Self-similarity may originate from two origins: i.e., the process memory and the process’ increments “infinite” variance. A distinction is attempted by employing the natural time $\chi$. Concerning the first origin, we analyze recent data on seismic electric signals, which support the view that they exhibit infinitely ranged temporal correlations. Concerning the second, slowly driven systems that emit bursts of various energies $E$ obeying the power-law distribution—i.e., $P\left(E\right)\sim E^{-\gamma }$—are studied. An interrelation between the exponent $\gamma$ and the variance ${\kappa }_1(\equiv ⟨{\chi }^2⟩-⟨\chi {⟩}^2)$ is obtained for the shuffled (randomized) data. For real earthquake data, the most probable value of ${\kappa }_1$ of the shuffled data is found to be approximately equal to that of the original data, the difference most likely arising from temporal correlation. Finally, it is found that the differential entropy associated with the probability $P\left({\kappa }_1\right)$ maximizes for $\gamma$ around $\gamma \approx 1.6–1.7$, which is comparable to the value determined experimentally in diverse phenomena: e.g., solar flares, icequakes, dislocation glide in stressed single crystals of ice, etc. It also agrees with the $b$ value in the Gutenberg-Richter law of earthquakes. In addition, the case of multiplicative cascades is studied in the natural time domain.

Within the replica symmetry breaking framework developed by Mézard and Parisi we investigate the occurrence of structural glass transitions in a model of fluid characterized by hard sphere repulsion together with short-range attraction. This model is appropriate for the description of a class of colloidal suspensions. The transition line in the density-temperature plane displays a reentrant behavior, in agreement with mode coupling theory and recent molecular dynamics simulations. Quantitative differences are found, together with the absence of the predicted glass-glass transition at high density. We also perform a systematic study of the pure hard-sphere fluid in order to ascertain the accuracy of the adopted method and the convergence of the numerical procedure.

Effects of charge-density fluctuations on a phase behavior of the restricted primitive model are studied within a field-theoretic formalism. We focus on a $\lambda$ line of continuous transitions between charge-ordered and charge-disordered phases that is observed in several mean-field theories, but is absent in simulation results. In our study the RPM is reduced to a ${\varphi }^6$ theory, and a fluctuation contribution to a grand thermodynamic potential is obtained by generalizing the Brazovskii approach. We find that in a presence of fluctuations the $\lambda$-line disappears. Instead, a fluctuation-induced first-order transition to a charge-ordered phase appears in the same region of a phase diagram, where the liquid–ionic-crystal transition is obtained in simulations. Our results indicate that the charge-ordered phase should be identified with an ionic crystal.

An expression for the anisotropy of the solid-liquid interfacial energy has been determined experimentally by an inverse method for the $\mathrm{Al}\text{−}43.4\mathrm{wt}\%\mathrm{Zn}\text{−}1.6\mathrm{wt}\%\mathrm{Si}$ system. Assuming that dendrite growth directions correspond to the minima of the surface stiffness, the anisotropy of the solid-liquid interfacial energy could be described by minimizing the errors between the calculated minima of a parametric interface stiffness function and experimentally measured growth directions of dendrites in thin coatings. In order to adequately describe the interfacial energy, it is found that a cubic harmonic expansion up to the third order is necessary to obtain the minima of interface stiffness along directions that depart from $⟨100⟩$ or $⟨110⟩$. Best agreement with observed growth directions is obtained for first, second, and third harmonic coefficients (${\epsilon }_1$, ${\epsilon }_2$, and ${\epsilon }_3$, respectively) satisfying the following relationships: ${\epsilon }_2∕{\epsilon }_1=-0.188$; ${\epsilon }_3∕{\epsilon }_1=-0.00776$. The corresponding interface stiffness function shows 24 minima lying along directions between $⟨100⟩$ and $⟨110⟩$. The minima are located at 28.5° from $⟨100⟩$ and only 5.1° from $⟨320⟩$, which was the growth direction suggested by Sémoroz et al. for this alloy [A. Sémoroz, Y. Durandet, and M. Rappaz, Acta Mater. 49, 529 (2001).]. It was also found that the strength of the effective in-plane anisotropy is directly reflected by the morphology of the dendritic microstructure.

