structure of the 2D solid dusty plasma perfectly matches the triangular substrate, two distinctive pinned and moving ordered states are observed as the external uniform driving force gradually increases from zero. When there is a mismatch between the lattice structure and the triangular substrate, however, on shallow substrates, it is discovered that all of the particles can slide freely on the substrate even when the applied driving force is tiny. This is a typical example of superlubricity, which is caused by the competition between the substrate-particle and particle-particle interactions. If the substrate depth increases further, as the driving force increases from zero, there are three dynamical states consisting of the pinned state, the disordered plastic flow state, and the moving ordered state. In an underdense system, where there are fewer particles than potential well minima, it is found that the occurrence of the three different dynamical states is controlled by the depth of the substrate, which is quantitatively characterized using the average mobility.

Rayleigh-Taylor instability in strongly coupled plasma

Rayleigh–Taylor instability (RTI) is the prominent energy mixing mechanism when heavy fluid lies on top of light fluid under the gravity. In this work, the RTI is studied in strongly coupled plasmas using two-dimensional molecular dynamics simulations. The motivation is to understand the evolution of the instability with the increasing correlation (Coulomb coupling) that happens when the average Coulombic potential energy becomes comparable to the average thermal energy. We report the suppression of the RTI due to a decrease in growth rate with increasing coupling strength. The caging effect is expected a physical mechanism for the growth suppression observed in both the exponential and the quadratic growth regimes. We also report that the increase in shielding due to background charges increases the growth rate of the instability. Moreover, the increase in the Atwood number, an entity to quantify the density gradient, shows the enhancement of the growth of the instability. The dispersion relation obtained from the molecular dynamics simulation of strongly coupled plasma shows a slight growth enhancement compared to the hydrodynamic viscous fluid. The RTI and its eventual impact on turbulent mixing can be significant in energy dumping mechanisms in inertial confinement fusion where, during the compressed phases, the coupling strength approaches unity.

Fast particles overtaking shock front in two-dimensional Yukawa solids

High-speed particles overtaking the shock front during the propagation of compressional shocks in two-dimensional (2D) Yukawa solids are investigated using molecular dynamical simulations. When the compressional speed is lower, all particles around the shock front are almost accelerated synchronously. However, when the compressional speed is much higher, some particles penetrate the shock front to enter the preshock region. Around the shock front, it is found that the particle velocity profile at the first peak of the dispersive shock wave (DSW) is able to be described using the Gaussian distribution, so that the amplitudes of the DSW can be well characterized. As the compressional speed increases, the particle velocity corresponding to these DSW's amplitudes increase more substantially than the shock front speed. These amplitudes of the DSW are found to be able to predict the occurrence of the fast particles. Combined with the previous study of the DSW's period, it is demonstrated that the properties of the DSW are nearly not affected by the conditions of the 2D Yukawa systems, but only related to the compressional speed.

Directional locking in a two-dimensional Yukawa solid modulated by a two-dimensional periodic substrate

Directional depinning dynamics of a two-dimensional (2D) dusty plasma solid modulated by a 2D square periodic substrate are investigated using Langevin dynamical simulations. We observe prominent directional locking effects when the direction of the external driving force is varied relative to the underlying square substrate. These locking steps appear when the direction of the driving force is close to the symmetry direction of the substrate, corresponding to the different dynamical flow patterns and the structures. In the conditions between the adjacent locking steps, moving ordered states are observed. Although the discontinuous transitions often occur between the locking steps and the nonlocking portion, the continuous transitions are also found around the locking step associated with the disordered plastic flow close to its termini. Our results show that directional locking also occurs for underdamped systems, which could be tested experimentally in dusty plasmas modulated by 2D substrates.

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.

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.

