We show that a scaling approach successfully characterizes clustering and intermittency in space and time, in systems of noninteracting particles driven by fluctuating surfaces. We study both the steady state and the approach to it, for passive particles sliding on one-dimensional Edwards-Wilkinson or Kardar-Parisi-Zhang (KPZ) surfaces, with particles moving either along (advection) or against (antiadvection) the growth direction in the latter case. Extensive numerical simulations are supplemented by analytical results for a sticky slider model in which particles coalesce when they meet. Results for single-particle displacement versus time show to what extent particle dynamics is slaved to the surface, while scaling properties of the probability distribution of the separation of two particles determine the scaling form of average overlap of a pair of trajectories. For the many-particle system, clustering in steady state is studied via moments of particle number fluctuations in a single stretch, revealing different degrees of spatial multiscaling with different drivings. Temporal intermittency in steady state is established by showing that the scaled flatness diverges as the stretch size scaled by system size approaches zero for all the three drivings, but with different exponents, reflecting strongest clustering for KPZ advection and weakest for KPZ antiadvection. Finally, we consider the approach to the steady state and study both the flatness and the evolution of equal-time correlation functions as in coarsening of phase-ordering systems. Our studies give clear evidence for a simple scaling description of the approach to steady state, with the scale set by a length that grows in time. An investigation of aging properties reveals that flatness is nonmonotonic in time with two distinct branches and that a scaling description holds for each one.

Active systems contain self-propelled particles and can spontaneously self-organize into patterns making them attractive candidates for the self-assembly of smart soft materials. One key limitation of our present understanding of these materials hinges on the complexity of the microscopic mechanisms driving its components forward. Here, by combining experiments, analytical theory, and simulations we explore such a mechanism for a class of active system, modular microswimmers, which self-assemble from colloids and ion-exchange resins on charged substrates. Our results unveil the self-assembly processes and the working mechanism of the ion-exchange driven motors underlying modular microswimmers, which have so far been illusive, even qualitatively. We apply these motors to show that modular microswimmers can circumvent corners in complex environments and move uphill. Our work closes a central knowledge gap in modular microswimmers and provides a facile route to extract mechanical energy from ion-exchange processes.

We use three-dimensional contact dynamics simulations to analyze the rheology of polydisperse packings of spherical particles subjected to simple shear. The macroscopic and microstructural properties of several packings are analyzed as a function of their size span (from nearly monodisperse to highly polydisperse). Consistently with previous two-dimensional simulations, we find that the shear strength is independent of the size span despite the increase of packing fraction with size polydispersity. At the grain scale, we analyze the particle connectivity, force transmission, and the corresponding anisotropies of the contact and force networks. We show that force distributions become increasingly broader as the size span increases. In particular, stronger forces are captured by large particles, which are also better connected creating the so-called granular backbone. Throughout this backbone friction mobilization is rare and compressive forces control the stability of such structure. In return, small particles create an important population of rattlers discarded of the strength and granular structure analysis. As a consequence, the contact anisotropy declines with size span, whereas the force and branch anisotropies increase. These microstructural compensations allow us to explain the independence of the shear strength from particle size polydispersity.

