The spatiotemporal pulse dynamics of a high-power relativistic laser pulse interacting with an electron-positron-ion plasmas is investigated theoretically and numerically. The occurrence of pulse compression is studied. The dependence of the mechanism on the concentration of the background ions in electron positron plasma is emphasized.

Many human diseases are associated with protein aggregation and fibrillation. We present experiments on in vitro glucagon fibrillation using total internal reflection fluorescence microscopy, providing real-time measurements of single-fibril growth. We find that amyloid fibrils grow in an intermittent fashion, with periods of growth followed by long pauses. The observed exponential distributions of stop and growth times support a Markovian model, in which fibrils shift between the two states with specific rates. Even if the individual rates vary considerably, we observe that the probability of being in the growing (stopping) state is very close to 1/4 (3/4) in all experiments.

It is well known that resonance can be induced by external noise or diversity. Here we show that resonance can be induced even by a phase disorder in coupled excitable neurons with subthreshold activity. In contrast to the case of identical phase, we find that phase disorder plays an active role in enhancing neuronal activity. We also uncover that the presence of phase disorder can induce a double resonance phenomenon: phase disorder and coupling strength both can enhance neuronal firing activity. A physical theory is formulated to help understand the mechanism behind this double resonance phenomenon.

Transport in random media is known to be affected by quenched disorder. From the point of view of random walks, quenching induces correlations between steps that may alter the dynamical properties of the medium. This paper is intended to provide more insight into the role of quenched disorder on superdiffusive transport in two-dimensional random media. The systems under consideration are disordered materials called Lévy glasses that exhibit large spatial fluctuations in the density of scattering elements. We show that in an ideal Lévy glass the influence of quenching can be neglected, in the sense that transport follows to very good approximation that of a standard Lévy walk. We also show that, by changing sample parameters, quenching effects can be increased intentionally, thereby making it possible to investigate systematically diverse regimes of transport. In particular, we find that strong quenching induces local trapping effects which slow down superdiffusion and lead to a transient subdiffusivelike transport regime close to the truncation time of the system.

Zipf’s law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical explanation has been shown to exist for its universality. Here, we show that Zipf’s law is, in fact, an inevitable outcome of a very general class of stochastic systems. Borrowing concepts from Algorithmic Information Theory, our derivation is based on the properties of the symbolic sequence obtained through successive observations over a system with an ubounded number of possible states. Specifically, we assume that the complexity of the description of the system provided by the sequence of observations is the one expected for a system evolving to a stable state between order and disorder. This result is obtained from a small set of mild, physically relevant assumptions. The general nature of our derivation and its model-free basis would explain the ubiquity of such a law in real systems.

We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: $f$, the fraction of vertices initially activated, and $p$, the fraction of undamaged vertices in the graph. We observe two transitions: the giant active component appears continuously at a first threshold. There may also be a second, discontinuous, hybrid transition at a higher threshold. Avalanches of activations increase in size as this second critical point is approached, finally diverging at this threshold. We describe the existence of a special critical point at which this second transition first appears. In networks with degree distributions whose second moment diverges (but whose first moment does not), we find a qualitatively different behavior. In this case the giant active component appears for any $f>0$ and $p>0$, and the discontinuous transition is absent. This means that the giant active component is robust to damage, and also is very easily activated. We also formulate a generalized bootstrap process in which each vertex can have an arbitrary threshold.

The control of chaos (suppression and enhancement) of a damped pendulum subjected to two perpendicular periodic excitations of its pivot (one chaos inducing and the other chaos controlling) is investigated. Analytical (Melnikov analysis) and numerical (Lyapunov exponents) results show that the initial phase difference between the two excitations plays a fundamental role in the control scenario. We demonstrate the effectiveness of the method in suppressing spatiotemporal chaos of chains of identical chaotic coupled pendula where homogeneous regularization is obtained under localized control on a minimal number of pendula. Additionally, we demonstrate the robustness of the control scenario against changes in the coupling function. In particular, synchronization-induced homogeneous regularization of chaotic chains can be highly enhanced by considering time-varying couplings instead of stationary couplings.