Phonon spectra of a two-dimensional solid dusty plasma modified by two-dimensional periodic substrates

Phonon spectra of a two-dimensional (2D) solid dusty plasma modulated by 2D square and triangular periodic substrates are investigated using Langevin dynamical simulations. The commensurability ratio, i.e., the ratio of the number of particles to the number of potential well minima, is set to 1 or 2. The resulting phonon spectra show that propagation of waves is always suppressed due to the confinement of particles by the applied 2D periodic substrates. For a commensurability ratio of 1, the spectra indicate that all particles mainly oscillate at one specific frequency, corresponding to the harmonic oscillation frequency of one single particle inside one potential well. At a commensurability ratio of 2, the substrate allows two particles to sit inside the bottom of each potential well, and the resulting longitudinal and transverse spectra exhibit four branches in total. We find that the two moderate branches come from the harmonic oscillations of one single particle and two combined particles in the potential well. The other two branches correspond to the relative motion of the two-body structure in each potential well in the radial and azimuthal directions. The difference in the spectra between the square and triangular substrates is attributed to the anisotropy of the substrates and the resulting alignment directions of the two-body structure in each potential well.

Stability of two-dimensional complex plasma monolayers in asymmetric capacitively coupled radio-frequency discharges

In this article, the stability of a complex plasma monolayer levitating in the sheath of the powered electrode of an asymmetric capacitively coupled radio-frequency argon discharge is studied. Compared to earlier studies, a better integration of the experimental results and theory is achieved by operating with actual experimental control parameters such as the gas pressure and the discharge power. It is shown that for a given microparticle monolayer at a fixed discharge power there exist two threshold pressures: (i) above a specific pressure p_{cryst}, the monolayer always crystallizes; (ii) below a specific pressure p_{MCI}, the crystalline monolayer undergoes the mode-coupling instability and the two-dimensional complex plasma crystal melts. In between p_{MCI} and p_{cryst}, the microparticle monolayer can be either in the fluid phase or the crystal phase: when increasing the pressure from below p_{MCI}, the monolayer remains in the fluid phase until it reaches p_{cryst} at which it recrystallizes; when decreasing the pressure from above p_{cryst}, the monolayer remains in the crystalline phase until it reaches p_{MCI} at which the mode-coupling instability is triggered and the crystal melts. A simple self-consistent sheath model is used to calculate the rf sheath profile, the microparticle charges, and the microparticle resonance frequency as a function of power and background argon pressure. Combined with calculation of the lattice modes the main trends of p_{MCI} as a function of power and background argon pressure are recovered. The threshold of the mode-coupling instability in the crystalline phase is dominated by the crossing of the longitudinal in-plane lattice mode and the out-of plane lattice mode induced by the change of the sheath profile. Ion wakes are shown to have a significant effect too.

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.

Shock width measured under liquid and solid conditions in a two-dimensional dusty plasma

Widths of shocks are compared, under liquid and solid conditions, for a two-dimensional layer of charged microspheres levitated in a plasma. In this strongly coupled dusty plasma, a shock was launched as a blast wave by moving an exciter wire at a supersonic speed and then bringing it to a halt. Runs were repeated with the layer of microspheres prepared two ways: a crystallinelike solid and a liquid. The liquid was sustained using laser heating, with conditions that were otherwise the same as in the solid. The shock width was found to be less in a liquid than in a solid, where it was four to six lattice constants. These measurements were based on the high-gradient region of density profiles. The profiles were obtained from particle coordinates, measured by high-speed video imaging. The spatial resolution was improved by combining particle coordinates, in the shock's frame of reference, from a sequence of images.

Data-driven criterion for the solid-liquid transition of two-dimensional self-propelled colloidal particles far from equilibrium

We establish an explicit data-driven criterion for identifying the solid-liquid transition of two-dimensional self-propelled colloidal particles in the far from equilibrium parameter regime, where the transition points predicted by different conventional empirical criteria for melting and freezing diverge. This is achieved by applying a hybrid machine learning approach that combines unsupervised learning with supervised learning to analyze a huge amount of the system's configurations in the nonequilibrium parameter regime on an equal footing. Furthermore, we establish a generic data-driven evaluation function, according to which the performance of different empirical criteria can be systematically evaluated and improved. In particular, by applying this evaluation function, we identify a new nonequilibrium threshold value for the long-time diffusion coefficient, based on which the predictions of the corresponding empirical criterion are greatly improved in the far from equilibrium parameter regime. These data-driven approaches provide a generic tool for investigating phase transitions in complex systems where conventional empirical ones face difficulties.

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.