The gravity-driven planar channel flow of a heated granular gas is analyzed using a kinetic model with stochastic forcing to understand the roles of inelasticity and forcing on its hydrodynamics and rheology. The closed-form analytical solutions up to the fourth order in gravitational acceleration have been determined to analyze the hydrodynamic and rheological fields as functions of the restitution coefficient ($e_n$) and the Froude number ${\mathrm{Fr}}_0$. It is found that the excess temperature [$\mathrm{\Delta }T=T_{max}/T\left(0\right)-1$, i.e., the deviation of the maximum temperature $T_{max}$ of the gas from its centerline value $T\left(0\right)$] increases monotonically with decreasing $e_n$ above a critical value of the Froude number (${\mathrm{Fr}}_0>{\mathrm{Fr}}_0^c$), but has a “nonmonotonic” dependence with $e_n$ [i.e., $\mathrm{\Delta }T$ decreases with decreasing $e_n$ for $e_n\in (1,0.5)$, but increases for $e_n<0.5$] at ${\mathrm{Fr}}_0<{\mathrm{Fr}}_0^c$. This changeover from nonmonotonic to monotonic dependence of $\mathrm{\Delta }T$ with $e_n$ at ${\mathrm{Fr}}_0={\mathrm{Fr}}_0^c$ also holds for both first (${\mathcal{N}}_1$) and second (${\mathcal{N}}_2$) normal-stress differences as well as for tangential heat flux ($q_x$). Phase diagrams are constructed in the (${\mathrm{Fr}}_0,1-e_n$) plane, demarcating two regions in which the dependencies of rarefaction effects ($\mathrm{\Delta }T, {\mathcal{N}}_1, {\mathcal{N}}_2$, and $q_x$) on $e_n$ are monotonic and nonmonotonic. The inelasticity plays a “dual” role of decreasing (at ${\mathrm{Fr}}_0<{\mathrm{Fr}}_0^c$) and increasing (at ${\mathrm{Fr}}_0>{\mathrm{Fr}}_0^c$) the rarefaction effects with decreasing restitution coefficient $e_n$ from the elastic limit. This finding, based on the fourth-order solution, is in variance with the leading-order solution that predicts only a nonmonotonic dependence of the above quantities on $e_n$ for all ${\mathrm{Fr}}_0$ [Tij and Santos, J. Stat. Phys. 117, 901 (2004)]. The role of inelasticity on the region of convergence of the asymptotic series solutions are subsequently analyzed by determining the Padé approximants for rheological fields [Rongali and Alam, Phys. Rev. E 98, 012115 (2018)]; the present solution is shown to have a larger range of validity in terms of both inelasticity and Froude number than its leading-order counterpart. Lastly, it is shown that the fourth-order solutions contain all Burnett-order terms (i.e., second order in the gradients of hydrodynamic fields) that can be obtained from the standard Chapman-Enskog expansion.

We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum thermalization to high-dimensional statistics. We find that the overlaps only depend on measurable quantities, and do not require the knowledge of the underlying “true” (noiseless) matrices. We apply our results to the case of empirical correlation matrices, that allow us to estimate reliably the width of the spectrum of the true correlation matrix, even when the latter is very close to the identity. We illustrate our results on the example of stock returns correlations, which clearly reveal a nontrivial structure for the bulk eigenvalues. We also apply our results to the problem of matrix denoising in high dimensions.

We study how a quantum heat engine performs across the critical value of an external parameter, pertaining to the quantum phase transition. Considering a two-ion system subjected to a magnetic field, we show that the system performs in a quantum Otto cycle above a critical value of the magnetic field, while below such critical point, it does not operate in a heat cycle at all. Moreover, at the critical point, its interaction with an ancillary ion deteriorates the performance of the system as a heat engine. We further show that a strong interaction between the constituent ions of an ion-based system is crucial for it to work in a heat-work cycle, while the coupling to the ancillary system must be minimized.

We numerically investigate the characteristics of chaos evolution during wave-packet spreading in two typical one-dimensional nonlinear disordered lattices: the Klein-Gordon system and the discrete nonlinear Schrödinger equation model. Completing previous investigations [Ch. Skokos et al., Phys. Rev. Lett. 111, 064101 (2013)], we verify that chaotic dynamics is slowing down for both the so-called weak and strong chaos dynamical regimes encountered in these systems, without showing any signs of a crossover to regular dynamics. The value of the finite-time maximum Lyapunov exponent $\mathrm{\Lambda }$ decays in time $t$ as $\mathrm{\Lambda }\propto t^{{\alpha }_{\mathrm{\Lambda }}}$, with ${\alpha }_{\mathrm{\Lambda }}$ being different from the ${\alpha }_{\mathrm{\Lambda }}=-1$ value observed in cases of regular motion. In particular, ${\alpha }_{\mathrm{\Lambda }}\approx -0.25$ (weak chaos) and ${\alpha }_{\mathrm{\Lambda }}\approx -0.3$ (strong chaos) for both models, indicating the dynamical differences of the two regimes and the generality of the underlying chaotic mechanisms. The spatiotemporal evolution of the deviation vector associated with $\mathrm{\Lambda }$ reveals the meandering of chaotic seeds inside the wave packet, which is needed for obtaining the chaotization of the lattice's excited part.

