The collisional-radiative model for hydrogenlike ions is used to investigate the scaling of recombination at low temperatures in order to identify the necessary conditions of electron density and temperature, which will allow population inversion between the first excited state and the ground state to be developed. Numerical calculations show that at low temperatures the population growth in the hydrogenic states can be represented by similarity relations. The physical origin of these forms is presented. A table of minimum densities at which inversion will occur is given as a function of temperature for ions of arbitrary atomic number.

For the nonlinear Schrödinger equation (NLSE), in the presence of disorder, exponentially localized stationary states are found. We demonstrate analytically that the localization length is typically independent of the strength of the nonlinearity and is identical to the one found for the corresponding linear equation. The analysis makes use of the correspondence between the stationary NLSE and the Langevin equation as well as of the resulting Fokker-Planck equation. The calculations are performed for the “white noise” random potential, and an exact expression for the exponential growth of the eigenstates is obtained analytically. It is argued that the main conclusions are robust.

Since the kinetic and potential energy terms of the real-time nonlinear Schrödinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well-known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even when the total energy is very well conserved. A detail error analysis reveals that the noise, or elementary excitations of the nonlinear Schrödinger equation, obeys the Bogoliubov spectrum and the instability is due to the exponential growth of high-wave-number noises caused by the splitting process. For a continuum wave function, this instability is unavoidable no matter how small the time step. For a discrete wave function, the instability can be avoided only for $\Delta t{k}_{\mathit{max}}^2\lesssim 2\pi$, where $k_{\mathit{max}}=\pi ∕\Delta x$.

In this paper, we propose a method for rapid computation of group betweenness centrality whose running time (after preprocessing) does not depend on network size. The calculation of group betweenness centrality is computationally demanding and, therefore, it is not suitable for applications that compute the centrality of many groups in order to identify new properties. Our method is based on the concept of path betweenness centrality defined in this paper. We demonstrate how the method can be used to find the most prominent group. Then, we apply the method for epidemic control in communication networks. We also show how the method can be used to evaluate distributions of group betweenness centrality and its correlation with group degree. The method may assist in finding further properties of complex networks and may open a wide range of research opportunities.

In nonequilibrium steady states (NESS) far from equilibrium, it is known that the Einstein relation is violated. Then, the ratio of the diffusion coefficient to the mobility is called an effective temperature, and the physical relevance of this effective temperature has been studied in several works. Although the physical relevance is not yet completely clear, it has been found that the role of an effective temperature in NESS is indeed analogous to that of the temperature in equilibrium systems in a number of respects. In this paper, we find further evidence establishing this analogy. We employ a nonequilibrium Langevin system as a thermostat for a Hamiltonian system and find that the kinetic temperature of this Hamiltonian system is equal to the effective temperature of the thermostat.

We study the structure of charged colloidal suspensions under confinement and determine a state diagram for the occurrence of electrostatic adsorption onto the confining walls, an effect that results in the accumulation of particles on the bounding surfaces and that could be relevant in experiments. We use Monte Carlo simulations to quantify this structural transition and perform theoretical calculations based on integral equations. Overall, our results provide a guide for experimentalists dealing with charged colloidal systems to determine the relevance of this purely electrostatic effect.

We study the statistical behavior of the Hermitian operators of complex systems with half-integer angular momentum and time-reversal symmetry. The complexity leads to randomization of the operators which can then be modeled, following maximum entropy hypothesis, by multiparametric Gaussian ensembles of real-quaternion matrices. The modeling shows that it is possible to classify the statistical behavior of spin-based complex systems into a continuum of universality classes characterized by a single parameter which is a function of all system parameters.

We present a biologically inspired electronic neuron based on a conductance model. The channels are constructed using linearly voltage controlled field effect transistors. A two channel and a three channel circuit is developed. The dynamical behavior of this system is studied, showing for the two channel circuit either class-I or class-II excitability and for the three channel circuit bursting and spike frequency adaptation. Voltage-clamp-type measurements, similar to the ones frequently used in neuroscience, are employed in order to determine the conductance characteristics of the electronic channels. We develop an empirical model based on these measurements that reproduces the different dynamical behaviors of the electronic neuron. We found that post-inhibitory rebound is present in the two channel circuit. Reliability and precision of spike timing is induced in the three channel circuit by injecting noise in the control variable of the slow channel that provides a negative feedback. The circuit is appropriate for the design of large scale electronic neural devices that can be used in mixed electronic-biological systems.