Head-on collision of compressional shocks in two-dimensional Yukawa systems

The head-on collision of compressional shocks in two-dimensional dusty plasmas is investigated using both molecular dynamical and Langevin simulations. Two compressional shocks are generated from the inward compressional boundaries in simulations. It is found that, during the collision of shocks, there is a generally existing time delay of shocks τ, which diminishes monotonically with the increasing compressional speed of boundaries, corresponding to the time resolution of the studied system. Dispersive shock waves (DSWs) are generated around the shock front for some conditions. It is also found that the period of the DSW decreases monotonically with the inward compressional speed of boundaries, more substantially than the time delay of shocks τ. When the inward compressional speed of boundaries increases further, the DSWs gradually vanish. We speculate that, for these high compressional speeds of boundaries, the period of the DSW might be reduced to a comparable timescale of the time delay of shocks τ, i.e., the time resolution of our studied system, or even shorter, thus the DSW reasonably vanishes.

Continuous and discontinuous transitions in the depinning of two-dimensional dusty plasmas on a one-dimensional periodic substrate

Langevin dynamical simulations are performed to study the depinning dynamics of two-dimensional dusty plasmas on a one-dimensional periodic substrate. From the diagnostics of the sixfold coordinated particles P_{6} and the collective drift velocity V_{x}, three different states appear, which are the pinning, disordered plastic flow, and moving ordered states. It is found that the depth of the substrate is able to modulate the properties of the depinning phase transition, based on the results of P_{6} and V_{x}, as well as the observation of hysteresis of V_{x} while increasing and decreasing the driving force monotonically. When the depth of the substrate is shallow, there are two continuous phase transitions. When the potential well depth slightly increases, the phase transition from the pinned to the disordered plastic flow states is continuous; however, the phase transition from the disordered plastic flow to the moving ordered states is discontinuous. When the substrate is even deeper, the phase transition from the pinned to the disordered plastic flow states changes to discontinuous. When the depth of the substrate further increases, as the driving force increases, the pinned state changes to the moving ordered state directly, so that the disordered plastic flow state disappears completely.

Melting, freezing, and dynamics of two-dimensional dipole systems in screening bulk media

This paper reports on the molecular dynamics simulations of classical two-dimensional (2D) electric dipole systems. The properties of 2D systems with bare (nonscreened) and screened dipole-dipole interactions have been investigated. Based on the polygon construction method, we present simulation results on the phase transition, and we locate the melting and freezing points of 2D dipole systems in terms of a polygon disorder parameter, with the polygon disorder parameter being the sum of nontriangular polygon order parameters. It was found that the phase transition of the system occurs when the polygon disorder parameter has a value 0.165. This result was cross-checked by using both local and overall orientational order parameters. We also identified that the value of the average local orientational order parameter at the phase transition point is 0.67. These results are valid for the ordinary (bare) dipole-dipole interaction as well as the screened dipole-dipole interaction, and they are expected to be general for other 2D systems with repulsive pair interaction. We observed that both melting and freezing points shift to lower values of temperature due to screening. In the liquid state, the radial distribution function and polygon construction method show the loss of order in a structure as screening becomes more severe. Furthermore, the impact of screening on the system's collective excitation spectra and diffusive characteristics at liquid and solid states has been studied. Results show the decrease in the values of both longitudinal and transverse sound speeds and the emergence of anomalous superdiffusive motion in the liquid state due to screening.

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.

Universal relationship of compression shocks in two-dimensional Yukawa systems

Using molecular dynamical simulations, compressional shocks in two-dimensional (2D) dusty plasmas are quantitatively investigated under various conditions. A universal relationship between the thermal and the drift velocities after shocks is discovered in 2D Yukawa systems. Using the equation of state of 2D Yukawa liquids, and the obtained pressure from the Rankine-Hugoniot relation, an analytical relation between the thermal and the drift velocities is derived, which well agrees with the discovered universal relationship for various conditions.

