We investigate the memory effect in a simple model for glassy relaxation, a trap model with a Gaussian density of states. In this model, thermal equilibrium is reached at all finite temperatures and we therefore can consider jumps from low to high temperatures in addition to the quenches usually considered in aging studies. We show that the evolution of the energy following the Kovacs protocol can approximately be expressed as a difference of two monotonously decaying functions and thus show the existence of a so-called Kovacs hump whenever these functions are not single exponentials. It is well established that the Kovacs effect also occurs in the linear response regime, and we show that most of the gross features do not change dramatically when large temperature jumps are considered. However, there is one distinguishing feature that only exists beyond the linear regime, which we discuss in detail. For the memory experiment with inverted temperatures, i.e., jumping up and then down again, we find a very similar behavior apart from an opposite sign of the hump.

In this paper experimental observations of self-organized patterns in resolidified thin films of liquid superheated metals are reported. The superheated melt layers represent an example of a system driven far from equilibrium, which undergoes explosive boiling and solidifies afterward. The melts appear in the course of single-shot femtosecond laser heating of metal samples. Self-organized cells, solitonlike structures, periodic stripes, and transient patterns are observed. Pattern properties and mechanisms leading to the pattern formation as well as possible applications for nanotechnology are discussed.

A discrete chemotactic predator-prey model is proposed in which the prey secrets a diffusing chemical which is sensed by the predator and vice versa. Two dynamical states corresponding to catching and escaping are identified and it is shown that steady hunting is unstable. For the escape process, the predator-prey distance is diffusive for short times but exhibits a transient subdiffusive behavior which scales as a power law $t^{1/3}$ with time $t$ and ultimately crosses over to diffusion again. This allows us to classify the motility and dynamics of various predatory microbes and phagocytes. In particular, there is a distinct region in the parameter space where they prove to be infallible predators.

In adaptive networks, fragmentation transitions have been observed in which the network breaks into disconnected components. We present an analytical approach for calculating the transition point in general adaptive network models. Using the example of an adaptive voter model, we demonstrate that the proposed approach yields good agreement with numerical results.

We demonstrate that a tree-based theory for various dynamical processes operating on static, undirected networks yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance $\ell$ is sufficiently small—that is, as long as it is close to the value of $\ell$ in a random network with negligible clustering and the same degree-degree correlations. We support this hypothesis numerically using both real-world networks from various domains and several classes of synthetic clustered networks. We present analytical calculations that further support our claim that tree-based theories can be accurate for clustered networks, provided that the networks are “sufficiently small” worlds.

We study time-delayed coupling in one-dimensional arrays of discrete excitable FitzHugh-Nagumo elements. For small time delays in an excitatory coupling, noise-triggered spikes undergo a slight prolongation. For larger delay times, the coupling to adjacent elements leads to a splitting of spikes and an “echo” effect that produces dampened series of spikes. For very large delay times, a transition to a stationary regime appears, as the spikes are sustained by mutual excitations, resulting in antiphase synchronization of all elements. We characterize several features exhibited by the system, such as speed and duration of pulses as well as bifurcations leading to the stationary regime.

A particular dynamic steady state emerging in the swarm oscillator model—a system of interacting motile elements with an internal degree of freedom—is presented. In the state, elements form a rotating triangle whose corners appear to catch and throw elements. This motion is referred to as “juggling motion” in this paper. How this motion is maintained is studied theoretically. In particular, the five-element system, the minimum system that exhibits the motion, is investigated. With the help of the analysis of the two-element system, several factors essential to maintaining this motion are obtained.

A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles’ trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order $-2$.

A completely generalized version of an inhomogeneous scaled particle theory (I-SPT) for hard particle fluids confined by hard walls is presented, whereby the reversible work of cavity insertion can be determined for a cavity of any radius located at any distance from the hard wall. New exact and approximate conditions on the central function $\mathrm{Ḡ}$ of I-SPT are developed, where $\mathrm{Ḡ}$ is related to the average value of the anisotropic density of hard-sphere centers at the surface of the cavity. The predictions of the work of insertion and the form of $\mathrm{Ḡ}$ are quite accurate up to moderate bulk densities as compared to molecular simulation results. The accuracy of I-SPT begins to decline at high densities, due to limitations of certain needed approximations required for a complete description of $\mathrm{Ḡ}$. Finally, interesting insights into the origin of depletion effects between a hard-sphere solute and the hard wall are generated via this version of I-SPT. The oscillatory nature of depletion forces, exhibiting both attractive and repulsive domains, is found to arise from the interplay between bulk SPT and I-SPT relations.

