We study the dynamics of perturbations in time-delay dynamical systems. Using a suitable space-time coordinate transformation, we find that the time evolution of the linearized perturbations (Lyapunov vector) can be described by the linear Zhang surface growth model [Y.-C. Zhang, J. Phys. (France) 51, 2129 (1990)], which is known to describe surface roughening driven by power-law distributed noise. As a consequence, Lyapunov vector dynamics is dominated by rare random events that lead to non-Gaussian fluctuations and multiscaling properties.

We develop models for the propagation of intense pulses in solid state media which can have either saturated absorption or reverse absorption. We model subluminal propagation in ruby and superluminal propagation in alexandrite as three and four level systems, respectively, coupled to Maxwell’s equations. We present results well beyond the traditional pump-probe approach and explain the experiments of Bigelow et al. [Phys. Rev. Lett. 90, 113903 (2003); Science 301, 200 (2003)] on solid state materials.

Weight measurements at the bottom of a quasi-2D vertical sheet of static cohesionless grains are carried out. The grains are held between two coaxial cylinders. This peculiar setup allows us to set either periodic or fixed lateral boundary conditions. Huge relative fluctuations in weight measurements appear in case of fixed lateral walls. This may be related to some indetermination in the mobilization state of friction forces on lateral walls. This argument would hold for any piling, but would lead to huge fluctuations in 2D systems only, because of averaging effects in 3D.

It is common knowledge that in an infinite periodic medium, for instance, an infinite photonic crystal, the direction of propagation of a monochromatic wave packet is given by the normal to the isofrequency diagram. We show that this is no longer true in a finite size medium, due to the existence of evanescent waves near the interfaces of the photonic crystal. We derive a renormalized isofrequency diagram giving the correct direction. We give a physical interpretation, showing that this phenomenon can be considered as a generalized Goos-Hänchen effect.

We observe the formation of optical precursors while propagating 540 fs pulses through 700 mm of deionized water. The launched pulses were strongly chirped to give them a bandwidth of approximately 60 nm to more readily excite the precursors. The precursors attenuated nonexponentially with distance.

We report the first experimental demonstration of time-reversal focusing with electromagnetic waves. An antenna transmits a $1\mathrm{\text{−}}\mathrm{\mu s}$ electromagnetic pulse at a central frequency of 2.45 GHz in a high-$Q$ cavity. Another antenna records the strongly reverberated signal. The time-reversed wave is built and transmitted back by the same antenna acting now as a time-reversal mirror. The wave is found to converge to its initial source and is compressed in time. The quality of focusing is determined by the frequency bandwidth and the spectral correlations of the field within the cavity.

Our experiments and molecular dynamics simulations on a projectile penetrating a two-dimensional granular medium reveal that the mean deceleration of the projectile is constant and proportional to the impact velocity. Thus, the time taken for a projectile to decelerate to a stop is independent of its impact velocity. The simulations show that the probability distribution function of forces on grains is time independent during a projectile’s deceleration in the medium. At all times the force distribution function decreases exponentially for large forces.

Turbulent Rayleigh-Bénard convection produces fields of intense updrafts and downdrafts that are responsible for much of the vertical heat transport. These structures, called plumes or thermals, have horizontal scales comparable to the thicknesses of the boundary layers in which they arise. In the three-dimensional numerical simulations reported here, we have observed that convective plumes organize themselves into clusters with horizontal scales that grow with time and reach the width of the computational domain. In this two-scale process, kinetic energy is transferred mainly to low horizontal wave numbers while the sizes of individual plumes remain on the scale of the boundary layer thickness.

We used the time correlation of shadowgraph images to determine the angle $\Theta$ of the horizontal component of the plume velocity above (below) the center of the bottom (top) plate of a cylindrical Rayleigh-Bénard cell of aspect ratio $\Gamma \equiv D/L=1$ ($D$ is the diameter and $L\simeq 87\mathrm{mm}$ is the height) in the Rayleigh-number range $7\times {10}^7\le R\le 3\times {10}^9$ for a Prandtl number $\sigma =6$. We expect that $\Theta$ gives the direction of the large-scale circulation. It oscillates time periodically. Near the top and bottom plates $\Theta (t)$ has the same frequency but is anticorrelated.

We introduce a novel approach for controlling fast chaos in time-delay dynamical systems and use it to control a chaotic photonic device with a characteristic time scale of $\sim 12\mathrm{ns}$. Our approach is a prescription for how to implement existing chaos-control algorithms in a way that exploits the system’s inherent time delay and allows control even in the presence of substantial control-loop latency (the finite time it takes signals to propagate through the components in the controller). This research paves the way for applications exploiting fast control of chaos, such as chaos-based communication schemes and stabilizing the behavior of ultrafast lasers.

A model to describe injection, due to footpoint motions, storage, and dissipation of MHD turbulence in coronal loops, is presented. The model is based on the use of the shell technique in the wave vector space applied to the set of reduced MHD equations. Numerical simulation showed that the energy injected is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions among these fluctuations give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. The statistical analysis performed on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics.