Sound speed in Yukawa one-component plasmas across coupling regimes

A many-body system of charged particles interacting via a pairwise Yukawa potential, the so-called Yukawa one-component plasma (YOCP), is a good approximation for a variety of physical systems. Such systems are completely characterized by two parameters: the screening parameter, κ, and the nominal coupling strength, Γ. It is well known that the collective spectrum of the YOCP is governed by a longitudinal acoustic mode, both in the weakly and strongly coupled regimes. In the long-wavelength limit, the linear term in the dispersion (i.e., ω=sk) defines the sound speed s. We study the evolution of this latter quantity from the weak- through the strong-coupling regimes by analyzing the dynamic structure function S(k,ω) in the low-frequency domain. Depending on the values of Γ and κ and w=s/v_{th} (i.e., the ratio between the phase velocity of the wave and the thermal speed of the particles), we identify five domains in the (κ,Γ) parameter space in which the physical behavior of the YOCP exhibits different features. The competing physical processes are the collective Coulomb-like versus binary-collision-dominated behavior and the individual particle motion versus quasilocalization. Our principal tool of investigation is molecular dynamics (MD) computer simulation from which we obtain S(k,ω). Recent improvements in the simulation technique have allowed us to obtain a large body of high-quality data in the range Γ={0.1-10000} and κ={0.5-5}. The theoretical results based on various models are compared in order to see which one provides the most cogent physical description and the best agreement with MD data in the different domains.

Entropy Measurement in Strongly Coupled Complex Plasmas

The change in entropy of a system that is transferred between two states at different temperatures is measured in a two-dimensional plasma crystal experiment. One- and especially two-component dust clusters are confined in the plasma sheath and heated to different temperatures using laser manipulation. We find that entropies obtained from the phase space yield consistent results for, i.e., the heat capacity which shows excellent agreement with the Dulong-Petit law. The implications for the validity of basic thermodynamical principles in finite size complex (dusty) plasmas are discussed.

Pressure and energy of compressional shocks in two-dimensional Yukawa systems

The propagation of compressional shocks in two-dimensional (2D) dusty plasmas is investigated using MD simulations under various conditions. The shock Hugoniot curves of the relationship between the shock front speed D and the mean particle speed v[over ¯] after shocks are obtained and analytically fit to parabolic expressions. As the screening parameter increases, the weaker Yukawa interparticle interaction cause the shock Hugoniot curves to be more linear. Combining the obtained shock Hugoniot curves with the Rankine-Hugoniot jump relations, analytic expressions of pressure and energy after the shocks in 2D Yukawa systems are obtained, which are functions of the observable quantities, like the shock front speed D or the mean particle speed v[over ¯] or the specific volume.

Slow Dynamics in a Quasi-Two-Dimensional Binary Complex Plasma

Slow dynamics in an amorphous quasi-two-dimensional complex plasma, comprised of microparticles of two different sizes, was studied experimentally. The motion of individual particles was observed using video microscopy, and the self-part of the intermediate scattering function as well as the mean-squared particle displacement was calculated. The long-time structural relaxation reveals the characteristic behavior near the glass transition. Our results suggest that binary complex plasmas can be an excellent model system to study slow dynamics in classical supercooled fluids.

Depinning dynamics of two-dimensional dusty plasmas on a one-dimensional periodic substrate

We investigate the depinning dynamics of two-dimensional dusty plasmas driven over one-dimensional periodic substrates using Langevin dynamical simulations. We find that, for a specific range of substrate strengths, as the external driving force increases from zero, there are three different states, which are the pinned, the disordered plastic flow, and the moving ordered states, respectively. These three states are clearly observed using different diagnostics, including the collective drift velocity, static structural measures, the particle trajectories, the mean-squared displacements, and the kinetic temperature. We compare the observed depinning dynamics here with the depinning dynamics in other systems.

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.

Experimental validation of interpolation method for pair correlations in model crystals

Accurate analysis of pair correlations in condensed matter allows us to establish relations between structures and thermodynamic properties and, thus, is of high importance for a wide range of systems, from solids to colloidal suspensions. Recently, the interpolation method (IM) that describes satisfactorily the shape of pair correlation peaks at short and at long distances has been elaborated theoretically and using molecular dynamics simulations, but it has not been verified experimentally as yet. Here, we test the IM by particle-resolved studies with colloidal suspensions and with complex (dusty) plasmas and demonstrate that, owing to its high accuracy, the IM can be used to experimentally measure parameters that describe interaction between particles in these systems. We used three- and two-dimensional colloidal crystals and monolayer complex (dusty) plasma crystals to explore suitability of the IM in systems with soft to hard-sphere-like repulsion between particles. In addition to the systems with pairwise interactions, if many-body interactions can be mapped to the pairwise ones with some effective (e.g., density-dependent) parameters, the IM could be used to obtain these parameters. The results reliably show that the IM can be effectively used for analysis of pair correlations and interactions in a wide variety of systems and therefore is of broad interest in condensed matter, complex plasma, chemical physics, physical chemistry, materials science, and soft matter.

