We use a recently developed order parameter expansion method to study the transition to synchronous firing occurring in a system of coupled active rotators under the exclusive presence of quenched noise. The method predicts correctly the existence of a transition from a rest state to a regime of synchronous firing and another transition out of it as the intensity of the quenched noise increases and leads to analytical expressions for the critical noise intensities in the large coupling regime. It also predicts the order of the transitions for different probability distribution functions of the quenched variables. Using numerical simulations and finite-size scaling theory to estimate the critical exponents of the transitions, we found values which are consistent with those reported in other scalar systems in the exclusive presence of additive static disorder.

This paper investigates surface roughness characteristics of localized plastic yield surface in a perfectly plastic disordered material. We model the plastic disordered material using perfectly plastic random spring model. Our results indicate that plasticity in a disordered material evolves in a diffusive manner until macroscopic yielding, which is in contrast to the localized failure observed in brittle fracture of disordered materials. On the other hand, the height-height fluctuations of the plastic yield surfaces generated by the spring model exhibit roughness exponents similar to those obtained in the brittle fracture of disordered materials, albeit anomalous scaling of plastic surface roughness is not observed. The local and global roughness exponents (${\zeta }_{loc}$ and $\zeta$, respectively) are equal to each other, and the two-dimensional crack roughness exponent is estimated to be ${\zeta }_{loc}=\zeta =0.67\pm 0.03$. The probability density distribution $p\left[\Delta h\left(\ell \right)\right]$ of the height differences $\Delta h\left(\ell \right)=\left[h\left(x+\ell \right)-h\left(x\right)\right]$ of the crack profile follows a Gaussian distribution.

We study the influence of white Gaussian noise in a system of two mutually coupled light-controlled oscillators (LCOs). We show that under certain noise intensity conditions, noise can destroy or enhance synchronization. We build some Arnold tonguelike structures in order to explain the effects due to noise. It is remarkable that noise-enhanced synchronization is possible only when the variances of the noise acting on each of the LCOs are different.

We review the fictitious integrable system approach which predicts dynamical tunneling rates from regular states to the chaotic region in systems with a mixed phase space. It is based on the introduction of a fictitious integrable system that resembles the regular dynamics within the regular island. We focus on the direct regular-to-chaotic tunneling process which dominates if nonlinear resonances within the regular island are not relevant. For quantum maps, billiard systems, and optical microcavities, we find excellent agreement with numerical rates for all regular states.

This paper describes an individual-based model for simulating the swarming behavior of prey in the presence of predators. Predators and prey are represented as agents that interact through radial force laws. The prey form swarms through attractive and repulsive forces. The predators interact with the prey through an anti-Newtonian force, which is a nonconservative force that acts in the same direction for both agents. Several options for forces between predators are explored. The resulting equations are solved numerically and the dynamics are described in the context of the swarm’s ability to realistically avoid the predators. The goal is to reproduce swarm behavior that has been observed in nature with the simplest possible model.

Glow discharge plasma in the excitable regime shows rich dynamical behavior under external forcing. By perturbing the plasma with a subthreshold sawtooth periodic signal, we obtained small subthreshold oscillations that showed resonance with the perturbation frequency. The resonance phenomenon can be useful to estimate characteristic of an excitable system. However, for suprathreshold perturbation, frequency entrainment was observed. In this case, the system showed harmonic frequency entrainment for the perturbation frequencies greater than the characteristic frequency of the system and the excitable behavior for the perturbation frequencies well below the characteristic frequency. The experiments were performed in a glow-discharge plasma where excitability was achieved at a suitable discharge voltage and gas pressure.

Bounding volume results in discreteness of eigenmodes in wave systems. This leads to a depletion or complete loss of wave resonances (three-wave, four-wave, etc.), which has a strong effect on wave turbulence (WT) i.e., on the statistical behavior of broadband sets of weakly nonlinear waves. This paper describes three different regimes of WT realizable for different levels of the wave excitations: discrete, mesoscopic and kinetic WT. Discrete WT comprises chaotic dynamics of interacting wave “clusters” consisting of discrete (often finite) number of connected resonant wave triads (or quarters). Kinetic WT refers to the infinite-box theory, described by well-known wave-kinetic equations. Mesoscopic WT is a regime in which either the discrete and the kinetic evolutions alternate or when none of these two types is purely realized. We argue that in mesoscopic systems the wave spectrum experiences a sandpile behavior. Importantly, the mesoscopic regime is realized for a broad range of wave amplitudes which typically spans over several orders on magnitude, and not just for a particular intermediate level.

