We study models of correlated percolation where there are constraints on the occupation of sites that mimic force balance, i.e., for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions. We prove rigorously that $p_c<1$ for the two-dimensional models studied. Numerical data indicate that the force-balance percolation transition is discontinuous with a growing crossover length, with perhaps the same form as the jamming percolation models, suggesting that all models belong to the same universality class with the same underlying mechanism driving the transition in both cases. We find a lower bound for the correlation length in the connected phase and that the correlation function does not appear to be a power law at the transition. Finally, we study the dynamics of the culling procedure invoked to obtain the force-balance configurations and find a dynamical exponent similar to that found in sandpile models.

We study critical properties of the relaxation time at a threshold point in switching processes between bistable states under change in external fields. In particular, we investigate the relaxation processes near the spinodal point of the infinitely long-range interaction model (the Husimi-Temperley model) by analyzing the scaling properties of the corresponding Fokker-Planck equation. We also confirm the obtained scaling relations by direct numerical solution of the original master equation, and by kinetic Monte Carlo simulation of the stochastic decay process. In particular, we study the asymptotic forms of the divergence of the relaxation time near the spinodal point and re-examine its scaling properties. We further extend the analysis to transient critical phenomena such as a threshold behavior with diverging switching time under a general external driving perturbation. This models photoexcitation processes in spin-crossover materials. In the ongoing development of nanosize fabrication, such size-dependence of switching processes should be an important issue, and the properties obtained here will be applicable to a wide range of physical processes.

We consider different Markovian embedding schemes of non-Markovian stochastic processes that are described by generalized Langevin equations and obey thermal detailed balance under equilibrium conditions. At thermal equilibrium, superdiffusive behavior can emerge if the total integral of the memory kernel vanishes. Such a situation of vanishing static friction is caused by a super-Ohmic thermal bath. One of the simplest models of ballistic superdiffusion is determined by a biexponential memory kernel that was proposed by [Bao J. Stat. Phys. 114, 503 (2004)]. We show that this non-Markovian model has infinitely many different four-dimensional Markovian embeddings. Implementing numerically the simplest one, we demonstrate that (i) the presence of a periodic potential with arbitrarily low barriers changes the asymptotic large-time behavior from free ballistic superdiffusion into normal diffusion; (ii) an additional biasing force renders the asymptotic dynamics superdiffusive again. The development of transients that display a qualitatively different behavior compared to the true large-time asymptotics presents a general feature of this non-Markovian dynamics. These transients though may be extremely long. As a consequence, they can be even mistaken as the true asymptotics. We find that such intermediate asymptotics exhibit a giant enhancement of superdiffusion in tilted washboard potentials and it is accompanied by a giant transient superballistic current growing proportional to $t^{{\alpha }_{\text{eff}}}$ with an exponent ${\alpha }_{\text{eff}}$ that can exceed the ballistic value of 2.

We examine the effect of the phase-resetting curve on the transfer of correlated input signals into correlated output spikes in a class of neural models receiving noisy superthreshold stimulation. We use linear-response theory to approximate the spike correlation coefficient in terms of moments of the associated exit time problem and contrast the results for type I vs type II models and across the different time scales over which spike correlations can be assessed. We find that, on long time scales, type I oscillators transfer correlations much more efficiently than type II oscillators. On short time scales this trend reverses, with the relative efficiency switching at a time scale that depends on the mean and standard deviation of input currents. This switch occurs over time scales that could be exploited by downstream circuits.

Mixing within sessile drops can be enhanced by generating internal flow patterns using ac electrowetting. While for low ac frequencies, the flow patterns have been attributed to oscillations of the drop surface, we provide here the driving mechanism of the hitherto unexplained high-frequency flows. We show that: (1) the electric field in the liquid bulk becomes important, leading to energy dissipation due to Joule heating and a temperature increase of several degrees Celsius, and (2) the fluid flow at these frequencies is generated by electrothermal effect, i.e., gradients in temperature give rise to gradients in conductivity and permittivity, the electric field acting on these inhomogeneities induces an electrical body force that generates the flow. We solved numerically the equations for the electric, temperature and flow fields. The temperature is obtained from a convection-diffusion equation where Joule heating is introduced as a source term. From the solution of the electric field and the temperature, we compute the electrical force that acts as a body force in Stokes equations. Our numerical results agree with previous experimental observations.

