We demonstrate that the quasi-equilibrium state in a self-gravitating $N$-body system after cold collapse is uniquely characterized by the local virial relation using numerical simulations. Conversely, assuming the constant local virial ratio and Jeans equation for a spherically steady-state system, we investigate the full solution space of the problem under the constant anisotropy parameter and obtain some relevant solutions. Specifically, the local virial relation always provides a solution which has a power-law density profile in both the asymptotic regions $r\to 0$ and $\infty$. This type of solution is commonly observed in many numerical simulations. Only the anisotropic velocity dispersion controls this asymptotic behavior of density profile.

We study scale-free simple graphs with an exponent of the degree distribution $\gamma$ less than 2. Generically one expects such extremely skewed networks—which occur very frequently in systems of virtually or logically connected units—to have different properties than those of scale free networks with $\gamma >2$: The number of links grows faster than the number of nodes and they naturally posses the small world property, because the diameter increases by the logarithm of the size of the network and the clustering coefficient is finite. We discuss a simple prototype model of such networks, inspired by real world phenomena, which exhibits these properties and allows for a detailed analytical investigation.

A method for numerical simulation of two-term exponentially correlated colored noise is proposed. The method is an extension of traditional method for one-term exponentially correlated colored noise. The validity of the algorithm is tested by comparing numerical simulations with analytical results in two physical applications.

This work investigates singularities occurring at finite real times in the classical dynamics of one-dimensional double-well systems with complex initial conditions. The objective is to understand the relationship between these singularities and the behavior of the systems for real initial conditions. An analytical treatment establishes that the dynamics of a quartic double well system possesses a doubly infinite sequence of singularities. These are associated with initial conditions that converge to those for the real separatrix as the singularity time becomes infinite. This confluence of singularities is shown to lead to the unstable behavior that characterizes the real motion at the separatrix. Numerical calculations confirm the existence of a large number of singularities converging to the separatrix for this and two additional double-well systems. The approach of singularities to the real axis is of particular interest since such behavior has been related to the formation of chaos in nonintegrable systems. The properties of the singular trajectories which cause this convergence to the separatrix are identified. The hyperbolic fixed point corresponding to the potential energy maximum, responsible for the characteristic motion at a separatrix, also plays a critical role in the formation of the complex singularities by delaying trajectories and then deflecting them into asymptotic regions of space from where they are directly repelled to infinity in a finite time.

In this paper we report numerically observed spontaneous vanishing of mean curvature on a developable cone made by pushing a thin elastic sheet into a circular container [E. Cerda, S. Chaieb, F. Melo, and L. Mahadevan, Nature (London) 401 46 (1999)]. We show that this feature is independent of thickness of the sheet, the supporting radius, and the amount of deflection. Several variants of the developable cone are studied to examine the necessary conditions that lead to the vanishing of mean curvature. It is found that the presence of appropriate amount of radial stress is necessary. The developable cone geometry somehow produces the right amount of radial stress to induce just enough radial curvature to cancel the conical azimuthal curvature. In addition, the circular symmetry of supporting container edge plays an important role. With an elliptical supporting edge, the radial curvature overcompensates the azimuthal curvature near the minor axis and undercompensates near the major axis. Our numerical finding is verified by a crude experiment using a reflective plastic sheet. We expect this finding to have broad importance in describing the general geometrical properties of forced crumpling of thin sheets.

We extend our previous work on soliton ratchet devices [L. Morales-Molina et al., Eur. Phys. J. B 37, 79 (2004)] to consider the joint effect of two ac forces including nonharmonic drivings, as proposed for particle ratchets by Savele’v et al. [Europhys. Lett. 67, 179 (2004); Phys. Rev. E 70, 066109 (2004)]. Current reversals due to the interplay between the phases, frequencies, and amplitudes of the harmonics are obtained. An analysis of the effect of the damping coefficient on the dynamics is presented. We show that solitons give rise to nontrivial differences in the phenomenology reported for particle systems that arise from their extended character. A comparison with soliton ratchets in homogeneous systems with biharmonic forces is also presented. This ratchet device may be an ideal candidate for Josephson junction ratchets with intrinsic large damping.