We apply the $\delta$-expansion method to nonlinear stochastic differential equations describing wave propagation in a random medium. In particular, we focus our attention on a model describing a nonlinear wave propagating in a turbulent atmosphere which has random variations in the refractive index (we take these variations to be stochastic). The method allows us to construct much more reasonable perturbation solutions with relatively few terms (compared to standard “small-parameter” perturbation methods) due to more accurate linearization used in constructing the initial approximation. We demonstrate that the method allows one to compute effective wave numbers more precisely than other methods applied to the problem in the literature. The method also picks up on the stochastic damping of the solutions quickly, holding all of the relevant data in the initial term. These properties allow for both a qualitative and a quantitative construction of physically meaningful solutions. In particular, we show that the method allows one to retain higher-order harmonics which are hard to capture with standard perturbation methods based on small parameters.

The isostatic jamming limit of frictionless spherical particles from Edwards’ statistical mechanics [Song et al., Nature (London) 453, 629 (2008)] is generalized to arbitrary dimension $d$ using a liquid-state description. The asymptotic high-dimensional behavior of the self-consistent relation is obtained by saddle-point evaluation and checked numerically. The resulting random close packing density scaling $\varphi \sim d{2}^{-d}$ is consistent with that of other approaches, such as replica theory and density-functional theory. The validity of various structural approximations is assessed by comparing with three- to six-dimensional isostatic packings obtained from simulations. These numerical results support a growing accuracy of the theoretical approach with dimension. The approach could thus serve as a starting point to obtain a geometrical understanding of the higher-order correlations present in jammed packings.

A mechanically based structural optimization method is utilized to explore the phenomena of jamming for assemblies of frictionless Platonic solids. Systems of these regular convex polyhedra exhibit mechanically stable phases with density substantially less than optimal for a given shape, revealing that thermal motion is necessary to access high-density phases. We confirm that the large system jamming threshold of $0.623\pm 0.003$ for tetrahedra is consistent with experiments on tetrahedral dice. Also, the extremely short-ranged translational correlations of packed tetrahedra observed in experiments are confirmed here, in contrast with those of thermally simulated glasses. Although highly ordered phases are observed to form for small numbers of cubes and dodecahedra, the short correlation length scale suppresses ordering in large systems, resulting in packings that are mechanically consistent with “orientationally disordered” contacts (point-face and edge-edge contacts). Mild nematic ordering is observed for large systems of cubes, whereas angular correlations for the remaining shapes are ultrashort ranged. In particular the angular correlation function of tetrahedra agrees with that recently observed experimentally for tetrahedral dice. Power-law scaling exponents for energy with respect to distance from the jamming threshold exhibit a clear dependence on the “highest-order” percolating contact topology. These nominal exponents are 6, 4, and 2 for configurations having percolating point-face (or edge-edge), edge-face, and face-face contacts, respectively. Jamming contact number is approximated for small systems of tetrahedra, icosahedra, dodecahedra, and octahedra with order and packing representative of larger systems. These Platonic solids exhibit hypostatic behavior, with average jamming contact number between the isostatic value for spheres and that of asymmetric particles. These shapes violate the isostatic conjecture, displaying contact number that decreases monotonically with sphericity. The common symmetry of dual polyhedra results in local translational structural similarity. Systems of highly spherical particles possessing icosahedral symmetry, such as icosahedra or dodecahedra, exhibit structural behavior similar to spheres, including jamming contact number and radial distribution function. These results suggest that although continuous rotational symmetry is broken by icosahedra and dodecahedra, the structural features of disordered packings of these particles are well replicated by spheres. Octahedra and cubes, which possess octahedral symmetry, exhibit similar local translational ordering, despite exhibiting strong differences in nematic ordering. In general, the structural features of systems with tetrahedra, octahedra, and cubes differ significantly from those of sphere packings.