An unsteady electrohydrodynamic flow of two viscous immiscible liquids in a channel is theoretically investigated. The flow is caused by an oscillating electric field whose intensity vector has both normal and tangential components on the interface between the liquids. The velocity profile and flow rates of the liquids are found for steady-state oscillatory flows. The limiting cases of constant and high-frequency fields are discussed.

Transformation-based cylindrical cloaks and concentrators are illuminated with nonmonochromatic waves and unusual effects are observed with interesting potential applications. The transient responses of the devices are studied numerically with the finite-difference time-domain method and the results are verified with analytical formulas. We compute the effective bandwidth of several cloaking schemes as well as the effect of losses on the performance of the structures. We also find that narrowband behavior, frequency shift effects, time delays, and spatial disturbances of the incoming waves are dominant due to the inherently dispersive nature of the devices. These effects are important and should be taken into account when designing metamaterial-based devices.

The nonlinear Schrödinger equation in the presence of disorder is considered. The dynamics of an initially localized wave packet is studied. A subdiffusive spreading of the wave packet is explained in the framework of a continuous time random walk. A probabilistic description of subdiffusion is suggested, and a transport exponent of subdiffusion is obtained to be 2/5.

Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional weakly site-diluted Ising model with spin concentrations $p=0.95$ and 0.8 at criticality. In contrast to studies of the critical behavior of the pure systems by the short-time dynamics method, our investigations of site-diluted Ising model have revealed three stages of the dynamic evolution characterizing a crossover phenomenon from the critical behavior typical for the pure systems to behavior determined by the influence of disorder. The static and dynamic critical exponents are determined with the use of the corrections to scaling for systems starting separately from ordered and disordered initial states. The obtained values of the exponents demonstrate a universal behavior of weakly site-diluted Ising model in the critical region. The values of the exponents are compared to results of numerical simulations which have been obtained in various works and, also, with results of the renormalization-group description of this model.

We develop a systematic coarse-graining procedure which establishes the connection between models of mixtures of immiscible fluids at different length and time scales. We start from the Cahn-Hilliard model of spinodal decomposition in a binary fluid mixture under flow from which we derive the coarse-grained description. The crucial step in this procedure is to identify the relevant coarse-grained variables and find the appropriate mapping which expresses them in terms of the more microscopic variables. In order to capture the physics of the Doi-Ohta level, we introduce the interfacial width as an additional variable at that level. In this way, we account for the stretching of the interface under flow and derive analytically the convective behavior of the relevant coarse-grained variables, which in the long wavelength limit recovers the familiar phenomenological Doi-Ohta model. In addition, we obtain the expression for the interfacial tension in terms of the Cahn-Hilliard parameters as a direct result of the developed coarse-graining procedure. Finally, by analyzing the numerical results obtained from the simulations on the Cahn-Hilliard level, we discuss that dissipative processes at the Doi-Ohta level are of the same origin as in the Cahn-Hilliard model. The way to estimate the interface relaxation times of the Doi-Ohta model from the underlying morphology dynamics simulated at the Cahn-Hilliard level is established.

The effects of the damaged car evacuation $\left(P_{exit}\right)$ and the collision $\left(P_{col}\right)$ probabilities on the traffic flow behavior of a car accident are investigated in the one-dimensional cellular automaton Nagel-Schreckenberg model, with injecting $\left(\alpha \right)$ and extracting $\left(\beta \right)$ rates in parallel dynamics. In this study, we suppose that the car involved in collision is evacuated from the road, with an exit probability $P_{exit}$. It is found that the behaviors of density, current, and $\left(\alpha ,\beta \right)$ phase diagram topology depend strongly on the values of $P_{exit}$ and $P_{col}$. Indeed, the high-density region shrinks when increasing $P_{exit}$. Moreover, the critical value ${\alpha }_c\left(\beta \right)$, at which the low-density–high-density transition occurs, increases when increasing $P_{col}$ and/or $P_{exit}$. Furthermore, the critical value at which the transition high-density–low-density occurs decreases when increasing $\beta$ and increases with $\alpha$.