Ensembles of quantum trajectories are evolved to study time-dependent reaction dynamics in multidimensional systems with up to 25 vibrational modes. The equations of motion are formulated in curvilinear reaction path coordinates and all coupling terms are retained, including those involving curvature of the reaction path. The model potential is a Gaussian barrier along the translational coordinate coupled to $M$ vibrational modes. Spatial derivatives needed to propagate the trajectories are evaluated by least squares fitting in a contracted basis set. Stable propagation of the trajectory ensembles was carried out until complete bifurcation into reflected and reactive subensembles. The reaction probabilities were evaluated by Monte Carlo integration of the multidimensional smooth transmitted densities. Computational results, including trajectory plots and time-dependent reaction probabilities, are presented for $M=1$, 5, and 25 vibrational modes.

We theoretically investigate the nonlinear dynamics and synchronization properties between two mutually coupled semiconductor lasers units. Each unit can self-oscillate by means of delayed optoelectronic feedback loops. The mutual optoelectronic interactions between the laser units take into account the finite propagation time of the signals. Under perfectly symmetric conditions, we find different “death by delay” islands that persist for instantaneous coupling. The appearance of (zero lag) isochronous chaotic synchronization, under appropriate driving conditions, is another distinctive feature of the delayed feedback loops in the laser units. For slightly asymmetric operation, we obtain frequency locked bands (Arnold Tongue) whose width periodically changes with the coupling delay time.

In this paper we present Hugoniot data for plastic foams obtained with laser-driven shocks. Relative equation-of-state data for foams were obtained using Al as a reference material. The diagnostics consisted in the detection of shock breakout from double layer Al/foam targets. The foams [poly(4-methyl-1-pentene) with density $130>\rho >60\mathrm{mg}∕{\mathrm{cm}}^3$] were produced at the Institute of Laser Engineering of Osaka University. The experiment was performed using the Prague PALS iodine laser working at $0.44\mu \mathrm{m}$ wavelength and irradiances up to a few ${10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. Pressures as high as $3.6\mathrm{Mbar}$ (previously unreached for such low-density materials) where generated in the foams. Samples with four different values of initial density were used, in order to explore a wider region of the phase diagram. Shock acceleration when the shock crosses the Al/foam interface was also measured.

In Phys. Rev. E 70, 047102 (2004), Torgerson and Lamoreaux investigated for the first time the real-frequency spectrum of the finite temperature correction to the Casimir force, for metallic plates of finite conductivity. The very interesting result of this study is that the large correction from the TE mode is dominated by low frequencies, for which the dielectric description of the metal is invalid, and the authors correctly point out that a more realistic description is provided by low-frequency metallic boundary conditions. However, their subsequent analysis uses an incorrect form of metallic boundary conditions for TE modes. After correcting this error, we find that their main conclusion was nevertheless qualitatively correct: contrary to the result of the dielectric model, the thermal TE mode correction leads to an increase in the TE mode force of attraction between the plates. The correction found by us, however, has a magnitude about 20 times larger than that quoted by Torgerson and Lamoreaux.

We respond to the “Comment on ‘Low-frequency character of the Casimir force between metallic films,’ ” by G. Bimonte, which points out an error in our earlier work [Phys. Rev. E 70, 047102(R) (2004)]. In particular, after correcting the error, the frequency range of the finite temperature contribution to the Casimir force is expanded and exceeds the range of validity for use of the Leontovich boundary. We estimate the size of the thermal effect with a modified boundary condition, and show that it agrees with the result of Bimonte, within the errors of previous experiments. An accurate (subpercent) calculation of the finite temperature contribution remains a theoretical challenge.

