We study the coherent exciton transport on Apollonian networks generated by simple iterative rules. The coherent exciton dynamics is modeled by continuous-time quantum walks and we calculate the transition probabilities between two nodes of the networks. We find that the transport depends on the initial nodes of the excitation. For networks up to the second generation the coherent transport shows perfect recurrences when the initial excitation starts at the central node. For networks of higher generation, the transport only shows partial revivals. Moreover, we find that the excitation is most likely to be found at the initial nodes while the coherent transport to other nodes has a very low probability. In the long time limit, the transition probabilities show characteristic patterns with identical values of limiting probabilities. Finally, the dynamics of quantum transport are compared with the classical transport modeled by continuous-time random walks.

The minimal density model for negative streamer ionization fronts is investigated. An earlier moving boundary approximation for this model consisted of a “kinetic undercooling” type boundary condition in a Laplacian growth problem of Hele-Shaw type. Here we derive a curvature correction to the moving boundary approximation that resembles surface tension. The calculation is based on solvability analysis with unconventional features, namely, there are three relevant zero modes of the adjoint operator, one of them diverging; furthermore, the inner-outer matching ahead of the front must be performed on a line rather than on an extended region; and the whole calculation can be performed analytically. The analysis reveals a relation between the fields ahead and behind a slowly evolving curved front, the curvature and the generated conductivity. This relation forces us to give up the ideal conductivity approximation, and we suggest to replace it by a charge neutrality approximation. This implies that the electric potential in the streamer interior is no longer constant but solves a Laplace equation; this leads to a Muskat-type problem.

The stabilization of steady states is studied in a modified Lang-Kobayashi model of a semiconductor laser. We show that multiple time-delayed feedback, realized by a Fabry-Perot resonator coupled to the laser, provides a valuable tool for the suppression of unwanted intensity pulsations, and leads to stable continuous-wave operation. The domains of control are calculated in dependence on the feedback strength, delay time (cavity round trip time), memory parameter (mirror reflectivity), latency time, feedback phase, and bandpass filtering. Due to the optical feedback, multistable behavior can also occur in the form of delay-induced intensity pulsations or other modes for certain choices of the control parameters. Control may then still be achieved by slowly ramping the injection current during turn-on.

It is demonstrated that a catastrophic relativistic self-focusing (RSF) of a high-power laser pulse can be prevented all-optically by a second, much weaker, copropagating pulse. RSF suppression occurs when the difference frequency of the pulses slightly exceeds the electron plasma frequency. The mutual defocusing is caused by the three-dimensional electron density perturbation driven by the laser beat wave slightly above the plasma resonance. A bienvelope model describing the early stage of the mutual defocusing is derived and analyzed. Later stages, characterized by the presence of a strong electromagnetic cascade, are investigated numerically. Stable propagation of the laser pulse with weakly varying spot size and peak amplitude over several Rayleigh lengths is predicted.

We study a generalized conserved lattice gas model in two dimensions by introducing an effective temperature to the conserved lattice gas model, where the number of particles is conserved during the dynamical process. We apply Monte Carlo simulation with the Metropolis transition rate. At zero temperature we find two transition behaviors; one between the localized active states and absorbing states and the other between the localized active states and active states. With a different definition of the order parameter for the second transition behavior, we obtain the critical exponents at the transition point.

This study is related to the fluctuation theory of electromagnetic fields, charges, and currents. The three-dimensional system under consideration is a semi-infinite conductor, modeled by the jellium, in vacuum. In previous theoretical studies it was found that the correlation functions of the surface charge density on the conductor decay as the inverse cube of the distance at asymptotically large distances. The prefactor to this asymptotic decay was obtained in the classical limit and in the quantum case without retardation effects. To describe the retarded regime, we study a more general problem of the semi-infinite jellium in thermal equilibrium with the radiated electromagnetic field. By using Rytov’s fluctuational electrodynamics we show that, for both static and time-dependent surface charge correlation functions, the inclusion of retardation effects causes the quantum prefactor to take its universal static classical form, for any temperature.