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.

Phase diagram for two-dimensional layer of soft particles

The phase diagram of a monolayer of soft particles described by the Daoud-Cotton model for star polymers is presented. Ground state calculations and grand canonical Monte Carlo simulations are used to determine the phase behavior as a function of the number of arms on the star and the areal coverage of the soft particles. The phase diagram exhibits rich behavior including reentrant melting and freezing and solid-solid transitions with triangular, stripe, honeycomb and kagome phases. These structures in 2D are analogous to the structures observed in 3D. The evolution of the structure factor with density is qualitatively similar to that measured in experiments for polymer grafted nanocrystals [Chen et al., Macromolecules, 2017, 50, 9636].

Two-dimensional crystals of star polymers: a tale of tails

The formation of non-hexagonal crystalline structures by the organisation of colloidal nanoparticles often involves the use of complex particles with anisotropic shape or interactions or the imposition of non-uniform external fields. Here we explore how unusual symmetries can be created using experimentally realistic particles that interact through isotropic and purely repulsive potentials. In particular, we use simulations to explore the phase behavior of two-dimensional systems of star polymers. We uncover how the tail of the pair potential has a large role in dictating the phase behavior. Star polymers interacting in the far field with a Gaussian potential only form hexagonal phases, while an exponential tail gives rise to stable primitive oblique and honeycomb lattices. We identify the ratio in strength between long and short range interactions and the nature of the transition between these regimes as crucial parameters to predict when non-hexagonal crystals of star polymers can be stable. This leads to experimental design rules for creating star polymers which should exhibit unusual lattice formation.

Thermoacoustic Instability in Two-Dimensional Fluid Complex Plasmas

Thermoacoustic instability in a fluid monolayer complex plasma is studied for the first time. Experiments, theory, and simulations demonstrate that nonreciprocal effective interactions between particles (mediated by plasma flows) provide positive thermal feedback leading to acoustic sound amplification. The form of the generated sound spectra obtained both in experiments and simulations excellently agrees with theory, justifying thermoacoustic instability in the fluid complex plasma. The results indicate a physical analogy between collective fluctuation dynamics in reactive media and in systems with nonreciprocal effective interactions exposing an activation behavior.

Dusty plasma experiment to confirm an expression for the decay of autocorrelation functions

Statistical physicists recently proposed an expression for an autocorrelation function (ACF) [Belousov and Cohen, Phys. Rev. E 94, 062124 (2016)2470-004510.1103/PhysRevE.94.062124] that has, until now, not been tested experimentally. The expression captures the early behavior of the ACF decay, when the ACF is flattened. Using experimental data from a nonequilibrium steady-state dusty plasma, we confirm that the expression's use extends to liquidlike strongly coupled plasmas. A transition in the shape of the ACF is identified, and we suggest that it corresponds to the onset of collisional scattering.

Spiral waves in driven strongly coupled Yukawa systems

Spiral wave formations are ubiquitous in nature. In the present paper, the excitation of spiral waves in the context of driven two-dimensional dusty plasma (Yukawa system) has been demonstrated at particle level using molecular-dynamics simulations. The interaction amidst dust particles is modeled by the Yukawa potential to take account of the shielding of dust charges by the lighter electron and ion species. The spatiotemporal evolution of these spiral waves has been characterized as a function of the frequency and amplitude of the driving force and dust neutral collisions. The effect of strong coupling has been studied, which shows that the excited spiral wave structures get clearer as the medium gets more strongly coupled. The radial propagation speed of the spiral wave is observed to remain unaltered with the coupling parameter. However, it is found to depend on the screening parameter of the dust medium and decreases when it is increased. In the crystalline phase (with screening parameter κ>0.58), the spiral wavefronts are shown to be hexagonal in shape. This shows that the radial propagation speed depends on the interparticle spacing.

