We have developed a general method for the description of separatrix chaos, based on the analysis of the separatrix map dynamics. Matching it with the resonant Hamiltonian analysis, we show that, for a given amplitude of perturbation, the maximum width of the chaotic layer in energy may be much larger than it was assumed before. We use the above method to explain the drastic facilitation of global chaos onset in time-periodically perturbed Hamiltonian systems possessing two or more separatrices, previously discovered [S. M. Soskin, O. M. Yevtushenko, and R. Mannella, Phys. Rev. Lett. 90, 174101 (2003)]. The theory well agrees with simulations. We also discuss generalizations and applications. The method may be generalized for single-separatrix cases. The facilitation of global chaos onset may be relevant to a variety of systems, e.g., optical lattices, magnetic and semiconductor superlattices, meandering flows in the ocean, and spinning pendulums. Apart from dynamical transport, it may facilitate noise-induced transitions and the stochastic web formation.

Based on the Riemannian geometric approach to Hamiltonian systems with many degrees of freedom, we study a chaotic nature of the SU(2) Yang-Mills field. Particularly, we study the Lyapunov exponent of the Wu-Yang magnetic-monopole solution of the SU(2) Yang-Mills field equation by use of an analytic formula which is determined by the average Ricci curvature and its fluctuation on the Riemannian manifold. It is shown that the system is chaotic from the positive values of the Lyapunov exponent. Furthermore, we find that the energy dependence of Lyapunov exponents exhibits a crossover phenomenon. By using the linear stability analysis, we point out that this crossover is related to the instability of the monopole solution.

The results of computer simulations are presented which give evidence for the existence of an interesting symmetry in a many-agent model which demonstrates, in special cases, both Bose-Einstein and Fermi-Dirac statistics. This symmetry is expressed in the close vicinity of the mean values of the degree of ultrametricity and the fraction of isosceles of the sets of agent memories (histories) coded by two different information-loss coding schemes. It is shown that this (in some sense) approximate statistical supersymmetry is probably broken at low temperatures—below some condensation limit. This breaking leads to the appearance of specific coding schemes for boson and fermion histories. The meaning of this specificity is revealed by applying the interpretation of the many-agent model described earlier [A. A. Ezhov and A. Yu. Khrennikov, Phys. Rev. E 71, 016138 (2005)].

The extension of the principle of critical-point universality to binary fluid mixtures, known as isomorphism of critical phenomena, has been reformulated in terms of complete scaling, a concept that properly matches asymmetric fluid-phase behavior with the symmetric Ising model. The controversial issue of the proper definition of the order parameter in binary fluid mixtures is clarified. We show that asymmetry of liquid-liquid coexistence in terms of mole fractions originates from two different sources: one is associated with a correlation between concentration and entropy fluctuations, whereas the other source is the correlation between concentration and density fluctuations. By analyzing the coexistence curves of liquid solutions of nitrobenzene in a series of hydrocarbons (from $n$-pentane to $n$-hexadecane), we have separated these two sources of asymmetry and found that the leading nonanalytical contribution to the asymmetry correlates linearly with the solute-solvent molecular-volume ratio. Other thermodynamic consequences of complete scaling for binary mixtures, such as an analog of the Yang-Yang anomaly in the behavior of the heat capacity and a curvature correction to the interfacial tension, are also discussed.

Invasion percolation is often used to simulate capillary-dominated drainage and imbibition in pore networks. More than a decade ago it was observed that the part of a pore network that is involved in an invasion bond percolation is a minimum-weight spanning tree of the network, where the weights indicate resistances associated with the bonds. Thus, one can determine a minimum-weight spanning tree first and then run the invasion bond percolation on the minimum-weight spanning tree. The time complexities of the two steps are $O\mathbf{\left(}m\alpha \left(m,n\right)\mathbf{\right)}$ and $O\left(n\right)$, respectively, where $m$ is the number of edges, $n$ is the number of vertices, and $\alpha \left(\cdot ,\cdot \right)$ denotes the inverse Ackermann function. In this paper we (1) formulate the property of minimum-weight spanning trees that justifies the two-step approach to invasion bond percolation, (2) extend the two-step approach to invasion site percolation, and (3) further extend it to simulations of drainage (imbibition) that include trapping of the wetting (nonwetting) phase. In case of imbibition we also take snap-off into account. As a consequence, all these simulations can now be done in $O\mathbf{\left(}m\alpha \left(m,n\right)\mathbf{\right)}$.

