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Abstract We discuss recent advances in developing a mode-coupling theory of the glass transition (MCT) of two-dimensional systems of active Brownian particles (ABPs). The theory describes the structural relaxation close to the active glass in terms of transient dynamical density correlation functions. We summarize the equations of motion that have been derived for the collective density-fluctuation dynamics and those for the tagged-particle motion. The latter allow to study the dynamics of both passive and active tracers in both passive and active host systems. In the limit of small wave numbers, they give rise to equations of motion describing the mean-squared displacements (MSDs) of these tracers and hence the long-time diffusion coefficients as a transport coefficient quantifying long-range tracer motion. We specifically discuss the case of a single ABP tracer in a glass-forming passive host suspension, a case that has recently been studied in experiments on colloidal Janus particles. We employ event-driven Brownian dynamics (ED-BD) computer simulations to test the ABP-MCT and find good agreement between the two for the MSD, provided that known errors in MCT already for the passive system (i.e., an overestimation of the glassiness of the system) are accounted for by an empirical mapping of packing fractions and host-system self-propulsion forces. The ED-BD simulation results also compare well to experimental data, although a peculiar non-monotonic mapping of self-propulsion velocities is required. The ABP-MCT predicts a specific self-propulsion dependence of the Stokes–Einstein relation between the long-time diffusion coefficient and the host-system viscosity that matches well the results from simulation. An application of ABP-MCT within the integration-through transients framework to calculate the density-renormalized effective swim velocity of the interacting ABP agrees qualitatively with the ED-BD simulation data at densities close to the glass transition and quantitatively for the full density range only after the mapping of packing fractions employed for the passive system. Graphic abstract

Reservoir computing is a very promising approach for the prediction of complex nonlinear dynamical systems. Besides capturing the exact short-term trajectories of nonlinear systems, it has also proved to reproduce its characteristic long-term properties very accurately. However, predictions do not always work equivalently well. It has been shown that both short- and long-term predictions vary significantly among different random realizations of the reservoir. In order to gain an understanding on when reservoir computing works best, we investigate some differential properties of the respective realization of the reservoir in a systematic way. We find that removing nodes that correspond to the largest weights in the output regression matrix reduces outliers and improves overall prediction quality. Moreover, this allows to effectively reduce the network size and, therefore, increase computational efficiency. In addition, we use a nonlinear scaling factor in the hyperbolic tangent of the activation function. This adjusts the response of the activation function to the range of values of the input variables of the nodes. As a consequence, this reduces the number of outliers significantly and increases both the short- and long-term prediction quality for the nonlinear systems investigated in this study. Our results demonstrate that a large optimization potential lies in the systematical refinement of the differential reservoir properties for a given dataset., 11 pages, 8 figures, published in Chaos

In a companion paper, we derived analytical expressions for the structure factor of the square-shoulder potential in a perturbative way around the high- and low-temperature regimes. Here, various physical properties of these solutions are derived. In particular, we investigate the large wave number sector, and relate it to the contact values of the pair-correlation function. Then, thermoelastic properties of the square-shoulder fluids are discussed., 25 pages , 16 figures

We present numerical evidence for an additional discontinuous transition inside the jammed regime for an asymmetric bidisperse granular packing upon compression. This additional transition line separates jammed states with networks of predominantly large particles from jammed networks formed by both large and small particles, and the transition is indicated by a discontinuity in the number of particles contributing to the jammed network. The additional transition line emerges from the curves of jamming transitions and terminates in an end-point where the discontinuity vanishes. The additional line is starting at a size ratio around $\delta = 0.22$ and grows longer for smaller $\delta$. For $\delta \to 0$, the additional transition line approaches a limit that can be derived analytically. The observed jamming scenarios are reminiscent of glass-glass transitions found in colloidal glasses., Comment: 4 pages, 3 figures

In contrast to molecular gases, granular gases are characterized by inelastic collisions and require therefore permanent driving to maintain a constant kinetic energy. The kinetic theory of granular gases describes how the average velocity of the particles decreases after the driving is shut off. Moreover it predicts that the rescaled particle velocity distribution will approach a stationary state with overpopulated high-velocity tails as compared to the Maxwell-Boltzmann distribution. While this fundamental theoretical result was reproduced by numerical simulations, an experimental confirmation is still missing. Using a microgravity experiment which allows the spatially homogeneous excitation of spheres via magnetic fields, we confirm the theoretically predicted exponential decay of the tails of the velocity distribution., Comment: 11 pages, 14 figures

We investigate the spatial structure of dense square-shoulder fluids. To this end we derive analytical perturbative solutions of the Ornstein-Zernike equation in the low- and high-temperature limits as expansions around the known hard sphere solutions. We then discuss the suitability of perturbative approaches in relation to the Ornstein-Zernike equation., 17 pages, 2 figures

Many natural and industrial processes rely on constrained transport, such as proteins moving through cells, particles confined in nanocomposite materials or gels, individuals in highly dense collectives and vehicular traffic conditions. These are examples of motion through crowded environments, in which the host matrix may retain some glass-like dynamics. Here we investigate constrained transport in a colloidal model system, in which dilute small spheres move in a slowly rearranging, glassy matrix of large spheres. Using confocal differential dynamic microscopy and simulations, here we discover a critical size asymmetry, at which anomalous collective transport of the small particles appears, manifested as a logarithmic decay of the density autocorrelation functions. We demonstrate that the matrix mobility is central for the observed anomalous behaviour. These results, crucially depending on size-induced dynamic asymmetry, are of relevance for a wide range of phenomena ranging from glassy systems to cell biology., The classical Lorentz gas model is widely used to describe constrained transport, but its assumption of an immobile environment is not applicable to many biological and industrial processes. Here, the authors show that the mobility of the matrix induces anomalous, logarithmic dynamics of the confined particles.