The coefficient of normal restitution of colliding viscoelastic spheres is computed as a function of the material properties and the impact velocity. From simple arguments it becomes clear that, in a collision of purely repulsively interacting particles, the particles lose contact slightly before the distance of the centers of the spheres reaches the sum of the radii, that is, the particles recover their shape only after they lose contact with their collision partner. This effect was neglected in earlier calculations, which leads erroneously to attractive forces and thus to an underestimation of the coefficient of restitution. As a result we find a different dependence of the coefficient of restitution on the impact rate.

We use analytical calculations and Monte Carlo simulations to determine the thermal fluctuation spectrum of a membrane patch of a few tens of nanometer in size, whose corners are located at a fixed distance $d$ above a plane rigid surface. Our analysis shows that the surface influence on the bilayer fluctuations can be effectively described in terms of a uniform confining potential that grows quadratically with the height of the membrane $h$ relative to the surface: $V=(1∕2)\gamma h^2$. The strength $\gamma$ of the harmonic confining potential vanishes when the corners of the membrane patch are placed directly on the surface $(d=0)$, and achieves its maximum value when $d$ is of the order of a few nanometers. However, even at maximum strength, the confinement effect is quite small and has a noticeable impact only on the amplitude of the largest bending mode.

A neuronal population model of the sleep-wake switch is extended to incorporate impulsive external stimuli. The model includes the mutual inhibition of the sleep-active neurons in the hypothalamic ventrolateral preoptic area (VLPO) and the wake-active monoaminergic brainstem populations (MA), as well as circadian and homeostatic drives. Arbitrary stimuli are described in terms of their relative effects on the VLPO and MA nuclei and represent perturbations on the normal sleep-wake dynamics. By separating the model’s intrinsic time scales, an analytic characterization of the dynamics in a reduced model space is developed. Using this representation, the model’s response to stimuli is studied, including the latency to return to wake or sleep, or to elicit a transition between the two states. Since sensory stimuli are known to excite the MA, we correspondingly investigate the model’s response to auditory tones during sleep, as in clinical sleep fragmentation studies. The arousal threshold is found to vary approximately linearly with the model’s total sleep drive, which includes circadian and homeostatic components. This relationship is used to reproduce the clinically observed variation of the arousal threshold across the night, which rises to a maximum near the middle of the night and decreases thereafter. In a further application of the model, time-of-night arousal threshold and body temperature variations in an experimental sleep fragmentation study are replicated. It is proposed that the shift of the extrema of these curves to a greater magnitude later in the night is due to the homeostatic impact of the frequent nocturnal disturbances. By modeling the underlying neuronal interactions, the methods presented here allow the prediction of arousal state responses to external stimuli. This methodology is fundamentally different to previous approaches that model the clinical data within a phenomenological framework. As a result, a broader understanding of how impulsive external stimuli modulate arousal is gained.

It is shown that the pulses which develop in the $\mathrm{N}\mathrm{O}+{\mathrm{H}}_2$ reaction on an alkali promoted Rh(110) surface reaction can transport alkali metal. This leads to the accumulation of a substantial alkali-metal concentration in the collision area of pulse trains. Realistic simulations revealed that the effect is due to the strong energetic interactions of the alkali metal with coadsorbates, i.e., the attractive interaction with coadsorbed oxygen and the effectively repulsive interaction with coadsorbed nitrogen.

In this paper we introduce a weighted complex networks model to investigate and recognize structures of patterns. The regular treating in pattern recognition models is to describe each pattern as a high-dimensional vector which however is insufficient to express the structural information. Thus, a number of methods are developed to extract the structural information, such as different feature extraction algorithms used in pre-processing steps, or the local receptive fields in convolutional networks. In our model, each pattern is attributed to a weighted complex network, whose topology represents the structure of that pattern. Based upon the training samples, we get several prototypal complex networks which could stand for the general structural characteristics of patterns in different categories. We use these prototypal networks to recognize the unknown patterns. It is an attempt to use complex networks in pattern recognition, and our result shows the potential for real-world pattern recognition. A spatial parameter is introduced to get the optimal recognition accuracy, and it remains constant insensitive to the amount of training samples. We have discussed the interesting properties of the prototypal networks. An approximate linear relation is found between the strength and color of vertexes, in which we could compare the structural difference between each category. We have visualized these prototypal networks to show that their topology indeed represents the common characteristics of patterns. We have also shown that the asymmetric strength distribution in these prototypal networks brings high robustness for recognition. Our study may cast a light on understanding the mechanism of the biologic neuronal systems in object recognition as well.

