Recent experiments and simulations of amorphous solids plastically deformed by an oscillatory drive have found a surprising behavior—for small strain amplitudes the dynamics can be reversible, which is contrary to the usual notion of plasticity as an irreversible form of deformation. This reversibility allows the system to reach limit cycles in which plastic events repeat indefinitely under the oscillatory drive. It was also found that reaching reversible limit cycles can take a large number of driving cycles and it was surmised that the plastic events encountered during the transient period are not encountered again and are thus irreversible. Using a graph representation of the stable configurations of the system and the plastic events connecting them, we show that the notion of reversibility in these systems is more subtle. We find that reversible plastic events are abundant and that a large portion of the plastic events encountered during the transient period are actually reversible in the sense that they can be part of a reversible deformation path. More specifically, we observe that the transition graph can be decomposed into clusters of configurations that are connected by reversible transitions. These clusters are the strongly connected components of the transition graph and their sizes turn out to be power-law distributed. The largest of these are grouped in regions of reversibility, which in turn are confined by regions of irreversibility whose number proliferates at larger strains. Our results provide an explanation for the irreversibility transition—the divergence of the transient period at a critical forcing amplitude. The long transients result from transition between clusters of reversibility in a search for a cluster large enough to contain a limit cycle of a specific amplitude. For large enough amplitudes, the search time becomes very large, since the sizes of the limit cycles become incompatible with the sizes of the regions of reversibility.

We perform experimental and numerical studies of a granular system under cyclic compression to investigate reversibility and memory effects. We focus on the quasistatic forcing of dense systems, which is most relevant to a wide range of geophysical, industrial, and astrophysical problems. We find that soft-sphere simulations with proper stiffness and friction quantitatively reproduce both the translational and rotational displacements of the grains. We then utilize these simulations to demonstrate that such systems are capable of storing the history of previous compressions. While both mean translational and rotational displacements encode such memory, the response is fundamentally different for translations compared to rotations. For translational displacements, this memory of prior forcing depends on the coefficient of static interparticle friction, but rotational memory is not altered by the level of friction.

We systematically analyze the tensorial structure of the lattice pressure tensors for a class of multiphase lattice Boltzmann models (LBM) with multirange interactions. Due to lattice discrete effects, we show that the built-in isotropy properties of the lattice interaction forces are not necessarily mirrored in the corresponding lattice pressure tensor. This finding opens a different perspective for constructing forcing schemes, achieving the desired isotropy in the lattice pressure tensors via a suitable choice of multirange potentials. As an immediate application, the obtained LBM forcing schemes are tested via numerical simulations of nonideal equilibrium interfaces and are shown to yield weaker and less spatially extended spurious currents with respect to forcing schemes obtained by forcing isotropy requirements only. From a general perspective, the proposed analysis yields an approach for implementing forcing symmetries, never explored so far in the framework of the Shan-Chen method for LBM. We argue this will be beneficial for future studies of nonideal interfaces.

We investigate the possibility of extending the notion of temperature in a stochastic model for the RNA or protein folding driven out of equilibrium. We simulate the dynamics of a small RNA hairpin subject to an external pulling force, which is time-dependent. First, we consider a fluctuation-dissipation relation (FDR) whereby we verify that various effective temperatures can be obtained for different observables, only when the slowest intrinsic relaxation timescale of the system regulates the dynamics of the system. Then, we introduce a different nonequilibrium temperature, which is defined from the rate of heat exchanged with a weakly interacting thermal bath. Notably, this “kinetic” temperature can be defined for any frequency of the external switching force. We also discuss and compare the behavior of these two emerging parameters, by discriminating the time-delayed nature of the FDR temperature from the instantaneous character of the kinetic temperature. The validity of our numerics are corroborated by a simple four-state Markov model which describes the long-time behavior of the RNA molecule.

