Coupled distinct arrays of nonlinear oscillators have been shown to have a regime of high frequency, or ultraharmonic, oscillations that are at multiples of the natural frequency of individual oscillators. The coupled array architectures generate an in-phase high-frequency state by coupling with an array in an antiphase state. The underlying mechanism for the creation and stability of the ultraharmonic oscillations is analyzed. A class of interarray coupling is shown to create a stable, in-phase oscillation having frequency that increases linearly with the number of oscillators, but with an amplitude that stays fairly constant. The analysis of the theory is illustrated by numerical simulation of coupled arrays of Stuart-Landau limit cycle oscillators.

For stochastic magnetic flux functions with percolative contours the test particle transport is investigated. The calculations make use of the stochastic Liouville approach. They start from the so-called $A$-Langevin equations, including stochastic magnetic field components and binary collisions. Using the decorrelation trajectory method, a relation between the Lagrangian velocity correlation function and the Eulerian magnetic field correlation is derived and introduced into the Green-Kubo formalism. Finite Larmor radius effects are included. Interesting results are presented in the percolation regime corresponding to high Kubo numbers. Previous results are found to be limiting cases for small Kubo numbers. For different percolative scenarios the diffusion is analyzed and strong influences of the percolative structures on the transport scaling are found. The finite Larmor radius effects are discussed in detail. Numerical simulations of the $A$-Langevin equation confirm the semianalytical predictions.

The response of complex ionized gas systems to the presence of nonuniform distribution of charged grains is investigated using a kinetic model. Contrary to an existing view that the electron temperature inevitably increases in the grain-occupied region because of enhanced ionization to compensate for the electrons lost to the grains, it is shown that this happens only when the ionizing electric field increases in the electron depleted region. The results for two typical plasma systems suggest that when the ionizing electric field depends on the spatially averaged electron density, the electron temperature in the grain containing region can actually decrease.

Experimental measurements of the coherent wave transmission for ultrasonic waves propagating in water through a random set of scatterers (metallic rods) are presented. Though the densities are moderate (6% and 14%) the experimental results show that the mean-free path deviates from the classical first-order approximation due to the existence of correlations between scatterers. Theoretical results for the mean free path obtained from different approaches are compared to the experimental measurements. The best agreement is obtained with the second-order diagrammatic expansion of the self-energy.

We present a Monte Carlo algorithm, which samples free energies of complex systems. Less probable configurations are populated with the help of a multitude of additional Gaussian weights and parallel tempering is used for efficient Monte Carlo moves within phase space. The algorithm is easily parallelized and can be applied to a wide class of problems. We discuss algorithmic performance for the case of low-temperature phase separation in two-dimensional and three-dimensional Ising models, where we determine the magnetic interface tension. Multiple Gaussian modified ensemble simulations, unlike multicanonical ensemble simulations do not require a priori knowledge of the free energy and are of similar efficiency as multicanonical ensemble and Wang-Landau simulations.

Molecular dynamic simulations are performed to investigate the melting process of two-dimensional clusters of classical charged particles trapped in an anisotropic parabolic potential. The confined particles interact through a repulsive potential. We find that the eccentricity of the confinement potential strongly affects the melting pattern of such clusters. Increasing the eccentricity of the confinement potential drives the system through three different melting regimes. Inhomogeneous melting is the typical melting process for anisotropically confined clusters and its appearance in small systems occurs in a distinct form called here internal intershell melting. The latter involves only particles in the center of the cluster while particles on the far left and right of the cluster are still ordered having a much higher melting temperature. Using the Lindemann’s criterion the melting temperatures are determined as a function of the different parameters. The internal intershell melting process is found for both long-range (i.e., logarithmic) and short-range (i.e., screened Coulomb) interparticle interaction. Decreasing the range of the interparticle interaction increases the eccentricity of the confinement potential for which internal intershell melting can occur.

Using molecular dynamics simulations, we study the Jagla model of a liquid which consists of particles interacting via a spherically symmetric two-scale potential with both repulsive and attractive ramps. This potential displays anomalies similar to those found in liquid water, namely expansion upon cooling and an increase of diffusivity upon compression, as well as a liquid-liquid (LL) phase transition in the region of the phase diagram accessible to simulations. The LL coexistence line, unlike in tetrahedrally coordinated liquids, has a positive slope, because of the Clapeyron relation, corresponding to the fact that the high density phase (HDL) is more ordered than low density phase (LDL). When we cool the system at constant pressure above the critical pressure, the thermodynamic properties rapidly change from those of LDL-like to those of HDL-like upon crossing the Widom line. The temperature dependence of the diffusivity also changes rapidly in the vicinity of the Widom line, namely the slope of the Arrhenius plot sharply increases upon entering the HDL domain. The properties of the glass transition are different in the two phases, suggesting that the less ordered phase is fragile, while the more ordered phase is strong, which is consistent with the behavior of tetrahedrally coordinated liquids such as water silica, silicon, and ${\mathrm{BeF}}_2$.

