We present measurements of the fast-electron-relaxation time in short-pulse $\left(0.5\mathrm{ps}\right)$ laser-solid interactions for laser intensities of ${10}^{17}$, ${10}^{18}$, and ${10}^{19}\mathrm{W}∕{\mathrm{cm}}^2$, using a picosecond time-resolved x-ray spectrometer and a time-integrated electron spectrometer. We find that the laser coupling to hot electrons increases as the laser intensity becomes relativistic, and that the thermalization of fast electrons occurs over time scales on the order of $10\mathrm{ps}$ at all laser intensities. The experimental data are analyzed using a combination of models that include $K\alpha$ generation, collisional coupling, and plasma expansion.

We study traffic clearance distributions (i.e., the instantaneous gap between successive vehicles) and time-headway distributions by applying the Beck and Cohen superstatistics. We model the transition from free phase to congested phase with the increase of vehicle density as a transition from the Poisson statistics to that of the random-matrix theory. We derive an analytic expression for the spacing distributions that interpolates from the Poisson distribution and Wigner’s surmise and apply it to the distributions of the net distance and time gaps among the succeeding cars at different densities of traffic flow. The obtained distribution fits the experimental results for single-vehicle data of the Dutch freeway A9 and the German freeway A5.

Two-dimensional melting transitions for model colloids in the presence of a one-dimensional external periodic potential are investigated using Monte Carlo simulation and finite size scaling techniques. Here we explore a hard disk system with commensurability ratio $p=\sqrt{3}{a}_s∕\left(2d\right)=2$, where $a_s$ is the mean distance between the disks and $d$ the period of the external potential. Three phases, the modulate liquid, the locked smectic, and the locked floating solid are observed, in agreement with other experimental and analytical studies. Various statistical quantities like order parameters, their cumulants, and response functions, are used to obtain a phase diagram for the transitions between these three phases.

We study the effects of local inhomogeneities, i.e., slow sites of hopping rate $q<1$, in a totally asymmetric simple exclusion process for particles of size $\ell ⩾1$ (in units of the lattice spacing). We compare the simulation results of $\ell =1$ and $\ell >1$ and notice that the existence of local defects has qualitatively similar effects on the steady state. We focus on the stationary current as well as the density profiles. If there is only a single slow site in the system, we observe a significant dependence of the current on the location of the slow site for both $\ell =1$ and $\ell >1$ cases. When two slow sites are introduced, more intriguing phenomena emerge, e.g., dramatic decreases in the current when the two are close together. In addition, we study the asymptotic behavior when $q\to 0$. We also explore the associated density profiles and compare our findings to an earlier study using a simple mean-field theory. We then outline the biological significance of these effects.

We present experimental results on the aggregation dynamics of a magnetorheological fluid, namely, an aqueous suspension of micrometer-sized superparamagnetic particles, under the action of a constant uniaxial magnetic field using video microscopy and image analysis. We find a scaling behavior in several variables describing the aggregation kinetics. The data agree well with the Family-Vicsek scaling ansatz for diffusion-limited cluster-cluster aggregation. The kinetic exponents $z$ and $z^{\prime }$ are obtained from the temporal evolution of the mean cluster size $S\left(t\right)$ and the number of clusters $N\left(t\right)$, respectively. The crossover exponent $\Delta$ is calculated in two ways: first, from the initial slope of the scaling function; second, from the evolution of the nonaggregated particles, $n_1\left(t\right)$. We report on results of Brownian two-dimensional dynamics simulations and compare the results with the experiments. Finally, we discuss the differences obtained between the kinetic exponents in terms of the variation in the crossover exponent and relate this behavior to the physical interpretation of the crossover exponent.

We argue that the impedance spectroscopy of an electrolytic cell in the low-frequency range can give information on the ambipolar diffusion. Our analysis is based on a theoretical investigation of the real part of the electrical impedance of an electrolytic cell. When the mobility of the positive ions differs from that of the negative ions, a second plateau of the resistance of the cell, in series representation, is expected close to the dc limit of the applied voltage. The effective diffusion coefficient, related to the measured resistance of the cell, in the dc limit, coincides with the ambipolar diffusion coefficient. The associated relaxation time corresponds to the ambipolar diffusion, and it is proportional to the square of the thickness of the sample. In the high-frequency range, the relaxation time coincides with the Debye relaxation time, connected to the free diffusion coefficient, and it is independent of the thickness of the sample. Finally, we propose a method to calculate the diffusion coefficients of the individual ions from the impedance spectrum and we discuss the implications of ambipolar diffusion in impedance measurements and interpretation of experimental quantities.

