The recently introduced entropic lattice Boltzmann model (ELBM) for multiphase flows [A. Mazloomi M., S. S. Chikatamarla, and I. V. Karlin, Phys. Rev. Lett. 114, 174502 (2015)] is extended to the simulation of dynamic fluid-solid interface problems. The thermodynamically consistent, nonlinearly stable ELBM together with a polynomial representation of the equation of state enables us to investigate the dynamics of the contact line in a wide range of applications, from capillary filling to liquid drop impact onto a flat surfaces with different wettability. The static interface behavior is tested by means of the liquid column in a channel to verify the Young-Laplace law. The numerical results of a capillary filling problem in a channel with wettability gradient show an excellent match with the existing analytical solution. Simulations of drop impact onto both wettable and nonwettable surfaces show that the ELBM reproduces the experimentally observed drop behavior in a quantitative manner. Results reported herein demonstrate that the present model is a promising alternative for studying the vapor-liquid-solid interface dynamics.

In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to ${\sigma }^{-1/2}, \sigma$ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.

We study various properties of the convex hull of a planar Brownian motion, defined as the minimum convex polygon enclosing the trajectory, in the presence of an infinite reflecting wall. Recently [Phys. Rev. E 91, 050104(R) (2015)], we announced that the mean perimeter of the convex hull at time $t$, rescaled by $\sqrt{Dt}$, is a nonmonotonous function of the initial distance to the wall. In this article, we first give all the details of the derivation of this mean rescaled perimeter, in particular its value when starting from the wall and near the wall. We then determine the physical mechanism underlying this surprising nonmonotonicity of the mean rescaled perimeter by analyzing the impact of the wall on two complementary parts of the convex hull. Finally, we provide a further quantification of the convex hull by determining the mean length of the portion of the reflecting wall visited by the Brownian motion as a function of the initial distance to the wall.

We study the crossover scaling behavior of the height-height correlation function in interface depinning in random media. We analyze experimental data from a fracture experiment and simulate an elastic line model with nonlinear couplings and disorder. Both exhibit a crossover between two different universality classes. For the experiment, we fit a functional form to the universal crossover scaling function. For the model, we vary the system size and the strength of the nonlinear term and describe the crossover between the two universality classes with a multiparameter scaling function. Our method provides a general strategy to extract scaling properties in depinning systems exhibiting crossover phenomena.

Chemical oscillators with a broad frequency distribution are photochemically coupled in network topologies. Experiments and simulations show that the network synchronization occurs by phase-lag synchronization of clusters of oscillators with zero- or nearly zero-lag synchronization. Symmetry also plays a role in the synchronization, the extent of which is explored as a function of coupling strength, frequency distribution, and the highest frequency oscillator location. The phase-lag synchronization occurs through connected synchronized clusters, with the highest frequency node or nodes setting the frequency of the entire network. The synchronized clusters successively “fire,” with a constant phase difference between them. For low heterogeneity and high coupling strength, the synchronized clusters are made up of one or more clusters of nodes with the same permutation symmetries. As heterogeneity is increased or coupling strength decreased, the phase-lag synchronization occurs partially through clusters of nodes sharing the same permutation symmetries. As heterogeneity is further increased or coupling strength decreased, partial synchronization and, finally, independent unsynchronized oscillations are observed. The relationships between these classes of behavior are explored with numerical simulations, which agree well with the experimentally observed behavior.

The symmetric four-strategy games are decomposed into a linear combination of 16 basis games represented by orthogonal matrices. Among these basis games four classes can be distinguished as it is already found for the three-strategy games. The games with self-dependent (cross-dependent) payoffs are characterized by matrices consisting of uniform rows (columns). Six of 16 basis games describe coordination-type interactions among the strategy pairs and three basis games span the parameter space of the cyclic components that are analogous to the rock-paper-scissors games. In the absence of cyclic components the game is a potential game and the potential matrix is evaluated. The main features of the four classes of games are discussed separately and we illustrate some characteristic strategy distributions on a square lattice in the low noise limit if logit rule controls the strategy evolution. Analysis of the general properties indicates similar types of interactions at larger number of strategies for the symmetric matrix games.