Using a real-space renormalization-group approximation, we study the anisotropic quantum Heisenberg model on hierarchical lattices, with interactions following aperiodic sequences. Three different sequences are considered, with relevant and irrelevant fluctuations, according to the Luck-Harris criterion. The phase diagram is discussed as a function of the anisotropy parameter $\Delta$ (such that $\Delta =0$ and 1 correspond to the isotropic Heisenberg and Ising models, respectively). We find three different types of phase diagrams, with general characteristics: the isotropic Heisenberg plane is always an invariant one (as expected by symmetry arguments) and the critical behavior of the anisotropic Heisenberg model is governed by fixed points on the Ising-model plane. Our results for the isotropic Heisenberg model show that the relevance or irrelevance of aperiodic models, when compared to their uniform counterpart, is as predicted by the Harris-Luck criterion. A low-temperature renormalization-group procedure was applied to the classical isotropic Heisenberg model in two-dimensional hierarchical lattices: the relevance criterion is obtained, again in accordance with the Harris-Luck criterion.

The Ivanov-Anderson model (and an earlier treatment by Kubo) envisages a decay of the orientational correlation by random but large amplitude molecular jumps, as opposed to infinitesimal small jumps assumed in Brownian diffusion. Recent computer simulation studies on water and viscous liquids have shown that large amplitude motions may indeed be more of a rule than exception. Existing theoretical studies on jump diffusion mostly assume an exponential (Poissonian) waiting time distribution for jumps, thereby again leading to an exponential decay. Here we extend the existing formalism of Ivanov and Anderson to include an algebraic waiting time distribution between two jumps. As a result, the first $(\ell =1)$ and second $(\ell =2)$ rank orientational time correlation functions show the same long time power law, but their short time decay behavior is quite different. The predicted Cole-Cole plot of dielectric relaxation reproduces various features of non-Debye behavior observed experimentally. We also developed a theory where both unrestricted small jumps and large angular jumps coexist simultaneously. The small jumps are shown to have a large effect on the long time decay, particularly in mitigating the effects of algebraic waiting time distribution, and in giving rise to an exponential-like decay, with a time constant, surprisingly, less than the time constant that arises from small amplitude decay alone.

A method of determining the physisorption energy of molecules on carbon nanostructures using field emission current fluctuation measurements is presented. A stochastic model, broken into birth and death processes, was applied to analyze the current fluctuation and determine the physisorption energy. This method yields a highly sensitive, precise determination of the physisorption energy of molecules, and we include the physisorption energies for various molecules on a graphene nanostructure.

Transition to burst synchronization (BS), where all the neurons start and end bursting simultaneously, has been studied on a diffusively coupled network of Hindmash-Rose bursting neurons. When the coupling strength $\epsilon$ is increased from zero, spatiotemporal chaos can be first tamed into one type of BS states with fold-homoclinic bursting, which then undergoes spike-adding and transits into another type of BS states with fold-Hopf bursting. The latter transition takes place via dynamic cluster separation, during which all the neurons with degree $k>k_c$ change to show fold-Hopf bursting, with $\epsilon k_c$ nearly a constant. A reasonable mechanism behind such phenomena is given by using local mean field approximation, and the role of network topology is also discussed. The case when the neurons are coupled via chemical synapses is also briefly discussed.

We studied synchronization between prisoner’s dilemma games with voluntary participation in two Newman-Watts small-world networks. It was found that there are three kinds of synchronization: partial phase synchronization, total phase synchronization, and complete synchronization, for varied coupling factors. Besides, two games can reach complete synchronization for the large enough coupling factor. We also discussed the effect of the coupling factor on the amplitude of oscillation of cooperator density.

We present simulations of granular flows in a modified Couette cell, using a continuum model recently proposed for dense granular flows. Based on a friction coefficient, which depends on an inertial number, the model captures the positions of the wide shear bands. We show that a smooth transition in velocity-profile shape occurs when the height of the granular material is increased, leading to a differential rotation of the central part close to the surface. The numerical predictions are in qualitative agreement with previous experimental results. The model provides predictions for the increase of the shear band width when the rotation rate is increased.

The identification of hidden interdependences among the parts of a complex system is a fundamental issue. Typically, the objective is, given only a sequence of scalar measurements, to infer as much as possible about the internal dynamics of the system and about the interactions between its subsystems. In general, such interactions are not only nonlinear but also asymmetric. Constraints on the estimation of hidden relationships are further posed by noise and by the length of signals sampled from real world systems. The focus of this paper is causal dependences between bivariate time series. We especially focus on the nonlinear extension of Granger causality with polynomial terms of the conventional embedding vector. In this paper, we study the performance of this measure in comparison with three alternative methods proposed recently in low-dimensional and low-order-nonlinearity systems. Those methods are tested with three different artificial chaotic maps with several noise contamination setups. As a result, we find that the polynomial embedding technique successfully detects asymmetric (causal) dependences between bivariate time series in many low-dimensional cases.