Ductile compaction is common in many natural systems, but the temporal evolution of such systems is rarely studied. We observe surprising oscillations in the weight measured at the bottom of a self-compacting ensemble of ductile grains. The oscillations develop during the first ten hours of the experiment, and usually persist through the length of an experiment (one week). The weight oscillations are connected to the grain-wall contacts, and are directly correlated with the observed strain evolution and the dynamics of grain-wall contacts during the compaction. Here, we present the experimental results and characteristic time constants of the system, and discuss possible reasons for the measured weight oscillations.

A continuum theory of dielectric relaxation within liquid crystal materials is described and used to model the response of dual frequency materials to single pulse voltage waveforms. The equations governing the anisotropic axis (director) angle, electric field, and induced polarizations are solved numerically to investigate pulsed addressing of a model zenithally bistable liquid crystal device. By suitably tailoring the voltage pulse, it is found to be possible to switch between both bistable states. For short pulses the high frequency components of the leading edge of the voltage pulse excites the perpendicular polarization and forces the director to lie parallel to the cell substrates. For longer voltage pulses the constant dc component of the voltage pulse excites the parallel polarization causing the director to lie perpendicular to the substrates. It is also found that reducing rotational viscosity and increasing the achievable dielectric anisotropies (particularly the high frequency value) can significantly reduce the operating voltages of such a device.

We present a quantitative picture of the separation of star polymers in a solution where part of the volume is influenced by a porous medium. To this end, we study the impact of long-range-correlated quenched disorder on the entropy and scaling properties of $f$-arm star polymers in a good solvent. We assume that the disorder is correlated on the polymer length scale with a power-law decay of the pair correlation function $g\left(r\right)\sim r^{-a}$. Applying the field-theoretical renormalization group approach we show in a double expansion in $\epsilon =4-d$ and $\delta =4-a$ that there is a range of correlation strengths $\delta$ for which the disorder changes the scaling behavior of star polymers. In a second approach we calculate for fixed space dimension $d=3$ and different values of the correlation parameter $a$ the corresponding scaling exponents ${\gamma }_f$ that govern entropic effects. We find that ${\gamma }_f-1$, the deviation of ${\gamma }_f$ from its mean field value is amplified by the disorder once we increase $\delta$ beyond a threshold. The consequences for a solution of diluted chain and star polymers of equal molecular weight inside a porous medium are that star polymers exert a higher osmotic pressure than chain polymers and in general higher branched star polymers are expelled more strongly from the correlated porous medium. Surprisingly, polymer chains will prefer a stronger correlated medium to a less or uncorrelated medium of the same density while the opposite is the case for star polymers.

We develop a generalized hyperdynamics method that is able to simulate slow dynamics in atomistic general (both energy- and entropy-dominated) systems. We show that a few functionals of the pair correlation function, involving two-body entropy, form a low-dimensional collective space, which is a good approximation that is able to distinguish stable and transitional conformations. A bias potential, which raises the energy in stable regions, is constructed on the fly. We examine the slow nucleation processes of a Lennard-Jones gas and show that our method can generate correct long-time dynamics without prior knowledge.

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity” over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.

We study second harmonic generation in a metallodielectric photonic-band-gap structure made of alternating layers of silver and a generic, dispersive, linear, dielectric material. We find that under ideal conditions the conversion efficiency can be more than two orders of magnitude greater than the maximum conversion efficiency achievable in a single layer of silver. We interpret this enhancement in terms of the simultaneous availability of phase matching conditions over the structure and good field penetration into the metal layers. We also give a realistic example of a nine-period, ${\mathrm{Si}}_3∕{\mathrm{N}}_4\mathrm{Ag}$ stack, where the backward conversion efficiency is enhanced by a factor of 50 compared to a single layer of silver.

We study the statistical properties of many Brownian particles under the influence of both a spatially homogeneous driving force and a periodic potential with period $\ell$ in a two-dimensional space. In particular, we focus on two asymptotic cases ${\ell }_{\mathrm{int}}⪡\ell$ and ${\ell }_{\mathrm{int}}⪢\ell$, where ${\ell }_{\mathrm{int}}$ represents the interaction length between two particles. We derive fluctuating hydrodynamic equations describing the evolution of a coarse-grained density field defined on scales much larger than $\ell$ for both cases. Using the obtained equations, we calculate the equal-time correlation functions of the density field to the lowest order of the interaction strength. We find that the system exhibits long-range correlation of the type $r^{-d}$ $(d=2)$ for the case ${\ell }_{\mathrm{int}}⪢\ell$, while no such behavior is observed for the case ${\ell }_{\mathrm{int}}⪡\ell$.

