Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological, and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street patterns of different world cities. Samples are turned into spatial valued graphs. In such graphs, the nodes are embedded in the two-dimensional plane and represent street intersections, the edges represent streets, and the edge values are equal to the street lengths. We evaluate the local properties of the graphs by measuring the meshedness coefficient and counting short cycles (of three, four, and five edges), and the global properties by measuring global efficiency and cost. We also consider, as extreme cases, minimal spanning trees (MST) and greedy triangulations (GT) induced by the same spatial distribution of nodes. The measures found in the real and the artificial networks are then compared. Surprisingly, cities of the same class, e.g., grid-iron or medieval, exhibit roughly similar properties. The correlation between a priori known classes and statistical properties is illustrated in a plot of relative efficiency vs cost.

Recently we proposed an extension to the traffic model of Aw, Rascle, and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse-$\lambda$ shape of the fundamental diagram of traffic flow. In the current work we analyze the steady-state solutions of the model and their stability properties. In addition to the equilibrium flow curve the trivial steady-state solutions form two additional branches in the flow-density diagram. We show that the characteristic structure excludes parts of these branches, resulting in the reverse-$\lambda$ shape of the flow-density relation. The upper branch is metastable against the formation of synchronized flow for intermediate densities and unstable for high densities, whereas the lower branch is unstable for intermediate densities and metastable for high densities. Moreover, the model can reproduce the typical speed of the downstream front of wide moving jams. It further reproduces a constant outflow from wide moving jams, which is far below the maximum free flow. Applying the model to simulate traffic flow at a bottleneck we observe a general pattern with wide moving jams traveling through the bottleneck.

We derive exact Langevin-type equations governing quasispecies dynamics. The inherent multiplicative noise has both real and imaginary parts. The numerical simulation of the underlying complex stochastic partial differential equations is carried out employing the Cholesky decomposition for the noise covariance matrix. This noise produces unavoidable spatiotemporal density fluctuations about the mean-field value. In two dimensions, the fluctuations are suppressed only when the diffusion time scale is much smaller than the amplification time scale for the master species.

A coarse-grained description of the restricted primitive model is considered in terms of the local charge- and number-density fields. Exact reduction to a one-field theory is derived, and exact expressions for the number-density correlation functions in terms of higher-order correlation functions for the charge-density are given. It is shown that in continuum space the singularity of the charge-density correlation function associated with short-wavelength charge-ordering disappears when charge-density fluctuations are included by following the Brazovskii approach. The related singularity of the individual Feynman diagrams contributing to the number-density correlation functions is cured when all the diagrams are segregated into disjoint sets according to their topological structure. By performing a resummation of all diagrams belonging to each set a regular expression represented by a secondary diagram is obtained. The secondary diagrams are again segregated into disjoint sets, and the series of all the secondary diagrams belonging to a given set is represented by a hyperdiagram. A one-to-one correspondence between the hyperdiagrams contributing to the number-density vertex functions, and diagrams contributing to the order-parameter vertex functions in a certain model system belonging to the Ising universality class is demonstrated. Corrections to scaling associated with irrelevant operators that are present in the model-system Hamiltonian, and other corrections specific to the RPM are also discussed.

Under certain conditions, focused laser excitation in semiconductor quantum well structures can lead to a charge separation and a circular reaction front, which is visible as a ring-shaped photoluminescence pattern. The diffusion-reaction equations governing the system are studied here with the aim of a detailed understanding of the steady state. The qualitative asymmetry in the sources for the two carriers is found to lead to unusual effects which dramatically affect the steady-state configuration. Analytic expressions are derived for carrier distributions and interface positions for a number of cases. These are compared with steady-state information obtained from simulations of the diffusion-reaction equations.

A thin disk-shaped container filled with a ferrofluid and suspended in a horizontal linearly polarized ac magnetic field can perform torsional vibrations around its vertical diameter. In contrast to a recently studied spherical pendulum, the cell is sensitive to the field direction: It exposes its edge to the stationary or slowly oscillating magnetic field, and its broad side to the field of a high frequency. When the amplitude of the latter field is increased, the state of rest gets destabilized, yielding to oscillations near the equilibrium. Further growth of the field strength results in the onset of the cell rotation. We describe sequences of local and global bifurcations which accompany those transitions.

Limitations of observer-based synchronization systems under information constraints (limited information capacity of the coupling channel) are evaluated. We give theoretical analysis for multidimensional drive-response systems represented in the Lurie form (linear part plus nonlinearity depending only on measurable outputs). It is shown that the upper bound of the limit synchronization error (LSE) is proportional to the upper bound of the transmission error. As a consequence, the upper and lower bounds of LSE are proportional to the maximum rate of the coupling signal and inversely proportional to the information transmission rate (channel capacity). Optimality of the binary coding for coders with one-step memory is established. The results are applied to synchronization of two chaotic Chua systems coupled via a channel with limited capacity.

