We study local search algorithms for networks with heterogeneous edge weights, testing them on scale-free and Erdös-Rényi networks. We assume that the location of the destination node is discovered when it is two edges away, and that the search cost is additive. It was previously shown that a search strategy preferring high-degree nodes reduces the average search cost over a simple random walk. In the prior work, for the case when the edge costs are randomly distributed, a different preference was investigated [high local betweenness centrality (LBC)], and was found to be superior to high-degree preference in scale-free networks, with the exception for the most sparse ones. We have found several preference criteria that are simpler and which, in all networks we tested, yield a lower cost than other criteria including high-degree, high-LBC, and low-edge cost.

We consider the effect of network topology on the optimality of packet routing which is quantified by ${\gamma }_c$, the rate of packet insertion beyond which congestion and queue growth occurs. We show that for any network, there exists an absolute upper bound, expressed in terms of vertex separators, for the scaling of ${\gamma }_c$ with network size $N$, irrespective of the static routing protocol used. We then derive an estimate to this upper bound for scale-free networks and introduce a static routing protocol, the “hub avoidance protocol,” which, for large packet insertion rates, is superior to the shortest path routing protocol.

Symplectic integrators evolve dynamical systems according to modified Hamiltonians whose error terms are also well-defined Hamiltonians. The error of the algorithm is the sum of each error Hamiltonian’s perturbation on the exact solution. When symplectic integrators are applied to the Kepler problem, these error terms cause the orbit to precess. In this work, by developing a general method of computing the perihelion advance via the Laplace-Runge-Lenz vector even for nonseparable Hamiltonians, I show that the precession error in symplectic integrators can be computed analytically. It is found that at leading order, each paired error Hamiltonians cause the orbit to precess oppositely by exactly the same amount after each period. Hence, symplectic corrector, or process integrators, which have equal coefficients for these paired error terms, will have their precession errors cancel at that order after each period. With the use of correctable algorithms, both the energy and precession error are of effective order $n+2$ where $n$ is the nominal order of the algorithm. Thus the physics of symplectic integrators determines the optimal algorithm for integrating long-time periodic motions.

Nucleation is considered near the pseudospinodal in a one-dimensional ${\varphi }^4$ model with a nonconserved order parameter and long-range interactions. For a sufficiently large system or a system with slow relaxation to metastable equilibrium, there is a non-negligible probability of nucleation occurring before reaching metastable equilibrium. This process is referred to as transient nucleation. The critical droplet is defined to be the configuration of maximum likelihood that is dynamically balanced between the metastable and stable wells. Time-dependent droplet profiles and nucleation rates are derived, and theoretical results are compared to computer simulations. The analysis reveals a distribution of nucleation times with a distinct peak characteristic of a nonstationary nucleation rate. Under the quench conditions employed, transient critical droplets are more compact than the droplets found in metastable equilibrium simulations and theoretical predictions.

The phenomena of radial and axial segregation in a horizontal rotating cylinder containing a mixture of granular particles of two different species have been modeled using discrete particle simulation. Space-time plots and detailed imagery provide a comprehensive description of what occurs in the system. As is the case experimentally, the nature of the segregation depends on the parameters defining the problem; the radial component of the segregation may be transient or long lasting, and the axial component may or may not develop. Simulations displaying the different kinds of behavior are described and the particle dynamics associated with the axially segregated state examined. The importance of an appropriate choice of interaction for representing the effective friction force is demonstrated.

We introduce an interacting random-walk model to describe the residence time of drug molecules undergoing a series of sojourn times in the body before being permanently eliminated under either homogeneous or heterogeneous conditions. We show that short-term correlations between drug molecules lead to Michaelis-Menten kinetics while long-term correlations lead to transient fractal-like kinetics. By combining both types of correlation, fractal-like Michaelis-Menten kinetics are achieved, and the simulations confirm previous analytical results.

We model information traffic on scale-free networks by introducing the node queue length $L$ proportional to the node degree and its delivering ability $C$ proportional to $L$. The simulation gives the overall capacity of the traffic system, which is quantified by a phase transition from free flow to congestion. It is found that the maximal capacity of the system results from the case of the local routing coefficient $\varphi$ slightly larger than zero, and we provide an analysis for the optimal value of $\varphi$. In addition, we report for the first time the fundamental diagram of flow against density, in which hysteresis is found, and thus we can classify the traffic flow with four states: free flow, saturated flow, bistable, and jammed.