The web of relations linking technological innovation can be fairly described in terms of patent citations. The resulting patent citation network provides a picture of the large-scale organization of innovations and its time evolution. Here we study the patterns of change of patents registered by the U.S. Patent and Trademark Office. We show that the scaling behavior exhibited by this network is consistent with a preferential attachment mechanism together with a Weibull-shaped aging term. Such an attachment kernel is shared by scientific citation networks, thus indicating a universal type of mechanism linking ideas and designs and their evolution. The implications for evolutionary theory of innovation are discussed.

In this study, the propagation of an action potential in a network of excitable elements is studied numerically. The network we consider consists of excitable elements arranged in the shape of a trifurcated structure having three cables. The system has a branch point, a Y junction, at which the three cables are joined. Two types of external stimulations are considered: a single impulsive stimulation at one of the cable terminals, and a pair of stimuli applied to two different terminals. We have found three basic phases depending on the excitability of the elements for a single external stimulus as follows: (1) signal distributor—as the excitability gets higher, the pulse generated by a stimulus splits into two at the branch point, and two pulses are transmitted to the opposite terminals, (2) propagation block—the pulse in the lower excitable chain is blocked at the branch point, and (3) transient propagation—as the excitability is decreased further, we see that the pulse vanishes before reaching the branch point. By the interaction between the pulses that originate from different sources, signal transmission is recovered if the pulses arrive at the branch point nearly synchronously or after a specific delay time. The effects of the repetition of these two types of stimulation are also investigated. Complex spatiotemporal patterns occur due to pulse-pulse interaction and collisions at the branch point. The input-output relationship, which depends crucially on the repetition period and the time lag between the pair of stimuli, is characterized by the stimulus-response ratio and the interspike interval. We also show the effects of noise on the distribution of the interspike interval.

The effect of a random phase screen on laser beam wander in a turbulent atmosphere is studied theoretically. The photon distribution function method is used to describe the photon kinetics of both weak and strong turbulence. By bringing together analytical and numerical calculations, we have obtained the variance of beam centroid deflections caused by scattering on turbulent eddies. It is shown that an artificial distortion of the initial coherence of the radiation can be used to decrease the wandering effect. The physical mechanism responsible for this reduction and the applicability of our approach are discussed.

We study the strong coupling (SC) limit of the anisotropic Kardar-Parisi-Zhang (KPZ) model. A systematic mapping of the continuum model to its lattice equivalent shows that in the SC limit, anisotropic perturbations destroy all spatial correlations but retain a temporal scaling which shows a remarkable crossover along one of the two spatial directions, the choice of direction depending on the relative strength of anisotropicity. The results agree with exact numerics and are expected to settle the long-standing SC problem of a KPZ model in the infinite range limit.

An instability is observed as a layer of dense granular material positioned above a layer of air falls in a gravitational field [Phys. Rev. Lett. 99, 048001 (2007)]. A characteristic pattern of fingers emerges along the interface defined by the grains, and a transient coarsening of the structure is caused by a coalescence of neighboring fingers. The coarsening is limited by the production of new fingers as the separation of the existing fingers reaches a certain distance. The experiments and simulations presented are shown to be comparable both qualitatively and quantitatively. The characteristic inverse length scale of the structures, obtained as the mean of the solid fraction power spectrum, relaxes toward a stable value shared by the numerical and experimental data. Further, the response of the numerical model to changes in various model parameters is investigated. These parameters include the density of the grains, the shape of the initial air-grain interface, and the dissipation of the granular phase. Also, the growth rates of the bulk solid fraction and the air-grain interface are obtained from Fourier power spectra of the numerical data. This analysis reveals that the instability is never in a linear regime, not even initially.

We study the interactions and directed assembly of dipolar nematic colloidal particles in planar nematic cells using laser tweezers. The binding energies for two stable configurations of a colloidal pair with homeotropic surface alignment are determined. It is shown that the orientation of the dipolar colloidal particle can efficiently be controlled and changed by locally quenching the nematic liquid crystal from the laser-induced isotropic phase. The interaction of a single colloidal particle with a single colloidal chain is determined and the interactions between pairs of colloidal chains are studied. We demonstrate that dipolar colloidal chains self-assemble into the two-dimensional (2D) dipolar nematic colloidal crystals. An odd-even effect is observed with increasing number of colloidal chains forming the 2D colloidal crystal.