We analyze the linear stability of the edge of a thin liquid metal layer subject to a transverse high-frequency ac magnetic field. The layer is treated as a perfectly conducting liquid sheet that allows us to solve the problem analytically for both a semi-infinite geometry with a straight edge and a thin disk of finite radius. It is shown that the long-wave perturbations of a straight edge are monotonically unstable when the wave number exceeds the critical value $k_c=F_0∕\left(\gamma l_0\right)$, which is determined by the linear density of the electromagnetic force $F_0$ acting on the edge, the surface tension $\gamma$, and the effective arclength of edge thickness $l_0$. Perturbations with wavelength shorter than critical are stabilized by the surface tension, whereas the growth rate of long-wave perturbations reduces as $\sim k$ for $k\to 0$. Thus, there is the fastest growing perturbation with the wave number $k_{\max }=2∕3k_c$. When the layer is arranged vertically, long-wave perturbations are stabilized by the gravity, and the critical perturbation is characterized by the capillary wave number $k_c=\sqrt{g\rho ∕\gamma }$, where $g$ is the acceleration due to gravity and $\rho$ is the density of metal. In this case, the critical linear density of electromagnetic force is $F_{0,c}=2k_c{l}_0\gamma$, which corresponds to the critical current amplitude $I_{0,c}=4\sqrt{\pi k_c{l}_{0}L\gamma ∕{\mu }_0}$ when the magnetic field is generated by a straight wire at the distance $L$ directly above the edge. By applying the general approach developed for the semi-infinite sheet, we find that a circular disk of radius $R_0$ placed in a transverse uniform high-frequency ac magnetic field with the induction amplitude $B_0$ becomes linearly unstable with respect to exponentially growing perturbation with the azimuthal wave number $m=2$ when the magnetic Bond number exceeds ${\mathrm{Bm}}_c=B_0^2{R}_0^2∕\left(2{\mu }_0{l}_0\gamma \right)=3\pi$. For $\mathrm{Bm}>{\mathrm{Bm}}_c$, the wave number of the fastest growing perturbation is $m_{\max }=[2\mathrm{Bm}∕(3\pi \left)\right]$. These theoretical results agree well with the experimental observations.

Druyvesteyn’s method finds the distribution of electron speeds from the second derivative of probe data using the assumption that the distribution is spherically symmetric. For the disk probe, the data are more directly related to the velocity distribution projected onto the direction normal to the probe surface. The projected distribution is less sensitive to noise because it is related to the first derivative of the data rather than the second. For the cylindrical probe, the data are more directly related to the distribution of energies projected onto the plane perpendicular to the probe axis. A method is developed for recovering this projected distribution from digitized probe data. The method is mathematically more complex than Druyvesteyn’s method, but has the advantage of being less sensitive to noise. The methods are compared using noise-free simulated data and using noisy data from a double-plasma device with multidipolar magnetic confinement.

The recent proposal to use highly charged ions as sources of electrons for laser acceleration [S. X. Hu and A. F. Starace, Phys. Rev. Lett. 88, 245003 (2002)] is investigated here in detail by means of three-dimensional, relativistic Monte Carlo simulations for a variety of system parameters, such as laser pulse duration, ionic charge state, and laser focusing spot size. Realistic laser focusing effects—e.g., the existence of longitudinal laser field components—are taken into account. Results of spatial averaging over the laser focus are also presented. These numerical simulations show that the proposed scheme for laser acceleration of electrons from highly charged ions is feasible with current or near-future experimental conditions and that electrons with GeV energies can be obtained in such experiments.

We study a system comprising a spheroidal particle with permittivity ${\epsilon }_2$ and conductivity ${\sigma }_2$ immersed in a host medium with permittivity ${\epsilon }_1$ and conductivity ${\sigma }_1$ in the ac external electric field with a strength ${\stackrel{\mathrm{⃗}}{\mathrm{E}}}_0$ and frequency $\omega$. We determined conditions when orientation of a spheroidal particle with a finite electric conductivity at $t\to \infty$ coincides with the orientation of the ideal dielectric spheroidal particle, when orientation of a spheroid at $t\to \infty$ is normal to the orientation of the ideal dielectric spheroidal particle, and when orientation of particle is not affected by the external electric field. We found the direct connection between the final orientation of the particle and the existence of two time intervals, $T_1\left(\omega \right)$ and $T_2\left(\omega \right)$, such that during time interval $T_1$ an equilibrium orientation of the particle is the same as the equilibrium orientation of an ideal dielectric particle while during time interval $T_2$ the direction of the stable equilibrium orientation is normal to the equilibrium orientation of an ideal dielectric particle. The values $T_1$ and $T_2$ depend on the frequency of the external field $\omega$ and $T=T_1\left(\omega \right)+T_2\left(\omega \right)$, where $T=2\pi ∕\omega$.