An Ising spin system under the critical temperature driven by a dichotomous Markov noise (magnetic field) with a finite correlation time is studied both numerically and theoretically. The order parameter exhibits a transition between two kinds of qualitatively different dynamics, symmetry-restoring and symmetry-breaking motions, as the noise intensity is changed. There exist regions called channels where the order parameter stays for a long time slightly above its critical noise intensity. Developing a phenomenological analysis of the dynamics, we investigate the distribution of the passage time through the channels and the power spectrum of the order parameter evolution. The results based on the phenomenological analysis turn out to be in quite good agreement with those of the numerical simulation.

We describe in detail how to implement a coarse-grained hybrid molecular dynamics and stochastic rotation dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length scales of this problem is emphasized. We systematically analyze how our coarse-graining scheme resolves dimensionless hydrodynamic numbers such as the Reynolds number Re, which indicates the importance of inertial effects, the Schmidt number Sc, which indicates whether momentum transport is liquidlike or gaslike, the Mach number, which measures compressibility effects, the Knudsen number, which describes the importance of noncontinuum molecular effects, and the Peclet number, which describes the relative effects of convective and diffusive transport. With these dimensionless numbers in the correct regime the many Brownian and hydrodynamic time scales can be telescoped together to maximize computational efficiency while still correctly resolving the physically relevant processes. We also show how to control a number of numerical artifacts, such as finite-size effects and solvent-induced attractive depletion interactions. When all these considerations are properly taken into account, the measured colloidal velocity autocorrelation functions and related self-diffusion and friction coefficients compare quantitatively with theoretical calculations. By contrast, these calculations demonstrate that, notwithstanding its seductive simplicity, the basic Langevin equation does a remarkably poor job of capturing the decay rate of the velocity autocorrelation function in the colloidal regime, strongly underestimating it at short times and strongly overestimating it at long times. Finally, we discuss in detail how to map the parameters of our method onto physical systems and from this extract more general lessons—keeping in mind that there is no such thing as a free lunch—that may be relevant for other coarse-graining schemes such as lattice Boltzmann or dissipative particle dynamics.

The influence of confinement, due to flat parallel structureless walls, on phase separation in colloid-polymer mixtures, is investigated by means of grand-canonical Monte Carlo simulations. Ultrathin films, with thicknesses between $D=3–10$ colloid diameters, are studied. The Asakura-Oosawa model [J. Chem. Phys. 22, 1255 (1954)] is used to describe the particle interactions. To simulate efficiently, a “cluster move” [J. Chem. Phys. 121, 3253 (2004)] is used in conjunction with successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)]. These techniques, when combined with finite size scaling, enable an accurate determination of the unmixing binodal. Our results show that the critical behavior of the confined mixture is described by “effective” critical exponents, which gradually develop from values near those of the two-dimensional Ising model, to those of the three-dimensional Ising model, as $D$ increases. The scaling predictions of and Fisher and Nakanishi [J. Chem. Phys. 75, 5875 (1981)] for the shift of the critical point are compatible with our simulation results. Surprisingly, however, the colloid packing fraction at criticality approaches its bulk $(D\to \infty )$ value nonmonotonically, as $D$ is increased. Far from the critical point, our results are compatible with the simple Kelvin equation, implying a shift of order $1∕D$ in the coexistence colloid chemical potential. We also present density profiles and pair distribution functions for a number of state points on the binodal, and the influence of the colloid-wall interaction is studied.

We have studied the phase diagram for chromatin within the framework of the two-angle model. Only a rough estimation of the forbidden surface of the phase diagram for chromatin was given in a previous work of Schiessel. We revealed the fine structure of this excluded-volume borderline numerically and analytically. Furthermore, we investigated the Coulomb repulsion of the DNA linkers to compare it with the previous results.

We study the spatiotemporal dynamics of a one-way coupled FitzHugh-Nagumo system of twenty neurons, which is subject to external noise at the first neuron. It is shown that noise-induced oscillation (NIO) triggered at the first neuron is propagated along the chain with noise suppression, such that a rather “regular” signal is obtained at the last neuron, which can provide a mechanism for the creation of the informative signal in a neural network. Coherence resonance or coherence biresonance behavior appears in the transmission of NIO at appropriate coupling and the information flow in each neuron can be simultaneously optimized at the optimal value of noise.

In this paper we derive the general equilibrium equations of a polymer chain with a noncircular cross section by the variation of the free energy functional. From the equilibrium equation of the elastic ribbon we derive analytically the equilibrium conformations both of the helical ribbons and the twisted ribbons. We find that the pitch angle of the helical ribbons depends on the ratio of the torsional rigidity to the bending one. For the twisted ribbons, the rotation rate depends on the spontaneous torsion, which is determined by the elastic properties of the polymers. Our results for helical and twisted ribbons strongly indicate that the formation of these structures is determined by their elastic properties.