We numerically study the dynamics of an ensemble of Marangoni surfers in a two-dimensional and unconfined space. The swimmers are modeled as Gaussian sources of surfactant generating surface tension gradients and are shown to follow the Marangoni flow filtered at their spatial scale in the lubrication regime, an unstable situation leading to spontaneous motion as soon as the Marangoni effect is intense enough. As the system is fully unconstrained, it is possible to study the various dynamical regimes from single swimmer, two-body interaction, to the many-particles case characterized by an efficient particle dispersion. We show that, although the present model is very simple, it reproduces the experimentally observed transition between a regime of dispersion by random agitation when the number of swimmers is moderate to the regime of crystallization with imperfect hexagonal lattice at high density.

An analytical theory is developed for acoustic streaming induced by an axisymmetric acoustic wave field around an isotropic solid spherical particle in a compressible viscoelastic fluid. The particle is assumed to undergo pulsation, translation, and shape deformations of all orders. The fluid motion is described by the compressible Oldroyd-B model. No restrictions are imposed on the particle size with respect to the acoustic wavelength and the viscous penetration depth. The obtained analytical solutions are used in numerical simulations. It is shown that in the general case, the streaming velocity magnitude decreases with increasing polymer viscosity. Increasing relaxation time (elasticity) of the polymer solution leads to increasing streaming velocity magnitude as long as the relaxation time remains relatively small. It is also observed that the variation of the polymer viscosity and the relaxation time can change the pattern of streamlines.

An analytical formula is derived for acoustic radiation force exerted by an axisymmetric acoustic wave on an isotropic solid spherical particle in a compressible viscoelastic fluid. The particle is assumed to undergo pulsation, translation, and shape deformations of all orders. The fluid motion is described by the compressible Oldroyd-B model. No restrictions are imposed on the particle size with respect to the acoustic wavelength and the viscous penetration depth. The obtained analytical formula is used in numerical simulations. The results show that the acoustic radiation force can be increased by more than a factor of 10 due to the viscoelastic nature of the fluid, depending on the parameters. It is also observed that the sign of the force can change so that the force becomes directed to the velocity node instead of the velocity antinode if the driving frequency, the particle size, and the relaxation time of the polymer solution are relatively small.

Theoretical studies of the characteristics of the spatial relaxation of the average energy of electrons in inert gases (He, Ne, Ar, Kr, Xe) in a uniform electric field had been carried out. Conditions were considered when spatial relaxation has the character of damped oscillations. The calculations were performed using the Monte Carlo technique both without and taking into account the secondary electrons that appeared due to the ionization of atoms by electron impact. It was shown that the inclusion of secondary electrons leads to a noticeable decrease in the spatial relaxation length even in the case when the contribution of the ionization process to the electron energy balance is relatively small. For these gases, the upper boundary of the the electric field strength was determined, where the spatial relaxation of the average energy has the character of damped oscillations.

Generalized mode-coupling theory (GMCT) has recently emerged as a promising first-principles theory to study the poorly understood dynamics of glass-forming materials. Formulated as a hierarchical extension of standard mode-coupling theory (MCT), it is able to systematically improve its predictions by including the exact dynamics of higher-order correlation functions into its hierarchy. However, in contrast to Newtonian dynamics, a fully generalized version of the theory based on Brownian dynamics is still lacking. To close this gap, we provide a detailed derivation of GMCT for colloidal mixtures obeying a many-body Smoluchowski equation. We demonstrate that a hierarchy of coupled equations can again be established and show that these, consistent with standard MCT, are identical to the ones obtained from Newtonian GMCT when taking the overdamped limit. Consequently, the nontrivial similarity between Brownian and Newtonian MCT is maintained for our multicomponent GMCT. As a proof of principle, we also solve the generalized mode-coupling equations for the binary Kob-Andersen Lennard-Jones mixture undergoing Brownian dynamics and confirm the improved predictive power of the theory upon using more levels of the GMCT hierarchy of equations.

