In this paper, global synchronization in coupled oscillator networks is investigated. We propose an adaptive weighted network and show that such a simple and quite general scheme is able to tip oscillator networks towards collective synchronization. In comparison with the results based on linear stability analysis of unweighted networks, the proposed scheme improves the synchronizability of network dynamics, and is beneficial to analyze the effect of network structure on synchronizability.

We study the evolution of three- and four-particle diffusion at large Reynolds numbers using kinematic simulation (KS) in isotropic turbulent flows. We vary the Reynolds number and find that the geometrical characteristics of triangles and tetrahedrons as functions of time do not depend on the Reynolds number but only on the ratio ${\Delta }_0∕L_1$ that is on the portion of the inertial range that was contained within the triangle or tetrahedron at the initial time. We also study the effect of the modeling of the unsteadiness term in the KS.

We apply the Bogoliubov-Krilov method of averaging to the study of the stability of the $\pi$-mode solution ($N∕2$ one-mode nonlinear solution) of the Fermi-Pasta-Ulam-$\beta$ system, with negative values of the nonlinearity parameter $\beta$ in the Hamiltonian of the system. The analysis is made as a function of the number $N$ of the particles and of the product $\lambda =ϵ\mid \beta \mid$, where $ϵ$ is the energy density. The results of this application are in excellent agreement with those obtained by the direct integration of motion equation.

How can we remove some interactions (generate shorter clauses) in a constraint satisfaction problem (CSP) such that it still remains satisfiable? In this paper we study a modified survey propagation algorithm that enables us to address this question for a prototypical CSP, i.e., random $K$-satisfiability problem. The average number of removed interactions is controlled by a tuning parameter in the algorithm. If the original problem is satisfiable then we are able to construct satisfiable subproblems ranging from the original one to a minimal one with minimum possible number of interactions. The minimal satisfiable subproblems will directly provide the solutions of the original problem.

We study numerically the aging dynamics of the two-dimensional $p$-state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior characteristic of nondisordered coarsening systems. For quenches to the ferromagnetic phase, the value of the dynamical exponents suggests that the model belongs to the Ising-type universality class. Specifically, for the integrated response function $\chi (t,s)\simeq s^{-a_{\chi }}f(t∕s)$, we find $a_{\chi }$ consistent with the value $a_{\chi }=0.28$ found in the two-dimensional Ising model.

We study the dynamics of precipitate coarsening in phase-separating alloys at late stages of phase separation by x-ray photon correlation spectroscopy (XPCS). For analyzing time series of fluctuating speckle intensities from small-angle scattering of coherent x rays, the method of detrended fluctuation analysis (DFA), which is ideal for determining power-law correlations, is applied. We discuss the application of DFA with respect to XPCS data by means of simulated time series. In particular, the effects of different signal-to-noise ratios are examined. Results from measurements of the two model systems $\mathrm{Al}\text{−}6\mathrm{at}.\%\mathrm{Ag}$ at $140°\mathrm{C}$ and $\mathrm{Al}\text{−}9\mathrm{at}.\%\mathrm{Zn}$ at $0°\mathrm{C}$ are presented. Since the DFA effectively removes adulterating trends in the data, quantitative agreement with Monte Carlo simulations is obtained. It is verified that two different coarsening mechanisms are predominant in the two systems—coarsening either by diffusion of single atoms or by movement of whole precipitates.

The entropic force exerted by the Brownian fluctuations of a grafted semiflexible polymer upon a rigid smooth wall are calculated both analytically and by Monte Carlo simulations. Such forces are thought to play an important role for several cellular phenomena, in particular, the physics of actin-polymerization-driven cell motility and movement of bacteria like Listeria. In the stiff limit, where the persistence length of the polymer is larger than its contour length, we find that the entropic force shows scaling behavior. We identify the characteristic length scales and the explicit form of the scaling functions. In certain asymptotic regimes, we give simple analytical expressions which describe the full results to a very high numerical accuracy. Depending on the constraints imposed on the transverse fluctuations of the filament, there are characteristic differences in the functional form of the entropic forces. In a two-dimensional geometry, the entropic force exhibits a marked peak.

The temperature-independent Wang-Landau Monte Carlo approach is implemented for an off-lattice model of flexible homopolymers and applied to the coil-globule and solidification transitions based on chain sizes up to $N=300$. An intermediate transformation from low-density liquid globule to high-density liquid globule is suggested. A scheme for identifying polymer structures representative of particular temperatures in the course of the simulation is presented and applied to illustrate intermediate states in the coil-globule transition. Transition temperatures are calculated and used to obtain a theta point of at least $\Theta =1.96$, distinctly higher than the solid-liquid transition temperature $T_M=1.26$.

The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of observables numerically computed along dynamical trajectories are found to reproduce results given by the statistical mechanics of homopolymer models. The dynamical treatment, however, indicates a nontrivial transition between regimes of slow and fast phase space mixing. Such a transition is inaccessible to a statistical mechanical treatment and reflects a bimodality in the relaxation of time averages to corresponding ensemble averages. It is also found that a change in the energy dependence of the largest Lyapunov exponent indicates the $\Theta$ transition between filamentary and globular polymer configurations, clearly detecting the transition even for a finite number of particles.

