Using a network model involving statistical mechanics we study the topological transition of complex networks with evolving wiring structure. The evolution rule of our network model contains both a structuring effect originated in a wiring decision metric (local clustering coefficient) and a randomizing effect due to thermal fluctuation. Monte Carlo simulation results show a dramatic topological transition between nonclustered networks and clustered networks in response to changes in the degree of randomness.

We show that the main results of the analysis of the friction factor for turbulent pipe flow reported by Gioia and Chakraborty [Phys. Rev. Lett. 96, 044502 (2006)] can be recovered by assuming the Heisenberg closure hypothesis for the turbulent spectrum. This highlights the structural features of the turbulent spectrum underlying the analysis of Gioia and Chakraborty.

The longitudinal oscillations of a string pendulum are discussed. The regime in which the oscillating bob executes free flight under gravity is studied. This regime arises if, during the motion in the upward direction, bob reaches a height at which no elastic force acts on bob, and its further motion occurs only under gravity. Thus, the string pendulum executes a motion of two types: the harmonic oscillations under the action of elastic force and free flights under gravity. In doing so, the height of flights can considerably exceed the amplitude of the forced oscillations, i.e., a noticeable amplitude amplification in the longitudinal oscillations of a string pendulum takes place. A mechanism of a resonance phenomenon related to the excitation of free oscillations is described. These free oscillations arising after each bob flight are the channel for energy pumping into the system in question. It turns out that the frequency of the above resonance is equal to the fundamental frequency of the string, and the resonance amplitude of the flights is proportional to the square of amplitude of regular forced oscillations.

We present a fluid-particle model for a polymer solution in nonisothermal situations. The state of the fluid particles is characterized by the thermodynamic variables and a configuration tensor that describes the underlying molecular orientation of the polymer molecules. The specification of very simple physical mechanisms inspired by the dynamics of single polymer molecules allows one, with the help of the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) formalism, to derive the equations of motion for a set of fluid particles carrying polymer molecules in suspension. In the simplest case of Hookean dumbbells we recover a fluid-particle version of the Oldroyd-B model in which thermal fluctuations are included consistently. Generalization to more complex viscoelastic models, such as finitely extensible nonlinear elastic Peterlin (FENE-P) model, with the proper introduction of thermal fluctuations is straightforward.

We present a semiclassical lattice Boltzmann method based on quantum kinetic theory. The method is directly derived by projecting the Uehling-Uhlenbeck Boltzmann-Bhatnagar-Gross-Krook equations onto the tensor Hermite polynomials following Grad’s moment expansion method. The intrinsic discrete nodes of the Gauss-Hermite quadrature provide the natural lattice velocities for the semiclassical lattice Boltzmann method. Gases of particles of arbitrary statistics can be considered. Simulation of one-dimensional compressible gas flow and two-dimensional hydrodynamic flows are shown. The results indicate distinct characteristics of the effects of quantum statistics.

We present an evolving network model in which the total numbers of nodes and edges are conserved, but in which edges are continuously rewired according to nonlinear preferential detachment and reattachment. Assuming power-law kernels with exponents $\alpha$ and $\beta$, the stationary states which the degree distributions evolve toward exhibit a second-order phase transition—from relatively homogeneous to highly heterogeneous (with the emergence of starlike structures) at $\alpha =\beta$. Temporal evolution of the distribution in this critical regime is shown to follow a nonlinear diffusion equation, arriving at either pure or mixed power laws of exponents $-\alpha$ and $1-\alpha$.

Self-avoiding polymers in two-dimensional $\left(d=2\right)$ melts are known to adopt compact configurations of typical size $R\left(N\right)\sim N^{1/d}$, with $N$ being the chain length. Using molecular-dynamics simulations we show that the irregular shapes of these chains are characterized by a perimeter length $L\left(N\right)\sim R{\left(N\right)}^{d_p}$ of fractal dimension $d_p=d-{\Theta }_2=5/4$, with ${\Theta }_2=3/4$ being a well-known contact exponent. Due to the self-similar structure of the chains, compactness and perimeter fractality repeat for subchains of all arclengths $s$ down to a few monomers. The Kratky representation of the intramolecular form factor $F\left(q\right)$ reveals a strong nonmonotonous behavior with $q^{2}F\left(q\right)\sim 1/{\left(q{N}^{1/d}\right)}^{{\Theta }_2}$ in the intermediate regime of the wave vector $q$. Measuring the scattering of labeled subchains the form factor may allow to test our predictions in real experiments.

