We study active run-and-tumble particles in two dimensions with an additional two-state internal variable characterizing their motile or nonmotile state. Motile particles change irreversibly into nonmotile ones upon collision with a nonmotile particle. The system evolves towards an absorbing state where all particles are nonmotile. We initialize the system with one nonmotile particle in a bath of motile ones and study numerically the kinetics of relaxation to the absorbing state and its structure as a function of the density of the initial bath of motile particles and of their tumbling rate. We find a crossover from fractal aggregates at low density to homogeneous ones at high density. The persistence of single-particle dynamics as quantified by the tumbling rate pushes this crossover to a higher density and can be used to tune the porosity of the aggregate. At the lowest density the fractal dimension of the aggregate approaches that obtained in single-particle diffusion-limited aggregation. Our results could be exploited for the design of structures of desired porosity. The model is a first step towards the study of the collective dynamics of active particles that can exchange biological information.

The Navier–Stokes transport coefficients for a model of a confined quasi-two-dimensional granular gas of smooth inelastic hard spheres are derived from the Enskog kinetic equation. A normal solution to this kinetic equation is obtained via the Chapman–Enskog method for states close to the local homogeneous state. The analysis is performed to first order in spatial gradients, allowing the identification of the Navier–Stokes transport coefficients associated with the heat and momentum fluxes. The transport coefficients are determined from the solution to a set of coupled linear integral equations analogous to those for elastic collisions. These integral equations are solved by using the leading terms in a Sonine polynomial expansion. The results are particularized to the relevant state with stationary temperature, where explicit expressions for the Navier–Stokes transport coefficients are given in terms of the coefficient of restitution and the solid volume fraction. The present work extends to moderate densities previous results [Brey et al. Phys. Rev. E 91, 052201 (2015)] derived for low-density granular gases.

The physics governing electron acceleration by a relativistically intense laser is not confined to the critical density surface; it also pervades the subcritical plasma in front of the target. Here particles can gain many times the ponderomotive energy from the overlying laser and strong fields can grow. Experiments using a high-contrast laser and a prescribed laser prepulse demonstrate that development of the preplasma has an unexpectedly strong effect on the most energetic, superponderomotive electrons. The presented two-dimensional particle-in-cell simulations reveal how strong, voluminous magnetic structures that evolve in the preplasma impact high-energy electrons more significantly than low-energy ones for longer pulse durations and how the common practice of tilting the target to a modest incidence angle can be enough to initiate strong deflection. The implications are that multiple angular spectral measurements are necessary to prevent misleading conclusions from past and future experiments.

It has been experimentally demonstrated that the geometry of a high-voltage electrode strongly affects the magnitude and structure of energy deposition into a thin metal wire before breakdown in vacuum. Additionally, two-dimensional electrostatic simulations provide evidence that the direction and magnitude of the radial electric field on a wire surface are dependent on the geometry of the electrodes. Increasing the size of the ground electrode leads to an increase in the radial electric field, but does not affect the direction of this field. However, modifications of the high-voltage electrode geometry alter the direction and magnitude of radial electric fields on the wire surface. Thus, the hot and homogeneous electrical explosion of a thin metal wire in vacuum can be realized with proper design of the wire's holding electrodes and independent from the polarity of the high-voltage electrode.

Unsupervised machine learning methods are used to identify structural changes using the melting point transition in classical molecular dynamics simulations as an example application of the approach. Dimensionality reduction and clustering methods are applied to instantaneous radial distributions of atomic configurations from classical molecular dynamics simulations of metallic systems over a large temperature range. Principal component analysis is used to dramatically reduce the dimensionality of the feature space across the samples using an orthogonal linear transformation that preserves the statistical variance of the data under the condition that the new feature space is linearly independent. From there, $k$-means clustering is used to partition the samples into solid and liquid phases through a criterion motivated by the geometry of the reduced feature space of the samples, allowing for an estimation of the melting point transition. This pattern criterion is conceptually similar to how humans interpret the data but with far greater throughput, as the shapes of the radial distributions are different for each phase and easily distinguishable by humans. The transition temperature estimates derived from this machine learning approach produce comparable results to other methods on similarly small system sizes. These results show that machine learning approaches can be applied to structural changes in physical systems.

