We investigate the phase diagram of the Sakaguchi-Kuramoto model with a higher-order interaction along with the traditional pairwise interaction. We also introduce asymmetry parameters in both the interaction terms and investigate the collective dynamics and their transitions in the phase diagrams under both unimodal and bimodal frequency distributions. We deduce the evolution equations for the macroscopic order parameters and eventually derive pitchfork and Hopf bifurcation curves. Transition from the incoherent state to standing wave pattern is observed in the presence of the unimodal frequency distribution. In contrast, a rich variety of dynamical states such as the incoherent state, partially synchronized state-I, partially synchronized state-II, and standing wave patterns and transitions among them are observed in the phase diagram via various bifurcation scenarios, including saddle-node and homoclinic bifurcations, in the presence of bimodal frequency distribution. Higher-order coupling enhances the spread of the bistable regions in the phase diagrams and also leads to the manifestation of bistability between incoherent and partially synchronized states even with unimodal frequency distribution, which is otherwise not observed with the pairwise coupling. Further, the asymmetry parameters facilitate the onset of several bistable and multistable regions in the phase diagrams. Very large values of the asymmetry parameters allow the phase diagrams to admit only the monostable dynamical states.

We investigate numerically how the motion of an intruder within a two-dimensional granular system affects its structure and produces drag on the intruder. We made use of discrete numerical simulations in which a larger disk (intruder) is driven at constant speed amid smaller disks confined in a rectangular cell. By varying the intruder's velocity and the basal friction, we obtained the resultant force on the intruder and the instantaneous network of contact forces, which we analyze at both the cell and grain scales. We found that there is a bearing network that percolates forces from the intruder toward the walls, being responsible for jammed regions and high values of the drag force, and a dissipative network that percolates small forces within the grains, in agreement with previous experiments on compressed granular systems. In addition, we found the anisotropy levels of the contact network for different force magnitudes and regions, that the force network can reach regions far downstream of the intruder by the end of the intruder's motion, that the extent of the force network decreases with decreasing the basal friction, and that the void region (cavity) that appears downstream of the intruder tends to disappear for lower values of the basal friction. Interestingly, our results show that grains within the bearing chains creep while the chains break, revealing the mechanism by which bearing chains collapse.

We developed an integer lattice gas method for the fluctuating diffusion equation. Such a method is unconditionally stable and able to recover the Poisson distribution for the microscopic densities. A key advance for integer lattice gases introduced in this paper is a sampling collision operator that replaces particle collisions with sampling from an equilibrium distribution. This can increase the efficiency of our integer lattice gas by several orders of magnitude.

We revisit the optimal performance of a thermoelectric generator within the endoreversible approximation, while imposing a finite physical dimensions constraint in the form of a fixed total area of the heat exchangers. Our analysis is based on the linear-irreversible law for heat transfer between the reservoir and the working medium, in contrast to Newton's law usually assumed in literature. The optimization of power output is performed with respect to the thermoelectric current as well as the fractional area of the heat exchangers. We describe two alternate designs for allocating optimal areas to the heat exchangers. Interestingly, for each design, the use of linear-irreversible law yields the efficiency at maximum power in the well-known form $2{\eta }_{\mathrm{C}}^{}/(4-{\eta }_{\mathrm{C}}^{})$, earlier obtained for the case of thermoelectric generator under exoreversible approximation, i.e., assuming only the internal irreversibility due to Joule heating. On the other hand, the use of Newton's law yields Curzon-Ahlborn efficiency.

There are few exactly solvable lattice models and even fewer solvable quantum lattice models. Here we address the problem of finding the spectrum of the tight-binding model (equivalently, the spectrum of the adjacency matrix) on Cayley trees. Recent approaches to the problem have relied on the similarity between the Cayley tree and the Bethe lattice. Here, we avoid to make any ansatz related to the Bethe lattice due to fundamental differences between the two lattices that persist even when taking the thermodynamic limit. Instead, we show that one can use a recursive procedure that starts from the boundary and then use the canonical basis to derive the complete spectrum of the tight-binding model on Cayley trees. Our resulting algorithm is extremely efficient, as witnessed with remarkable large trees having hundreds of shells. We also show that, in the thermodynamic limit, the density of states is dramatically different from that of the Bethe lattice.