At the superfluid-solid ${}^4\text{H}\text{e}$ interface there exist crystallization waves having much in common with gravitational-capillary waves at the interface between two normal fluids. The Rayleigh-Taylor instability is an instability of the interface which can be realized when the lighter fluid is propelling the heavier one. We investigate here the analogs of the Rayleigh-Taylor instability for the superfluid-solid ${}^4\text{H}\text{e}$ interface. In the case of a uniformly accelerated interface the instability occurs only for a growing solid phase when the magnitude of the acceleration exceeds some critical value independent of the surface stiffness. For the Richtmyer-Meshkov limiting case of an impulsively accelerated interface, the onset of instability does not depend on the sign of the interface acceleration. In both cases the effect of crystallization wave damping is the reduction in the perturbation growth rate of the Taylor unstable interface.

Cilia and flagella are hairlike extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consists of a cylindrical arrangement of nine microtubule doublets, called the axoneme. The axoneme is an actively bending structure whose motility results from the action of dynein motor proteins cross-linking microtubule doublets and generating stresses that induce bending deformations. The periodic beat patterns are the result of a mechanical feedback that leads to self-organized bending waves along the axoneme. Using a theoretical framework to describe planar beating motion, we derive a nonlinear wave equation that describes the fundamental Fourier mode of the axonemal beat. We study the role of nonlinearities and investigate how the amplitude of oscillations increases in the vicinity of an oscillatory instability. We furthermore present numerical solutions of the nonlinear wave equation for different boundary conditions. We find that the nonlinear waves are well approximated by the linearly unstable modes for amplitudes of beat patterns similar to those observed experimentally.

The influence of coexisting correlated and noncorrelated impurities on the critical behavior of the three-dimensional Ising model is studied using Monte Carlo numerical simulations and finite-size scaling. The amount of correlated and noncorrelated vacancies is modified and controlled during the simulations. The long-range correlated (LRC) critical behavior is always found for any value of the concentration of correlated vacancies. The smaller the amount of correlated vacancies the larger the system size needed to detect the LRC universality class. This result explains why critical values measured in xerogel liquid-vapor experiments, where the concentration of correlated vacancies is marginal, seem to correspond to a short-range correlated disorder.

We propose an experimental setup based on a single oscillator for studying large networks formed by identical unidirectionally coupled systems. A chaotic wave form generated by the oscillator is stored in a computer to adjust the signal according to the desired network configuration to feed it again into the same oscillator. No previous theoretical knowledge about the oscillator dynamics is needed. To visualize network synchronization we introduce a network synchronization bifurcation diagram that should prove to be an effective tool for analysis, design, and optimization of complex networks.

We have identified the existence of globally clustered chimera states in delay-coupled oscillator populations and find that these states can breathe periodically and aperiodically and become unstable depending upon the value of coupling delay. We also find that the coupling delay induces frequency suppression in the desynchronized group. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.

The nonlinear propagation of the dust-acoustic (DA) waves in a strongly coupled dusty plasma containing strongly correlated arbitrarily (positively or negatively) charged dust and weakly correlated Boltzmann electrons and ions has been investigated by employing the generalized hydrodynamic model and the reductive perturbation method. It has been shown that the strong correlation among the charged dust is a source of dissipation and is responsible for the formation of the DA shock waves in such a strongly coupled dusty plasma. It has also been found that the DA shock waves with positive (negative) potential are formed for positively (negatively) charged dust. The basic features of such DA shock waves have been identified. It has been suggested that a laboratory experiment be performed to test the theory presented here.

We investigate the two components of the total daily return (close-to-close), the overnight return (close-to-open), and the daytime return (open-to-close), as well as the corresponding volatilities of the 2215 New York Stock Exchange stocks for the 20 year period from 1988 to 2007. The tail distribution of the volatility, the long-term memory in the sequence, and the cross correlation between different returns are analyzed. Our results suggest that (i) the two component returns and volatilities have features similar to that of the total return and volatility. The tail distribution follows a power law for all volatilities, and long-term correlations exist in the volatility sequences but not in the return sequences. (ii) The daytime return contributes more to the total return. Both the tail distribution and the long-term memory of the daytime volatility are more similar to that of the total volatility, compared to the overnight records. In addition, the cross correlation between the daytime return and the total return is also stronger. (iii) The two component returns tend to be anticorrelated. Moreover, we find that the cross correlations between the three different returns (total, overnight, and daytime) are quite stable over the entire 20 year period.