Epidemic processes are common out-of-equilibrium phenomena of broad interdisciplinary interest. Recently, dynamic message-passing (DMP) has been proposed as an efficient algorithm for simulating epidemic models on networks, and in particular for estimating the probability that a given node will become infectious at a particular time. To date, DMP has been applied exclusively to models with one-way state changes, as opposed to models like SIS and SIRS where nodes can return to previously inhabited states. Because many real-world epidemics can exhibit such recurrent dynamics, we propose a DMP algorithm for complex, recurrent epidemic models on networks. Our approach takes correlations between neighboring nodes into account while preventing causal signals from backtracking to their immediate source, and thus avoids “echo chamber effects” where a pair of adjacent nodes each amplify the probability that the other is infectious. We demonstrate that this approach well approximates results obtained from Monte Carlo simulation and that its accuracy is often superior to the pair approximation (which also takes second-order correlations into account). Moreover, our approach is more computationally efficient than the pair approximation, especially for complex epidemic models: the number of variables in our DMP approach grows as $2mk$ where $m$ is the number of edges and $k$ is the number of states, as opposed to $m{k}^2$ for the pair approximation. We suspect that the resulting reduction in computational effort, as well as the conceptual simplicity of DMP, will make it a useful tool in epidemic modeling, especially for high-dimensional inference tasks.

The paper investigates shock-induced vortical flows within inhomogeneous media of nonuniform thermodynamic properties. Numerical simulations are performed using a Eulerian type mathematical model for compressible multicomponent flow problems. The model, which accounts for pressure nonequilibrium and applies different equations of state for individual flow components, shows excellent capabilities for the resolution of interfaces separating compressible fluids as well as for capturing the baroclinic source of vorticity generation. The developed finite volume Godunov type computational approach is equipped with an approximate Riemann solver for calculating fluxes and handles numerically diffused zones at flow component interfaces. The computations are performed for various initial conditions and are compared with available experimental data. The initial conditions promoting a shock-bubble interaction process include weak to high planar shock waves with a Mach number ranging from $1.2$ to 3 and isolated cylindrical bubble inhomogeneities of helium, argon, nitrogen, krypton, and sulphur hexafluoride. The numerical results reveal the characteristic features of the evolving flow topology. The impulsively generated flow perturbations are dominated by the reflection and refraction of the shock, the compression, and acceleration as well as the vorticity generation within the medium. The study is further extended to investigate the influence of the ratio of the heat capacities on the interface deformation.

In this paper, we consider the physical mechanism for the clustering of inertial particles in the inertial range of isotropic turbulence. We analyze the exact, but unclosed, equation governing the radial distribution function (RDF) and compare the mechanisms it describes for clustering in the dissipation and inertial ranges. We demonstrate that in the limit ${\mathrm{St}}_r\ll 1$, where ${\mathrm{St}}_r$ is the Stokes number based on the eddy turnover time scale at separation $r$, the clustering in the inertial range can be understood to be due to the preferential sampling of the coarse-grained fluid velocity gradient tensor at that scale. When ${\mathrm{St}}_r\gtrsim O\left(1\right)$ this mechanism gives way to a nonlocal clustering mechanism. These findings reveal that the clustering mechanisms in the inertial range are analogous to the mechanisms that we identified for the dissipation regime [see New J. Phys. 16, 055013 (2014)]. Further, we discuss the similarities and differences between the clustering mechanisms we identify in the inertial range and the “sweep-stick” mechanism developed by Coleman and Vassilicos [Phys. Fluids 21, 113301 (2009)]. We show that the idea that initial particles are swept along with acceleration stagnation points is only approximately true because there always exists a finite difference between the velocity of the acceleration stagnation points and the local fluid velocity. This relative velocity is sufficient to allow particles to traverse the average distance between the stagnation points within the correlation time scale of the acceleration field. We also show that the stick part of the mechanism is only valid for ${\mathrm{St}}_r\ll 1$ in the inertial range. We emphasize that our clustering mechanism provides the more fundamental explanation since it, unlike the sweep-stick mechanism, is able to explain clustering in arbitrary spatially correlated velocity fields. We then consider the closed, model equation for the RDF given in Zaichik and Alipchenkov [Phys. Fluids 19, 113308 (2007)] and use this, together with the results from our analysis, to predict the analytic form of the RDF in the inertial range for ${\mathrm{St}}_r\ll 1$, which, unlike that in the dissipation range, is not scale invariant. The results are in good agreement with direct numerical simulations, provided the separations are well within the inertial range.