We consider a Kuramoto model with weakly conformed oscillators, for which the tendency of catching up with each other varies with the degree of synchronization, to study conformity effects. The bifurcation diagrams and dynamical behaviors of conformed oscillators are examined for unimodal and bimodal frequency distributions, respectively. For a unimodal distribution, a hysteresis loop emerges in the bifurcation diagram and the branch of unstable fixed points corresponds to the threshold, or quorum, over which systems move toward more synchronized states. For a bimodal distribution, saddle-node and homoclinic bifurcation lines shift with conformity which reflects the fact that conformity generally demotes the incoherent state. In addition, to shed light on how two groups of phase-locked oscillators reach synchronization subject to conformity, we analyze the period of limit cycles with a perturbation theory and numerics. Two groups of oscillators would reach a synchronized state when a threshold conformity parameter is met.

A random geometric graph (RGG) ensemble is defined by the disordered distribution of its node locations. We investigate how this randomness drives sample-to-sample fluctuations in the dynamical properties of these graphs. We study the distributional properties of the algebraic connectivity which is informative of diffusion and synchronization time scales in graphs. We use numerical simulations to provide a characterization of the algebraic connectivity distribution for RGG ensembles. We find that the algebraic connectivity can show fluctuations relative to its mean on the order of $30\%$, even for relatively large RGG ensembles ($N={10}^5$). We explore the factors driving these fluctuations for RGG ensembles with different choices of dimensionality, boundary conditions, and node distributions. Within a given ensemble, the algebraic connectivity can covary with the minimum degree and can also be affected by the presence of density inhomogeneities in the nodal distribution. We also derive a closed-form expression for the expected algebraic connectivity for RGGs with periodic boundary conditions for general dimension.

Recent technological development has enabled researchers to study social phenomena in detail, and financial markets have attracted the attention of physicists particularly since key concepts in Brownian motion are applicable to the description of financial systems. In our previous Letter [Kanazawa et al., Phys. Rev. Lett. 120, 138301 (2018)], we presented a microscopic model of high-frequency traders (HFTs) through direct data analyses of individual trajectories of HFTs and revealed its theoretical dynamics by introducing the Boltzmann and Langevin equations for finance. However, the formulation therein was rather heuristic and a more mathematically exact derivation is necessary from the microscopic dynamics of the HFT model. We hereby establish the mathematical foundation of kinetic theory for financial Brownian motion in a manner parallel to traditional statistical physics. We first derive the exact time-evolution equation for the phase-space distribution for the HFT model, corresponding to the Liouville equation in analytical mechanics. By a systematic reduction of the Liouville equation for finance, the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchal equations are generalized for financial Brownian motion. We then derive the Boltzmann and Langevin equations for the order book and the price dynamics by assuming molecular chaos. The asymptotic solutions to these equations are presented for a large number of HFTs, which qualitatively reveal how the strategies of traders at the microscopic level impact the macroscopic dynamics of market price. Our theoretical prediction was numerically examined via Monte Carlo simulations. Our kinetic description highlights the parallel mathematical structure between the financial and physical Brownian motions by a straightforward extension of statistical mechanics.