We study collective modes in a classical system of particles with repulsive inverse-power-law (IPL) interactions in the fluid phase, near the fluid-solid coexistence (IPL melts). The IPL exponent is varied from $n=10$ to $n=100$ to mimic the transition from moderately soft to hard-sphere-like interactions. We compare the longitudinal dispersion relations obtained using molecular dynamic (MD) simulations with those calculated using the quasi-crystalline approximation (QCA) and find that this simple theoretical approach becomes grossly inaccurate for $n\gtrsim 20$. Similarly, conventional expressions for high-frequency (instantaneous) elastic moduli, predicting their divergence as $n$ increases, are meaningless in this regime. Relations of the longitudinal and transverse elastic velocities of the QCA model to the adiabatic sound velocity, measured in MD simulations, are discussed for the regime where QCA is applicable. Two potentially useful freezing indicators for classical particle systems with steep repulsive interactions are discussed., Full text access to the paper using the link: http://rdcu.be/uVRO

Thermodynamics of two-dimensional Yukawa (screened Coulomb or Debye-H\"uckel) 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, ions absorbed to interfaces in electrolytes is pointed out., Comment: 11 pages, 3 figures, 5 tables

We study a complex plasma under microgravity conditions that is first stabilized with an oscillating electric field. Once the stabilization is stopped, the so-called heartbeat instability develops. We study how the kinetic energy spectrum changes during and after the onset of the instability and compare with the double cascade predicted by Kraichnan and Leith for two-dimensional turbulence. The onset of the instability manifests clearly in the ratio of the reduced rates of cascade of energy and enstrophy and in the power-law exponents of the energy spectra., 7 pages, 7 figures

International audience; In this paper, we discuss the relations between the exact shape of interparticle interactions in complex (dusty) plasmas and the dispersion relation of the longitudinal collective mode. Several representative repulsive potentials, predicted previously theoretically, are chosen, and the corresponding dispersion relations are calculated using the quasi-crystalline approximation. Both weakly coupled and strongly coupled regimes are considered. It is shown that the long-wavelength portions of the dispersion curves can be sensitive to the long-range asymptote of the interaction potential. This can be used to discriminate between different interaction mechanisms operational in complex plasmas experimentally. Main requirements are briefly discussed. Published by AIP Publishing.

Granular materials are complex multi-particle ensembles in which macroscopic properties are largely determined by inter-particle interactions between their numerous constituents. In order to understand and to predict their macroscopic physical behavior, it is necessary to analyze the composition and interactions at the level of individual contacts and grains. To do so requires the ability to image individual particles and their local configurations to high precision. A variety of competing and complementary imaging techniques have been developed for that task. In this introductory paper accompanying the Focus Issue, we provide an overview of these imaging methods and discuss their advantages and drawbacks, as well as their limits of application., Comment: Submitted to Review of Scientific Instruments as introduction for: Focus on Imaging Methods in Granular Physics

Complex microscopic many-body processes are often interpreted in terms of so-called "reaction coordinates," i.e., in terms of the evolution of a small set of coarse-grained observables. A rigorous method to produce the equation of motion of such observables is to use projection operator techniques, which split the dynamics of the observables into a main contribution and a marginal one. The basis of any derivation in this framework is the classical Heisenberg equation for an observable. If the Hamiltonian of the underlying microscopic dynamics and the observable under study do not explicitly depend on time, this equation is obtained by a straightforward derivation. However, the problem is more complicated if one considers Hamiltonians which depend on time explicitly as, e.g., in systems under external driving, or if the observable of interest has an explicit dependence on time. We use an analogy to fluid dynamics to derive the classical Heisenberg picture and then apply a projection operator formalism to derive the nonstationary generalized Langevin equation for a coarse-grained variable. We show, in particular, that the results presented for time-independent Hamiltonians and observables in the study by Meyer, Voigtmann, and Schilling, J. Chem. Phys. 147, 214110 (2017) can be generalized to the time-dependent case.

International audience; The collective modes of a familiar two-dimensional one-component-plasma with the repulsive logarithmic interaction between the particles are analysed using the quasi-crystalline approximation (QCA) combined with the molecular dynamic simulation of the equilibrium structural properties. It is found that the dispersion curves in the strongly coupled regime are virtually independent of the coupling strength. Arguments based on the excluded volume consideration for the radial distribution function allow us to derive very simple expressions for the dispersion relations, which show excellent agreement with the exact QCA dispersion over the entire domain of wavelengths. Comparison with the results of the conventional fluid analysis is performed, and the difference is explained. Published by AIP Publishing.