A detailed study is undertaken of the $v_{\max }=1$ limit of the cellular automaton traffic model proposed by Nagel and Paczuski [Phys. Rev. E 51, 2909 (1995)]. The model allows one to analyze the behavior of a traffic jam initiated in an otherwise freely flowing stream of traffic. By mapping onto a discrete-time queueing system, itself related to various problems encountered in lattice combinatorics, exact results are presented in relation to the jam lifetime, the maximum jam length, and the jam mass (the space-time cluster size or integrated vehicle waiting time), both in terms of the critical and the off-critical behavior. This sets existing scaling results in their natural context and also provides several other interesting results in addition.

We study the space-time correlation and response functions in nonequilibrium growth processes described by linear stochastic Langevin equations. Exploiting exclusively the existence of space- and time-dependent symmetries of the noiseless part of these equations, we derive expressions for the universal scaling functions of two-time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion. The usefulness of the space-time functions is illustrated through the investigation of two atomistic growth models, the Family model and the restricted Family model, which are shown to belong to a unique universality class in $1+1$ and $2+1$ space dimensions. This corrects earlier studies which claimed that in $2+1$ dimensions the two models belong to different universality classes.

A highly efficient photonic band edge dye-doped cholesteric liquid crystal (CLC) laser is demonstrated. By sandwiching an active CLC cell within a resonator consisting of two passive CLC reflectors, the lasing efficiency is dramatically enhanced. Theoretical analysis using the improved $4\times 4$ transfer matrix and scattering matrix shows that the band edge laser mode can be supported by the external CLC resonator and its optimal output can be achieved by a relatively thin active CLC layer and thin passive CLC reflectors. Theoretical analysis agrees well with the experimental results.

We inject an angularly collimated laser beam into a scattering medium of a nondairy creamer-water solution and examine the distribution of the scattered light along the optical axis as a function of the source-detector spacing. The experimental and simulated data obtained from a Monte Carlo simulation suggest four regimes characterizing the transition from unscattered to diffusive light. We compare the data also with theoretical predictions based on a first-order scattering theory for regions close to the source, and with diffusionlike theories for larger source-detector spacings. We demonstrate the impact of the measurement process and the effect of the unavoidable absorption of photons by the detection fiber on the light distribution inside the medium. We show that the range of validity of these theories can depend on the experimental parameters such as the diameter and acceptance angle of the detection fiber.

We examine the response of type II excitable neurons to trains of synaptic pulses, as a function of the pulse frequency and amplitude. Similarly to the case of harmonic inputs, these neurons exhibit a resonant behavior also for pulsed inputs. We interpret this phenomenon in terms of the subthreshold response of the neuron. In the presence of dynamical trains of input pulses whose frequency varies continuously in time, the receiving neuron synchronizes episodically to the input pulses, whenever the pulse frequency lies within the neuron’s locking range. The results are obtained both in numerical simulations of the Morris-Lecar model and in an electronic implementation of the FitzHugh-Nagumo system, evidencing the robustness of the phenomenon.

Random networks of coupled phase oscillators, representing an approximation for systems of coupled limit-cycle oscillators, are considered. Entrainment of such networks by periodic external forcing applied to a subset of their elements is numerically and analytically investigated. For a large class of interaction functions, we find that the entrainment window with a tongue shape becomes exponentially narrow for networks with higher hierarchical organization. However, the entrainment is significantly facilitated if the networks are directionally biased—i.e., closer to the feedforward networks. Furthermore, we show that the networks with high entrainment ability can be constructed by evolutionary optimization processes. The neural network structure of the master clock of the circadian rhythm in mammals is discussed from the viewpoint of our results.

Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase or decrease their utility by linking to nodes with a higher or lower degree than their own. We interpret utility as an equivalent to energy in physical systems and discuss the temperature dependence of the emerging networks. We observe the existence of a critical temperature $T_c$ where total energy (utility) and network architecture undergo radical changes. Along this topological transition we obtain ensemble averages of scale-free networks with complex hierarchical topology. The scale-free nature emerges strictly within equilibrium, with a clearly defined microcanonical ensemble and the principle of detailed balance fulfilled. This provides evidence that “complex” networks may arise without irreversibility. The utility approach establishes a link between classical statistical physics and a wide variety of applications in socioeconomic statistical systems.

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the microlevel behavior at each node, we develop a macroscopic description of the system in terms of the statistical features of the subnetwork of active nodes. We find that very different networks evolve to active subnetworks with similar asymptotic characteristics: the size of the active set is independent of the total number of nodes in the network, and the average degree of the active nodes is independent of both the network size and its connectivity. This robustness has strong implications for dynamical networks observed in the natural world, notably the existence of a characteristic range of links per species across ecological systems.