It has been shown theoretically and observationally that the Green’s function for acoustic and elastic waves can be retrieved by cross-correlating fluctuations recorded at two locations. We extend the concept of the extraction of the Green’s function to a wide class of scalar linear systems. For systems that are not invariant under time reversal, the fluctuations must be excited by volume sources in order to satisfy the energy balance (equipartitioning) that is needed to extract the Green’s function. The general theory for retrieving the Green’s function is illustrated with examples that include the diffusion equation, Schrödinger’s equation, a vibrating string, the acoustic wave equation, a vibrating beam, and the advection equation. Examples are also shown of situations where the Green’s function cannot be extracted from ambient fluctuations. The general theory opens up new applications for the extraction of the Green’s function from field correlations that include flow in porous media, quantum mechanics, and the extraction of the response of mechanical structures such as bridges.

We investigate the dispersion relations of nonlinear periodic wave trains in excitable systems which describe the dependence of the propagation velocity on the wavelength. Pulse interaction by oscillating pulse tails within a wave train leads to bistable wavelength bands, in which two stable and one unstable wave train coexist for the same wavelength. The essential spectra of the unstable wave trains exhibit a circle of eigenvalues with positive real parts which is detached from the imaginary axis. We describe the destruction of the bistable dispersion curve and the formation of isolas of wave trains in a sequence of transcritical bifurcations unfolding into pairs of saddle-node bifurcations. It turns out that additional dispersion curves of unstable wave trains play an important role in the destruction of the bistable dispersion curve.

The eigenfrequencies of the potential-flow equilibria of a symmetric vortex pair behind an elliptic cylinder in uniform flow are calculated through the use of conformal mapping. These frequencies are shown to have values in agreement with measured Strouhal numbers reported in various papers. The special cases of the potential-flow equilibrium of a symmetric vortex pair behind a circular cylinder and the equilibrium behind a flat plate perpendicular to the uniform flow, are related to the measured Strouhal numbers of about 0.21 and 0.15, respectively. It is suggested that in the range of subcritical Reynolds numbers, $3\times {10}^2$ to $5\times {10}^5$ for the circular cylinder, a part of the drag is the result of the presence of a mean recirculation region in the near wake, which sheds vortices in the far wake and which is fed by vorticity from the cylinder wall.

The effects of strong Coulomb correlations in dense three-dimensional electron-hole plasmas are studied by means of unbiased direct path integral Monte Carlo simulations. The formation and dissociation of bound states, such as excitons and biexcitons, is analyzed and the density-temperature region of their appearance is identified. At high density, the Mott transition to the fully ionized metallic state (electron-hole liquid) is detected. Particular attention is paid to the influence of the hole to electron mass ratio $M$ on the properties of the plasma. Above a critical value of about $M=80$ formation of a hole Coulomb crystal was recently verified [Bonitz et al., Phys. Rev. Lett. 95, 235006 (2005)] which is supported by additional results. Results are related to the excitonic phase diagram of intermediate valent Tm[Se,Te], where large values of $M$ have been observed experimentally.

In a recent article Kengne and Liu [Phys. Rev. E 73, 026603 (2006)] have presented a number of exact elliptic solutions for a derivative nonlinear Schrödinger equation. It is the aim of this Comment to point out that all these solutions given in Secs. II and III of this article (referred to as KL in the following) are subcases of the general solution of Eq. (KL.9). Conditions for the parameters $A\text{−}E$ of the solutions given by Kengne and Liu can be found from general conditions for solitary and periodic elliptic solutions as shown in the following. Positive and bounded solutions can be found by considering the phase diagram. Therefore, the comment of Kengne and Liu that “we find its particular positive bounded solutions” can be specified.

The anomalous translational diffusion including inertial effects of nonlinear Brownian oscillators in a double well potential $V\left(x\right)=a{x}^2∕2+b{x}^4∕4$ is considered. An exact solution of the fractional Klein-Kramers (Fokker-Planck) equation is obtained allowing one to calculate via matrix continued fractions the positional autocorrelation function and dynamic susceptibility describing the position response to a small external field. The result is a generalization of the solution for the normal Brownian motion in a double well potential to fractional dynamics (giving rise to anomalous diffusion).