Stochastic thermodynamics provides an important framework to explore small physical systems where thermal fluctuations are inevitable. In the studies of stochastic thermodynamics, some thermodynamic quantities, such as the trajectory work, associated with the complete Langevin equation (the Kramers equation) are often assumed to converge to those associated with the overdamped Langevin equation (the Smoluchowski equation) in the overdamped limit under the overdamped approximation. Nevertheless, a rigorous mathematical proof of the convergence of the work distributions to our knowledge has not been reported so far. Here we study the convergence of the work distributions explicitly. In the overdamped limit, we rigorously prove the convergence of the extended Fokker-Planck equations including work using a multiple timescale expansion approach. By taking the linearly dragged harmonic oscillator as an exactly solvable example, we analytically calculate the work distribution associated with the Kramers equation, and verify its convergence to that associated with the Smoluchowski equation in the overdamped limit. We quantify the accuracy of the overdamped approximation as a function of the damping coefficient. In addition, we experimentally demonstrate that the data of the work distribution of a levitated silica nanosphere agrees with the overdamped approximation in the overdamped limit, but deviates from the overdamped approximation in the low-damping case. Our work fills a gap between the stochastic thermodynamics based on the complete Langevin equation (the Kramers equation) and the overdamped Langevin equation (the Smoluchowski equation), and deepens our understanding of the overdamped approximation in stochastic thermodynamics.

We consider a thermal quantum harmonic oscillator weakly coupled to a heat bath at a different temperature. We analytically study the quantum heat exchange statistics between the two systems using the quantum-optical master equation. We exactly compute the characteristic function of the heat distribution and show that it verifies the Jarzynski-Wójcik fluctuation theorem. We further evaluate the heat probability density in the limit of long thermalization times, both in the low- and the high-temperature regimes, and investigate its time evolution by calculating its first two cumulants.

The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov exponents, that help predict the system's transitions into globally organized states. However, the local, microscopic, description of this emergent process continues to elude us. Here we show that at the microscopic level, synchronization is captured through a gradual process of topological adjustment in phase space, in which the strange attractors of the two coupled systems continuously converge, taking similar form, until complete topological synchronization ensues. We observe the local nucleation of topological synchronization in specific regions of the system's attractor, providing early signals of synchrony, that appear significantly before the onset of complete synchronization. This local synchronization initiates at the regions of the attractor characterized by lower expansion rates, in which the chaotic trajectories are least sensitive to slight changes in initial conditions. Our findings offer an alternative description of synchronization in chaotic systems, exposing its local embryonic stages that are overlooked by the currently established global analysis. Such local topological synchronization enables the identification of configurations where prediction of the state of one system is possible from measurements on that of the other, even in the absence of global synchronization.

Many-body states that are invariant under particle relabeling, the permutation symmetric states, occur naturally when the system dynamics is described by symmetric processes or collective spin operators. We derive expressions for the reduced density matrix for arbitrary subsystem decomposition for these states and study properties of permutation symmetric states and their subsystems when the joint system is picked randomly and uniformly. Thus defining an appropriate random matrix ensemble, we find the average linear entropy and von Neumann entropy, which implies that random permutation symmetric states are marginally entangled and as a consequence the tripartite mutual information (TMI) is typically positive, preventing information from being shared globally. Applying these results to the quantum kicked top viewed as a multiqubit system, we find that entanglement, mutual information, and TMI all increase for large subsystems across the Ehrenfest or logarithmic time and saturate at the random state values if there is global chaos. During this time the out-of-time-order correlators evolve exponentially, implying scrambling in phase space. We discuss how positive TMI may coexist with such scrambling.