The zeroth law is one of the oldest conjectures in turbulence that is still unproven. Here, we consider weak solutions of one-dimensional compressible magnetohydrodynamics and demonstrate that the lack of smoothness of the fields introduces a dissipative term, named inertial dissipation, into the expression of energy conservation that is neither viscous nor resistive in nature. We propose exact solutions assuming that the kinematic viscosity and the magnetic diffusivity are equal, and we demonstrate that the associated inertial dissipation is positive and equal on average to the mean viscous dissipation rate in the limit of small viscosity, proving the conjecture of the zeroth law of turbulence and the existence of an anomalous dissipation. As an illustration, we evaluate the shock heating produced by discontinuities detected by Voyager in the solar wind around 5 AU. We deduce a heating rate of $\sim {10}^{-18}\mathrm{J}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$, which is significantly higher than the value obtained from the turbulent fluctuations. This suggests that collisionless shocks can be a dominant source of heating in the outer solar wind.

Motivated from a wide range of applications, various methods to control synchronization in coupled oscillators have been proposed. Previous studies have demonstrated that global feedback typically induces three macroscopic behaviors: synchronization, desynchronization, and oscillation quenching. However, analyzing all of these transitions within a single theoretical framework is difficult, and thus the feedback effect is only partially understood in each framework. Herein, we analyze a model of globally coupled phase oscillators exposed to global feedback, which shows all of the typical macroscopic dynamical states. Analytical tractability of the model enables us to obtain detailed phase diagrams where transitions and bistabilities between different macroscopic states are identified. Additionally, we propose strategies to steer the oscillators into targeted states with minimal feedback strength. Our study provides a useful overview of the effect of global feedback and is expected to serve as a benchmark when more sophisticated feedback needs to be designed.

Airlines use different boarding policies to organize the queue of passengers waiting to enter the airplane. We analyze three policies in the many-passenger limit by a geometric representation of the queue position and row designation of each passenger and apply a Lorentzian metric to calculate the total boarding time. The boarding time is governed by the time each passenger needs to clear the aisle, and the added time is determined by the aisle-clearing time distribution through an effective aisle-clearing time parameter. The nonorganized queues under the common random boarding policy are characterized by large effective aisle-clearing time. We show that, subject to a mathematical assumption which we have verified by extensive numerical computations in all realistic cases, the average total boarding time is always reduced when slow passengers are separated from faster passengers and the slow group is allowed to enter the airplane first. This is a universal result that holds for any combination of the three main governing parameters: the ratio between effective aisle-clearing times of the fast and the slow groups, the fraction of slow passengers, and the congestion of passengers in the aisle. Separation into groups based on aisle-clearing time allows for more synchronized seating, but the result is nontrivial, as the similar fast-first policy—where the two groups enter the airplane in reverse order—is inferior to random boarding for a range of parameter settings. The asymptotic results conform well with discrete-event simulations with realistic numbers of passengers. Parameters based on empirical data, with hand luggage as criteria for separating passengers into the slow and fast groups, give an 8% reduction in total boarding time for slow first compared to random boarding.

A variety of theoretical models have been proposed to calculate the stopping power of charged particles in matter, which is a fundamental issue in many fields. However, the approximation adopted in these theories will be challenged under warm dense matter conditions. Molecular dynamics (MD) simulation is a good way to validate the effectiveness of these models. We investigate the stopping power of warm dense hydrogen for electrons with projectile energies ranging from 400–10000 eV by means of an electron force field (eFF) method, which can effectively avoid the Coulomb catastrophe in conventional MD calculations. It is found that the stopping power of warm dense hydrogen decreases with increasing temperature of the sample at those high projectile velocities. This phenomenon could be explained by the effect of electronic structure dominated by bound electrons, which is further explicated by a modified random phase approximation (RPA) model based on local density approximation proper to inhomogeneous media. Most of the models extensively accepted by the plasma community, e.g., Landau-Spitzer model, Brown-Preston-Singleton model and RPA model, cannot well address the effect caused by bound electrons so that their predictions of stopping power contradict our result. Therefore, the eFF simulations of this paper reveals the important role played by the bound electrons on stopping power in warm dense plasmas.