In this paper, the collapse of a granular column over an erodible bed is investigated experimentally and numerically. Four series of experiments are performed using different materials in order to understand the occurrence of the erosion and its evolution. Three different erosion-deposition regimes are observed in experiments, which primarily depend on the difference in material properties between the column and erodible bed but vary little with the initial aspect ratio of the column. Once the erosion process occurs, the collapsing flow has both longer initial acceleration and final deceleration phases but a shorter intermediate period of constant-velocity flow, a phenomenon that is more prominent when the flow front of collapsing material eventually penetrates into bed material. However, the overall flowing duration satisfies a proportional relationship with the free-fall time of granular column ${\tau }_c$ for both erosion regimes, almost identical to that observed on a rigid substrate. Furthermore, the mechanism of the erosion is discussed based on the evolution of velocity field and the migration of the interface between static and flowing materials. The proposed equation of motion for the flow front shows that the particle density ratio of the column and the erodible bed plays a crucial role in the formation of different erosion-deposition regimes. In addition to reproducing various deposit morphologies observed in our experiments, our numerical simulation results also confirm the existence of critical particle density ratios that correspond to regime transitions and are almost independent of the initial aspect ratio of the column.

In this paper, a coupled discrete unified gas kinetic scheme (CDUGKS) with a flexible Prandtl number is developed for the thermal compressible flows in all Knudsen number regimes. Different from the existing thermal discrete unified gas kinetic scheme based on the Shakhov model, the proposed CDUGKS based on the total energy double-distribution-function model can well preserve the nonnegative property of the distribution function, especially for the strong shock in the continuum regime. In the CDUGKS, the velocity distribution function (VDF) is used to recover the compressible continuity and momentum equations, while the energy distribution function (EDF) is used to recover the energy equation. The VDF and EDF are evaluated in a similar way and then coupled via the thermal equation of state. With the un-splitting treatment of the particle transport and collision in the distribution function evolution and the flux evaluation, the time step in CDUGKS is not limited by the particle collision time. Furthermore, the CDUGKS is an asymptotic preserving scheme, in which the Navier-Stokes solution in the hydrodynamic regime and the free transport mechanism in the kinetic regime can be precisely recovered with the second-order accuracy in both space and time. Finally, several numerical experiments, including the weak shock tube and the strong one in the whole Knudsen number flows, as well as the two-dimensional Riemann problem and the Rayleigh-Taylor instability in both hydrodynamic regime and kinetic regimes, are performed to validate the method. Numerical results agree fairly well with other benchmark results in different flow regimes, which demonstrates the current CDUGKS is a reliable and efficient method for multiscale flow problems.

We present an energy conserving lattice Boltzmann model on a body-centered-cubic arrangement for thermohydrodynamics. It exhibits accurate thermohydrodynamic behavior with a high degree of accuracy and is therefore capable of simulating compressible and thermal hydrodynamics. The theoretical requirements and the methodology to construct this model have been described in detail and can be employed to construct even more accurate models. Simulations of canonical test cases related to compressible flows like shock tube and thermoacoustic convection and thermal flows like viscous heat dissipation and the Rayleigh-Bénard convection are performed to demonstrate the effectiveness of the model.

Using molecular dynamics simulations, we study particle transport in a system of interacting colloidal particles on a ring, where the system is driven by a time-dependent external potential, moving along the ring. We consider two driving protocols: (i) the external potential barrier moves with a uniform velocity $v$ along the ring, and (ii) it moves in discrete jumps with jump length $l$ and waiting time $\tau$ with an effective velocity $v=l/\tau$. The time-averaged (dc) particle current, which always remains positive in case (i), interestingly reverses its direction in case (ii) upon tuning the particle-number density ${\rho }_0$ and the effective barrier velocity $v$. We also find a scaling form for the current in terms of number density, barrier velocity, barrier height, and temperature of the system.

We investigate the behavior of the shortest path on a directed two-dimensional square lattice for bond percolation at the critical probability $p_c$. We observe that flipping an edge lying on the shortest path has a nonlocal effect in the form of power-law distributions for both the differences in shortest path lengths and for the minimal enclosed areas. Using maximum likelihood estimation and extrapolation, we find the exponents $\alpha =1.36\pm 0.01$ for the path length differences and $\beta =1.186\pm 0.001$ for the enclosed areas.