I introduce a method to derive mesoscopic particle interactions by macroscopic thermodynamics, which is suitable for simulation of multiphase fluids by means of the lattice Boltzmann equation. For van der Waals fluids, the interaction possesses a high-density strong repulsive core and a low-density weak attractive tail, which looks like the Lennard-Jones potential with replacement of the distance between particles with mass density. Numerical results on phase separation show a droplet growth scheme rather than spinodal decomposition, and exhibit accurately the equilibrium phase diagram, a convincing interfacial energy property, and irreversible thermodynamics.

The reflection properties of cholesteric films with thermally induced pitch gradients are theoretically and experimentally studied. It is shown that the optical behavior of such films corresponds to the averaged contribution of a number of stochastic pitch variation profiles, due to the transversal and longitudinal nonuniformities that develop in the helical structure of such samples. Depending on the annealing time, both narrow-band and broadband behavior can be selectively achieved. The influence of the pitch profile gradient on the broadband reflection performance of cholesteric samples is theoretically analyzed, and a multi-slab structure for achieving optimum efficiency is proposed.

We investigate the return-volatility correlation both local and nonlocal in time with daily and minutely data of the German DAX and Chinese indices, and observe a leverage effect for the German DAX, while an antileverage effect for the Chinese indices. In the negative time direction, i.e., for the volatility-return correlation, an antileverage effect nonlocal in time is detected for both the German DAX and Chinese indices, although the duplicate local in time does not exist. A retarded volatility model may describe the asymmetric properties of the financial indices in the positive time direction.

We report the observation of a square superlattice pattern in a dielectric barrier discharge system. The correlation measurements indicate that the square superlattice pattern is an interleaving of two different transient square sublattices. The interplay between the charge pattern and the discharge filament pattern is discussed.

We study the stability of compressible differentially rotating flows in the presence of the magnetic field, and we show that the compressibility profoundly alters the previous results for a magnetized incompressible flow. The necessary condition of newly found instability can be easily satisfied in various flows in laboratory and astrophysical conditions and reads $B_s{B}_{\phi }{\Omega }^{\prime }\ne 0$, where $B_s$ and $B_{\phi }$ are the radial and azimuthal components of the magnetic field, ${\Omega }^{\prime }=d\Omega ∕ds$ with $s$ being the cylindrical radius. Contrary to the well-known magnetorotational instability that occurs only if $\Omega$ decreases with $s$, the instability considered in this paper may occur at any sign of ${\Omega }^{\prime }$. The instability can operate even in a very strong magnetic field that entirely suppresses the standard magnetorotational instability. The growth time of instability can be as short as a few rotation periods.

The effective thermal conductivity of composites with embedded self-similar $\mathsf{H}$-shaped fractal-like tree networks is studied. It is found that the effective thermal conductivity of the composites with these networks is related to the structures of the networks and the ratio of the component thermal conductivities: the longer the branches, the lower the thermal conductivity; the smaller the ratio $\left(\beta \right)$ of successive branch diameters, the lower the thermal conductivity; the denser the network, the lower the thermal conductivity. It is also found that the thermal conductivity of the $\mathsf{H}$-shaped fractal-like tree networks does not obey Murray’s law. The present results show that a network embedded in a composite plays an important role, and the thermal conductivity of the network itself may be less than that of the original material by several orders of magnitude. Fractal-like tree networks can significantly reduce the thermal conductivity compared to an equivalent single cylinder.

We use Rice’s theory of shot noise random processes to provide a statistical analysis of the evolution of the amplitude and phase of the chaotic optical field from a high-gain, self-amplified, spontaneous-emission (SASE) free-electron laser. The theoretical framework developed is compared with recent frequency-resolved optical-gating measurements of the SASE output at the LEUTL facility at Argonne National Laboratory.

We study stability and dynamics of the single cylindrically symmetric solitary structures and dipolar solitonic molecules in spatially nonlocal media. The main properties of the solitons, vortex solitons, and dipolar solitons are investigated analytically and numerically. The vortices and higher-order solitons show the transverse symmetry-breaking azimuthal instability below some critical power. We find the threshold of the vortex soliton stabilization using the linear stability analysis and direct numerical simulations. The higher-order solitons, which have a central peak and one or more surrounding rings, are also demonstrated to be stabilized in nonlocal nonlinear media. Using direct numerical simulations, we find a class of radially asymmetric, dipolelike solitons and show that, at sufficiently high power, these structures are stable.

We have examined the rational solitons in the Generalized Coupled Mode model for a deep nonlinear Bragg grating. These solitons are the degenerate forms of the ordinary solitons and appear at the transition lines in the parameter plane. A simple formulation is presented for the investigation of the bifurcations induced by detuning the carrier wave frequency. The analysis yields among others the appearance of in-gap dark and antidark rational solitons unknown in the nonlinear shallow grating. The exact expressions for the corresponding rational solitons are also derived in the process, which are characterized by rational algebraic functions. It is further demonstrated that certain effects in the soliton energy variations are to be expected when the frequency is varied across the values where the rational solitons appear.