An accurate understanding of ion-beam transport in plasmas is crucial for applications in inertial fusion energy and high-energy-density physics. We present an experimental measurement on the energy spectrum of a proton beam at 270 keV propagating through a gas-discharge hydrogen plasma. We observe the energies of the beam protons changing as a function of the plasma density and spectrum broadening due to a collective beam-plasma interaction. Supported by linear theory and three-dimensional particle-in-cell simulations, we attribute this energy modulation to a two-stream instability excitation and further saturation by beam ion trapping in the wave. The widths of the energy spectrum from both experiment and simulation agree with the theory.

Collective behavior, both in real biological systems and in theoretical models, often displays a rich combination of different kinds of order. A clear-cut and unique definition of “phase” based on the standard concept of the order parameter may therefore be complicated, and made even trickier by the lack of thermodynamic equilibrium. Compression-based entropies have been proved useful in recent years in describing the different phases of out-of-equilibrium systems. Here, we investigate the performance of a compression-based entropy, namely, the computable information density, within the Vicsek model of collective motion. Our measure is defined through a coarse graining of the particle positions, in which the key role of velocities in the model only enters indirectly through the velocity-density coupling. We discover that such entropy is a valid tool in distinguishing the various noise regimes, including the crossover between an aligned and misaligned phase of the velocities, despite the fact that velocities are not explicitly used. Furthermore, we unveil the role of the time coordinate, through an encoding recipe, where space and time localities are both preserved on the same ground, and find that it enhances the signal, which may be particularly significant when working with partial and/or corrupted data, as is often the case in real biological experiments.

It is known that the distribution of nonreversible Markov processes breaking the detailed balance condition converges faster to the stationary distribution compared to reversible processes having the same stationary distribution. This is used in practice to accelerate Markov chain Monte Carlo algorithms that sample the Gibbs distribution by adding nonreversible transitions or nongradient drift terms. The breaking of detailed balance also accelerates the convergence of empirical estimators to their ergodic expectation in the long-time limit. Here, we give a physical interpretation of this second form of acceleration in terms of currents associated with the fluctuations of empirical estimators using the level 2.5 of large deviations, which characterizes the likelihood of density and current fluctuations in Markov processes. Focusing on diffusion processes, we show that there is accelerated convergence because estimator fluctuations arise in general with current fluctuations, leading to an added large deviation cost compared to the reversible case, which shows no current. We study the current fluctuation most likely to arise in conjunction with a given estimator fluctuation and provide bounds on the acceleration, based on approximations of this current. We illustrate these results for the Ornstein-Uhlenbeck process in two dimensions and the Brownian motion on the circle.

We investigate the asymptotic distributions of periodically driven anharmonic Langevin systems. Utilizing the underlying ${\text{SL}}_2$ symmetry of the Langevin dynamics, we develop a perturbative scheme in which the effect of periodic driving can be treated nonperturbatively to any order of perturbation in anharmonicity. We spell out the conditions under which the asymptotic distributions exist and are periodic and show that the distributions can be determined exactly in terms of the solutions of the associated Hill equations. We further find that the oscillating states of these driven systems are stable against anharmonic perturbations.

Multiple double-pole bright-bright and bright-dark soliton solutions for the multicomponent nonlinear Schrödinger (MCNLS) system comprising three types of nonlinearities, namely, focusing, defocusing, and mixed (focusing-defocusing) nonlinearities, arising in different physical settings are constructed. An interesting type of energy-exchanging phenomenon during collision of these double-pole solitons is unraveled. To explore the objectives, we consider the general solutions of a set of generalized MCNLS equations and by taking the long-wavelength limit with proper parameter choices of single-pole bright-bright and bright-dark soliton pairs, the multiple double-pole bright-bright and bright-dark soliton solutions are constructed in terms of determinants. The regular double-pole bright-bright solitons exist in the focusing and focusing-defocusing MCNLS equations and undergo a particular type of energy-sharing collision for $M\ge 2$ in addition to the usual elastic collisions. A striking feature observed in the process of energy-sharing collisions is that the double-pole two-soliton possessing unequal intensities before collision indeed exactly exchange their intensities after collision. Further, the existence of double-pole bright-dark solitons in the MCNLS equations with focusing, defocusing, and mixed (focusing-defocusing) nonlinearities is analyzed by constructing explicit determinant form solutions, where the double-pole bright solitons exhibit elastic and energy-exchanging collisions while the double-pole dark solitons undergo mere elastic collision. The double-pole bright-dark solitons possess much richer localized coherent patterns than their counterpart double-pole bright-bright solitons. For particular choices of parameters, we demonstrate that the solitons would degenerate into the background, resulting in a lower number of solitons. Another important observation is the formation of doubly localized rogue waves with extreme amplitude, in the case of double-pole bright-dark four-solitons. Our results should stimulate interest in such special multipole localized structures and are expected to have ramifications in nonlinear optics.