An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of nontrivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be predicted from the phase response of a single oscillator to a given impulsive perturbation. We present a theory based on phase reduction of a jump stochastic process describing a Poisson-driven limit-cycle oscillator, and verify the results through numerical simulations and electric circuit experiments. We also give a geometrical interpretation of the synchronizing mechanism, a perturbative expansion to the stationary phase distribution, and the diffusion limit of our jump stochastic model.

A bifurcation of excitation fronts induced by cross diffusion in two-component bistable reaction-diffusion systems of activator-inhibitor type is discovered. This bifurcation is similar to the nonequilibrium Ising-Bloch bifurcation. A different type of fronts, whose spatial profiles are characterized by oscillating tails, are associated with this bifurcation. These fronts are described using exact analytical solutions of piecewise linear reaction-diffusion equations.

We have developed a one-dimensional fluid dynamics model for the ablation of water-rich targets by nanosecond infrared laser pulses at atmospheric pressure. To describe the laser-target interaction and the plume expansion dynamics, in light of recent experimental results the model incorporates phase explosion due to superheating and the nonlinear light absorption properties of water. In the model, the phase explosion is treated as a prolonged process that lasts for a finite time. Once a thin layer beneath the target surface exceeds the phase explosion temperature, this layer is transformed from target material into a mixture of water vapor and droplets and become part of the plume. This process is sustained for some time until the laser energy cannot maintain it. The simulation results show that as a result of two different phase transition mechanisms, i.e., surface evaporation and phase explosion, a first, slower plume expansion phase is followed by a more vigorous accelerated expansion phase. The calculated time evolution of the shock front at various fluence levels agrees well with the experimental observations of Apitz and Vogel [I. Apitz and A. Vogel, Appl. Phys. A. 81, 329 (2005)]. This model sheds light on the effect of phase explosion in laser ablation dynamics and its results are relevant for material synthesis, surface analysis, and medical (surgery) applications.

We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case, even to lowest order, because of the complicated discontinuous boundary conditions on the electric field at such an interface. Our final expression is simply a surface integral, over the material interface, of the continuous field components from the unperturbed structure. The derivation is based on a “localized” coordinate-transformation technique, which avoids both the problem of field discontinuities and the challenge of constructing an explicit coordinate transformation by taking the limit in which the coordinate perturbation is infinitesimally localized around the boundary. Not only is our result potentially useful in evaluating boundary perturbations, e.g., from fabrication imperfections, in highly anisotropic media such as many metamaterials, but it also has a direct application in numerical electromagnetism. In particular, we show how it leads to a subpixel smoothing scheme to ameliorate staircasing effects in discretized simulations of anisotropic media, in such a way as to greatly reduce the numerical errors compared to other proposed smoothing schemes.

We find the static multisoliton solutions of the baby Skyrme model on the two-sphere for topological charges $1\le B\le 14$. Numerical full-field results show that the charge-one Skyrmion is spherical, the charge-two Skyrmion is toroidal, and Skyrmions with higher charge all have point symmetries which are subgroups of O(3). We find that a rational map ansatz yields very good approximations to the full-field solutions. We point out a strong connection between the discrete symmetries of our solutions and those of corresponding solutions of the three-dimensional Skyrme model.

We present an algorithmic framework for a variant of the quantum Monte Carlo operator-loop algorithm, where nonlocal cluster updates are constructed in a way that makes each individual loop smaller. The algorithm is designed to increase simulation efficiency in cases where conventional loops become very large, do not close altogether, or otherwise behave poorly. We demonstrate and characterize some aspects of the short loop on a square lattice spin-1/2 $XXZ$ model where, remarkably, a significant increase in simulation efficiency is observed in some parameter regimes. The simplicity of the model provides a prototype for the use of short loops on more complicated quantum systems.

The lattice Boltzmann equation replaces continuous particle velocity space by a finite set; the velocity distribution function then varies over a finite-dimensional vector space instead of over an infinite-dimensional function space. The number of linearly independent moments of the distribution function in a lattice Boltzmann model cannot exceed the number of velocities; finite dimensionality therefore necessarily induces linear dependences among the moments that do not exist in a continuous theory. Given a finite velocity set, it is important to know which moments are free of these dependences. Elementary group theory is applied to the solution of this problem. It is found that decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group makes it straightforward to uncover linear dependences among the moments. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing higher-dimensional models are suggested.

Active cellular transport is a fundamental mechanism for protein and vesicle delivery, cell cycle, and molecular degradation. Viruses can hijack the transport system and use it to reach the nucleus. Most transport processes consist of intermittent dynamics, where the motion of a particle, such as a virus, alternates between pure Brownian and directed movement along microtubules. In this Rapid Communication, we estimate the mean time for a particle to attach to a microtubule network. This computation leads to a coarse grained equation of the intermittent motion in radial and cylindrical geometries. Finally, by using the degradation activity inside the cytoplasm, we obtain refined asymptotic estimations for the probability and the mean time a virus reaches a small nuclear pore.