Properties of the Olami-Feder-Christensen (OFC) model of earthquakes are studied by numerical simulations. The previous study indicated that the model exhibited “asperity”-like phenomena, i.e., the same region ruptures many times near periodically [T. Kotani et al., Phys. Rev. E 77, 010102(R) (2008)]. Such periodic or characteristic features apparently coexist with power-law-like critical features, e.g., the Gutenberg-Richter law observed in the size distribution. In order to clarify the origin and the nature of the asperity-like phenomena, we investigate here the properties of the OFC model with emphasis on its stress distribution. It is found that the asperity formation is accompanied by self-organization of the highly concentrated stress state. Such stress organization naturally provides the mechanism underlying our observation that a series of asperity events repeat with a common epicenter site and with a common period solely determined by the transmission parameter of the model. Asperity events tend to cluster both in time and in space.

We describe a molecular-dynamics framework for the direct calculation of the short-ranged structural forces underlying grain-boundary premelting and grain coalescence in solidification. The method is applied in a comparative study of (i) a $\Sigma 9⟨115⟩120°$ twist and (ii) a $\Sigma 9⟨110⟩\left\{411\right\}$ symmetric tilt boundary in a classical embedded-atom model of elemental Ni. Although both boundaries feature highly disordered structures near the melting point, the nature of the temperature dependence of the width of the disordered regions in these boundaries is qualitatively different. The former boundary displays behavior consistent with a logarithmically diverging premelted layer thickness as the melting temperature is approached from below, while the latter displays behavior featuring a finite grain-boundary width at the melting point. It is demonstrated that both types of behavior can be quantitatively described within a sharp-interface thermodynamic formalism involving a width-dependent interfacial free energy, referred to as the disjoining potential. The disjoining potential for boundary (i) is calculated to display a monotonic exponential dependence on width, while that of boundary (ii) features a weak attractive minimum. The results of this work are discussed in relation to recent simulation and theoretical studies of the thermodynamic forces underlying grain-boundary premelting.

We present an effective contour model for electrical discharges deduced as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, in the limit of small electron diffusion. The incorporation of curvature effects to the velocity propagation and not to the boundary conditions is a feature and makes it different from the classical Laplacian growth models. The dispersion relation for a nonplanar two-dimensional discharge is calculated. The development and propagation of fingerlike patterns are studied and their main features quantified.

We present an experimental study of a droplet interacting with an ultrasonic surface acoustic wave. Depending on the amplitude of the wave, the drop can either experience an internal flow with its contact line pinned, or (at higher amplitude) move along the direction of the wave also with internal flow. Both situations come with oscillations of the drop free surface. The physical origins of the internal mixing flow as well as the drop displacement and surface waves are still not well understood. In order to give insights of the underlying physics involved in these phenomena, we carried out an experimental and numerical study. The results suggest that the surface deformation of the drop can be related to a combination between acoustic streaming effect and radiation pressure inside the drop.

Crossing sea states can occur during adverse weather conditions. The instability of such wave trains has been suggested as a possible mechanism for the formation of rogue (freak or extreme) waves. One model for crossing sea states is weakly nonlinear and finite-amplitude short-crested waves (SCWs) on deep water. SCWs are the resonant interaction of two wave systems each with a different direction of propagation. Recently, it has been shown that the stability of these wave interactions is closely associated with the stability of the oblique nonresonant interaction between two waves. The long-wave instability of such waves is considered here; SCWs are used as a benchmark. By using a mismatch of amplitudes, it is demonstrated that instability growth rates of two crossing waves can be larger than those given by SCWs. This indicates that only considering true resonant interactions can underestimate the contribution from unstable crossing sea states to the possible formation of rogue waves.

A useful approximation for the thermal operator $\text{exp}\left(-\beta \widehat{H}\right)$ is based on its representation in terms of either frozen or thawed Gaussian states. Such approximate representations are leading-order terms in respective series representations of the thermal operator. A numerical study of the convergence properties of the frozen Gaussian series representation has been recently published. In this paper, we extend the previous study to include also the convergence properties of the more expensive thawed Gaussian series representation of the thermal operator. We consider three different formulations for the series representation and apply them to a quartic double-well potential to find that the thawed Gaussian series representation converges faster than the frozen Gaussian one. Further analysis is presented as to the convergence properties and the numerical efficiency of three different thawed Gaussian series representation. The unsymmetrized form converges most rapidly, however, the lower order approximations of the symmetrized forms are more accurate. Comparison with a standard discretized path-integral evaluation demonstrates that the Gaussian based perturbation series representation converges much faster.

Instead of the problematic reasoning presented in the work of D. J. Braun [Phys. Rev. E 78, 016213 (2008)], a rigorous argument is provided to show the validity of the adaptive controller proposed by Braun under some particular assumptions. Without these assumptions, this controller may be failed to stabilize the unsteady state, which is numerically shown by specific examples. Also, the choice of parameters to guarantee the validity of these assumptions is illustrated.