Recent atomic force microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick-shell models are proposed for two capsids: the spherical cowpea chlorotic mottle virus (CCMV), and the ellipsocylindrical bacteriophage $\varphi 29$. As analyzed by the finite-element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive particulars, and greatly influenced by geometric and kinematic details. Nonlinear stiffening and softening of the force response is dependent on the AFM tip dimensions and shell thickness. Fits of the models capture the roughly linear behavior observed in experimental measurements and result in estimates of Young’s moduli of $\approx 280–360\mathrm{MPa}$ for CCMV and $\approx 4.5\mathrm{GPa}$ for $\varphi 29$.

We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, strategies for enhancing robustness and immunization of a geographical network are proposed. Using the generating function formalism, we obtain an explicit form of the percolation threshold $q_c$ for networks containing arbitrary order cycles. For three-cycles, the dependence of $q_c$ on the clustering coefficients is ascertained. The analysis substantiates the validity of the strategies with analytical evidence.

The thermodynamic formalism for dynamical systems with many degrees of freedom is extended to deal with time averages and fluctuations of some macroscopic quantity along typical orbits, and applied to coupled map lattices exhibiting phase transitions. Thereby, it turns out that a seed of phase transition is embedded as an anomalous distribution of unstable periodic orbits, which appears as a so-called $q$-phase transition in the spatiotemporal configuration space. This intimate relation between phase transitions and $q$-phase transitions leads to one natural way of defining transitions and their order in extended chaotic systems. Furthermore, a basis is obtained on which we can treat locally introduced control parameters as macroscopic “temperature” in some cases involved with phase transitions.

The saturation curve of a sample of paper board was measured with mercury-intrusion porosimetry, and the three-dimensional structure of its pore space was determined by x-ray tomographic imaging. Ab initio numerical simulation of intrusion on the tomographic reconstruction, based on the lattice-Boltzmann method, was in excellent agreement with the measured saturation curve. A numerical invasion-percolation simulation in the same tomographic reconstruction showed good agreement with the lattice-Boltzmann simulation. The access function of the sample, determined from the saturation curve and the pore-throat distribution determined from the tomographic reconstruction, indicated that the ink-bottle effect is significant in paperlike materials.

We present a pair of coupled partial differential equations to describe the evolution of the average total intensity and intensity flux of a wave field inside a randomly layered medium. These equations represent a modification of the Kubelka-Munk equations, or radiative transfer. Our modification accounts for wave interference (e.g., localization), which is neglected in radiative transfer. We numerically solve the modified Kubelka-Munk equations and compare the results to radiative transfer as well as to simulations of the wave equation with randomly located thin layers.

It has long been known that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks (SAWs) on percolation clusters and their critical exponent ${\nu }_{\mathrm{SAW}}$, with the SAW implicitly referring to the average SAW. Hitherto, static averaging has been commonly used, e.g., in numerical simulations, to determine what the average SAW is. We assert that only kinetic, rather than static, averaging can lead to asymptotic scaling behavior and corroborate our assertion by heuristic arguments and a renormalizable field theory. Moreover, we calculate to two-loop order ${\nu }_{\mathrm{SAW}}$, the exponent ${\nu }_{\max }$ for the longest SAW, and a family of multifractal exponents ${\nu }^{\left(\alpha \right)}$.

Numerical and analytical results are presented for the maximal relative height distribution of stationary periodic Gaussian signals (one-dimensional interfaces) displaying a $1∕f^{\alpha }$ power spectrum. For $0\le \alpha <1$ (regime of decaying correlations), we observe that the mathematically established limiting distribution (Fisher-Tippett-Gumbel distribution) is approached extremely slowly as the sample size increases. The convergence is rapid for $\alpha >1$ (regime of strong correlations) and a highly accurate picture gallery of distribution functions can be constructed numerically. Analytical results can be obtained in the limit $\alpha \to \infty$ and, for large $\alpha$, by perturbation expansion. Furthermore, using path integral techniques we derive a trace formula for the distribution function, valid for $\alpha =2n$ even integer. From the latter we extract the small argument asymptote of the distribution function whose analytic continuation to arbitrary $\alpha >1$ is found to be in agreement with simulations. Comparison of the extreme and roughness statistics of the interfaces reveals similarities in both the small and large argument asymptotes of the distribution functions.