In this paper, we study the quantum self-contained refrigerator [Linden et al., Phys. Rev. Lett. 105, 130401 (2010)] in the strong internal coupling regime with engineered reservoirs. We find that if some modes of the three thermal reservoirs can be properly filtered out, the efficiency and the working domain of the refrigerator can be improved in contrast to the those in the weak internal coupling regime, which indicates one advantage of the strong internal coupling. In addition, we find that the background natural vacuum reservoir could cause the filtered refrigerator to stop working and the background natural thermal reservoir could greatly reduce the cooling efficiency.

The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial “temperature” $T$ and the sign of the Ising coupling. Based on our numerical results, we propose that at the Ising critical temperature $T_c$ the model is compatible with the universality class of two-dimensional (2D) self-avoiding walk (SAW). Especially the fractal dimension of the loops, which are defined as the external frontier of the avalanches, is very close to $D_f^{\text{SAW}}=\frac{4}{3}$. Also, the corresponding open curves has conformal invariance with the root-mean-square distance $R_{\text{rms}}\sim t^{3/4}$ ($t$ being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at $T=T_c$ the model has some aspects compatible with the 2D BTW model (e.g., the $1/log\left(L\right)$-dependence of the exponents of the distribution functions) and some in accordance with the Ising model (e.g., the $1/L$-dependence of the fractal dimensions). The finite-size scaling theory is tested and shown to be fulfilled for all statistical observables in $T=T_c$. In the off-critical temperatures in the close vicinity of $T_c$ the exponents show some additional power-law behaviors in terms of $T-T_c$ with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with $L^{\frac{1}{2}}$, which is different from the regular 2D BTW model.

Experimental evidence of the scalar convergence towards a global strange eigenmode independent of the scalar initial condition in chaotic mixing is provided. This convergence, underpinning the independent nature of chaotic mixing in any passive scalar, is presented by scalar fields with different initial conditions casting statistically similar shapes when advected by periodic unsteady flows. As the scalar patterns converge towards a global strange eigenmode, the scalar filaments, locally aligned with the direction of maximum stretching, as described by the Lagrangian stretching theory, stack together in an inhomogeneous pattern at distances smaller than their asymptotic minimum widths. The scalar variance decay becomes then exponential and independent of the scalar diffusivity or initial condition. In this work, mixing is achieved by advecting the scalar using a set of laminar flows with unsteady periodic topology. These flows, that resemble the tendril-whorl map, are obtained by morphing the forcing geometry in an electromagnetic free surface 2D mixing experiment. This forcing generates a velocity field which periodically switches between two concentric hyperbolic and elliptic stagnation points. In agreement with previous literature, the velocity fields obtained produce a chaotic mixer with two regions: a central mixing and an external extensional area. These two regions are interconnected through two pairs of fluid conduits which transfer clean and dyed fluid from the extensional area towards the mixing region and a homogenized mixture from the mixing area towards the extensional region.

The stability of powergrid is crucial since its disruption affects systems ranging from street lightings to hospital life-support systems. While short-term dynamics of single-event cascading failures have been extensively studied, less is understood on the long-term evolution and self-organization of powergrids. In this paper, we introduce a simple model of evolving powergrid and establish its connection with the sandpile model and earthquakes, i.e., self-organized systems with intermittent strain releases. Various aspects during its self-organization are examined, including blackout magnitudes, their interevent waiting time, the predictability of large blackouts, as well as the spatiotemporal rescaling of blackout data. We examined the self-organized strain releases on simulated networks as well as the IEEE 118-bus system, and we show that both simulated and empirical blackout waiting times can be rescaled in space and time similarly to those observed between earthquakes. Finally, we suggested proactive maintenance strategies to drive the powergrids away from self-organization to suppress large blackouts.

An alternative approach for deriving the equation of state for a two-dimensional lattice gas is proposed, based on arguments similar to those used in the derivation of the Langmuir-Szyszkowski equation of state for localized adsorption. The relationship between surface coverage and excluded area is first extracted from random sequential adsorption simulations incorporating surface diffusion (RSAD). The adsorption isotherm is then obtained using kinetic arguments, and the Gibbs equation gives the relation between surface pressure and coverage. Provided surface diffusion is fast enough to ensure internal equilibrium within the monolayer during the RSAD simulations, the resulting equations of state are very close to the most accurate equivalents obtained by cumbersome thermodynamic methods. An internal test of the accuracy of the method is obtained by noting that adsorption RSAD simulations starting from an empty lattice and desorption simulations starting from a full lattice provide convergent upper and lower bounds on the surface pressure.