We investigate the ground-state quantum entanglement in a one-dimensional incarnation of deconfined quantum critical point by making use of the finite-size density matrix renormalization group method. We observe two distinct behaviors of two-site entanglement calculated on odd and even bonds, and the difference ${\mathcal{O}}_E$ is shown to obey conventional scaling relations for order parameters. Accurate deconfined critical point and associated critical exponents are numerically extracted from finite-size scaling analyses. We further notice a close similarity between ${\mathcal{O}}_E$ and the valence-bond-solid order parameter and same observations are also obtained for quantum coherence and trace distance. Furthermore, the deconfined critical point is suggested to possess rich quantum entanglement other than the two-site entanglement from the residual entanglement perspective. Our work explores the critical characteristics of the one-dimensional deconfined quantum critical point from the quantum information aspect and provides insights for its ground-state entanglement structure.

We study site- and bond-percolation on a class of lattices referred to as Lieb lattices. In two dimensions the Lieb lattice (LL) is also known as the decorated square lattice, or as the ${\mathrm{CuO}}_2$ lattice; in three dimensions it can be generalized to a layered Lieb lattice or to a perovskite lattice. Emergent electronic phenomena, such as topological states and ferrimagnetism, have been predicted to occur in these systems, which may be realized in optical lattices as well as in solid state. Since the study of the interplay between quantum fluctuations and disorder in these systems requires the availability of accurate estimates of geometrical critical parameters, such as percolation thresholds and correlation length exponents, here we use Monte Carlo simulations to obtain these data for LLs when a site (or bond) is present with probability $p$. We have found that the thresholds satisfy a mean-field (Bethe lattice) trend, namely that the critical concentration, $p_c$, increases as the average coordination number decreases; our estimates for the correlation length exponent are in line with the expectation that there is no change in the universality class.

Although the gravity dependence of granular friction is crucial to understand various natural phenomena, its precise characterization is difficult. We propose a method to characterize granular friction under various gravity (body force) conditions controlled by centrifugal force; specifically, the deformation of a rotated granular pile was measured. To understand the mechanics governing the observed nontrivial deformation of this pile, we introduced an analytic model considering local force balance. The excellent agreement between the experimental data and theoretical model suggests that the deformation is simply governed by the net body force (sum of gravity and centrifugal force) and friction angle. The body-force dependence of granular friction was precisely measured from the experimental results. The results reveal that the grain shape affects the degree of body-force dependence of the granular friction.

We revisit the associating lattice gas (ALG) introduced by Henriques et al. [Phys. Rev. E 71, 031504 (2005)] in its symmetric version. In this model, defined on the triangular lattice, interaction between molecules occupying nearest-neighbor sites depends on their relative orientation, mimicking the formation of hydrogen bonds in network-forming fluids. Although all previous studies of this model agree that it has a disordered fluid (DF), a low-density liquid (LDL), and a high-density liquid (HDL) phase, quite different forms have been reported for its phase diagram. Here, we present a thorough investigation of its phase behavior using both transfer matrix calculations and Monte Carlo (MC) simulations, along with finite-size scaling extrapolations. Results in striking agreement are found using these methods. The critical point associated with the DF-HDL transition at full occupancy, identified by Furlan et al. [Phys. Rev. E 100, 022109 (2019)] is shown to be one terminus of a critical line separating these phases. In opposition to previous simulation studies, we find that the transition between the DF and LDL phases is always discontinuous, similar to the LDL-HDL transition. The associated coexistence lines meet at the point where the DF-HDL critical line ends, making it a critical-end-point. Overall, the form of the phase diagram observed in our simulations is very similar to that found in the exact solution of the model on a Husimi lattice. Our results confirm that, despite the existence of some waterlike anomalies in this model, it is unable to reproduce key features of the phase behavior of liquid water.

We investigate consensus dynamics on temporal hypergraphs that encode network systems with time-dependent, multiway interactions. We compare these consensus processes with dynamics evolving on projections that remove the temporal and/or the multiway interactions of the higher-order network representation. For linear average consensus dynamics, we find that the convergence of a randomly switching time-varying system with multiway interactions is slower than the convergence of the corresponding system with pairwise interactions, which in turn exhibits a slower convergence rate than a consensus dynamics on the corresponding static network. We then consider a nonlinear consensus dynamics model in the temporal setting. Here we find that in addition to an effect on the convergence speed, the final consensus value of the temporal system can differ strongly from the consensus on the aggregated, static hypergraph. In particular, we observe a first-mover advantage in the consensus formation process: If there is a local majority opinion in the hyperedges that are active early on, then the majority in these first-mover groups has a higher influence on the final consensus value—a behavior that is not observable in this form in projections of the temporal hypergraph.