Floating particles that are initially distributed uniformly on the surface of a turbulent fluid, subsequently coagulate, until finally a steady state is reached. This being so, they manifestly form a compressible system. In this experiment, the information dimension $D_1$, and the Lyapunov exponents of the coagulated floaters, is measured. The trajectories and the velocity fields of the particles are captured in a sequence of rapidly acquired images. Then the velocity sequence is randomly shuffled in time to generate new trajectories. This analysis mimics the Kraichnan ensemble and yields properties of a velocity correlation function that is delta correlated in time (but not in space). The measurements are compared with theoretical expectations and with simulations of Boffetta et al., that closely mimic the laboratory experiment reported here.

Results are presented for the nonequilibrium dynamics of a quantum $XXZ$-spin chain whose spins are initially arranged in a domain wall profile via the application of a magnetic field in the $z$ direction, which is spatially varying along the chain. The system is driven out of equilibrium in two ways: a). by rapidly turning off the magnetic field, b). by rapidly quenching the interactions at the same time as the magnetic field is turned off. The time evolution of the domain wall profile as well as various two-point spin correlation functions are studied by the exact solution of the fermionic problem for the $XX$ chain and via a bosonization approach and a mean-field approach for the $XXZ$ chain. At long times the magnetization is found to equilibrate (reach the ground state value), while the two-point correlation functions in general do not. In particular, for quenches within the gapless $XX$ phase, the spin correlation function transverse to the $z$ direction acquires a spatially inhomogeneous structure at long times whose details depend on the initial domain wall profile. The spatial inhomogeneity is also recovered for the case of classical spins initially arranged in a domain wall profile and shows that the inhomogeneities arise due to the dephasing of transverse spin components as the domain wall broadens. A generalized Gibbs ensemble approach is found to be inadequate in capturing this spatially inhomogeneous state.

The existence of the important similarities between gelation and glass transition makes it hard to distinguish between the two types of nonergodic states experimentally. Here, we report on a stochastic analysis of the scattered light intensity through a colloidal particles suspension during the gel and glass formation. In this analysis, we exploit the methods developed for complex hierarchical systems, such as turbulence. Using the multiplicative log-normal cascade models, we provide a criterion to distinguish gels from glasses.

A relation between equilibrium, steady state, and waiting-time-dependent dynamical two-time correlation functions in dense glass-forming liquids subject to homogeneous steady shear flow is discussed. The systems under study show pronounced shear thinning, i.e., a significant speedup in their steady-state slow relaxation as compared to equilibrium. An approximate relation that recovers the exact limit for small waiting times is derived following the integration through transients (ITT) approach for the nonequilibrium Smoluchowski dynamics, and is exemplified within a schematic model in the framework of the mode-coupling theory of the glass transition (MCT). Computer simulation results for the tagged-particle density correlation functions corresponding to wave vectors in the shear-gradient directions from both event-driven stochastic dynamics of a two-dimensional hard-disk system and from previously published Newtonian-dynamics simulations of a three-dimensional soft-sphere mixture are analyzed and compared with the predictions of the ITT-based approximation. Good qualitative and semiquantitative agreement is found. Furthermore, for short waiting times, the theoretical description of the waiting time dependence shows excellent quantitative agreement to the simulations. This confirms the accuracy of the central approximation used earlier to derive fluctuation dissipation ratios [M. Krüger and M. Fuchs, Phys. Rev. Lett. 102, 135701 (2009)]. For intermediate waiting times, the correlation functions decay faster at long times than the stationary ones. This behavior is predicted by our theory and observed in simulations.

It is well known that at the gel-liquid phase-transition temperature a lipid bilayer membrane exhibits an increased ion permeability. We analyze the quantized currents in which the increased permeability presents itself. The open time histogram shows a “$-3/2$” power law which implies an open-closed transition rate that decreases like $k\left(t\right)\propto t^{-1}$ as time evolves. We propose a “pore freezing” model to explain the observations. We discuss how this model also leads to the $1/f^{\alpha }$ noise that is commonly observed in currents across biological and artificial membranes.