Thinner parts (the so-called holes) and thicker parts (islands) move in free-standing smectic films due to gravity if the film is inclined. The velocity of the movement depends on the viscosity coefficient ${\eta }_3$ of the film. Therefore, this measurement is a direct method to determine ${\eta }_3$ in smectic phases. This paper contains the corresponding hydrodynamic calculations for the flow patterns in and around a circular hole in a circular two-dimensional film under various conditions. The viscous force on the hole is calculated. Experiments are performed with the liquid crystal $n$-octyl-cyano-biphenyl (8CB) in the smectic phase. The influence of the disclination which surrounds the hole and the influence of the gas which surrounds the film on the movement is studied. It is shown that the influence of these effects on the determination of ${\eta }_3$ can be neglected if the film is thick and the difference in the thicknesses between film and hole is small. The temperature dependence of ${\eta }_3$ is determined for 8CB.

The diffusion effect on chirality selection in a two-dimensional reaction-diffusion model is studied by Monte Carlo simulations. The model consists of achiral reactants $A$ which turn into either of the chiral products $R$ or $S$ in a solvent of chemically inactive vacancies $V$. The reaction contains a nonlinear autocatalysis as well as a recycling process, and the chiral symmetry breaking is monitored by an enantiomeric excess (ee) $\varphi$. Without dilution a strong nonlinear autocatalysis ensures chiral symmetry breaking. By diluting a diffusionless system, the ee $\varphi$ decreases and a racemic state is recovered below a critical concentration $c_c$. When the diffusion is allowed, the steady value of $\varphi$ increases and $c_c$ decreases. As for the relation between the ee $\varphi$ and the concentration $c$, a formula interpolating between the diffusionless $(D=0)$ and the homogeneous $(D=\infty )$ limits is proposed by incorporating the diffusional enhancement of the concentrations of chiral species. Diffusion also accelerates the development of the chiral order, and the time required to establish the order in a system of a size $L^2$ is inversely proportional to the diffusion constant $D$ as $L^2∕D$.

We study a competition dynamics, based on the minority game, endowed with various substrate network structures. We observe the effects of the network topologies by investigating the volatility of the system and the structure of follower networks. The topology of substrate structures significantly influences the system efficiency represented by the volatility and such substrate networks are shown to amplify the herding effect and cause inefficiency in most cases. The follower networks emerging from the leadership structure show a power-law incoming degree distribution. This study shows the emergence of scale-free structures of leadership in the minority game and the effects of the interaction among players on the networked version of the game.

In this paper a topic regarding the synchronization of chaotic systems is dealt with: the case of separation and synchronization of many chaotic signals generated by different chaotic circuits and combined together is examined. In particular, an observer based strategy has been adopted, and an approach for the simultaneous stabilization of many Luenberger observers has been investigated to face the problem of separation and synchronization. The design strategy is based on linear matrix inequalities (LMIs). Indeed, the LMI problem is referred to have a solution if a dual optimization problem admits a solution. In our case the feasibility condition, if it does exist, allows us to establish that the separation and synchronization problem for the chosen circuit admits a solution. Some numerical simulations are reported. Further results refer to an experimental circuit showing the suitability of the approach. Furthermore, the use of the proposed scheme to transmit two or more information masked into two or more multiplexed chaotic signals and the design of suitable parameters through the introduced technique based on LMIs are discussed.

In the spectral region where the refractive index of the negative index material is approximately zero, at oblique incidence, the linear transmission of a finite structure composed of alternating layers of negative and positive index materials manifests the formation of a new type of band gap with exceptionally narrow band-edge resonances. In particular, for TM-polarized (transverse magnetic) incident waves, field values that can be achieved at the band edge may be much higher compared to field values achievable in standard photonic band-gap structures. We exploit the unique properties of these band-edge resonances for applications to nonlinear frequency conversion, second-harmonic generation, in particular. The simultaneous availability of high field localization and phase matching conditions may be exploited to achieve second-harmonic conversion efficiencies far better than those achievable in conventional photonic band-gap structures. Moreover, we study the role played by absorption within the negative index material, and find that the process remains efficient even for relatively high values of the absorption coefficient.