The flow of cohesive granular materials in a two-dimensional rotating drum is investigated using discrete element method simulations. Contacts between particles are modeled based on the widely used model of the spring-dashpot and Coulomb's friction law. A simplified model of intermediate range attraction between grains (i.e., cohesion) has been used in order to reproduce the flow of electrostatic or wet granular materials. Granular flow is generated by means of a rotating drum and the effect of the rotation speed, the friction between the grains, and the cohesion are studied. Significantly different flow behaviors are observed when cohesion is added. Plug flow appears in the rotating drum for a wide range of rotation speeds when cohesion becomes sufficiently strong. We propose a measurement of surface flow fluctuations to quantify the strength of cohesion, inspired by the previous observation of plug flow. Then, we make use of the results to include the effect of cohesion into a theoretical flow model. A good agreement is obtained between theory and numerical measurements of the granular bed's dynamic angle of repose, which allows us to propose a method for estimating the microscopic cohesion between grains based on the measurement of surface fluctuations.

An isolated positive wedge disclination deforms an initially flat elastic sheet into a perfect cone when the sheet is of infinite extent and is elastically inextensible. The latter requires the elastic stretching strains to be vanishingly small. In this paper, rigorous analytical and numerical results are obtained for the disclination-induced deformed shape and stress field of a bounded Föppl–von Kármán elastic sheet with finite extensibility, while emphasizing the deviations from the perfect cone solution. In particular, the Gaussian curvature field is no longer localized as a Dirac singularity at the defect location whenever elastic extensibility is allowed and is necessarily negative in large regions away from the defect. The stress field, similarly, has no Dirac singularity in the presence of elastic extensibility. However, with increasing Young's modulus of the sheet, while keeping the bending modulus and the domain size fixed, both of these fields tend to develop a Dirac singularity. Noticeably, in this limiting behavior, inextensibility eludes the bounded elastic sheet due to persisting regions of nontrivial Gaussian curvature away from the defect. Other results in the paper include studying the effect of specific boundary conditions (free, simply supported, or partially clamped) on the Gaussian curvature field away from the defect and on the buckling transition from the flat to a conical solution.

Acoustophoresis mainly deals with the manipulation of subwavelength scatterers in an incident acoustic field. The geometric details of manipulated particles are often neglected by replacing them with equivalent symmetric geometries such as spheres, spheroids, cylinders, or disks. It has been demonstrated that geometric asymmetry, represented by Willis coupling terms, can strongly affect the scattering of a small object; hence neglecting these terms may miss important force contributions. In this work, we present a generalized formalism of acoustic radiation force and radiation torque based on the polarizability tensor, where Willis coupling terms are included to account for geometric asymmetry. Following Gorkov's approach, the effects of geometric asymmetry are explicitly formulated as additional terms in the radiation force and torque expressions. By breaking the symmetry of a sphere along one axis using intrusion and protrusion, we characterize the changes in the force and torque in terms of partial components, associated with the direct and Willis coupling coefficients of the polarizability tensor. We investigate the cases of standing and traveling plane waves and show how the equilibrium positions and angles are shifted by these additional terms. We show that while the contributions of asymmetry to the force are often negligible for small particles, these terms greatly affect the radiation torque. Our presented theory, providing a way of calculating radiation force and torque directly from polarizability coefficients, shows that it is essential to account for shape of objects undergoing acoustophoretic manipulation, with important implications for applications such as the manipulation of biological cells.

Recent experiments have shown that femtosecond filamentation plasmas generate ultrabroadband radio frequency radiation (RF). We show that a combination of plasma dynamics is responsible for the RF: A plasma wake field develops behind the laser pulse, and this wake excites (and copropagates with) a surface wave on the plasma column. The surface wave proceeds to detach from the end of the plasma and propagates forward as the RF pulse. We have developed a four-stage model of these plasma wake surface waves and find that it accurately predicts the RF from a wide range of experiments, including both 800-nm and $3.9\text{−}\mu \mathrm{m}$ laser systems.