A drop translating in the presence of an electric field is studied analytically. The flow is a combination of a Hadamard-Rybczynski and a Taylor circulation due to the translation and electric field, respectively. We consider chaotic advection that is generated by (1) tilting and (2) time-dependent modulation of the electric field. For the analysis we consider small perturbations in time and space to what is otherwise an integrable flow. By using a robust analytical technique we find an adiabatic invariant (AI) for the system by averaging the equations of motion. The chaotic advection is due to quasirandom jumps of the AI after crossing the separatrix of the unperturbed flow. We demonstrate that the asymptotic analysis leads to a set of criteria that can be used to optimize stirring in these systems.

We investigate a quantum heat engine with a working substance of two particles, one with a spin-$1/2$ and the other with an arbitrary spin (spin $s$), coupled by Heisenberg exchange interaction, and subject to an external magnetic field. The engine operates in a quantum Otto cycle. Work harvested in the cycle and its efficiency are calculated using quantum thermodynamical definitions. It is found that the engine has higher efficiencies at higher spins and can harvest work at higher exchange interaction strengths. The role of exchange coupling and spin $s$ on the work output and the thermal efficiency is studied in detail. In addition, the engine operation is analyzed from the perspective of local work and efficiency. We develop a general formalism to explore local thermodynamics applicable to any coupled bipartite system. Our general framework allows for examination of local thermodynamics even when global parameters of the system are varied in thermodynamic cycles. The generalized definitions of local and cooperative work are introduced by using mean field Hamiltonians. The general conditions for which the global work is not equal to the sum of the local works are given in terms of the covariance of the subsystems. Our coupled spin quantum Otto engine is used as an example of the general formalism.

We derive analogs of the Jarzynski equality and Crooks relation to characterize the nonequilibrium work associated with changes in the spring constant of an overdamped oscillator in a quadratically varying spatial temperature profile. The stationary state of such an oscillator is described by Tsallis statistics, and the work relations for certain processes may be expressed in terms of $q$-exponentials. We suggest that these identities might be a feature of nonequilibrium processes in circumstances where Tsallis distributions are found.

The critical properties of the spin-1 Blume-Capel model in two dimensions is studied on Voronoi-Delaunay random lattices with quenched connectivity disorder. The system is treated by applying Monte Carlo simulations using the heat-bath update algorithm together with single histograms re-weighting techniques. We calculate the critical temperature as well as the critical exponents as a function of the crystal field $\mathrm{\Delta }$. It is found that this disordered system exhibits phase transitions of first- and second-order types that depend on the value of the crystal field. For values of $\mathrm{\Delta }\le 3$, where the nearest-neighbor exchange interaction $J$ has been set to unity, the disordered system presents a second-order phase transition. The results suggest that the corresponding exponent ratio belongs to the same universality class as the regular two-dimensional ferromagnetic model. There exists a tricritical point close to ${\mathrm{\Delta }}_t=3.05\left(4\right)$ with different critical exponents. For ${\mathrm{\Delta }}_t\le \mathrm{\Delta }<3.4$ this model undergoes a first-order phase transition. Finally, for $\mathrm{\Delta }\ge 3.4$ the system is always in the paramagnetic phase.

In a previous paper [Phys. Rev. E 83, 021801 (2011)] we performed neutron reflectivity (NR) measurements on a five-layer polystyrene (PS) thin film consisting of alternatively stacked deuterated polystyrene (dPS) and hydrogenated polystyrene (hPS) layers (dPS/hPS/dPS/hPS/dPS, $\sim 100$ nm thick) on a Si substrate to reveal the distribution of $T_g$ along the depth direction. Information on the $T_g$ distribution is very useful to understand the interesting but unusual properties of polymer thin films. However, one problem that we have to clarify is if there are effects of deuterium labeling on $T_g$ or not. To tackle the problem we performed low-energy muon spin relaxation ($\mu \mathrm{SR}$) measurements on the above-mentioned deuterium-labeled five-layer PS thin film as well as dPS and hPS single-layer thin films $\sim 100$ nm thick as a function of muon implantation energy. It was found that the deuterium labeling had no significant effects on the $T_g$ distribution, guaranteeing that we can safely discuss the unusual thin film properties based on the $T_g$ distribution revealed by NR on the deuterium-labeled thin films. In addition, the $\mu \mathrm{SR}$ result suggested that the higher $T_g$ near the Si substrate is due to the strong orientation of phenyl rings.