We report the results of molecular-dynamics simulations of solvophobic nanoparticles in $n$-decane solvent. We observe that solvent ordering in the interparticle gap and solvation forces depend on the particle size and shape. Analogous to hydrophobic hydration, we observe dewetting of the interparticle region when the nanoparticle separation becomes smaller than a critical value of ${\delta }_c$. We observe that ${\delta }_c$ exhibits a nonmonotonic dependence on nanoparticle size, in contrast to what is expected from studies of water. While studies of hydrophobic hydration indicate that two solute length scales govern hydrophobic interactions, our studies indicate that a third length scale can be important in the more general phenomenon of solvophobic solvation.

Dynamical systems that operate near the onset of coupling-induced oscillations can exhibit enhanced sensitivity to external perturbations under suitable operating parameters. This cooperative behavior and the attendant enhancement in the system response (quantified here via a signal-to-noise ratio at the fundamental of the coupling-induced oscillation frequency) are investigated in this work. As a prototype, we study an array of dc superconducting quantum interference device (SQUID) rings locally coupled, unidirectionally as well as bidirectionally, in a ring configuration; it is well known that each individual SQUID can be biased through a saddle-node bifurcation to oscillatory behavior. We show that biasing the array near the bifurcation point of coupling-induced oscillations can lead to a significant performance enhancement.

We have performed systematic experiments on vane intruders of different sizes and aspect ratios that are immersed and slowly rotated in beds of monodisperse glass beads of different diameters. We find that the torque and lift force on the vane increase with bead size. The measured torque on the rotating vanes follows a scaling behavior that depends on the effective immersion depth and the effective vane diameter. The torque increases with the square of the effective immersion depth and the square of the effective vane diameter, and closely resembles the scaling behavior previously reported for the torque on rotating cylinders. We also find that the vertical lift forces have a supralinear dependence on the effective immersion depth, and qualitatively resemble the plunging forces produced when an intruder is slowly immersed into beds of glass beads.

The stress and optical relaxation of an initially straight stiff polymer chain are studied through Brownian dynamics simulations (based on a semiflexible bead-rod model) covering a broad range of time scales and polymer lengths. The strong stress component ${\sigma }_{11}$ (where “1” is the direction of the original alignment) is shown to be associated with the chain’s longitudinal relaxation while the weak stress component ${\sigma }_{22}={\sigma }_{33}$ is shown to depend on the chain’s transverse relaxation. The two independent stress components follow a different relaxation; this anisotropy is shown to result from the participation of the different relaxation modes in the transverse direction. The chain’s optical relaxation is shown to be affected by the longitudinal dynamics only. The early relaxation of the strong stress component ${\sigma }_{11}$ and that of the chain’s optical properties constitute a universal behavior—i.e., valid for any stiffness of the bead-rod chain, since at the early times the bending forces do not affect the longitudinal dynamics. Based on the knowledge of the physical mechanism and the chain’s conformational behavior, we predict and explain the polymer stress and optical relaxation. A nonlinear stress-optic law (valid for any time and chain stiffness) is derived based on the identified relation of the chain configuration with the optical properties and the polymer stress. A coarse-grain model describing extended semiflexible bead road chains is also derived.

Multistable systems can exhibit stochastic resonance which is characterized by the amplification of small periodic signals by additive noise. Here we consider a nonmultistable linear system with a multiplicative noise forced by an external periodic signal. The noise is the sum of a colored noise of mean value zero and a noise with a definite sign. We show that the system exhibits stochastic resonance through the numerical study of an exact analytical expression for the mean value obtained by functional integral techniques. This is proof of the effect for a very general kind of noise which can even have a definite sign.