We observe stable holes in a vertically oscillated 0.5 cm deep aqueous suspension of cornstarch. Holes appear only if a finite perturbation is applied to the layer for accelerations $a$ above $10g$. Holes are circular and approximately 0.5 cm wide, and can persist for more than ${10}^6$ cycles. Above $a\simeq 17g$ the rim of the hole becomes unstable, producing fingerlike protrusions or hole division. At higher acceleration, the hole delocalizes, growing to cover the entire surface with erratic undulations. We find similar behavior in an aqueous suspension of glass microspheres.

We show that extraordinary light transmission of periodic subwavelength hole arrays, generally attributed to surface-plasmon resonances, is strongly influenced by the hole shape. Both experiments and calculations, based on a Fourier modal method, demonstrate that a shape change from circular to rectangular increases the normalized transmission by an order of magnitude while the hole area decreases. Moreover, the spectra exhibit large redshifts ($\sim 2500{\mathrm{cm}}^{-1}$). A comparison with the transmission of isolated holes shows that shape resonances of the rectangular holes play a dominant role.

The spontaneous clustering of a vibrofluidized granular gas is employed to generate directed transport in two different compartmentalized systems: a granular fountain in which the transport takes the form of convection rolls, and a granular ratchet with a spontaneous particle current perpendicular to the direction of energy input. In both instances, transport is not due to any system-intrinsic anisotropy, but arises as a spontaneous collective symmetry breaking effect of many interacting granular particles. The experimental and numerical results are quantitatively accounted for within a flux model.

We find a renormalized “time-dependent diffusion coefficient,” $D(t)$, for pulsed excitation of a nominally diffusive sample by solving the Bethe-Salpeter equation with recurrent scattering. We observe a crossover in dynamics in the transformation from a quasi-1D to a slab geometry implemented by varying the ratio of the radius, $R$, to the length, $L$, of the cylindrical sample with reflecting side walls and open ends. Immediately after the peak of the transmitted pulse, $D(t)$ falls linearly with a nonuniversal slope that approaches an asymptotic value for $R/L\gg 1$. The value of $D(t)$ extrapolated to $t=0$ depends only upon the dimensionless conductance $g$ for $R/L\ll 1$ and only upon $k{\ell }_0$ for $R/L\gg 1$, where $k$ is the wave vector and ${\ell }_0$ is the bare mean free path.

We report two phenomena, induced by dynamical correlations, that occur during the free cooling of a two-dimensional mixture of inelastic hard disks. First, we show that, due to the onset of velocity correlations, the ratio of the kinetic energies associated with the two species changes from the value corresponding to the homogeneous cooling state to a value approximately given by the mass ratio $m_1/m_2$ of the two species. Second, we report a novel segregation effect that occurs in the late stage of cooling, where interconnected domains appear. Spectral analysis of the composition field reveals the emergence of a growing characteristic length.

We study the dynamics of chemically or biologically active particles advected by open flows of chaotic time dependence, which can be modeled by a random time dependence of the parameters on a stroboscopic map. We develop a general theory for reactions in such random flows, and derive the reaction equation for this case. We show that there is a singular enhancement of the reaction in random flows, and this enhancement is increased as compared to the nonrandom case. We verify our theory in a model flow generated by four point vortices moving chaotically.

We study fluctuations in a vertically oscillated layer of grains below the critical acceleration for the onset of ordered standing waves. As onset is approached, transient disordered waves with a characteristic length scale emerge and increase in power and coherence. The scaling behavior and the shift in the onset of order agrees with the Swift-Hohenberg theory for convection in fluids. However, the noise in the granular system is an order of magnitude larger than the thermal noise in the most sensitive convecting fluid experiments to date; the effect of the granular noise is observable 20% below the onset of order.

Corrugated, hydrophilic particles with diameters between 30 and $150\mu \mathrm{m}$ are found to cause cavitation inception at their surfaces when they are exposed to a short, intensive tensile stress wave. The growing cavity accelerates the particle into translatory motion until the tensile stress decreases, and subsequently the particle separates from the cavity. The cavity growth and particle detachment are modeled by considering the momentum of the particle and the displaced liquid. The analysis suggests that all particles which cause cavitation are accelerated into translatory motion, and separate from the cavities they themselves nucleate. Thus, in the research of cavitation nuclei the link is established between developed cavitation bubbles and their origin.

Mesoscopic correlations are observed in the polarization of microwave radiation transmitted through a random waveguide. These measurements, supported by diagrammatic theory, permit an unambiguous decomposition of the intensity correlation function of a vector wave into short, long, and infinite range components. Infinite range correlation that leads to universal conductance fluctuations is measured and found to be in agreement with calculations. The long and infinite range components include nonuniversal frequency-independent terms associated with coupling into and out of the sample.