In this work we describe the electrorheology of suspensions consisting of hematite $\left(\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3\right)$ particles dispersed in silicone oil in the presence of large dc electric fields. If an electric field pulse is applied to the systems, it is possible to estimate the time that the electrorheological (ER) fluid takes to reach its final microstructure in the presence of the field. Our results indicate that response times of several seconds are typical, and that this time decreases with the field strength. Conventional shear-rate sweeps indicate the existence of a well-defined dynamic yield stress and a shear-thinning behavior. Interestingly, both the yield stress and the shear-thinning slope $a$ [relating the viscosity, $\eta$, and the shear rate, $\dot{\gamma }$, as $\eta =a{\dot{\gamma }}^{-b}+\eta \left(\infty \right)$] show a linear dependence on the field strength, $E$, in disagreement with the $E^2$ dependence often reported. This deviation is associated with changes in the conductivity of the dispersion medium with the field strength. A simple calculation of the interactions present in our ER fluid demonstrates that the ER behavior is entirely controlled by hydrodynamic $(\propto \dot{\gamma })$ and electrical forces $(\propto E)$. This is confirmed by the collapse of all experimental results in a single master curve when the relative viscosity is plotted against the ratio $\dot{\gamma }∕E$. Careful attention has been paid in this work to the microstructure of the suspensions in the presence of both shear and electric fields simultaneously: the particles gather themselves on the walls of the electrorheological measurement cell, forming aggregates with cylindrical symmetry, shaped as rings or lamellas of solids. The electric field induced increase in viscosity is the consequence of the balance between two actions: that of the electric field, tending to keep particles together, and that of the shear field, forcing the flow of the liquid phase in the regions between rings or between rings and walls.

The principal theme of this paper is that anomalously slow, super-Arrhenius relaxations in glassy materials may be activated processes involving chains of molecular displacements. As pointed out in a preceding paper with Lemaitre, the entropy of critically long excitation chains can enable them to grow without bound, thus activating stable thermal fluctuations in the local density or molecular coordination of the material. I argue here that the intrinsic molecular-scale disorder in a glass plays an essential role in determining the activation rate for such chains, and show that a simple disorder-related correction to the earlier theory recovers the Vogel-Fulcher law in three dimensions. A key feature of this theory is that the spatial extent of critically long excitation chains diverges at the Vogel-Fulcher temperature. I speculate that this diverging length scale implies that, as the temperature decreases, increasingly large regions of the system become frozen and do not contribute to the configurational entropy, and thus ergodicity is partially broken in the super-Arrhenius region above the Kauzmann temperature $T_K$. This partially broken ergodicity seems to explain the vanishing entropy at $T_K$ and other observed relations between dynamics and thermodynamics at the glass transition.

We study the fundamental vibration mode of supported submillimeter-size droplets. Using an analogy with a simple oscillator we derive a semianalytical expression for the eigenfrequency and the scaling law of the energy dissipation within the droplet. The experimental results obtained for mercury drops deposited on glass are compared with the model. The agreement is satisfactory for the eigenfrequencies on the whole range of size we considered (from $0.04$ to $0.9\mathrm{mm}$). The scaling law for the dissipation is recovered for radii larger than $0.1\mathrm{mm}$ but fails for smaller droplets. We finally discuss possible applications related to the use of vibrations to effectively reduce the hysteresis of the wetting angle and therefore increase the mobility of the supported droplets.

Propagator theory of brain dynamics is generalized to incorporate a new class of patchy propagators that enable treatment of approximately periodic structures such as are seen in the visual cortex. Complex response fields are also incorporated to allow for features such as orientation preference and wave-number selectivity. The results are applied to the corticothalamic system associated with the primary visual cortex. It is found that this system can generate gamma $(\gtrsim 30\mathrm{Hz})$ oscillations during stimulation, whose properties are consistent with experimental findings on gamma frequency and bandwidth, and existence of fine-scale spatial structure. It is found that a potential resonance is associated with each reciprocal lattice vector corresponding to periodic modulations of the propagators. It is found that the lowest resonances are the most likely to give rise to noticeable spectral peaks and increases of correlation amplitude, length, and time, and that these aspects are prominent only if the system is close to marginal stability, in accord with previous measurements and discussions of cortical stability. These features also enable gamma resonances to be stimulus-evoked, with substantial resonance sharpening for relatively small changes in mean neural firing rate. The results also imply dependence of gamma frequency on stimulus features.