We study the critical properties of a nonequilibrium statistical model, the majority-vote model, on heptagonal and dual heptagonal lattices. Such lattices have the special feature that they only can be embedded in negatively curved surfaces. We find, by using Monte Carlo simulations and finite-size analysis, that the critical exponents $1/\nu$, $\beta /\nu$, and $\gamma /\nu$ are different from those of the majority-vote model on regular lattices with periodic boundary condition, which belongs to the same universality class as the equilibrium Ising model. The exponents are also from those of the Ising model on a hyperbolic lattice. We argue that the disagreement is caused by the effective dimensionality of the hyperbolic lattices. By comparative studies, we find that the critical exponents of the majority-vote model on hyperbolic lattices satisfy the hyperscaling relation $2\beta /\nu +\gamma /\nu =D_{\text{eff}}$, where $D_{\text{eff}}$ is an effective dimension of the lattice. We also investigate the effect of boundary nodes on the ordering process of the model.

The physics of the heat conduction and viscous dissipation in rarefied gases is analyzed and discussed. A heat transfer model valid for arbitrary Knudsen numbers, defined as the ratio of the molecular mean free path to the characteristic length of channels, is derived by treating the heat transfer behavior in the slip and transition regimes as an intermediate function of continuum heat transfer model and free molecular heat transfer model. Comparison studies reveal that this model not only shows good agreement with the numerical results based on the direct simulation Monte Carlo method, but also has some unique features that can overcome the deficiencies existing in the previous models. Therefore, this model is capable to study the heat transport phenomena in very dilute gas Couette flows through micro/nanochannels more accurately.

We present a detailed analysis of the fluctuation-dissipation theorem (FDT) close to the glass transition in colloidal suspensions under steady shear using mode coupling approximations. Starting point is the many-particle Smoluchowski equation. Under shear, detailed balance is broken and the response functions in the stationary state are smaller at long times than estimated from the equilibrium FDT. An asymptotically constant relation connects response and fluctuations during the shear driven decay, restoring the form of the FDT with, however, a ratio different from the equilibrium one. At short times, the equilibrium FDT holds. We follow two independent approaches whose results are in qualitative agreement. To discuss the derived fluctuation-dissipation ratios, we show an exact reformulation of the susceptibility which contains not the full Smoluchowski operator as in equilibrium, but only its well defined Hermitian part. This Hermitian part can be interpreted as governing the dynamics in the frame comoving with the probability current. We present a simple toy model which illustrates the FDT violation in the sheared colloidal system.

The relaxation of straight contact lines is considered in the context of the Wilhelmy-plate experiment: a homogeneous solid plate is moving vertically at constant velocity in a tank of liquid in the partial wetting regime. We apply the contact line dissipation approach to describe the quasistatic relaxation of the contact line toward the stationary state (below the entrainment transition). Asymptotic solutions are derived from the differential equations describing the capillary rise height and the contact angle relaxation for small initial deviations of the height from the final stationary value in the model considering the friction dissipation at the moving contact line, in the model considering the viscous flow dissipation in the wedge, and in the combined model taking into account both channels of dissipation. We find that for all models the time relaxation of the height and the cosine of the contact angle are given by sums of exponential functions up to a second order in the expansion of the small parameter. We analyze the implications which follow when only one dissipation channel is taken into account and compare them to the case when both dissipation channels are included. The asymptotic solutions are compared with experimental results and with numerically obtained solutions which are based on hydrodynamic approach in lubrication approximation with and without a correction factor for finite contact angles. The best description of the experimental data, based on multicriteria testing, is obtained with the combined contact line dissipation model which takes into account both channels of dissipation.