Thermodynamics of two-dimensional Yukawa systems across coupling regimes

Thermodynamics of two-dimensional Yukawa (screened Coulomb or Debye-Hückel) systems is studied systematically using molecular dynamics (MD) simulations. Simulations cover very broad parameter range spanning from weakly coupled gaseous states to strongly coupled fluid and crystalline states. Important thermodynamic quantities, such as internal energy and pressure, are obtained and accurate physically motivated fits are proposed. This allows us to put forward simple practical expressions to describe thermodynamic properties of two-dimensional Yukawa systems. For crystals, in addition to numerical simulations, the recently developed shortest-graph interpolation method is applied to describe pair correlations and hence thermodynamic properties. It is shown that the finite-temperature effects can be accounted for by using simple correction of peaks in the pair correlation function. The corresponding correction coefficients are evaluated using MD simulation. The relevance of the obtained results in the context of colloidal systems, complex (dusty) plasmas, and ions absorbed to interfaces in electrolytes is pointed out.

Full melting of a two-dimensional complex plasma crystal triggered by localized pulsed laser heating

The full melting of a two-dimensional plasma crystal was induced in a principally stable monolayer by localized laser stimulation. Two distinct behaviors of the crystal after laser stimulation were observed depending on the amount of injected energy: (i) below a well-defined threshold, the laser melted area recrystallized; (ii) above the threshold, it expanded outwards in a similar fashion to mode-coupling instability-induced melting, rapidly destroying the crystalline order of the whole complex plasma monolayer. The reported experimental observations are due to the fluid mode-coupling instability, which can pump energy into the particle monolayer at a rate surpassing the heat transport and damping rates in the energetic localized melted spot, resulting in its further growth. This behavior exhibits remarkable similarities with impulsive spot heating in ordinary reactive matter.

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.

Coupling of Noncrossing Wave Modes in a Two-Dimensional Plasma Crystal

We report an experimental observation of the coupling of the transverse vertical and longitudinal in-plane dust-lattice wave modes in a two-dimensional complex plasma crystal in the absence of mode crossing. A new large-diameter rf plasma chamber was used to suspend the plasma crystal. The observations are confirmed with molecular dynamics simulations. The coupling manifests itself in traces of the transverse vertical mode appearing in the measured longitudinal spectra and vice versa. We calculate the expected ratio of the trace to the principal mode with a theoretical analysis of the modes in a crystal with finite temperature and find good agreement with the experiment and simulations.

Flame propagation in two-dimensional solids: Particle-resolved studies with complex plasmas

Using two-dimensional (2D) complex plasmas as an experimental model system, particle-resolved studies of flame propagation in classical 2D solids are carried out. Combining experiments, theory, and molecular dynamics simulations, we demonstrate that the mode-coupling instability operating in 2D complex plasmas reveals all essential features of combustion, such as an activated heat release, two-zone structure of the self-similar temperature profile ("flame front"), as well as thermal expansion of the medium and temperature saturation behind the front. The presented results are of relevance for various fields ranging from combustion and thermochemistry, to chemical physics and synthesis of materials.

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.

Cage correlation and diffusion in strongly coupled three-dimensional Yukawa systems in magnetic fields

The influence of an external homogeneous magnetic field on the quasilocalization of the particles-characterized quantitatively by cage correlation functions-in strongly coupled three-dimensional Yukawa systems is investigated via molecular dynamics computer simulations over a wide domain of the system parameters (coupling and screening strengths, and magnetic field). The caging time is found to be enhanced by the magnetic field B. The anisotropic migration of the particles in the presence of magnetic field is quantified via computing directional correlation functions, which indicate a more significant increase of localization in the direction perpendicular to B, while a moderate increase is also found along the B field lines. Associating the particles' escapes from the cages with jumps of a characteristic length, a connection is found with the diffusion process: the diffusion coefficients derived from the decay time of the directional correlation functions in both the directions perpendicular to and parallel with B are in very good agreement with respective diffusion coefficients values obtained from their usual computation based on the mean-squared displacement of the particles.