In a recent article [D. J. Braun, Phys. Rev. E 78, 016213 (2008)], the author has proposed a controller to stabilize a steady-state of a nonlinear dynamical system without requiring explicit knowledge of the system dynamics. In the related Comment [W. Lin, Phys. Rev. E 81, 038201 (2010)], Lin has criticized the analytical verification of the controller, and provided an alternative proof to verify its feasibility. While this proof is acknowledged here, we will show that the example used by Lin to demonstrate failure of the controller is a counterexample on the Comment itself.

Starting from a continuous-time random-walk (CTRW) model of particles that may evanesce as they walk, our goal is to arrive at macroscopic integrodifferential equations for the probability density for a particle to be found at point $\mathbf{r}$ at time $t$ given that it started its walk from ${\mathbf{r}}_0$ at time $t=0$. The passage from the CTRW to an integrodifferential equation is well understood when the particles are not evanescent. Depending on the distribution of stepping times and distances, one arrives at standard macroscopic equations that may be “normal” (diffusion) or “anomalous” (subdiffusion and/or superdiffusion). The macroscopic description becomes considerably more complicated and not particularly intuitive if the particles can die during their walk. While such equations have been derived for specific cases, e.g., for location-independent exponential evanescence, we present a more general derivation valid under less stringent constraints than those found in the current literature.

By subjecting a dynamical system to a series of short pulses and varying several time delays, we can obtain multidimensional characteristic measures of the system. Multidimensional Kullback-Leibler response function (KLRF), which are based on the Kullback-Leibler distance between the initial and final states, are defined. We compare the KLRF, which are nonlinear in the probability density, with ordinary response functions obtained from the expectation value of a dynamical variable, which are linear. We show that the KLRF encode different level of information regarding the system’s dynamics. For overdamped stochastic dynamics two-dimensional KLRF shows a qualitatively different variation with the time delays between pulses, depending on whether the system is initially in a steady state or in thermal equilibrium.

We define a percolation problem on the basis of spin configurations of the two-dimensional $XY$ model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting angle. The percolation properties of this model are studied by means of Monte Carlo simulations and a finite-size scaling analysis. Our simulations show the existence of percolation transitions when the conducting angle is varied, and we determine the transition point for several values of the $XY$ coupling. It appears that the critical behavior of this percolation model can be well described by the standard percolation theory. The critical exponents of the percolation transitions, as determined by finite-size scaling, agree with the universality class of the two-dimensional percolation model on a uniform substrate. This holds over the whole temperature range, even in the low-temperature phase where the $XY$ substrate is critical in the sense that it displays algebraic decay of correlations.

The family of Vicsek fractals is one of the most important and frequently studied regular fractal classes, and it is of considerable interest to understand the dynamical processes on this treelike fractal family. In this paper, we investigate discrete random walks on the Vicsek fractals, with the aim to obtain the exact solutions to the global mean-first-passage time (GMFPT), defined as the average of first-passage time (FPT) between two nodes over the whole family of fractals. Based on the known connections between FPTs, effective resistance, and the eigenvalues of graph Laplacian, we determine implicitly the GMFPT of the Vicsek fractals, which is corroborated by numerical results. The obtained closed-form solution shows that the GMFPT approximately grows as a power-law function with system size (number of all nodes), with the exponent lies between 1 and 2. We then provide both the upper bound and lower bound for GMFPT of general trees, and show that the leading behavior of the upper bound is the square of system size and the dominating scaling of the lower bound varies linearly with system size. We also show that the upper bound can be achieved in linear chains and the lower bound can be reached in star graphs. This study provides a comprehensive understanding of random walks on the Vicsek fractals and general treelike networks.

We have investigated the dielectric properties of water-in-oil microemulsions composed of sodium bis(2-ethyl-hexyl)sulfosuccinate, water, and decane, using radiofrequency impedance spectroscopy, below the percolation threshold, where the system behaves as surfactant-coated individual water droplets dispersed in a continuous oil phase. The analysis of the dielectric spectra has evidenced that the whole dielectric response below percolation is due to two different contributions, which give rise to two partially overlapping dielectric relaxations, approximately in the frequency range from 10 to 500 MHz. The first of these mechanisms is originated by the bulk polarization of counterions distributed in the electrical double layer of the droplet interior. The second mechanism is associated with a correlated motion of the anionic head groups ${\text{SO}}_3^{-}$ at the surfactant-water interface. The introduction of this latter contribution allows us to justify the experimentally observed increase in the low-frequency permittivity as a function of temperature up to temperatures very close to percolation. The present study shows that deviations from the expected values on the basis of dielectric theories of heterogeneous systems (Maxwell-Wagner effect) observed when percolation is approaching can be accounted for, in a reasonable way, by the introduction of a further polarization mechanism, which involves the anionic surfactant groups. Only very close to percolation, when microemulsions undergo a scaling behavior, deviations of the permittivity (and electrical conductivity as well) are a print of the structural rearrangement of the whole system and models based on colloidal particle suspension theories fail. Even if the whole picture of the dielectric properties of microemulsion systems does not change in deep, nevertheless, the refinement introduced in this paper demonstrates how different polarization mechanisms could be simultaneously present in these rather complex systems and, above all, how the individual particle colloidal properties are maintained up to very close to the percolation threshold.