We model a sheared disordered solid using the theory of shear transformation zones (STZs). In this mean-field continuum model the density of zones is governed by an effective temperature that approaches a steady state value as energy is dissipated. We compare the STZ model to simulations by Shi et al. [Phys. Rev. Lett. 98, 185505 (2007)], finding that the model generates solutions that fit the data, exhibit strain localization, and capture important features of the localization process. We show that perturbations to the effective temperature grow due to an instability in the transient dynamics, but unstable systems do not always develop shear bands. Nonlinear energy dissipation processes interact with perturbation growth to determine whether a material exhibits strain localization. By estimating the effects of these interactions, we derive a criterion that determines which materials exhibit shear bands based on the initial conditions alone. We also show that the shear band width is not set by an inherent diffusion length scale but instead by a dynamical scale that depends on the imposed strain rate.

We present a shear-transformation-zone (STZ)-based analysis of numerical simulations by Haxton and Liu [Phys. Rev. Lett. 99, 195701 (2007)]. The extensive Haxton and Liu (HL) data sharply test the basic assumptions of the STZ theory, especially the central role played by the effective disorder temperature as a dynamical state variable. We find that the theory survives these tests, and that the HL data provide important and interesting constraints on some of its specific ingredients. Our most surprising conclusion is that, when driven at various constant shear rates in the low-temperature glassy state, the HL system exhibits a classic glass transition, including super-Arrhenius behavior, as a function of the effective temperature.

The neighbor network in a two-dimensional polydisperse hard-disk fluid with diameter distribution $p\left(\sigma \right)\sim {\sigma }^{-4}$ is examined using constant-pressure Monte Carlo simulations. Graphs are constructed from vertices (disks) with edges (links) connecting each vertex to $k$ neighboring vertices defined by a radical tessellation. At packing fractions in the range $0.24\le \eta \le 0.36$, the decay of the network degree distribution is observed to be consistent with the power law $k^{-\gamma }$ where the exponent lies in the range $5.6\le \gamma \le 6.0$. Comparisons with the predictions of a maximum-entropy theory suggest that this apparent power-law behavior is not the asymptotic one and that $p_k\sim k^{-4}$ in the limit $k\to \infty$. This is consistent with the simple idea that for large disks, the number of neighbors is proportional to the disk diameter. A power-law decay of the network degree distribution is one of the characteristics of a scale-free network. The assortativity of the network is measured and is found to be positive, meaning that vertices of equal degree are connected more often than in a random network. Finally, the equation of state is determined and compared with the prediction from a scaled-particle theory. Very good agreement between simulation and theory is demonstrated.

In this work, we carried out an extensive numerical exploration of the delicate global dynamics of pulse self-replication and analyzed the stability of singular homoclinic stationary solutions and their bifurcations in the one-dimensional Gray-Scott model. This stability analysis has several implications for understanding the recently discovered phenomena of self-replicating pulses. The solutions of the ordinary differential equation are organized around a codimension-2 global bifurcation from which two or $N$ branches of homoclinic orbits originate, corresponding to solitary pulse solutions in the partial differential equation. A careful analysis of the bifurcation scenarios in the global bifurcation diagram suggests that the dynamics of the self-replicating system are related to a hierarchy structure of folding bifurcation branches in parameter space. The numerical simulation suggests that the Bogdanov-Takens points, together with the presence of critical points emanating from a particular codimension-2 homoclinic orbit, play a central role for the global bifurcation of periodic orbits, the homoclinic solutions, and the complex chaotic dynamics. The numerical simulation also reveals the existence of a modulating two-pulse or multipulse, which accompanies the procedure of pulse self-replication in reaction-diffusion systems.