Solid-oxide fuel cells produce electric current from energy released by a spontaneous electrochemical reaction. The efficiency of these devices depends crucially on the microstructure of their electrodes and in particular on the three-phase boundary (TPB) length, along which the energy-producing reaction occurs. We present a systematic maximization of the TPB length as a function of four readily controllable microstructural parameters, for any given mean hydraulic radius, which is a conventional measure of the permeability to gas flow. We identify the maximizing parameters and show that the TPB length can be increased by a factor of over 300% compared to current common practices. We support this result by calculating the TPB of several numerically simulated structures. We also compare four models for a single intergranular contact in the sintered electrode and show that the model commonly used in the literature is oversimplified and unphysical. We then propose two alternatives.

We investigate the erosive growth of channels in a thin subsurface sedimentary layer driven by hydrodynamic drag toward understanding subterranean networks and their relation to river networks charged by ground water. Building on a model based on experimental observations of fluid-driven evolution of bed porosity, we focus on the characteristics of the channel growth and their bifurcations in a horizontal rectangular domain subject to various fluid source and sink distributions. We find that the erosion front between low- and high-porosity regions becomes unstable, giving rise to branched channel networks, depending on the spatial fluctuations of the fluid flow near the front and the degree to which the flow is above the erodibility threshold of the medium. Focusing on the growth of a network starting from a single channel, and by identifying the channel heads and their branch points, we find that the number of branches increases sublinearly and is affected by the source distribution. The mean angles between branches are found to be systematically lower than river networks in humid climates and depend on the domain geometry.

Hydraulic fracture trajectories in rocks and other materials are highly affected by spatial heterogeneity in their mechanical properties. Understanding the complexity and structure of fluid-driven fractures and their deviation from the predictions of homogenized theories is a practical problem in engineering and geoscience. We conduct a Monte Carlo simulation study to characterize the influence of heterogeneous mechanical properties on the trajectories of hydraulic fractures propagating in elastic media. We generate a large number of random fields of mechanical properties and simulate pressure-driven fracture propagation using a phase-field model. We model the mechanical response of the material as that of an elastic isotropic material with heterogeneous Young modulus and Griffith energy release rate, assuming that fractures propagate in the toughness-dominated regime. Our study shows that the variance and the spatial covariance of the mechanical properties are controlling factors in the tortuousness of the fracture paths. We characterize the deviation of fracture paths from the homogenous case statistically, and conclude that the maximum deviation grows linearly with the distance from the injection point. Additionally, fracture path deviations seem to be normally distributed, suggesting that fracture propagation in the toughness-dominated regime may be described as a random walk.

Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms. The latent representation of the Boltzmann machines can be designed to mediate complex interactions and identify clusters of the physical system. We demonstrate these findings with concrete examples of the classical Ising model with and without four-spin plaquette interactions. In the future, automatic searches in the algorithm space parametrized by Boltzmann machines may discover more innovative Monte Carlo updates.

If a system is driven at finite rate through a phase transition by varying an intensive parameter, the order parameter shatters into finite domains. The Kibble-Zurek mechanism predicts the typical size of these domains, which are governed only by the rate of driving and the spatial and dynamical critical exponents. We show that also the irreversible entropy production fulfills a universal behavior, which however is determined by an additional critical exponent corresponding to the intensive control parameter. Our universal prediction is numerically tested in two systems exhibiting noise-induced phase transitions.

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth $b$ and a QKR of chaos parameter $\alpha$, the appropriate FRCG model has the effective range $d=b^2/N={\alpha }^2/N$, for large $N$ matrix dimensionality. As $d$ increases, there is a transition from Poisson to classical random matrix statistics.

Patra et al. [Int. J. Bifurcat. Chaos 26, 1650089 (2016)] recently showed that the time-averaged rates of entropy production and phase-space volume contraction are equal for several different molecular dynamics methods used to simulate nonequilibrium steady states in Hamiltonian systems with thermostated temperature gradients. This equality is a plausible statistical analog of the second law of thermodynamics. Here we show that those two rates are identically equal in a wide class of methods in which the thermostat variables $\mathbf{z}$ are determined by ordinary differential equations of motion (i.e., methods of the Nosé-Hoover or integral feedback control type). This class of methods is defined by three relatively innocuous restrictions which are typically satisfied in methods of this type.