The Turing instability is a paradigmatic route to pattern formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a consequence, the system evolves towards a stationary, nonhomogeneous attractor. Stable patterns can be also obtained via oscillation quenching of an initially synchronous state of diffusively coupled oscillators. In the literature this is known as the oscillation death phenomenon. Here, we show that oscillation death is nothing but a Turing instability for the first return map of the system in its synchronous periodic state. In particular, we obtain a set of approximated closed conditions for identifying the domain in the parameter space that yields the instability. This is a natural generalization of the original Turing relations, to the case where the homogeneous solution of the examined system is a periodic function of time. The obtained framework applies to systems embedded in continuum space, as well as those defined on a networklike support. The predictive ability of the theory is tested numerically, using different reaction schemes.

In a recent paper [Phys. Rev. E 91, 012920 (2015)] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.

We have found a strongly pulsating regime of dissipative solitons in the laser model described by the complex cubic-quintic Ginzburg-Landau equation. The pulse energy within each period of pulsations may change more than two orders of magnitude. The soliton spectra in this regime also experience large variations. Period doubling phenomena and chaotic behaviors are observed in the boundaries of existence of these pulsating solutions.

To model waves, surface flows, and particle dispersion at the air-water interface one needs to know the essential mechanisms affecting the fluid motion at the surface. We show that a thin film (less than 10-nm thick) of adsorbed protein dramatically affects two-dimensional turbulence generated by Faraday waves at the fluid surface. Extremely low concentrations ($\approx 1$ ppm) of soluble proteins form a strong viscoelastic layer which suppresses turbulent diffusion at the surface, changes wave patterns, and shows strong resilience to the wave-induced droplet generation. Surface shear properties of the film play a key role in this phenomenon by inhibiting the creation of vorticity at the surface. The addition of surfactants, on the other hand, destroys the nanolayer and restores the fluid mobility.

The interaction between a magnetic field and plasma close to a nonconductive surface is of interest for both science and technology. In space, crustal magnetic fields on celestial bodies without atmosphere can interact with the solar wind. In advanced technologies such as those used in fusion or spaceflight, magnetic fields can be used to either control a plasma or protect surfaces exposed to the high heat loads produced by plasma. In this paper, a method will be discussed for investigating magnetic field plasma interactions close to a nonconductive surface inside a Gaseous Electronics Conference reference cell employing dust particles as probes. To accomplish this, a magnet covered by a glass plate was exposed to a low power argon plasma. The magnetic field was strong enough to magnetize the electrons, while not directly impacting the dynamics of the ions or the dust particles used for diagnostics. In order to investigate the interaction of the plasma with the magnetic field and the nonconductive surface, micron-sized dust particles were introduced into the plasma and their trajectories were recorded with a high-speed camera. Based on the resulting particle trajectories, the accelerations of the dust particles were determined and acceleration maps over the field of view were generated which are representative of the forces acting on the particles. The results show that the magnetic field is responsible for the development of strong electric fields in the plasma, in both horizontal and vertical directions, leading to complex motion of the dust particles.

Field-induced magnetostatic interaction in a pair of identical particles made of a magnetically soft ferromagnet is studied. It is shown that due to saturation of the ferromagnet magnetization, this case differs significantly from the (super)paramagnetic one. A numerical solution is given, discussed, and compared with that provided by a simpler model (nonlinear mutual dipoles). We show that for multidomain ferromagnetic particles embedded in an elastomer matrix, as for paramagnetic ones in the same environment, pair clusters may form or break by a hysteresis scenario. However, the magnetization saturation brings in important features to this effect. First, the bistability state and the hysteresis take place only in a limited region of the material parameters of the system. Second, along with the hysteresis jumps occurring under the sole influence of the field, the “latent” hysteresis is possible which realizes only if the action of the field is combined with some additional (nonmagnetic) external factor. The obtained conditions, when used to assess the possibility of clustering in real magnetorheological polymers, infer an important role of mesoscopic magnetomechanical hysteresis for the macroscopic properties of these composites.