We present a method for efficiently exciting a Bragg soliton with a spectral content located mostly within the bandgap of a one-dimensional periodic structure. The method is based on a new interaction between Bragg solitons and on a high intensity enhancement, caused owing to the reduced propagation velocity inside periodic structures. Our method can also be used for efficient compression of optical pulses. We have theoretically demonstrated pulse compression with a compression ratio of 2800—over two orders of magnitude higher than previously reported. The results open new possibilities for experimental demonstration of Bragg soliton propagation and for pulse compression in one-dimensional periodic structures.

We theoretically study the statistics of record-breaking daily temperatures and validate these predictions using both Monte Carlo simulations and $126\text{years}$ of available data from the city of Philadelphia. Using extreme statistics, we derive the number and the magnitude of record temperature events, based on the observed Gaussian daily temperature distribution in Philadelphia, as a function of the number of years of observation. We then consider the case of global warming, where the mean temperature systematically increases with time. Over the $126\text{−}\text{year}$ time range of observations, we argue that the current warming rate is insufficient to measurably influence the frequency of record temperature events, a conclusion that is supported by numerical simulations and by the Philadelphia data. We also study the role of correlations between temperatures on successive days and find that they do not affect the frequency or magnitude of record temperature events.

The first detailed analysis of the two-dimensional (2D) NMR $T_2\text{−}{T}_2$ exchange experiment with a period of magnetization storage between the two $T_2$ relaxation encoding periods $\left(T_2\text{−}\mathrm{store}\text{−}{T}_2\right)$ is presented. It is shown that this experiment has certain advantages over the $T_1\text{−}{T}_2$ variant for the quantization of chemical exchange. New $T_2\text{−}\mathrm{store}\text{−}{T}_2$ 2D ${}^1\mathrm{H}$ NMR spectra of the pore water within white cement paste are presented. Based on these spectra, the exchange rate of water between the two smallest porosity reservoirs is estimated for the first time. It is found to be of the order of $5{\mathrm{ms}}^{-1}$. Further, a careful estimate of the pore sizes of these reservoirs is made. They are found to be of the order of $1.4\mathrm{nm}$ and $10–30\mathrm{nm}$, respectively. A discussion of the results is developed in terms of possible calcium silicate hydrate products. A water diffusion coefficient inferred from the exchange rate and the cement particle size is found to compare favorably with the results of molecular-dynamics simulations to be found in the literature.

We have recorded the swarming-like collective migration of a large number of keratocytes (tissue cells obtained from the scales of goldfish) using long-term videomicroscopy. By increasing the overall density of the migrating cells, we have been able to demonstrate experimentally a kinetic phase transition from a disordered into an ordered state. Near the critical density a complex picture emerges with interacting clusters of cells moving in groups. Motivated by these experiments we have constructed a flocking model that exhibits a continuous transition to the ordered phase, while assuming only short-range interactions and no explicit information about the knowledge of the directions of motion of neighbors. Placing cells in microfabricated arenas we found spectacular whirling behavior which we could also reproduce in simulations.

We experimentally observe the dynamics of a two-mode $\mathrm{Nd}:\mathrm{Y}\mathrm{V}{\mathrm{O}}_4$ microchip solid-state laser with optoelectronic feedback. The total laser output is detected and fed back to the injection current of the laser diode for pumping. Chaotic oscillations are observed in the microchip laser with optoelectronic self-feedback. We also observe the dynamics of two microchip lasers coupled mutually with optoelectronic link. The output of one laser is detected by a photodiode and the electronic signal converted from the laser output is sent to the pumping of the other laser. Chaotic fluctuation of the laser output is observed when the relaxation oscillation frequency is close to each other between the two microchip lasers. Synchronization of periodic wave form is also obtained when the microchip lasers have a single-longitudinal mode.

The evolution of the large-scale magnetic field in a turbulent flow of conducting fluid is considered in the framework of a multiscale ${\alpha }^2$-dynamo model, which includes the poloidal and the toroidal components for the large-scale magnetic field and a shell model for the small-scale magnetohydrodynamical turbulence. The conjugation of the mean-field description for the large-scale field and the shell formalism for the small-scale turbulence is based on strict conformity to the conservation laws. The model displays a substantial magnetic contribution to the $\alpha$ effect. It was shown that a large-scale magnetic field can be generated by current helicity even solely. The $\alpha$ quenching and the role of the magnetic Prandtl number $\left(P_m\right)$ are studied. We have determined the dynamic nature of the saturation mechanism of dynamo action. Any simultaneous cross correlation of $\alpha$ and large-scale magnetic field energy $E^B$ is negligible, whereas coupling between $\alpha$ and $E^B$ becomes substantial for moderate time lags. An unexpected result is the behavior of the large-scale magnetic energy with variation of the magnetic Prandtl number. Diminishing of $P_m$ does not have an inevitable ill effect on the magnetic field generation. The most efficient large-scale dynamo operates under relatively low Prandtl numbers—then the small-scale dynamo is suppressed and the decrease of $P_m$ can lead even to superequipartition of the large-scale magnetic field (i.e., $E_B>E_u$). In contrast, the growth of $P_m$ does not promote the large-scale magnetic field generation. A growing counteraction of the magnetic $\alpha$ effect reduces the level of mean large-scale magnetic energy at the saturated state.