The cumulant representation of the Fourier path integral method is examined to determine the asymptotic convergence characteristics of the imaginary-time density matrix with respect to the number of path variables $N$ included. It is proved that when the cumulant expansion is truncated at order $p$, the asymptotic convergence rate of the density matrix behaves like $N^{-\left(2p+1\right)}$. The complex algebra associated with the proof is simplified by introducing a diagrammatic representation of the contributing terms along with an associated linked-cluster theorem. The cumulant terms at each order are expanded in a series such that the asymptotic convergence rate is maintained without the need to calculate the full cumulant at order $p$. Using this truncated expansion of each cumulant at order $p$, the numerical cost in developing Fourier path integral expressions having convergence order $N^{-\left(2p+1\right)}$ is shown to be approximately linear in the number of required potential energy evaluations making the method promising for actual numerical implementation.

A characterization of reconnection of vorticity contours is made by direct numerical simulations of the two-dimensional Navier-Stokes flow at a relatively low Reynolds number. We identify all the critical points of the vorticity field and classify them by solving an eigenvalue problem of its Hessian matrix on the basis of critical-point theory. The numbers of hyperbolic (saddles) and elliptic (minima and maxima) points are confirmed to satisfy Euler’s index theorem numerically. Time evolution of these indices is studied for a simple initial condition. Generally speaking, we have found that the indices are found to decrease in number with time. This result is discussed in connection with related works on streamline topology, in particular, the relationship between stagnation points and the dissipation. Associated elementary procedures in physical space, the merging of vortices, are studied in detail for a number of snapshots. A similar analysis is also done using the stream function.

We show that the relative entropy, $S_{\text{rel}}$, suggests a fundamental indicator of the success of multiscale studies, in which coarse-grained (CG) models are linked to first-principles (FP) ones. We demonstrate that $S_{\text{rel}}$ inherently measures fluctuations in the differences between CG and FP potential energy landscapes, and develop a theory that tightly and generally links it to errors associated with coarse graining. We consider two simple case studies substantiating these results, and suggest that $S_{\text{rel}}$ has important ramifications for evaluating and designing coarse-grained models.

Experiments were conducted to investigate pattern formation during the defluidization of a partially fluidized bimodal granular mixture. Partial fluidization occurs when the system is driven at gas velocities that are insufficient to fluidize all of the constituent particles. Over time, the granular mixture evolves into a variety of patterns depending on the concentrations of large and small particles and the gas velocity. We show how vertically oriented pipes, containing large particles, grow at the interface between the fluidized and static zones. The heterogeneities in the permeability field focus the flow, causing localized fluidization, which in turn localizes the sedimentation of the large particles segregating the system. We discuss how the interplay between heterogeneities in material properties, fluid flow and fluid induced deformation may be relevant to a variety of geological processes.

The dynamics of flexible polymer molecules are often assumed to be governed by hydrodynamics of the solvent. However there is considerable evidence that internal dissipation of a polymer contributes as well. Here we investigate the dynamics of a single chain in the absence of solvent to characterize the nature of this internal friction. We model the chains as freely hinged but with localized bond angles and threefold symmetric dihedral angles. We show that the damping is close but not identical to Kelvin damping, which depends on the first temporal and second spatial derivative of monomer position. With no internal potential between monomers, the magnitude of the damping is small for long wavelengths and weakly damped oscillatory time dependent behavior is seen for a large range of spatial modes. When the size of the internal potential is increased, such oscillations persist, but the damping becomes larger. However underdamped motion is present even with quite strong dihedral barriers for long enough wavelengths.

We study a large population of globally coupled phase oscillators subject to common white Gaussian noise and find analytically that the critical coupling strength between oscillators for synchronization transition decreases with an increase in the intensity of common noise. Thus, common noise promotes the onset of synchronization. Our prediction is confirmed by numerical simulations of the phase oscillators as well as of limit-cycle oscillators.

Chimera states occur in networks of coupled oscillators, and are characterized by having some fraction of the oscillators perfectly synchronized, while the remainder are desynchronized. Most chimera states have been observed in networks of phase oscillators with coupling via a sinusoidal function of phase differences, and it is only for such networks that any analysis has been performed. Here we present the first analysis of chimera states in a network of planar oscillators, each of which is described by both an amplitude and a phase. We find that as the attractivity of the underlying periodic orbit is reduced chimeras are destroyed in saddle-node bifurcations, and supercritical Hopf and homoclinic bifurcations of chimeras also occur.