We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, that represent here populations of cells involved in cancerous proliferation and cytotoxic response of the immune system, the overall kinetics can be approximated by a one-dimensional overdamped Langevin equation. The modulating activity of the immune response is here modeled as a dichotomous random process of the relative rate of neoplastic cell destruction. We discuss physical aspects of environmental noises acting in such a system, pointing out the possibility of coexistence of dynamical regimes where noise-enhanced stability and resonant activation phenomena can be observed together. We explain the underlying mechanisms by analyzing the behavior of the variance of first passage times as a function of the noise intensity.

An extended FitzHugh-Nagumo model coupled with dynamical heat transfer in tissue, as described by a bioheat equation, is derived and confronted with experiments. The main outcome of this analysis is that traveling pulses and spiral waves of electric activity produce temperature variations on the order of tens of $\mu °\mathrm{C}$. In particular, the model predicts that a spiral wave’s tip, heating the surrounding medium as a consequence of the Joule effect, leads to characteristic hot spots. This process could possibly be used to have a direct visualization of the tip’s position by using thermal detectors.

We propose two types of evolving networks: evolutionary Apollonian networks (EANs) and general deterministic Apollonian networks (GDANs), established by simple iteration algorithms. We investigate the two networks by both simulation and theoretical prediction. Analytical results show that both networks follow power-law degree distributions, with distribution exponents continuously tuned from 2 to 3. The accurate expression of clustering coefficient is also given for both networks. Moreover, the investigation of the average path length of EAN and the diameter of GDAN reveals that these two types of networks possess small-world feature. In addition, we study the collective synchronization behavior on some limitations of the EAN.

We present a heuristic algorithm for the optimization of transport on complex networks. Previously proposed network transport optimization algorithms aim at avoiding or reducing link overload. Our algorithm balances traffic on a network by minimizing the maximum node betweenness with as little path lengthening as possible, thus being useful in cases when networks are jamming due to node congestion. By using the resulting routing, a network can sustain significantly higher traffic without jamming than in the case of shortest path routing.

We formulate a fictitious-time-flow equation which drives an initial guess torus to a torus invariant under a given dynamics, provided such a torus exists. The method is general and applies in principle to continuous time flows and discrete time maps in arbitrary dimension and to both Hamiltonian and dissipative systems.

The effect of a stationary electric field on a water droplet with a diameter of several tens micrometers in oil was examined. Such a droplet exhibits repetitive translational motion between the electrodes in a spontaneous manner. The state diagram of this oscillatory motion was deduced; at $0–20\mathrm{V}$ the droplet is fixed at the surface of the electrode, at $20–70\mathrm{V}$ the droplet exhibits small-amplitude oscillatory motion between the electrodes, and at $70–100\mathrm{V}$ the droplet shows large-amplitude periodic motion between the electrodes. The observed rhythmic motion is explained in a semiquantitative manner by using differential equations, which includes the effect of charging the droplet under an electric field. We also found that twin droplets exhibit synchronized rhythmic motion between the electrodes.

By numerically solving the coupled laser Ginzburg-Landau equations and using the pulse tracing technique to incorporate the cavity effect in the simulation, we have explicitly calculated the soliton polarization ellipses throughout the cavity of a fiber-ring laser mode-locked by the nonlinear polarization rotation technique, and investigated the soliton polarization dynamics in laser cavities. It was found that in a conventional stable soliton operation state, although the soliton polarization varies as the pulse propagates, at a fixed position inside the laser cavity the soliton polarization is invariant with time. However, in the presence of laser dynamics, at a fixed location within the cavity the soliton could either have multiple alternating fixed polarization states or no fixed polarization state at all, depending on the soliton dynamics.

Transmission dips in the response of metallic compound gratings formed by several wires and slits in each period have been recently reported for normal illumination. These anomalies are generated by a particular arrangement of the magnetic field phases inside the subwavelength slits, and they are characterized by a significant enhancement of the interior field. We investigate the microwave response of such systems under non-normal illumination and show that new phase modes appear in this configuration. Contrary to the effect produced by a defect in a photonic crystal, these systems exhibit forbidden channels within a permitted band. We also found that the appearance of these resonances is not highly dependent on the slits' width and thickness, even though these parameters modify the overall transmittance.

Diffusion in a quasi-one-dimensional channel, with cross section varying along the longitudinal coordinate, is considered. Using a rigorous mapping of the diffusion equation onto one dimension, eliminating transients in transverse direction(s), we derive an expansion of the effective diffusion coefficient $D\left(x\right)$, which represents corrections to the Fick-Jacobs equation.

The transition from surface to bulk normal dielectric rolls in a nematic liquid crystal is imaged by fluorescence confocal polarizing microscopy. The three-dimensional director structure and the liquid flow are scanned in both the layer plane and the transverse plane. Two systems of small-scale convective flow are formed, one at each electrode. Strong anchoring makes director oscillations difficult and charges accumulate by the Carr-Helfrich mechanism. The middle region is a structureless convection where the director oscillates with the frequency of the applied voltage. The small-scale flow eventually fills the cell from one electrode to the other as one system of thin and elongated rolls. The true dielectric mode is not a director pattern, rather a surface flow instability.

We have performed exhaustive multicanonical Monte Carlo simulations of three 12-residue synthetic peptides in order to investigate the thermodynamic and structural properties as well as the characteristic helix-coil transitions. In these studies, we employ a realistic model where the interactions between all atoms are taken into account. Effects of solvation are also simulated by using an implicit-solvent model.