Multiscale mixing efficiencies for passive scalar advection are defined in terms of the suppression of variance weighted at various length scales. We consider scalars maintained by temporally steady but spatially inhomogeneous sources, stirred by statistically homogeneous and isotropic incompressible flows including fully developed turbulence. The mixing efficiencies are rigorously bounded in terms of the Péclet number and specific quantitative features of the source. Scaling exponents for the bounds at high Péclet number depend on the spectrum of length scales in the source, indicating that molecular diffusion plays a more important quantitative role than that implied by classical eddy diffusion theories.

We investigate the classical chaotic diffusion of atoms subjected to pairs of closely spaced pulses (“kicks”) from standing waves of light (the $2\delta \text{−}\mathrm{KP}$). Recent experimental studies with cold atoms implied an underlying classical diffusion of a type very different from the well-known paradigm of Hamiltonian chaos, the standard map. The kicks in each pair are separated by a small time interval $ϵ⪡1$, which together with the kick strength $K$, characterizes the transport. Phase space for the $2\delta \text{−}\mathrm{KP}$ is partitioned into momentum “cells” partially separated by momentum-trapping regions where diffusion is slow. We present here an analytical derivation of the classical diffusion for a $2\delta \text{−}\mathrm{KP}$ including all important correlations which were used to analyze the experimental data. We find an asymptotic $(t\to \infty )$ regime of “hindered” diffusion: while for the standard map the diffusion rate, for $K⪢1$, $D\sim K^2∕2[1-2J_2\left(K\right)\cdots ]$ oscillates about the uncorrelated rate $D_0=K^2∕2$, we find analytically, that the $2\delta \text{−}\mathrm{KP}$ can equal, but never diffuses faster than, a random walk rate. We argue this is due to the destruction of the important classical “accelerator modes” of the standard map. We analyze the experimental regime $0.1\lesssim Kϵ\lesssim 1$, where quantum localization lengths $L\sim {\hslash }^{-0.75}$ are affected by fractal cell boundaries. We find an approximate asymptotic diffusion rate $D\propto K^3ϵ$, in correspondence to a $D\propto K^3$ regime in the standard map associated with the “golden-ratio” cantori.

Dynamical tunneling between symmetry-related stable modes is studied in the periodically driven pendulum. We present strong evidence that the tunneling process is governed by nonlinear resonances that manifest within the regular phase-space islands on which the stable modes are localized. By means of a quantitative numerical study of the corresponding Floquet problem, we identify the trace of such resonances not only in the level splittings between near-degenerate quantum states, where they lead to prominent plateau structures, but also in overlap matrix elements of the Floquet eigenstates, which reveal characteristic sequences of avoided crossings in the Floquet spectrum. The semiclassical theory of resonance-assisted tunneling yields good overall agreement with the quantum-tunneling rates, and indicates that partial barriers within the chaos might play a prominent role.

A regular pattern of surface waves is observed on a liquid curtain falling from a horizontal, wetted tube, maintained between two vertical wires. Since the upper boundary is not constrained in the transverse direction, the top of the curtain enters a pendulumlike motion, when the flow rate is progressively reduced, coupled to the propagation of curtain undulations, structured as a checkerboard. This structure is formed by two patterns of propagating waves. In some sense, these propagating patterns replace the stationary pattern of liquid columns observed at a lower flow rate. Measurements of phase velocity, frequency, and wavelength are reported. The data are in agreement with a simple dimensional argument suggesting that the wave velocity is proportional to the surface tension divided by the mass flux of liquid per unit length. This scaling is also that followed by the fluid velocity at the so-called transonic point, i.e., the point where the fluid velocity equals that of sinuous waves. We finally discuss the implications of these results for the global stability of liquid curtains.

We propose a modified x-ray form factor that describes the scattering cross section in warm dense matter valid for both the plasma and the solid (crystalline) state. Our model accounts for the effect of lattice correlations on the electron-electron dynamic structure, as well as provides a smooth transition between the solid and the plasma scattering cross sections. In addition, we generalize the expression of the dynamic structure in the case of a two-temperature system (with different electron and ion temperatures). This work provides a unified description of the x-ray scattering processes in warm and dense matter, as the one encountered in inertial confinement fusion, laboratory astrophysics, material science, and high-energy density physics and it can be used to verify temperature relaxation mechanisms in such environments.