We consider the Kuramoto model of globally coupled phase oscillators subject to Ornstein-Uhlenbeck and non-Gaussian colored noise and investigate the influence of noise on the order parameter of the synchronization process. We use numerical methods to study the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise, and find that the threshold of synchronization strongly depends on the nature of the noise. It is found to be lower for both the Ornstein-Uhlenbeck and non-Gaussian processes compared to the case of white noise. A finite correlation time also favors the achievement of the full synchronization of the system, in contract to the white noise process, which does not allow that. Finally, we discuss possible applications of the stochastic Kuramoto model to oscillations taking place in biochemical systems.

We propose an algorithm to estimate the Hurst exponent of high-dimensional fractals, based on a generalized high-dimensional variance around a moving average low-pass filter. As working examples, we consider rough surfaces generated by the random midpoint displacement and by the Cholesky-Levinson factorization algorithms. The surrogate surfaces have Hurst exponents ranging from 0.1 to 0.9 with step 0.1, and different sizes. The computational efficiency and the accuracy of the algorithm are also discussed.

For an underdamped Brownian particle in a one-dimensional periodic potential we theoretically predict three unusual transport properties: (i) A static bias force (of either sign) generates an average particle motion in the opposite direction. (ii) A small bias leads to a particle transport in the direction of the bias, but upon increasing the bias the particle velocity reverses direction. (iii) For a given bias force, the particle motion follows the direction of the force for low temperatures, but upon increasing the temperature reverses its direction. The considered model is shown to be minimal for the occurrence of these phenomena. A detailed analysis of its deterministic properties and the influence of thermal noise is carried out with numerical simulations that are complemented by analytical approximations. Intuitive explanations of the basic mechanism behind the three effects are provided; their origin is attributed to a subtle interplay between the stability of coexisting attractors, noise induced metastability, and transient chaos. An experimental system for the realization of the predicted effects is given within the Stewart-McCumber model for Josephson junctions. Suitable parameter values for which these effects can be observed are quite realistic experimentally.

We present an analytic mean-field theory for relaxational dynamics in spatially extended systems that undergo purely noise-induced phase transitions to ordered states. The theory augments the usual mean-field approach with a Gaussian ansatz that yields quantitatively accurate results for strong coupling. We obtain analytic results not only for steady-state mean fields and distribution widths, but also for the dynamical approach to a steady state or to collective oscillatory behaviors in multifield systems. Because the theory yields dynamical information, it can also predict the initial-condition-dependent final state (disordered state, steady or oscillatory ordered state) in multistable arrays.

The fluctuation spectra and the intermembrane interaction of two membranes at a fixed average distance are investigated. Each membrane can either be a fluid or a solid membrane, and in isolation, its fluctuations are described by a bare or a wave-vector-dependent bending modulus, respectively. The membranes interact via their excluded-volume interaction; the average distance is maintained by an external, homogeneous pressure. For strong coupling, the fluctuations can be described by a single, effective membrane that combines the elastic properties. For weak coupling, the fluctuations of the individual, noninteracting membranes are recovered. The case of a composite membrane consisting of one fluid and one solid membrane can serve as a microscopic model for the plasma membrane and cytoskeleton of the red blood cell. We find that, despite the complex microstructure of bilayers and cytoskeletons in a real cell, the fluctuations with wavelengths $\lambda \gtrsim 400\mathrm{nm}$ are well described by the fluctuations of a single, polymerized membrane (provided that there are no inhomogeneities of the microstructure). The model is applied to the fluctuation data of discocytes (“normal” red blood cells), a stomatocyte, and an echinocyte. The elastic parameters of the membrane and an effective temperature that quantifies active, metabolically driven fluctuations are extracted from the experiments.