A discrete and periodic complex Ginzburg-Landau equation, coupled to a mean equation, is systematically derived from a driven and dissipative lattice oscillator model, close to the onset of a supercritical Andronov-Hopf bifurcation. The oscillator model is inspired by recent experiments exploring active vibrations of quasi-one-dimensional lattices of self-propelled millimetric droplets bouncing on a vertically vibrating fluid bath. Our systematic derivation provides a direct link between the constitutive properties of the lattice system and the coefficients of the resultant amplitude equations, paving the way to compare the emergent nonlinear dynamics—namely, the onset and formation of discrete dark solitons, breathers, and traveling waves—against experiments. The framework presented herein is expected to be applicable to a wider class of oscillators characterized by the presence of a dynamic coupling potential between particles. More broadly, our results point to deeper connections between nonlinear oscillators and the physics of active and driven matter.

Integrable dynamical systems play an important role in many areas of science, including accelerator and plasma physics. An integrable dynamical system with $n$ degrees of freedom possesses $n$ nontrivial integrals of motion, and can be solved, in principle, by covering the phase space with one or more charts in which the dynamics can be described using action-angle coordinates. To obtain the frequencies of motion, both the transformation to action-angle coordinates and its inverse must be known in explicit form. However, no general algorithm exists for constructing this transformation explicitly from a set of $n$ known (and generally coupled) integrals of motion. In this paper we describe how one can determine the dynamical frequencies of the motion as functions of these $n$ integrals in the absence of explicitly known action-angle variables, and we provide several examples.

The permeability of packs of spheres is important in a wide range of physical scenarios. Here, we create numerically generated random periodic domains of spheres that are polydisperse in size and use lattice-Boltzmann simulations of fluid flow to determine the permeability of the pore phase interstitial to the spheres. We control the polydispersivity of the sphere size distribution and the porosity across the full range from high porosity to a close packing of spheres. We find that all results scale with a Stokes permeability adapted for polydisperse sphere sizes. We show that our determination of the permeability of random distributions of spheres is well approximated by models for cubic arrays of spheres at porosities greater than $\sim 0.38$, without any fitting parameters. Below this value, the Kozeny-Carman relationship provides a good approximation for dense, closely packed sphere packs across all polydispersivity.

For quantum Otto engine driven quasistatically, we provide exact full statistics of heat and work for a class of working fluids that follow a scale-invariant energy eigenspectra under driving. Equipped with the full statistics we go on to derive a universal expression for the ratio of $n\mathrm{th}$ cumulant of output work and input heat in terms of the mean Otto efficiency. Furthermore, for nonadiabatic driving of quantum Otto engine with working fluid consisting of either a (i) qubit or (ii) a harmonic oscillator, we show that the relative fluctuation of output work is always greater than the corresponding relative fluctuation of input heat absorbed from the hot bath. As a result, the ratio between the work fluctuation and the input heat fluctuation receives a lower bound in terms of the square value of the average efficiency of the engine. The saturation of the lower bound is received in the quasistatic limit of the engine.

This paper studies numerically the Weeks-Chandler-Andersen system, which is shown to obey hidden scale invariance with a density-scaling exponent that varies from below 5 to above 500. This unprecedented variation makes it advantageous to use the fourth-order Runge-Kutta algorithm for tracing out isomorphs. Good isomorph invariance of structure and dynamics is observed over more than three orders of magnitude temperature variation. For all state points studied, the virial potential-energy correlation coefficient and the density-scaling exponent are controlled mainly by the temperature. Based on the assumption of statistically independent pair interactions, a mean-field theory is developed that rationalizes this finding and provides an excellent fit to data at low temperatures.