We study the dynamics of priority-queue networks, generalizations of the binary interacting priority-queue model introduced by Oliveira and Vazquez [Physica A 388, 187 (2009)]. We found that the original AND-type protocol for interacting tasks is not scalable for the queue networks with loops because the dynamics becomes frozen due to the priority conflicts. We then consider a scalable interaction protocol, an OR-type one, and examine the effects of the network topology and the number of queues on the waiting time distributions of the priority-queue networks, finding that they exhibit power-law tails in all cases considered, yet with model-dependent power-law exponents. We also show that the synchronicity in task executions, giving rise to priority conflicts in the priority-queue networks, is a relevant factor in the queue dynamics that can change the power-law exponent of the waiting time distribution.

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

It is known from experiments that the radiated x-ray energy appears to exceed the calculated implosion kinetic energy and Spitzer resistive heating [C. Deeney et al., Phys. Rev. A 44, 6762 (1991)] but possible mechanisms of the enhanced x-ray production are still being discussed. Enhanced plasma heating in small-diameter wire arrays with decreased calculated kinetic energy was investigated, and a review of experiments with cylindrical arrays of 1–16 mm in diameter on the 1 MA Zebra generator is presented in this paper. The implosion and x-ray generation in cylindrical wire arrays with different diameters were compared to find a transition from a regime where thermalization of the kinetic energy is the prevailing heating mechanism to regimes with other dominant mechanisms of plasma heating. Loads of 3–8 mm in diameter generate the highest x-ray power at the Zebra generator. The x-ray power falls in 1–2 mm loads which can be linked to the lower efficiency of plasma heating with the lack of kinetic energy. The electron temperature and density of the pinches also depend on the array diameter. In small-diameter arrays, 1–3 mm in diameter, ablating plasma accumulates in the inner volume much faster than in loads of 12–16 mm in diameter. Correlated bubblelike implosions were observed with multiframe shadowgraphy. Investigation of energy balance provides evidence for mechanisms of nonkinetic plasma heating in $Z$ pinches. Formation and evolution of bright spots in $Z$ pinches were studied with a time-gated pinhole camera. A comparison of x-ray images with shadowgrams shows that implosion bubbles can initiate bright spots in the pinch. Features of the implosions in small-diameter wire arrays are discussed to identify mechanisms of energy dissipation.

We present an improved space-discretization scheme for the numerical solutions of the time-dependent Schrödinger equation. Compared to the scheme of W. van Dijk and F. M. Toyama [Phys. Rev. E 75, 036707 (2007)], the present one, which contains more terms of second-order partial derivatives, greatly reduces the error resulting from the spatial integration. For a $\left(2l+1\right)$-point formula with $\left(2l+1\right)$ terms of second-order partial derivatives, the local truncation error can decrease from the order of ${\left(\Delta x\right)}^{2l}$ to ${\left(\Delta x\right)}^{4l}$, while the previous one contains only one term of second-order partial derivative. Two well-known numerical examples and the corresponding error analysis demonstrate that the present scheme has an advantage in the precision and efficiency over the previous one.

A nonisotropic tensorial extension of the single-component Shan-Chen pseudopotential Lattice Boltzmann method for nonideal fluids is presented. Direct comparison with experimental data shows that this extension is able to capture relevant features of ferrofluid behavior, such as the deformation and subsequent rupture of a liquid droplet as a function of an externally applied magnetic field. The present model offers an economic lattice-kinetic pathway to the simulation of complex ferrofluid hydrodynamics.

Using nonequilibrium molecular-dynamics simulations, we study the temperature dependence of the negative differential thermal resistance that appears in two-segment Frenkel-Kontorova lattices. We apply the theoretical method based on Landauer equation to obtain the relationship between the heat current and the temperature, which states a fundamental interpretation about the underlying physical mechanism of the negative differential thermal resistance. The temperature profiles and transport coefficients are demonstrated to explain the crossover from diffusive to ballistic transport. The finite-size effect is also discussed.