In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion, we determine how the critical density depends on the form of the initial perturbation. Specifically, we employ a renormalization-group improved perturbative method to analyze the model equations and show analytically, up to first order in the perturbation parameter, how the critical density is modified by the strength of the initial angular perturbation in the system.

We introduce the concept of random sequential renormalization (RSR) for arbitrary networks. RSR is a graph renormalization procedure that locally aggregates nodes to produce a coarse grained network. It is analogous to the (quasi)parallel renormalization schemes introduced by C. Song et al. [C. Song et al., Nature (London) 433, 392 (2005)] and studied by F. Radicchi et al. [F. Radicchi et al., Phys. Rev. Lett. 101, 148701 (2008)], but much simpler and easier to implement. Here we apply RSR to critical trees and derive analytical results consistent with numerical simulations. Critical trees exhibit three regimes in their evolution under RSR. (i) For $N_0^{\nu }\lesssim N<N_0$, where $N$ is the number of nodes at some step in the renormalization and $N_0$ is the initial size of the tree, RSR is described by a mean-field theory, and fluctuations from one realization to another are small. The exponent $\nu =1/2$ is derived using random walk and other arguments. The degree distribution becomes broader under successive steps, reaching a power law $p_k~1/k^{\gamma }$ with $\gamma =2$ and a variance that diverges as $N_0^{1/2}$ at the end of this regime. Both of these latter results are obtained from a scaling theory. (ii) For $N_0^{{\nu }_{\mathrm{star}}}\lesssim N\lesssim N_0^{1/2}$, with ${\nu }_{\mathrm{star}}\approx 1/4$ hubs develop, and fluctuations between different realizations of the RSR are large. Trees are short and fat with an average radius that is $\mathcal{O}(1)$. Crossover functions exhibiting finite-size scaling in the critical region $N~N_0^{1/2}\to \infty$ connect the behaviors in the first two regimes. (iii) For $N\lesssim N_0^{{\nu }_{\mathrm{star}}}$, star configurations appear with a central hub surrounded by many leaves. The distribution of stars is broadly distributed over this range. The scaling behaviors found under RSR are identified with a continuous transition in a process called “agglomerative percolation” (AP), with the coarse-grained nodes in RSR corresponding to clusters in AP that grow by simultaneously attaching to all their neighboring clusters.

Fat-tail distributions of sizes abound in natural, physical, economic, and social systems. The lognormal and the power laws have historically competed for recognition with sometimes closely related generating processes and hard-to-distinguish tail properties. This state-of-affair is illustrated with the debate between Eeckhout [Amer. Econ. Rev. 94, 1429 (2004)] and Levy [Amer. Econ. Rev. 99, 1672 (2009)] on the validity of Zipf’s law for US city sizes. By using a uniformly most powerful unbiased (UMPU) test between the lognormal and the power-laws, we show that conclusive results can be achieved to end this debate. We advocate the UMPU test as a systematic tool to address similar controversies in the literature of many disciplines involving power laws, scaling, “fat” or “heavy” tails. In order to demonstrate that our procedure works for data sets other than the US city size distribution, we also briefly present the results obtained for the power-law tail of the distribution of personal identity (ID) losses, which constitute one of the major emergent risks at the interface between cyberspace and reality.

Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [Phys. Rev. E 78, 056202 (2008)] the trace formula for both the smooth and the oscillating parts of the resonance density was proposed and checked for the circular cavity. The present paper deals with numerous shapes which would be integrable (square, rectangle, and ellipse), pseudointegrable (pentagon), and chaotic (stadium), if the cavities were closed (billiard case). A good agreement is found between the theoretical predictions, the numerical simulations, and experiments based on organic microlasers.

The curved channel appears to be indispensable for the lab-on-chips systems because it provides a convenient scheme for increasing the channel length per unit chip area in the direction of net flow. A secondary Dean flow in curved rectangular microchannels is examined by applying the finite-volume scheme with a semi-implicit method for pressure-linked equations (SIMPLE) algorithm for the pressure-driven electrokinetic transport. This framework is based on the theoretical model coupled with the full Poisson-Boltzmann, Navier-Stokes, and the Nernst-Planck principles of net charge conservation [Yun et al., Phys. Fluids 22, 052004 (2010)]. The effect of a dissimilar wall condition on the secondary flow at the turn is explored by considering different configurations of channel wall having complementary aspect ratios (i.e., ratio of the channel height to the channel width, $H$/$W$ $=$ 0.25 and 4.0) with combinations of hydrophilic glass and hydrophobic polydimethylsiloxane surfaces. Simulation results exhibit that, contrary to the case of general narrow-bore channels, the streamwise axial velocity tends to shift toward the inner wall caused by a stronger effect of the spanwise pressure gradient, according to a sufficiently low Dean number. The increasing rate of this shift with increasing curvature ratio is more significant in the shallow (or low-aspect-ratio) channel, due to the effect of greater distance traveled by the fluid along the outer wall. The curvature introduces the presence of pairs of counter-rotating vortices perpendicular to the flow direction. Comparing between shallow and deep (or high-aspect-ratio) channels allows us to identify that the patterns of axial velocity and vorticity are altered by the heterogeneity effect of surfaces occupying a large area. The total magnitude of vorticity at the cross section of the channel increases with increasing slip length, due to the contribution of enhanced axial velocity driven by the slip, while there is no fluid-slip dependency for the slip length of less than about 50 nm.