We study a biological autoregulation process, involving a protein that enhances its own transcription, in a parameter region where bistability would be present in the absence of fluctuations. We calculate the rate of fluctuation-induced rare transitions between locally stable states using a path integral formulation and Master and Chapman-Kolmogorov equations. As in simpler models for rare transitions, the rate has the form of the exponential of a quantity $S_0$ (a “barrier”) multiplied by a prefactor $\eta$. We calculate $S_0$ and $\eta$ first in the bursting limit (where the ratio $\gamma$ of the protein and mRNA lifetimes is very large). In this limit, the calculation can be done almost entirely analytically, and the results are in good agreement with simulations. For finite $\gamma$ numerical calculations are generally required. However, $S_0$ can be calculated analytically to first order in $1/\gamma$, and the result agrees well with the full numerical calculation for all $\gamma >1$. Employing a method used previously on other problems, we find we can account qualitatively for the way the prefactor $\eta$ varies with $\gamma$, but its value is 15–20% higher than that inferred from simulations.

A theory for the frequency-dependent magnetic susceptibility of a ferrofluid in a static uniform magnetic field is developed, including the dipolar interactions between the constituent particles. Interactions are included within the framework of modified mean-field theory. Predictions are given for the linear responses of the magnetization to a probing ac field both parallel and perpendicular to the static field and are tested against results from Brownian dynamics simulations. The effects of the particle concentration and dipolar coupling constant on the field-dependent static susceptibilities and the frequency dispersions are shown to be substantial, which justifies taking proper account of the interactions between particles. The theory is reliable provided that the volume concentration and dipolar coupling constant are not too large and within the range of values for real ferrofluids.

We use density functional theory to explore the stable adsorption geometries of the liquid crystal molecule 5CB on a graphene sheet. First, we calculate the dependence of the polarizability of 5CB on its geometry. Our results break down the contributions of the cyano, biphenyl, and alkyl groups to the optical properties of 5CB, confirming the biphenyl group as the most influential. Second, we quantify possible adsorption structures of 5CB on graphene. We find that 5CB can stably adsorb with its biphenyl group oriented intermediate to the armchair and zigzag crystallographic directions, in addition to adsorbing with the biphenyl oriented along those directions.

We use topological data analysis to study the post buckling behavior of laboratory scale cylindrical silos under gravity driven granular discharges. Thin walled silos buckle during the discharge if the initial height of the granular column is large enough. The deformation of the silo is reversible as long as the filling height does not exceed a critical value, $L_c$. Beyond this threshold the deformation becomes permanent and the silo often collapses. We study the dynamics of reversible and irreversible deformation processes, varying the initial filling height around $L_c$. We find that all reversible processes exhibit striking similarities and they alternate between regimes of slow and fast dynamics. The patterns that occur at the beginning of irreversible deformation processes are topologically very similar to those that arise during reversible processes. However, the dynamics of reversible and irreversible processes is significantly different. In particular, the evolution of irreversible processes is much faster. This allows us to make an early prediction of the collapse of the silo based solely on observations of the deformation patterns.

The friction for sliding objects over partially water-saturated granular materials is investigated as a function of the water volume fraction. We find that ploughing friction is the main sliding mechanism: The slider leaves a deep trace in the sand after its passage. In line with previous research and everyday experience, we find that the friction force varies nonmonotonically with the water volume fraction. The addition of a small amount of water makes the friction force sharply drop, whereas too much added water causes the friction force to increase again. We present a ploughing model that quantitatively reproduces the nonmonotonic variation of the friction force as a function of water volume fraction without adjustable parameters. In this model, the yield stress of the water-sand mixture controls the depth to which the hemisphere sinks into the sand and the force that is required to plough through the water-sand mixture. We show that the model can also be used for other ploughing friction experiments, such as an ice skate that leaves a ploughing track on ice.

We report on the pattern formation in a horizontal rotating cylinder fully filled with bidispersed suspension composed of non-Brownian settling and floating particles. The effect of particle mixing of different buoyancy and shape on the axial and radial pattern formation was investigated using flow visualization and particle image velocimetry techniques. The experimental investigations involved two cases divided according to the shape of the particles making up the suspension. In the first case, both the floating and settling particles were spherical in shape while the second one was composed of buoyant spherical and settling cylindrical particles. A detailed analysis of the difference between the monodispersed and bidispersed suspension for various rotational speeds is provided. The radial and axial patterns for the bidispersed suspension was found to strongly depend on the rotation rate. The behavior at low rotation was similar to that of monodispersed systems, but at higher speeds, hybrid patterns emerged that were driven by the complementary influence of the two kinds of particles. The patterns observed were seen to be primarily influenced by the particle-particle hydrodynamic interaction. The nonspherical nature of the cylindrical particles produces radial and axial patterns that are distinctly different from the spherical particles.