We study the dynamics and statistics of the Rule 150 reversible cellular automaton (RCA). This is a one-dimensional lattice system of binary variables with synchronous (Floquet) dynamics that corresponds to a bulk deterministic and reversible discretized version of the kinetically constrained “exclusive one-spin facilitated” (XOR) Fredrickson-Andersen (FA) model, where the local dynamics is restricted: A site flips if and only if its adjacent sites are in different states from each other. Similar to other RCA that have been recently studied, such as Rule 54 and Rule 201, the Rule 150 RCA is integrable, however, in contrast is noninteracting: The emergent quasiparticles, which are identified by the domain walls, behave as free fermions. This property allows us to solve the model by means of matrix product ansatz. In particular, we find the exact equilibrium and nonequilibrium stationary states for systems with closed (periodic) and open (stochastic) boundaries, respectively, resolve the full spectrum of the time evolution operator and, therefore, gain access to the relaxation dynamics, and obtain the exact large deviation statistics of dynamical observables in the long-time limit.

Systems of interacting bosons in triple-well potentials are of significant theoretical and experimental interest. They are explored in contexts that range from quantum phase transitions and quantum dynamics to semiclassical analysis. Here, we systematically investigate the onset of quantum chaos in a triple-well model that moves away from integrability as its potential gets tilted. Even in its deepest chaotic regime, the system presents features reminiscent of integrability. Our studies are based on level spacing distribution and spectral form factor, structure of the eigenstates, and diagonal and off-diagonal elements of observables in relationship to the eigenstate thermalization hypothesis. With only three sites, the system's eigenstates are at the brink of becoming fully chaotic, so they do not yet exhibit Gaussian distributions, which resonates with the results for the observables.

The existence of two structural forms in liquid water has been a point of discussion for a long time. A phase transition between these two forms of liquid water has been proposed based on evidence from molecular simulations, and experiments have also been very recently able to track the proposed transition of the low-density liquid form to the high-density liquid form. We propose to use the average angle an oxygen atom makes with its neighbors to describe the structural environment of a water molecule. The distribution of this order parameter is observed to have two peaks with one peak at $\sim 109.5^{\circ }$, corresponding to the internal angle of a regular tetrahedron, indicating tetrahedral arrangement. The other peak corresponds to an environment with a tighter arrangement of neighboring molecules. The distribution of O-O-O angles is decomposed into two skewed distributions to estimate the fractions of the two liquid forms in water. A good similarity is observed between the temperature and pressure trends of fractions of locally favored tetrahedral structure (LFTS) form estimated using the new order parameter and the reports in the literature, over a range of temperatures and pressures. We also compare the structural environments indicated by different order parameters and find that the order parameter proposed in this paper captures the structure of first solvation shell of the LFTS accurately.

There is great interest in using near-term quantum computers to simulate and study foundational problems in quantum mechanics and quantum information science, such as the scrambling measured by an out-of-time-ordered correlator (OTOC). Here we use an IBM Q processor, quantum error mitigation, and weaved Trotter simulation to study high-resolution operator spreading in a four-spin Ising model as a function of space, time, and integrability. Reaching four spins while retaining high circuit fidelity is made possible by the use of a physically motivated fixed-node variant of the OTOC, allowing scrambling to be estimated without overhead. We find clear signatures of a ballistic operator spreading in a chaotic regime, as well as operator localization in an integrable regime. The techniques developed and demonstrated here open up the possibility of using cloud-based quantum computers to study and visualize scrambling phenomena, as well as quantum information dynamics more generally.

We simulate Korteweg–de Vries (KdV) and dissipationless Burgers equations using $\delta$-correlated random noise as an initial condition. We observe that the energy fluxes of the two equations remain zero throughout, thus, indicating their equilibrium nature. We characterize the equilibrium states using Gaussian probability distribution for the real space field, and using Boltzmann distribution for the modal energy. We show that the single soliton of the KdV equation too exhibits zero energy flux, hence, it is in equilibrium. We argue that the energy flux is a good measure for ascertaining whether a system is in equilibrium or not.

The dynamics of two active nonlinear resonators coupled to a linear resonator is studied theoretically. Possible stationary states and their dynamical stability are considered in detail. Spontaneous symmetry breaking is found and it is shown that this bifurcation results in the formation of asymmetric states. It is also found that the oscillating states can occur in the system in a certain range of parameters. The results of the analysis of the stationary states are confirmed by direct numerical simulations. The possibility of switching between different states is also demonstrated by numerical experiments.