Instabilities in a two-phase electromagnetohydrodynamic (EMHD) flow between a pair of parallel electrodes are explored. A linear stability analysis has been performed based on a coupled Orr-Sommerfeld system generated from the conservation laws. The study shows the presence of a finite-wave-number EMHD mode of instability in addition to the two commonly observed instability modes in the pressure-driven two-layer flows, namely, the long-wave interfacial mode arising from the viscosity or density stratification and the finite-wave-number shear flow mode engendered by the Reynolds stresses. This extra EMHD mode originates from the additional stresses generated by the Lorenz force acting at the liquid layers and is found to exist under all conditions beyond a critical strength of the externally applied magnetic field. The EMHD mode either can exist as a singular dominant mode or can coexist as a dominant or subdominant mode with the conventional interfacial mode or shear flow instabilities in the two-layer flows. The EMHD flow studied here has numerous potential applications in fluid transport, enhanced heat and mass transfer, mixing, and emulsification because of the low energy requirement, flow reversibility, absence of moving parts, and facile control over flow rate. The parametric study presented here on the instabilities in the two-layer EMHD flow will thus be of great practical use.

The Weibull function is widely used to describe skew distributions observed in nature. However, the origin of this ubiquity is not always obvious to explain. In the present paper, we consider the well-known Galton-Watson branching process describing simple replicative systems. The shape of the resulting distribution, about which little has been known, is found essentially indistinguishable from the Weibull form in a wide range of the branching parameter; this can be seen from the exact series expansion for the cumulative distribution, which takes a universal form. We also find that the branching process can be mapped into a process of aggregation of clusters. In the branching and aggregation process, the number of events considered for branching and aggregation grows cumulatively in time, whereas, for the binomial distribution, an independent event occurs at each time with a given success probability.

We propose a simple complexity indicator of classical Liouvillian dynamics, namely the separability entropy, which determines the logarithm of an effective number of terms in a Schmidt decomposition of phase space density with respect to an arbitrary fixed product basis. We show that linear growth of separability entropy provides a stricter criterion of complexity than Kolmogorov-Sinai entropy, namely it requires that the dynamics be exponentially unstable, nonlinear, and non-Markovian.

We explore the issue of a quantum-noise-induced directed transport of an overdamped Brownian particle that is allowed to move in a spatially periodic potential. The established system-reservoir model has been employed here to study the quantum-noise-induced transport of a Brownian particle in a periodic potential, where the reservoir is being modulated externally by a Gaussian-colored noise. The mobility of the Brownian particle in the linear response regime has been calculated. Then, using Einstein’s relation, the analytical expression for the diffusion rate is evaluated for any arbitrary periodic potential for the high-temperature quantum regime.

We present a new formulation of the jamming phase diagram for a class of glass-forming fluids consisting of spheres interacting via finite-ranged repulsions at temperature $T$, packing fraction $\varphi$ or pressure $p$, and applied shear stress $\Sigma$. We argue that the natural choice of axes for the phase diagram are the dimensionless quantities $T/p\sigma {}^3$, $p\sigma {}^3/\epsilon$, and $\Sigma /p$, where $T$ is the temperature, $p$ is the pressure, $\Sigma$ is the stress, $\sigma$ is the sphere diameter, $\epsilon$ is the interaction energy scale, and $m$ is the sphere mass. We demonstrate that the phase diagram is universal at low $p\sigma {}^3/\epsilon$; at low pressure, observables such as the relaxation time are insensitive to details of the interaction potential and collapse onto the values for hard spheres, provided the observables are nondimensionalized by the pressure. We determine the shape of the jamming surface in the jamming phase diagram, organize previous results in relation to the jamming phase diagram, and discuss the significance of various limits.