Chaos-synchronization-based multiparameter estimation of a multiply delayed feedback system is investigated. We propose an adaptive method that can estimate all the parameters of the response system using the driving signal only. In the past few years, various methods have been developed for estimation of multiparameters of a chaotic system but most of them require more than one time series to estimate all the parameters of a chaotic or hyperchaotic system. The proposed method requires only a single chaotic time series to estimate all the parameters. A sufficient condition for synchronization is derived and it is shown that the numerical results well support the analytic calculations. The synchronized system has applications in cryptographic encoding for digital and analog signals, which is shown with an example.

The development of thermovibrational convection in a cubic cell filled with high Prandtl number liquid (isopropanol) is studied. Direct nonlinear simulations are performed by solving three-dimensional Navier-Stokes equations in the Boussinesq approximation. The cell is subjected to high frequency periodic oscillations perpendicular to the applied temperature gradient under zero gravity. Two types of vibrations are imposed: either as a sine or cosine function of time. It is shown that the initial vibrational phase plays a significant role in the transient behavior of thermovibrational convective flow. Such knowledge is important to interpret correctly short-duration experimental results performed in microgravity, among which the most accessible are drop towers $(\sim 5\mathrm{s})$ and parabolic flights $(\sim 20\mathrm{s})$. It is obtained that under sine vibrations, the flow reaches steady state within less than one thermal time. Under cosine acceleration, this time is 2 times longer. For cosine excitations, the Nusselt number is approximately 10 times smaller in comparison with the sine case. Besides, in the case of cosine, the Nusselt number oscillates with double frequency. However, at the steady state, time-averaged and oscillatory characteristics of the flow are independent of the vibrational start-up. The only feature that always differs the two cases is the phase difference between the velocity, temperature, and accelerations. We have found that due to nonlinear response of the system to the imposed vibrations, the phase shift between velocity and temperature is never equal exactly to $\pi ∕2$, at least in weightlessness. Thus, heat transport always exists from the beginning of vibrations, although it might be weak.

A recently established mathematical equivalence—between weakly perturbed Huygens fronts (e.g., flames in weak turbulence or geometrical-optics wave fronts in slightly nonuniform media) and the inviscid limit of white-noise-driven Burgers turbulence—motivates theoretical and numerical estimates of Burgers-turbulence properties for specific types of white-in-time forcing. Existing mathematical relations between Burgers turbulence and the statistical mechanics of directed polymers, allowing use of the replica method, are exploited to obtain systematic upper bounds on the Burgers energy density, corresponding to the ground-state binding energy of the directed polymer and the speedup of the Huygens front. The results are complementary to previous studies of both Burgers turbulence and directed polymers, which have focused on universal scaling properties instead of forcing-dependent parameters. The upper-bound formula can be heuristically understood in terms of renormalization of a different kind from that previously used in combustion models, and also shows that the burning velocity of an idealized turbulent flame does not diverge with increasing Reynolds number at fixed turbulence intensity, a conclusion that applies even to strong turbulence. Numerical simulations of the one-dimensional inviscid Burgers equation using a Lagrangian finite-element method confirm that the theoretical upper bounds are sharp within about 15% for various forcing spectra (corresponding to various two-dimensional random media). These computations provide a quantitative test of the replica method. The inferred nonuniversality (spectrum dependence) of the front speedup is of direct importance for combustion modeling.

We report the determination of the Kerr constant $\left(B\right)$ and the real part of the third-order nonlinear optic susceptibility $\left({\chi }^{\left(3\right)}\right)$ above the nematic-isotropic phase transition temperature $\left(T_{NI}\right)$ of a liquid crystal composed of bent-shaped molecules. The values of $B$ and ${\chi }^{\left(3\right)}$ just above $(\sim 0.3°\mathrm{C})$ $T_{NI}$ are $\sim 8\times {10}^{-12}\mathrm{m}∕{\mathrm{V}}^2$ and $5\times {10}^{-20}{\mathrm{m}}^2∕{\mathrm{V}}^2$, respectively. The estimated critical temperature $T_C^{*}$ is about $1.5°\mathrm{C}$ below $T_{NI}$ indicating that the nematic-isotropic $\left(NI\right)$ transition is weakly first order as in the case of calamitic liquid crystals. The temperature-dependent Kerr constant is found to be in good agreement with the predictions of the Landau–de Gennes theory. The experimental results are compared with those in a calamitic liquid crystal material with negative dielectric anisotropy in the nematic phase.