In this work, for the constant speed kinetic model (CSKM) of Zadehgol and Ashrafizaadeh [J. Comput. Phys. 274, 803 (2014)], a different nonuniform and unsteady mass and force source term is proposed. Employing a Fourier series expansion of the source term and applying the standard Chapnan-Enskog analysis, we show that the desired source term can be determined by evaluating the expansion coefficients of the Fourier series in terms of the mass and force sources and the known macroscopic properties of the fluid. To rectify the pressure and speed of sound, rest particles are introduced. Moreover, it is shown that the present results can be applied to three-dimensional (3D) cases by employing four-dimensional (4D) Fourier series in the 4D hypercomplex space and projecting the results into the 3D space. The accuracy and thermodynamic consistency of the present method are numerically verified by simulating the following 2D and 3D benchmark flows: (i) Womersley flow, (ii) unsteady Taylor-Green vortex flow, (iii) flow in a concentric annular pipe, and (iv) the force-driven flow of a fluid inside a 3D channel. The present results are in excellent agreement with the exact and analytical solutions, and it is shown that the implementation of the present formulation of source term does not affect the thermodynamic consistency of the CSKM.

A feedforward neural network has a remarkable property which allows the network itself to be a universal approximator for any function. Here we present a universal machine-learning based solver for multivariable partial differential equations. The algorithm approximates the target functions by neural networks and adjusts the network parameters to approach the desirable solutions. The idea can be easily adopted for dealing with multivariable coupled integrodifferential equations, such as those in the self-consistent field theory for predicting polymer microphase-separated structures.

We present a theory for the dynamics of binary mixtures with particle size swaps. The general structure of the theory shows that, in accordance with physical intuition, particle size swaps open up an additional channel for the relaxation of density fluctuations. Thus, allowing particle size swaps speeds up the dynamics. To make explicit predictions, we use a factorization approximation similar to that employed in the mode-coupling theory of glassy dynamics. We calculate an approximate dynamic glass transition phase diagram for an equimolar binary hard-sphere mixture. We find that in the presence of particle size swaps, with increasing ratio of the hard-sphere diameters the dynamic glass transition line moves toward higher volume fractions, up to the ratio of the diameters approximately equal to 1.2, and then saturates. We comment on the implications of our findings for the theoretical description of the glass transition.

Low-mode asymmetries prevent effective compression, confinement, and heating of the fuel in inertial confinement fusion (ICF) implosions, and their control is essential to achieving ignition. Ion temperatures ($T_{\mathrm{ion}}$) in ICF experiments are inferred from the broadening of primary neutron spectra. Directional motion (flow) of the fuel at burn also impacts broadening and will lead to artificially inflated “$T_{\mathrm{ion}}$” values. Flow due to low-mode asymmetries is expected to give rise to line-of-sight variations in measured $T_{\mathrm{ion}}$. We report on intentionally asymmetrically driven experiments at the OMEGA laser facility designed to test the ability to accurately predict and measure line-of-sight differences in apparent $T_{\mathrm{ion}}$ due to low-mode asymmetry-seeded flows. Contrasted to chimera and xrage simulations, the measurements demonstrate how all asymmetry seeds have to be considered to fully capture the flow field in an implosion. In particular, flow induced by the stalk that holds the target is found to interfere with the seeded asymmetry. A substantial stalk-seeded asymmetry in the areal density of the implosion is also observed.

We study the occupation fluctuations of drifted Brownian motion in a closed interval and show that they undergo a dynamical phase transition in the long-time limit without an additional low-noise limit. This phase transition is similar to wetting and depinning transitions, and arises here as a switching between paths of the random motion leading to different occupations. For low occupations, the motion essentially stays in the interval for some fraction of time before escaping, while for high occupations the motion is confined in an ergodic way in the interval. This is confirmed by studying a confined version of the model, which points to a further link between the dynamical phase transition and quantum phase transitions. Other variations of the model, including the geometric Brownian motion used in finance, are considered to discuss the role of recurrent and transient motion in dynamical phase transitions.