Using a model of wealth distribution where traders are characterized by quenched random saving propensities and trade among themselves by bipartite transactions, we mimic the enhanced rates of trading of the rich by introducing the preferential selection rule using a pair of continuously tunable parameters. The bipartite trading defines a growing trade network of traders linked by their mutual trade relationships. With the preferential selection rule this network appears to be highly heterogeneous characterized by the scale-free nodal degree and the link weight distributions and presents signatures of nontrivial strength-degree correlations. With detailed numerical simulations and using finite-size scaling analysis we present evidence that the associated critical exponents are continuous functions of the tuning parameters. However the wealth distribution has been observed to follow the well-known Pareto law robustly for all positive values of the tuning parameters.

Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination or cooperation of interacting entities will occur, be it spins, particles, bacteria, animals, or humans. Here, we analyze the case, where the entities are heterogeneous, particularly the case of two populations with conflicting interactions and two possible states. For such systems, explicit mathematical formulas will be determined for the stationary solutions and the associated eigenvalues, which determine their stability. In this way, four different types of system dynamics can be classified and the various kinds of phase transitions between them will be discussed. While these results are interesting from a physics point of view, they are also relevant for social, economic, and biological systems, as they allow one to understand conditions for (1) the breakdown of cooperation, (2) the coexistence of different behaviors (“subcultures”), (3) the evolution of commonly shared behaviors (“norms”), and (4) the occurrence of polarization or conflict. We point out that norms have a similar function in social systems that forces have in physics.

For years, astrophysicists, plasma fusion, and fluid physicists have puzzled over Rayleigh-Taylor turbulent mixing layers. In particular, strong discrepancies in the growth rates have been observed between experiments and numerical simulations. Although two phenomenological mechanisms (mode-coupling and mode-competition) have brought some insight on these differences, convincing theoretical arguments are missing to explain the observed values. In this paper, we provide an analytical expression of the growth rate compatible with both mechanisms and is valid for a self-similar, low Atwood Rayleigh-Taylor turbulent mixing subjected to a constant or time-varying acceleration. The key step in this work is the presentation of foliated averages and foliated turbulent spectra highlighted in our three-dimensional numerical simulations. We show that the exact value of the Rayleigh-Taylor growth rate not only depends upon the acceleration history but is also bound to the power-law exponent of the foliated spectra at large scales.

This paper presents the results from direct numerical simulations of homogeneous ferrofluid turbulence with a spatially uniform, applied oscillating magnetic field. Due to the strong coupling that exists between the magnetic field and the ferrofluid, we find that the oscillating field can affect the characteristics of the turbulent flow. The magnetic field does work on the turbulent flow and typically leads to an increased rate of energy loss via two dissipation modes specific to ferrofluids. However, under certain conditions this magnetic work results in injection, or a forcing, of turbulent kinetic energy into the flow. For the cases considered here, there is no mean shear and the mean components of velocity, vorticity, and particle spin rate are all zero. Thus, the effects shown are entirely due to the interactions between the turbulent fluctuations of the ferrofluid and the magnetic field. In addition to the effects of the oscillation frequency, we also investigate the effects of the choice of magnetization equation. The calculations focus on the approximate centerline conditions of the relatively low Reynolds number turbulent ferrofluid pipe flow experiments described previously [K. R. Schumacher et al., Phys. Rev. E 67, 026308 (2003)].

Using computations of three-dimensional magnetohydrodynamic (MHD) turbulence with a Taylor-Green flow, whose inherent time-independent symmetries are implemented numerically, and in the absence of either a forcing function or an imposed uniform magnetic field, we show that three different inertial ranges for the energy spectrum may emerge for three different initial magnetic fields, the selecting parameter being the ratio of nonlinear eddy to Alfvén time. Equivalent computational grids range from ${128}^3$ to ${2048}^3$ points with a unit magnetic Prandtl number and a Taylor Reynolds number of up to 1500 at the peak of dissipation. We also show a convergence of our results with Reynolds number. Our study is consistent with previous findings of a variety of energy spectra in MHD turbulence by studies performed in the presence of both a forcing term with a given correlation time and a strong, uniform magnetic field. However, in contrast to the previous studies, here the ratio of characteristic time scales can only be ascribed to the intrinsic nonlinear dynamics of the paradigmatic flows under study.