We carry out overdamped simulations in a simple model of jamming—a collection of bidisperse soft core frictionless disks in two dimensions—with the aim to explore the finite size dependence of different quantities, both the relaxation time obtained from the relaxation of the energy and the pressure equivalent of the shear viscosity. The motivation for the paper is the observation [Nishikawa et al., J. Stat. Phys. 182, 37 (2021)] that there are finite size effects in the relaxation time, $\tau$, that give problems in the determination of the critical divergence, and the claim that this is due to a finite size dependence, $\tau \sim lnN$, which makes $\tau$ an ill-defined quantity. Beside analyses to determine the relaxation time for the whole system we determine particle relaxation times which allow us to determine both histograms of particle relaxation times and the average particle relaxation times—two quantities that are very useful for the analyses. The starting configurations for the relaxation simulations are of two different kinds—completely random or taken from steady shearing simulations—and we find that the difference between these two cases are bigger than previously noted and that the observed problems in the determination of the critical divergence obtained when starting from random configurations are not present when instead starting the relaxations from shearing configurations. We also argue that the the effect that causes the $lnN$ dependence is not as problematic as asserted. When it comes to the finite size dependence of the pressure equivalent of the shear viscosity we find that our data don't give support for the claimed strong finite size dependence, but also that the finite size dependence is at odds with what one would normally expect for a system with a diverging correlation length, and that this calls for an alternative understanding of the phenomenon of shear-driven jamming.

Transport processes in porous media are controlled by the characteristics of the flow field which are determined by the porous material properties and the boundary conditions of the system. This work provides experimental evidence of the relation between mixing and flow field topology in porous media at the continuum scale. The setup consists of a homogeneously packed quasi-two-dimensional flow-through chamber in which transient flow conditions, dynamically controlled by two external reservoirs, impact the transport of a dissolved tracer. The experiments were performed at two different flow velocities, corresponding to Péclet numbers of 191 and 565, respectively. The model-based interpretation of the experimental results shows that high values of the effective Okubo-Weiss parameter, driven by the changes of the boundary conditions, lead to high rates of increase of the Shannon entropy of the tracer distribution and, thus, to enhanced mixing. The comparison between a hydrodynamic dispersion model and an equivalent pore diffusion model demonstrates that despite the spatial and temporal variability in the hydrodynamic dispersion coefficients, the Shannon entropy remains almost unchanged because it is controlled by the Okubo-Weiss parameter. Overall, our work demonstrates that under highly transient boundary conditions, mixing dynamics in homogeneous porous media can also display complex patterns and is controlled by the flow topology.

Important microfluidic phenomena, such as droplet deformation and cell motion, are impacted by the formation of Debye layers at charged interfaces. Previous studies examined interface problems with leaky dielectrics or the formation of diffuse charge layers. In most cases, the results are derived for weakly curved spherical geometries. Moreover, many studies of streaming-potential phenomena at fluid-solid interfaces lack a macroscale description of effects that are higher than first order. An asymptotic methodology capturing both complex surface geometries and an accurate description of higher-order phenomena is presented in this study. For this purpose, we consider a generic streaming-potential problem. As a result, the complex three-dimensional electrohydrodynamics in the Debye layer are entailed in two-dimensional discontinuity conditions. The latter contain a free parameter, the layer thickness, which mathematically represents the discontinuity position within the Debye layer. It can be used to derive an alternative definition of the Debye thickness capturing the influence of the $\zeta$ potential. We introduce a virtual particle whose outer boundary envelopes the solid particle plus a fraction of the Debye layer. It interacts with the macroscopic flow while incorporating the detailed electrohydrodynamics inside the layer.

Instabilities in stratified precessing fluid are investigated. We extend the study by Mahalov [Phys. Fluids A 5, 891 (1993)] in the stably stratified Boussinesq framework, with an external Coriolis force (with rate ${\mathrm{\Omega }}_p$) altering the base flow through the distortion of the circular streamlines of the unperturbed axially stratified rotating columns (with constant vorticity $2\mathrm{\Omega }.$) It is shown that the inviscid part of the modified velocity flow $(0,\mathrm{\Omega }r,-2\varepsilon \mathrm{\Omega }rsin\phi )$ and buoyancy with gradient $N^2(-2\varepsilon cos\phi ,2\varepsilon sin\phi ,1)$ are an exact solution of Boussinesq-Euler equations. Here $(r,\phi ,z)$ is a cylindrical coordinate system, with $\varepsilon ={\mathrm{\Omega }}_p/\mathrm{\Omega }$ being the Poincaré number and $N$ the Brunt-Väisälä frequency. The base flow is transformed into a Cartesian coordinate system, and the stability of a superimposed perturbation is studied in terms of Fourier (or Kelvin) modes. The resulting Floquet system for the Fourier modes has three parameters: $\varepsilon ,$ $\mathcal{N}=N/\mathrm{\Omega }$, and $\mu$, which is the angle between the wave vector $\mathit{k}$ and the solid-body rotation axis in the limit $\varepsilon =0.$ In this limit, there are inertia-gravity waves propagating with frequency $\pm \omega$ and the resonant cases are those for which $2\omega =n\mathrm{\Omega }$, $n$ being an integer. We perform an asymptotic analysis to leading order in $\varepsilon$ and characterize the destabilizing resonant case of order $n=1$ (i.e., the subharmonic instability) which exists and for $0\le N<\mathrm{\Omega }/2.$ In this range, the subharmonic instability remains the strongest with a maximal growth rate ${\sigma }_m=[\varepsilon (5\sqrt{15}/8)\sqrt{1-4{\mathcal{N}}^2}/(4-{\mathcal{N}}^2)].$ Stable stratification acts in such a way as to make the subharmonic instability less efficient, so as it disappears for $N\ge 0.5\mathrm{\Omega }.$ The destabilizing resonant cases of order $n=2,3,4,5$ are investigated in detail by numerical computations. The effect of viscosity on these instabilities is briefly addressed assuming the diffusive coefficients (kinematic and thermal) are equal. Likewise, we briefly investigate the case where $N^2<0$ and show that the instability associated to the mode with $k_3=0$ is the strongest.