Remarkably little is known about the higher-order folding motifs of the chromatin fiber inside the cell nucleus. Folding depends among others on local gene density and transcriptional activity and plays an important role in gene regulation. Strikingly, at fiber lengths above $5\text{to}10\mathrm{Mb}$ the measured mean square distance $⟨R^2⟩$ between any two points on the chromatin fiber is independent of polymer length. We propose a polymer model that can explain this leveling-off by means of random looping. We derive an analytical expression for the mean square displacement between two arbitrary beads. Here the average is taken over the thermal ensemble with a fixed but random loop configuration, while quenched averaging over the ensemble of different loop configurations—which turns out to be equivalent to averaging over an ensemble of random matrices—is performed numerically. A detailed investigation of this model shows that loops on all scales are necessary to fit experimental data.

We consider a low-temperature plasma within a newly developed magnetohydrodynamic fluid model. In addition to the standard terms, the electron spin, quantum particle dispersion, and degeneracy effects are included. It turns out that the electron spin properties can give rise to ferromagnetic behavior in certain regimes. If additional conditions are satisfied, a homogeneous magnetized plasma can even be unstable. This happens in the low-temperature high-density regime, when the magnetic properties associated with the spin can overcome the stabilizing effects of the thermal and Fermi pressure, to cause a Jeans-like instability.

In the study of complex systems a fundamental issue is the mapping of the networks of interaction between constituent subsystems of a complex system or between multiple complex systems. Such networks define the web of dependencies and patterns of continuous and dynamic coupling between the system’s elements characterized by directed flow of information spanning multiple spatial and temporal scales. Here, we propose a wavelet-based extension of transfer entropy to measure directional transfer of information between coupled systems at multiple time scales and demonstrate its effectiveness by studying (a) three artificial maps, (b) physiological recordings, and (c) the time series recorded from a chaos-controlled simulated robot. Limitations and potential extensions of the proposed method are discussed.

For many years it was believed that an unstable periodic orbit with an odd number of real Floquet multipliers greater than unity cannot be stabilized by the time-delayed feedback control mechanism of Pyragas. A recent paper by Fiedler et al. Phys. Rev. Lett. 98, 114101 (2007) uses the normal form of a subcritical Hopf bifurcation to give a counterexample to this theorem. Using the Lorenz equations as an example, we demonstrate that the stabilization mechanism identified by Fiedler et al. for the Hopf normal form can also apply to unstable periodic orbits created by subcritical Hopf bifurcations in higher-dimensional dynamical systems. Our analysis focuses on a particular codimension-two bifurcation that captures the stabilization mechanism in the Hopf normal form example, and we show that the same codimension-two bifurcation is present in the Lorenz equations with appropriately chosen Pyragas-type time-delayed feedback. This example suggests a possible strategy for choosing the feedback gain matrix in Pyragas control of unstable periodic orbits that arise from a subcritical Hopf bifurcation of a stable equilibrium. In particular, our choice of feedback gain matrix is informed by the Fiedler et al. example, and it works over a broad range of parameters, despite the fact that a center-manifold reduction of the higher-dimensional problem does not lead to their model problem.

An inert dynamically passive scalar in a constant density fluid forced by a statistically homogeneous field of turbulence has been investigated using the results of a ${256}^3$ grid direct numerical simulation. Mixing characteristics are characterized in terms of either principal curvatures or mean and Gauss curvatures. The most probable small-scale scalar geometries are flat and tilelike isosurfaces. Preliminary correlations between flow and scalar small-scale structures associate highly curved saddle points with large-strain regions and elliptic points with vorticity-dominated zones. The concavity of the scalar profiles along the isosurface normal coordinate $x_n$ correlates well with negative mean curvatures, Gauss curvatures displaying any sign, which correspond to scalar minima, tiles, or saddle points; on the other hand, convexity along $x_n$ is associated with positive mean curvatures, Gauss curvatures ranging from negative to positive signs, featuring maxima, tiles, or saddle points; inflection points along $x_n$ correlate well with small values of the mean curvature and zero or negative values of $k_g$, corresponding to plane isosurfaces or saddle points with curvatures of equal and opposite signs. Small values of the scalar gradient are associated with elliptic points, either concave or convex $\left(k_g>0\right)$, for both concave and convex scalar profiles along $x_n$. Large values of the scalar gradient (or, equivalently, scalar fluctuation dissipation rates) are generally connected with small values of the Gauss curvature (either flat or moderate-curvature tilelike local geometries), with both concave and convex scalar profiles along $x_n$ equally probable. Vortical local flow structures correlate well with small and moderate values of the scalar gradient, while strain-dominated regions are associated with large values.