We develop a lattice model for the splay flexoelectric effect in nematic liquid crystals. In this model, each lattice site has a spin representing the local molecular orientation, and the interaction between neighboring spins represents pear-shaped molecules with shape polarity. We perform Monte Carlo simulations and mean-field calculations to find the behavior as a function of interaction parameters, temperature, and applied electric field. The resulting phase diagram has three phases: isotropic, nematic, and polar. In the nematic phase, there is a large splay flexoelectric effect, which diverges as the system approaches the transition to the polar phase. These results show that flexoelectricity can be a statistical phenomenon associated with the onset of polar order.

We develop a semiquantitative theory to describe the experimentally observed energy gain when two light beams intersect in hybrid organic-inorganic photorefractives. These systems consist of a nematic liquid-crystal (LC) layer placed between two photorefractive windows. A periodic space-charge field is induced by the interfering light beams in the photorefractive windows. The field penetrates into the LC, interacting with the nematic director and giving rise to a diffraction grating. LC flexoelectricity is the principal physical mechanism driving the grating structure. Each light beam diffracts from the induced grating, leading to an apparent energy gain and loss within each beam. The LC optics is described in the Bragg regime. In the theory the exponential gain coefficient is a product of a beam interference term, a flexoelectricity term and a space-charge term. The theory has been compared with results of an experimental study on hybrid cells filled with the LC mixture TL 205. Experimentally the energy gain is maximal at much lower grating wave numbers than is predicted by naïve theory. However, if the director reorientation is cubic rather than linear in the space-charge field term, then good agreement between theory and experiment can be achieved using only a single fitting parameter. We provide a semiquantitative argument to justify this nonlinearity in terms of electric-field-induced local phase separation between different components of the liquid crystal.

An attempt is made to measure the vibron-phonon coupling strength in a finite size lattice of H-bonded peptide units. Within a finite temperature density matrix approach, we compare separately the influence of both the vibron-phonon coupling and the dipole-dipole interaction on the coherence between the ground state and a local one-vibron state. Due to the confinement, it is shown that the vibron-phonon coupling yields a series of dephasing-rephasing mechanisms that prevents the coherence to decay. Similarly, the dipole-dipole interaction gives rise to quantum recurrences for specific revival times. Nevertheless, intense recurrences are rather rare events so that the coherence behaves as a random variable whose most probable value vanishes. By comparing the degree of the coherence for each interaction, a critical coupling ${\chi }^{\ast }\left(L\right)$ is defined to discriminate between the weak and the strong coupling limits. Its size dependence indicates that the smaller the lattice size is, the weaker the vibron-phonon coupling relative to the dipole-dipole interaction is.

We develop a method for calculating the equilibrium properties of the liquid-solid phase transition in a classical, ideal, multicomponent plasma. Our method is a semianalytic calculation that relies on extending the accurate fitting formulas available for the one-, two-, and three-component plasmas to the case of a plasma with an arbitrary number of components. We compare our results to those of C. J. Horowitz et al. [Phys. Rev. E 75, 066101 (2007)], who used a molecular-dynamics simulation to study the chemical properties of a 17-species mixture relevant to the ocean-crust boundary of an accreting neutron star at the point where half the mixture has solidified. Given the same initial composition as Horowitz et al., we are able to reproduce to good accuracy both the liquid and solid compositions at the half-freezing point; we find abundances for most species within 10% of the simulation values. Our method allows the phase diagram of complex mixtures to be explored more thoroughly than possible with numerical simulations. We briefly discuss the implications for the nature of the liquid-solid boundary in accreting neutron stars.

Recent work has revealed that success-driven migration can promote cooperation among selfish individuals in evolutionary games. This migration mechanism relies, however, on nonlocal information about the states of the individuals and their computational capabilities for prediction. We investigate the role of adaptive migration in cooperative behavior in the framework of spatial game by proposing an alternative migration strategy that requires only local information obtainable through game interactions. Our results demonstrate that adaptive migration can be effective in promoting cooperation in two ways. First, there exists an optimal degree of migration associated with the density of empty sites and migration speed, which leads to the highest level of cooperation. Second, adaptive migration can induce an outbreak of cooperation from an environment dominated by defectors. These findings hold for common types of evolutionary games that involve pairwise interactions.

In this paper, we deal with a kinetic model to describe the evolution of the opinion in a closed group with respect to a choice between multiple options (e.g., political parties), which takes into account two main mechanisms of opinion formation, namely, the interaction between individuals and the effect of the mass media. We numerically test the model in some relevant cases and eventually provide an existence and a uniqueness result for it.

In the tangent space of some spatially extended dissipative systems one can observe “physical” modes which are highly involved in the dynamics and are decoupled from the remaining set of hyperbolically “isolated” degrees of freedom representing strongly decaying perturbations. This mode splitting is studied for the Ginzburg-Landau equation at different strength of the spatial coupling. We observe that isolated modes coincide with eigenmodes of the homogeneous steady state of the system; that there is a local basis where the number of nonzero components of the state vector coincides with the number of “physical” modes; that in a system with finite number of degrees of freedom the strict mode splitting disappears at finite value of coupling; that above this value a fussy mode splitting is observed.