We introduce a stochastic equation for the microscopic motion of a tagged particle in the single-file model. This equation provides a compact representation of several of the system’s properties such as fluctuation-dissipation and linear-response relations, achieved by means of a diffusion noise approach. Most importantly, the proposed Langevin equation reproduces quantitatively the three temporal regimes and the corresponding time scales: ballistic, diffusive, and subdiffusive.

We present a rice-pile cellular automaton model that includes inertial and friction effects. This model is studied in one dimension, where the updating of metastable sites is done according to a stochastic dynamics governed by a probabilistic toppling parameter $p$ that depends on the accumulated energy of moving grains. We investigate the scaling properties of the model using finite-size scaling analysis. The avalanche size, the lifetime, and the residence time distributions exhibit a power-law behavior. Their corresponding critical exponents, respectively, $\tau$, $y$, and $y_r$, are not universal. They present continuous variation versus the parameters of the system. The maximal value of the critical exponent $\tau$ that our model gives is very close to the experimental one, $\tau =2.02$ [Frette et al., Nature (London) 379, 49 (1996)], and the probability distribution of the residence time is in good agreement with the experimental results. We note that the critical behavior is observed only in a certain range of parameter values of the system which correspond to low inertia and high friction.

Using the five-site transferable intermolecular potential (TIP5P) we perform molecular dynamics simulations to investigate the relationship between the excess entropy and anomalies of water. We find that the two-body excess entropy is an ideal quantity to predict the regions of structural, dynamic, and thermodynamic anomalies of water in its pressure-temperature and density-temperature phase diagrams. From the excess entropy we can also predict the location of the Widom line, associated with the hypothesized liquid-liquid critical point in supercooled water.

The dynamics of an isolated polymer chain has irreversible aspects that lead to the decorrelation of configurational properties over time. For simple mechanical models with time reversible equations of motion, the irreversibility is a consequence of the chaotic nature of the dynamics which, for a many body system, is expected to result in ergodic mixing. Here we study a fixed bond length $N$-mer interaction-site chain with fixed total energy and angular momentum. For $N⩾4$ the equations of motion for such a chain are nonintegrable and chaotic dynamics is expected. We directly assess the ergodicity of short repulsive Lennard-Jones chains by comparing phase space and time averages for structural and energetic properties. The phase space averages are determined from the exact microcanonical partition function while the time averages are obtained from molecular dynamics (MD) simulations. For $N=4$ and 5 we find that our exact phase space averages agree with the MD time averages, as expected for an ergodic system. The $N=3$ system is integrable and thus displays regular dynamics for which time averages are found to depend on initial conditions. In all cases, the total angular momentum is found to have a large effect on both the average chain conformation and the partitioning of the total energy between potential, vibrational, and rotational contributions. Compared to a nonrotating chain, a small to moderate angular momentum slightly speeds up the internal chain dynamics, while a large angular momentum dramatically slows the internal dynamics.

It has been shown that the analysis of electroencephalographic (EEG) signals submitted to an appropriate external stimulation (active paradigm) is efficient with respect to anticipating epileptic seizures [S. Kalitzin et al., Clin. Neurophysiol. 116, 718 (2005)]. To better understand how an active paradigm is able to detect properties of EEG signals by means of which proictal states can be identified, we performed a simulation study using a computational model of seizure generation of a hippocampal network. Applying the active stimulation methodology, we investigated (i) how changes in model parameters that lead to a transition from the normal ongoing EEG to an ictal pattern are reflected in the properties of the simulated EEG output signals and (ii) how the evolution of neuronal excitability towards seizures can be reconstructed from EEG data using an active paradigm, rather than passively, using only ongoing EEG signals. The simulations indicate that a stimulation paradigm combined with appropriate analytical tools, as proposed here, may yield information about the change in excitability that precedes the transition to a seizure. Such information is apparently not fully reflected in the ongoing EEG activity. These findings give strong support to the development and application of active paradigms with the aim of predicting the occurrence of a transition to an epileptic seizure.