We examine phase separation in aqueous mixtures due to preferential solvation with a low-density solute (hydrophilic ions or hydrophobic particles). For hydrophilic ions, preferential solvation can stabilize water domains enriched with ions. This precipitation occurs above a critical solute density $n_{\text{p}}$ in wide ranges of the temperature and the average composition, where the mixture solvent would be in a one-phase state without solute. The volume fraction of precipitated domains tends to zero as the average solute density $\overline{n}$ is decreased to $n_{\text{p}}$ or as the interaction parameter $\chi$ is decreased to a critical value ${\chi }_{\text{p}}$. If we start with one-phase states with $\overline{n}>n_{\text{p}}$ or $\chi >{\chi }_{\text{p}}$, precipitation proceeds via homogeneous nucleation or via heterogeneous nucleation, for example, around suspended colloids. In the latter case, colloid particles are wrapped by thick wetting layers. We also predict a first-order prewetting transition for $\overline{n}$ or $\chi$ slightly below $n_{\text{p}}$ or ${\chi }_{\text{p}}$ for neutral colloids.

We present a model for actin-based motility that combines the dynamics of the semiflexible region at the leading edge of the lamellipodium with actomyosin gel properties in the bulk described by the theory of active polar gels. We calculate the velocity of the lamellipodium determined by the interaction of the gel and adhesion with forces in the semiflexible region. The stationary concave force-velocity relation of the model reproduces experimental results. We suggest that it is determined by retrograde flow at small forces and gel formation and retrograde flow at large ones. The variety of dynamic regimes of the semiflexible region reproducing experimentally observed morphodynamics is conserved when we couple the leading edge to the gel.

We investigate the coevolution dynamics of node activities and coupling strengths in coupled chaotic oscillators via a simple threshold adaptive scheme. The coupling strength is synchronous activity regulated, which in turn is able to boost the synchronization remarkably. In the case of weak coupling, the globally coupled oscillators present a highly clustered functional connectivity with a power-law distribution in the tail with $\gamma \simeq 3.1$, while for strong coupling, they self-organize into a network with a heterogeneously rich connectivity at the onset of synchronization but exhibit rather sparse structure to maintain the synchronization in noisy environment. The relevance of the results is briefly discussed.

Strong terahertz (THz) radiation can be generated by intense femtosecond laser pulses propagating in air. The excitation of transient current induced in the wake just behind the laser pulse is studied in detail using numerical simulations on the basis of Maxwell’s equations for THz-band fields and hydrodynamic model for the plasma motion. It is shown that the thermal effects, anisotropic in character in the case of linear polarized laser field, can explain observed quadrupole-type THz radiation pattern in the experiment performed by Akhmedzhanov et al. [Radiophys. Quantum Electron. 52, 482 (2009)]. Taking into account the transverse structure of the plasma filament, our numerical code enables us to calculate the spatial distribution and temporal evolution of terahertz electron current, its spectrum, and angular emission pattern. It is shown that an expansion of full fields in terms of azimuthal modes is a useful tool for research of THz generation in many situations of practical interest.

The polarization of the two beam (driver-probe) high-order harmonic generation from solids is measured. The experiments, together with computer simulations, allow us to distinguish two different coupling mechanisms of the driver and the probe, resulting in different harmonic efficiencies and spectral slopes. We find that in the nonrelativistic regime the coupling is mostly due to the nonlinear plasma density modulation.

Human blood flow is a multiscale problem: in first approximation, blood is a dense suspension of plasma and deformable red cells. Physiological vessel diameters range from about one to thousands of cell radii. Current computational models either involve a homogeneous fluid and cannot track particulate effects or describe a relatively small number of cells with high resolution but are incapable to reach relevant time and length scales. Our approach is to simplify much further than existing particulate models. We combine well-established methods from other areas of physics in order to find the essential ingredients for a minimalist description that still recovers hemorheology. These ingredients are a lattice Boltzmann method describing rigid particle suspensions to account for hydrodynamic long-range interactions and—in order to describe the more complex short-range behavior of cells—anisotropic model potentials known from molecular-dynamics simulations. Paying detailedness, we achieve an efficient and scalable implementation which is crucial for our ultimate goal: establishing a link between the collective behavior of millions of cells and the macroscopic properties of blood in realistic flow situations. In this paper we present our model and demonstrate its applicability to conditions typical for the microvasculature.