This work examines the emergence of autoresonance (AR) in a one-dimensional chain of strongly nonlinear oscillators subjected to a harmonic force with a slowly varying frequency applied at the end of the chain. The dynamics of the chain is studied assuming 1:1 (fundamental) resonance, when the response of each nonlinear oscillator has a dominant harmonic component with the frequency close to the frequency of the external excitation. Explicit asymptotic equations describing the amplitudes and the phases of the oscillations are derived. These equations demonstrate that, in contrast to the chain with a linear attachment, the strongly nonlinear chain can be entirely captured into resonance provided that its structural and excitation parameters exceed certain critical thresholds but the frequency detuning rate is small enough. It is shown that at large times the amplitudes of all oscillators captured into AR converge to a common monotonically growing quasisteady backbone curve. This implies asymptotic equipartition of energy between the oscillators under the condition of AR. Numerical simulations have been performed for two-, four-, and 12-particle arrays with fixed forcing and coupling parameters and different detuning rates. The obtained results demonstrate the existence of two intervals of the rate's values corresponding to AR and small-amplitude oscillations in the entire chain, respectively, and a narrow gap between these two intervals, wherein each oscillator may escape from resonance individually or in combination with neighboring particles. This implies a negligibly small interval of energy localization in a part of the chain adjacent to the source of energy compared to the interval of the emergence of AR in the entire chain.

Quantum kicked top is a fundamental model for time-dependent, chaotic Hamiltonian system and has been realized in experiments as well. As the quantum kicked top can be represented as a system of qubits, it is also popular as a test bed for the study of measures of quantum correlations, such as entanglement, quantum discord, and other multipartite entanglement measures. Further, earlier studies on kicked top have led to a broad understanding of how these measures are affected by the classical dynamical features. In this work, relying on the invariance of quantum correlation measures under local unitary transformations, it is shown exactly these measures display periodic behavior either as a function of time or as a function of the chaos parameter in this system. As the kicked top has been experimentally realized using cold atoms as well as superconducting qubits, it is pointed out that these periodicities must be factored in while choosing experimental parameters so that repetitions can be avoided.

An outstanding problem of interdisciplinary interest is to understand quantitatively the role of social contacts in contagion dynamics. In general, there are two types of contacts: close ones among friends, colleagues and family members, etc., and ordinary contacts from encounters with strangers. Typically, social reinforcement occurs for close contacts. Taking into account both types of contacts, we develop a contact-based model for social contagion. We find that, associated with the spreading dynamics, for random networks there is coexistence of continuous and discontinuous phase transitions, but for heterogeneous networks the transition is continuous. We also find that ordinary contacts play a crucial role in promoting large-scale spreading, and the number of close contacts determines not only the nature of the phase transitions but also the value of the outbreak threshold in random networks. For heterogeneous networks from the real world, the abundance of close contacts affects the epidemic threshold, while its role in facilitating the spreading depends on the adoption threshold assigned to it. We uncover two striking phenomena. First, a strong interplay between ordinary and close contacts is necessary for generating prevalent spreading. In fact, only when there are propagation paths of reasonable length which involve both close and ordinary contacts are large-scale outbreaks of social contagions possible. Second, abundant close contacts in heterogeneous networks promote both outbreak and spreading of the contagion through the transmission channels among the hubs, when both values of the threshold and transmission rate among ordinary contacts are small. We develop a theoretical framework to obtain an analytic understanding of the main findings on random networks, with support from extensive numerical computations. Overall, ordinary contacts facilitate spreading over the entire network, while close contacts determine the way by which outbreaks occur, i.e., through a second- or first-order phase transition. These results provide quantitative insights into how certain social behaviors can emerge and become prevalent, which has potential implications not only to social science but also to economics and political science.