We construct a semiclassical theory for propagation of an optical wave packet in a nonconducting medium with a periodic structure of dielectric permittivity and magnetic permeability, i.e., a nonconducting photonic crystal. We employ a quantum-mechanical formalism in order to clarify its link to those of electronic systems. It involves the geometrical phase, i.e., Berry’s phase, in a natural way, and describes an interplay between orbital motion and internal rotation. Based on the above theory, we discuss the geometrical aspects of the optical Hall effect. We also consider a reduction of the theory to a system without periodic structure and apply it to the transverse shift of an optical beam at an interface reflection or refraction. For a generic incident beam with an arbitrary polarization, an identical result for the transverse shift of each reflected or transmitted beam is given by the following different approaches: (i) analytic evaluation of wave-packet dynamics, (ii) total angular momentum (TAM) conservation for individual photons, and (iii) numerical simulation of wave-packet dynamics. It is consistent with a result by classical electrodynamics. This means that the TAM conservation for individual photons is already taken into account in wave optics, i.e., classical electrodynamics. Finally, we show an application of our theory to a two-dimensional photonic crystal, and propose an optimal design for the enhancement of the optical Hall effect in photonic crystals.

Wilkie [Phys. Rev. E 70, 017701 (2004)] used a heuristic approach to derive Runge-Kutta-based numerical methods for stochastic differential equations based on methods used for solving ordinary differential equations. The aim was to follow solution paths with high order. We point out that this approach is invalid in the general case and does not lead to high order methods. We warn readers against the inappropriate use of deterministic calculus in a stochastic setting.

We consider random energy landscapes constructed from $d$-dimensional lattices or trees. The distribution of the number of local minima in such landscapes follows a large-deviation principle and we derive the associated law exactly for dimension 1. Also of interest is the probability of the maximum possible number of minima; this probability scales exponentially with the number of sites. We calculate analytically the corresponding exponent for the Cayley tree and the two-leg ladder; for two- to five-dimensional hypercubic lattices, we compute the exponent numerically and compare to the Cayley tree case.

We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we compute the probability distribution functions of the entropy and satisfactorily test many of the predictions based on Seifert’s integral fluctuation theorem. The results presented for this simple model clearly illustrate the practical features and implications derived from such a result of nonequilibrium statistical mechanics.

Equilibria of a nematic liquid crystal confined between two eccentric cylinders are studied within a purely director approach. A planar equilibrium configuration competes against a three-dimensional one. A stability diagram is obtained in terms of both the ratio between the radii of the bounding cylinders and the distance between their axes. It turns out that the nonplanar minimizer has a structure more complex than that envisaged in the tensorial approach employed by McKay and Virga [Phys. Rev. E 71, 041702 (2005)] and that the planar configuration cannot be the absolute minimizer when the outer cylinder becomes a plane wall. The mechanical actions transmitted by the nematic liquid crystal on both bounding cylinders are computed and compared with other results available in the literature.

This study reports deuterium nuclear-magnetic-resonance (NMR) spectra collected at $61.4\mathrm{MHz}$ in the chiral smectic-$C$ phase of liquid crystal $4^{\prime }\left(\text{octyloxy}\right)\text{−}{d}_{17}$ biphenyl-4-$y\mathrm{l}2$-chloro-3-methylpentanoate (BP8Cl). By using a goniometer probe, the oriented sample was rotated to collect spectra at different rotation $\left(\theta \right)$ angles. These spectra were simulated to gain information on solitonlike distortions in the helical superstructure. The Landau theory was adopted to study the distortion of the helix by the NMR magnetic field. Deuterium two-dimensional exchange experiments were also used on the aligned sample at $\theta =15°$ to obtain dynamic parameters through the spectral simulation. The interlayer diffusion constants in the $\mathrm{Sm}{C}^{*}$ phase were estimated from a proton $T_1$ dispersion study. The pitch length of BP8Cl is estimated to be circa 2–3 microns at one temperature.