Samples of the cuticle taken from the body of Buprestidae Chrysochroa vittata have been studied by scanning electron microscopy and optical reflectance measurements, related to numerical simulations. The cause of the metallic coloration of the body of these insects is determined to be the structure of the hard carapace constructed as a stack of thin chitin layers separated by very thin irregular air gaps. In particular the change of color as a function of the observation angle is elucidated in terms of an infinite photonic-crystal model, confirmed by finite multilayer calculations. These mechanisms are used to develop an artificial bioinspired multilayer system which reproduces the visual effects provided by the insect surface.

A theoretical framework is developed for moment neuronal networks (MNNs). Within this framework, the behavior of the system of spiking neurons is specified in terms of the first- and second-order statistics of their interspike intervals, i.e., the mean, the variance, and the cross correlations of spike activity. Since neurons emit and receive spike trains which can be described by renewal—but generally non-Poisson—processes, we first derive a suitable diffusion-type approximation of such processes. Two approximation schemes are introduced: the usual approximation scheme (UAS) and the Ornstein-Uhlenbeck scheme. It is found that both schemes approximate well the input-output characteristics of spiking models such as the IF and the Hodgkin-Huxley models. The MNN framework is then developed according to the UAS scheme, and its predictions are tested on a few examples.

Empirical and numerical microscopic features of moving traffic jams are presented. Based on a single vehicle data analysis, it is found that within wide moving jams, i.e., between the upstream and downstream jam fronts there is a complex microscopic spatiotemporal structure. This jam structure consists of alternations of regions in which traffic flow is interrupted and flow states of low speeds associated with “moving blanks” within the jam. Moving blanks within a wide moving jam resemble electron holes in the valence band of semiconductors: As the moving blanks that propagate upstream appear due to downstream vehicle motion within the jam, so appearance of electron holes moving with the electric field results from electron motion against the electric field in the valence band of semiconductors. Empirical features of moving blanks are found. Based on microscopic models in the context of the Kerner’s three-phase traffic theory, physical reasons for moving blanks emergence within wide moving jams are disclosed. Microscopic nonlinear effects of moving jam emergence, propagation, and dissolution as well as a diverse variety of hysteresis effects in freeway traffic associated with phase transitions and congested traffic propagation are numerically investigated. Microscopic structure of moving jam fronts is numerically studied and compared with empirical results.

We propose a routing strategy to improve the transportation efficiency on complex networks. Instead of using the routing strategy for shortest path, we give a generalized routing algorithm to find the so-called efficient path, which considers the possible congestion in the nodes along actual paths. Since the nodes with the largest degree are very susceptible to traffic congestion, an effective way to improve traffic and control congestion, as our strategy, can be redistributing traffic load in central nodes to other noncentral nodes. Simulation results indicate that the network capability in processing traffic is improved more than 10 times by optimizing the efficient path, which is in good agreement with the analysis.

The bifurcation diagram of steady convective flow patterns inside a cubical cavity with adiabatic lateral walls heated from below and filled with silicone oil $(\mathrm{Pr}=130)$ was determined for values of the Rayleigh number (Ra) up to $1.5\times {10}^5$. A continuation procedure based on the Galerkin spectral method was used to determine the steady convective solutions as a function of Ra. Bifurcations leading to either new steady or time-dependent solutions were identified and new steady solution branches were also continued. A total of fifteen steady solutions were tracked and the stability analysis predicted that six flow patterns were stable and that two, three, or even four of these patterns coexisted over certain ranges of Ra in the studied domain. Predicted flow patterns and transitions are in agreement with flow visualizations previously reported in the literature. The variation of the Nusselt number (Nu) as a function of Pr was investigated for three of the stable flow patterns identified: a $x$ or $y$ roll, a diagonal oriented roll and a pattern formed by four connected half rolls. It was found that whereas the Nusselt changes within the region $0.71⩽\mathrm{Pr}⩽10$ it tends to an asymptotic value with increasing Pr.