We present a method for minimizing additive potential-energy functions. Our hidden-force algorithm can be described as an intricate multiplayer tug-of-war game in which teams try to break an impasse by randomly assigning some players to drop their ropes while the others are still tugging until a partial impasse is reached, then, instructing the dropouts to resume tugging, for all teams to come to a new overall impasse. Utilizing our algorithm in a non-Markovian parallel Monte Carlo search, we found 17 new putative global minima for binary Lennard-Jones clusters in the size range of 90–100 particles. The method is efficient enough that an unbiased search was possible; no potential-energy surface symmetries were exploited. All new minima are comprised of three nested polyicosahedral or polytetrahedral shells when viewed as a nested set of Connolly surfaces (though the shell structure has previously gone unscrutinized, known minima are often qualitatively similar). Unlike known minima, in which the outer and inner shells are comprised of the larger and smaller atoms, respectively, in 13 of the new minima, the atoms are not as clearly separated by size. Furthermore, while some known minima have inner shells stabilized by larger atoms, four of the new minima have outer shells stabilized by smaller atoms.

In a recent publication [E. Y. Petrov and A. V. Kudrin, Phys. Rev. Lett. 104, 190404 (2010)], a method for constructing exact axisymmetric solutions of the Maxwell equations in a nonlinear nondispersive medium has been put forward. In this Brief Report, we will use the proposed method to deal with problems of wave propagation in an inhomogeneous nonlinear and nondispersive medium. The inhomogeneous factor is chosen in the form as $r^{\beta }$, where $\beta$ is a certain constant. By solving the Maxwell equations an exact axisymmetric solution is obtained, starting from the corresponding solution of linear field equations, to describe the propagation of cylindrical electromagnetic waves in the medium. In the limit $\beta \to 0$, our solutions go into a nonlinear but homogeneous case, which is the same as prevenient results. We analyze the initial value problem and boundary value problem, to compare the differences between homogeneous and inhomogeneous conditions. It is found that the amplitude and frequency of the electromagnetic wave can be controlled with different $\beta$. Our results can be used for analysis of inhomogeneous ferroelectric resonators.

Stochastic resonance is numerically and analytically studied using a model wherein two coupled particles are exposed to noise of heterogeneous (i.e., particle-dependent) amplitude. In a certain range of coupling constant and under noise of heterogeneous amplitude, a particle is observed to resonate intensively to the external field. In other words, one particle under noise of very small or zero amplitude exhibits intensive resonance with the assistance of a highly fluctuating second particle under noise of large amplitude. This intensive resonance is interpreted as a product of the unique combinatory dynamics between one particle that stochastically fluctuates and another particle that classically resonates to the external field.

When studying the motion of optically trapped particles on the microsecond time scale, in low-viscosity media such as air, inertia cannot be neglected. Resolution of unusual and interesting behavior not seen in colloidal trapping experiments is possible. In an attempt to explain the phenomena we use power-spectral methods to perform a parameter study of the Brownian motion of optically trapped liquid aerosol droplets concentrated around the critically damped regime. We present evidence that the system is suitably described by a simple harmonic oscillator model which must include a description of Faxén’s correction, but not necessarily frequency dependent hydrodynamic corrections to Stokes’ law. We also provide results describing how the system behaves under several variables and discuss the difficulty in decoupling the parameters responsible for the observed behavior. We show that due to the relatively low dynamic viscosity and high trap stiffness, it is easy to transfer between over- and underdamped motion by experimentally altering either trap stiffness or damping. Our results suggest stable aerosol trapping may be achieved in underdamped conditions, but the onset of deleterious optical forces at high trapping powers prevents the probing of the upper stability limits due to Brownian motion.