We investigate the properties of a two-state sandpile model subjected to a confining potential in two dimensions. From the microdynamical description, we derive a diffusion equation, and find a stationary solution for the case of a parabolic confining potential. By studying the systems at different confining conditions, we observe two scale-invariant regimes. At a given confining potential strength, the cluster size distribution takes the form of a power law. This regime corresponds to the situation in which the density at the center of the system approaches the critical percolation threshold. The analysis of the fractal dimension of the largest cluster frontier provides evidence that this regime is reminiscent of gradient percolation. By increasing further the confining potential, most of the particles coalesce in a giant cluster, and we observe a regime where the jump size distribution takes the form of a power law. The onset of this second regime is signaled by a maximum in the fluctuation of energy.

The quantum fluctuations of the entropy production for fermionic systems in the Landauer-Büttiker nonequilibrium steady state are investigated. The probability distribution, governing these fluctuations, is explicitly derived by means of quantum field theory methods and analyzed in the zero frequency limit. It turns out that microscopic processes with positive, vanishing and negative entropy production occur in the system with nonvanishing probability. In spite of this fact, we show that all odd moments (in particular, the mean value of the entropy production) of the above distribution are non-negative. This result extends the second principle of thermodynamics to the quantum fluctuations of the entropy production in the Landauer-Büttiker state. The effect of the time reversal is also discussed.

The classical self-oscillations can collapse merely due to their mutual couplings. We investigate this oscillation collapse in quantum van der Pol oscillators. For a pair of quantum oscillators, the steady-state mean phonon number is shown to be lower than in the corresponding classical model with a Gaussian white noise that mimics quantum noise. We further show within the mean-field theory that a number of globally coupled oscillators undergo a transition from the synchronized periodic motion to the collective oscillation collapse. A quantum many-body simulation suggests that the increase in the number of oscillators leads to a lower steady-state mean phonon number, bounded below by the mean-field result.

Crawling cell motility is vital to many biological processes such as wound healing and the immune response. Using a minimal model we investigate the effects of patterned substrate adhesiveness and biophysical cell parameters on the direction of cell motion. We show that cells with low adhesion site formation rates may move perpendicular to adhesive stripes while those with high adhesion site formation rates results in motility only parallel to the substrate stripes. We explore the effects of varying the substrate pattern geometry and the strength of actin polymerization on the directionality of the crawling cell. These results reveal that high strength of actin polymerization results in motion perpendicular to substrate stripes only when the substrate is relatively nonadhesive; in particular, this suggests potential applications in motile cell sorting and guiding on engineered substrates.

Microscopic swimming particles, which dissipate energy to execute persistent directed motion, are a classic example of a nonequilibrium system. We investigate the noninteracting Ornstein-Uhlenbeck Particle (OUP), which is propelled through a viscous medium by a force which is correlated over a finite time. We obtain an exact expression for the steady-state phase-space density of a single OUP confined by a quadratic potential, and use the result to explore more complex geometries, both through analytical approximations and numerical simulations. In a “Casimir”-style setup involving two narrowly spaced walls, we describe a particle-trapping phenomenon, which leads to a repulsive effective interaction between the walls, while in a two-dimensional annulus geometry, we observe net stresses which resemble the Laplace pressure.

In compressive fracture of dry plexiform bone, we examine the individual roles of overall mean porosity, the connectivity of the porosity network, and the elastic as well as the failure properties of the nonporous matrix, using a random spring network model (RSNM). Porosity network structure is shown to reduce the compressive strength by up to 30%. However, the load-bearing capacity increases with an increase in either of the matrix properties—the elastic modulus or the failure strain threshold. To validate the porosity-based RSNM model with available experimental data, bone-specific failure strain thresholds for the ideal matrix of similar elastic properties were estimated to be within 60% of each other. Further, we observe the avalanche size exponents to be independent of the bone-dependent parameters as well as the structure of the porosity network.

Strong collisional shocks in multi-ion plasmas are featured in many high-energy-density environments, including inertial confinement fusion implosions. However, their basic structure and its dependence on key parameters (e.g., the Mach number and the plasma ion composition) are poorly understood, and inconsistencies in that regard remain in the literature. In particular, the shock width's dependence on the Mach number has been hotly debated for decades. Using a high-fidelity Vlasov-Fokker-Planck code, iFP, and direct comparisons to multi-ion hydrodynamic simulations and semianalytic predictions, we resolve the structure of steady-state planar shocks in D-${}^3\mathrm{He}$ plasmas. Additionally, we derive and confirm with kinetic simulations a quantitative description of the dependence of the shock width on the Mach number and initial ion concentration.