Amplitude equations are derived that describe the spatiotemporal dynamics of cardiac alternans during periodic pacing of one- [B. Echebarria and A. Karma, Phys. Rev. Lett. 88, 208101 (2002)] and two-dimensional homogeneous tissue and one-dimensional anatomical reentry in a ring of homogeneous tissue. These equations provide a simple physical understanding of arrhythmogenic patterns of period-doubling oscillations of action potential duration with a spatially varying phase and amplitude, as well as explicit quantitative predictions that can be compared to ionic model simulations or experiments. The form of the equations is expected to be valid for a large class of ionic models but the coefficients are derived analytically only for a two-variable ionic model and calculated numerically for the original Noble model of Purkinje fiber action potential. In paced tissue, this theory explains the formation of “spatially discordant alternans” by a linear instability mechanism that produces a periodic pattern of out-of-phase domains of alternans. The wavelength of this pattern, equal to twice the spacing between nodes separating out-of-phase domains, is shown to depend on three fundamental length scales that are determined by the strength of cell-to-cell coupling and conduction velocity (CV) restitution. Moreover, the patterns of alternans can be either stationary, with fixed nodes, or traveling, with moving nodes and hence quasiperiodic oscillations of action potential duration, depending on the relative strength of the destabilizing effect of CV restitution and the stabilizing effect of diffusive coupling. For the ring geometry, we recover the results of Courtemanche, Glass, and Keener [Phys. Rev. Lett. 70, 2182 (1993)] with two important modifications due to cell-to-cell diffusive coupling. First, this coupling breaks the degeneracy of an infinite-dimensional Hopf bifurcation such that the most unstable mode of alternans corresponds to the longest quantized wavelength of the ring. Second, the Hopf frequency, which determines the velocity of the node along the ring, depends both on the steepness of CV restitution and the strength of this coupling, with the net result that quasiperiodic behavior can arise with a constant conduction velocity. In both the paced geometries and the ring, the onset of alternans is different in tissue than for a paced isolated cell. The implications of these results for alternans dynamics during two-dimensional reentry are briefly discussed.

Here we address the effect of large delay on the statistical characteristics of noise-induced oscillations in a nonlinear system below Andronov-Hopf bifurcation. In particular, we introduce a theory of these oscillations that does not involve the eigenmode expansion, and can therefore be used for arbitrary delay time. In particular, we show that the correlation matrix (CM) oscillates on two different time scales: on the scale of the main period of noise-induced oscillations, and on the scale close to the delay time. At large values of the delay time, the CM is shown to decay exponentially only for large values of its argument, while for the arguments comparable with the value of the delay, the CM remains finite disregarding the delay time. The definition of the correlation time of the system with delay is discussed.

Magnetic fluctuations generated by a tangling of the mean magnetic field by velocity fluctuations are studied in a developed turbulent convection with large magnetic Reynolds numbers. We show that the energy of magnetic fluctuations depends on the magnetic Reynolds number only when the mean magnetic field is smaller than $B_{\mathrm{eq}}∕4{\mathrm{Rm}}^{1∕4}$, where $B_{\mathrm{eq}}$ is the equipartition mean magnetic field determined by the turbulent kinetic energy and $\mathrm{Rm}$ is the magnetic Reynolds number. Generation of magnetic fluctuations in a turbulent convection with a nonzero mean magnetic field results in a decrease of the total turbulent pressure and may cause the formation of large-scale inhomogeneous magnetic structures even in an originally uniform mean magnetic field. This effect is caused by a negative contribution of the turbulent convection to the effective mean Lorentz force. The inhomogeneous large-scale magnetic fields are formed due to excitation of the large-scale instability. The energy for this instability is supplied by small-scale turbulent convection. The discussed effects might be useful for understanding the origin of solar nonuniform magnetic fields: e.g., sunspots.

Autocatalytic reaction fronts propagating in a Poiseuille flow present a change of speed and curvature depending on the strength of the flow and on the direction of front propagation. These chemical fronts separate reacted and unreacted fluids of different densities, consequently convection will always be present due to the horizontal density gradient of the curved front. In this paper, we find the change of speed caused by gravity for fronts propagating in vertical tubes under a Poiseuille flow. For small density differences, we find axisymmetric fronts. Our theory predicts a transition to nonaxisymmetric fronts as the distance between the walls is increased. The transition depends on the average speed of the Poiseuille flow.

We report the observation of acoustic Bloch oscillations at megahertz frequency in a two-dimensional phononic crystal. By creating periodically arrayed cavities with a decreasing gradient in width along one direction in the phononic crystal, acoustic Wannier-Stark ladders are created in the frequency domain. The oscillatory motion of an incident Gaussian pulse inside the sample is demonstrated by both simulation and experiment.