Beginning with the assumption that the quantum state of a many-particle system is a functional on the internal space of the particles, a unified quantum statistics, which may interpolate smoothly between Bose-Einstein and Fermi-Dirac statistics, is proposed. The commutation relations for such particle creation and annihilation operators are derived, and statistical partition function and thermodynamical properties of an ideal gas of the particles are investigated. Besides the Bose-Einstein condensation, another kind of particle condensation may appear.

In the original invasion percolation model, a random number quantifies the role of necks, or generally the quality of pores, ignoring the structure of pores and impermeable regions (to which the invader cannot enter). In this paper, we investigate invasion percolation (IP), taking into account the impermeable regions, the configuration of which is modeled by ordinary and Ising-correlated site percolation (with short-range interactions, SRI), on top of which the IP dynamics is defined. We model the long-ranged correlations of pores by a random Coulomb potential (RCP). By examining various dynamical observables, we suggest that the critical exponents of Ising-correlated cases change considerably only in the vicinity of the critical point (critical temperature), while for the ordinary percolation case the exponents are robust against the occupancy parameter $p$. The properties of the model for the long-range interactions [LRI (RCP)] are completely different from the normal IP. In particular, the fractal dimension of the external frontier of the largest hole is nearly $\frac{4}{3}$ for SRI far from the critical points, which is compatible with normal IP, while it converges to $1.099\pm 0.04$ for RCP. For the latter case, the time dependence of our observables is divided into three parts: the power law (short time), the logarithmic (moderate time), and the linear (long time) regimes. The second crossover time is shown to go to infinity in the thermodynamic limit, whereas the first crossover time is nearly unchanged, signaling the dominance of the logarithmic regime. The average gyration radius of the growing clusters, the length of their external perimeter, and the corresponding roughness are shown to be nearly constant for the long-time regime in the thermodynamic limit.

In this article, we present a dynamical scheme to obtain a reconfigurable noise-aided logic gate that yields all six fundamental two-input logic operations, including the xor operation. The setup consists of two coupled bistable subsystems that are each driven by one subthreshold logic input signal, in the presence of a noise floor. The synchronization state of their outputs robustly maps to two-input logic operations of the driving signals, in an optimal window of noise and coupling strengths. Thus the interplay of noise, nonlinearity, and coupling leads to the emergence of logic operations embedded within the collective state of the coupled system. This idea is manifested using both numerical simulations and proof-of-principle circuit experiments. The regions in parameter space that yield reliable logic operations were characterized through a stringent measure of reliability, using both numerical and experimental data.

We determined bulk crystal nucleation rates in aqueous suspensions of charged spheres at low metastability. Experiments were performed in dependence on electrolyte concentration and for two different particle number densities. The time-dependent nucleation rate shows a pronounced initial peak, while postsolidification crystal size distributions are skewed towards larger crystallite sizes. At each concentration, the nucleation rate density initially drops exponentially with increasing salt concentration. The full data set, however, shows an unexpected scaling of the nucleation rate densities with metastability times the number density of particles. Parameterization of our results in terms of classical nucleation theory reveals unusually low interfacial free energies of the nucleus surfaces and nucleation barriers well below the thermal energy. We tentatively attribute our observations to the presence of doublets introduced by the employed conditioning technique. We discuss the conditions under which such small seeds may induce nucleation.

Theory of absolute stimulated Brillouin side scattering in an inhomogeneous flowing plasma is presented and verified numerically. The linearized coupling equations are transformed into a Schrödinger equation in $k$ space and solved as an eigenvalue problem. Analytic threshold, growth rate, and scattering geometry are obtained for the pump laser with arbitrary incidence angle. Numerical solutions of the coupling equations show good agreements between the theoretical and numerical absolute thresholds when ion-acoustic wave damping is not too large, and thus an old but famous threshold in [Phys. Fluids 17, 1211 (1974)] is corrected. It also indicates that the theoretical analysis is not accurate for strong dampings, since it will overestimate the absolute threshold. Possibility of finding such instability in the current experiments is also discussed.