We extend the paradigmatic and versatile totally asymmetric simple exclusion process (TASEP) for stochastic 1D transport to allow for two different particle species, each having specific entry and exit rates. We offer a complete mean-field analysis, including a phase diagram, by mapping this model onto an effective one-species TASEP. Stochastic simulations confirm the results, but indicate deviations when the particle species have very different exit rates. We illustrate that this is due to a phenomenon of intermittency, and formulate a refined “intermittent” mean-field theory for this regime. We discuss how nonstationary effects may further enrich the phenomenology.

We study the percolation of randomly rotating patchy particles on 11 Archimedean lattices in two dimensions. Each vertex of the lattice is occupied by a particle, and in each model the patch size and number are monodisperse. When there are more than one patches on the surface of a particle, they are symmetrically decorated. As the proportion $\chi$ of the particle surface covered by the patches increases, the clusters connected by the patches grow and the system percolates at the threshold ${\chi }_c$. We combine Monte Carlo simulations and the critical polynomial method to give precise estimates of ${\chi }_c$ for disks with one to six patches and spheres with one to two patches on the 11 lattices. For one-patch particles, we find that the order of ${\chi }_c$ values for particles on different lattices is the same as that of threshold values $p_c$ for site percolation on these lattices, which implies that ${\chi }_c$ for one-patch particles mainly depends on the geometry of lattices. For particles with more patches, symmetry becomes very important in determining ${\chi }_c$. With the estimates of ${\chi }_c$ for disks with one to six patches, using analyses related to symmetry, we are able to give precise values of ${\chi }_c$ for disks with an arbitrary number of patches on all 11 lattices. The following rules are found for patchy disks on each of these lattices: (1) as the number of patches $n$ increases, values of ${\chi }_c$ repeat in a periodic way, with the period $n_0$ determined by the symmetry of the lattice; (2) when $mod(n,n_0)=0$, the minimum threshold value ${\chi }_{\min }$ appears, and the model is equivalent to site percolation with ${\chi }_{\min }=p_c$; and (3) disks with $mod(n,n_0)=m$ and $n_0-m$ ($m<n_0/2$) share the same ${\chi }_c$ value. The results can be useful references for studying the connectivity of patchy particles on two-dimensional lattices at finite temperatures.

Temperature-dependent Smoluchowski equations describe the ballistic agglomeration. In contrast to the standard Smoluchowski equations for the evolution of cluster densities, with constant rate coefficients, the temperature-dependent equations describe both—the evolution of the densities as well as cluster temperatures, which determine the agglomeration rates. To solve these equations, we develop a Monte Carlo technique based on the low-rank approximation for the aggregation kernel. Using this highly effective approach, we perform a comprehensive study of the kinetic phase diagram of the system and reveal a few surprising regimes, including permanent temperature growth and “density separation” regime, with a large gap in the size distribution for middle-size clusters. We perform scaling analysis and classify the aggregation kernels for the temperature-dependent equations. Furthermore, we conjecture the lack of gelation in such systems. The results of the scaling theory agree well with the simulation data.

Classical density functional theory for finite temperatures is usually formulated in the grand-canonical ensemble where arbitrary variations of the local density are possible. However, in many cases the systems of interest are closed with respect to mass, e.g., canonical systems with fixed temperature and particle number. Although the tools of standard, grand-canonical density functional theory are often used in an ad hoc manner to study closed systems, their formulation directly in the canonical ensemble has so far not been known. In this work, the fundamental theorems underlying classical DFT are revisited and carefully compared in the two ensembles showing that there are only trivial formal differences. The practicality of DFT in the canonical ensemble is then illustrated by deriving the exact Helmholtz functional for several systems: the ideal gas, certain restricted geometries in arbitrary numbers of dimensions, and, finally, a system of two hard spheres in one dimension (hard rods) in a small cavity. Some remarkable similarities between the ensembles are apparent even for small systems with the latter showing strong echoes of the famous exact of result of Percus in the grand-canonical ensemble.