We report the first spatially resolved measurements of the time dependence of high-order harmonic radiation. We have measured the time evolution of the harmonic distribution at the exit of the gas jet for the 13th harmonic $(\lambda =60\mathrm{}\mathrm{nm})$ generated in a low-density xenon jet by a 780 nm, 1 ps chirped laser pulse in the ${10}^{13}–{10}^{14}\mathrm{W}{\mathrm{cm}}^{-2\mathrm{}}$ range. We show that the harmonic source can become annular with a radius that increases in time during the laser pulse owing primarily to ionization depletion of the neutral medium. Under certain focusing conditions, we demonstrate that this can lead to significant harmonic pulse shortening.

The first experimentally observed ultrasonic full band gap in periodic bidimensional composites for the longitudinal wave mode is described in this Letter. The structure consists of an aluminum alloy plate with a square periodic arrangement of cylindrical holes filled with mercury. No propagation wave exists at the frequency range between 1000–1120 kHz irrespective of the measurement direction. The experiment was performed by means of an ultrasonic transmission technique, and a measurement of the position dependence of the acoustic amplitude was also performed.

The Rayleigh-Taylor instability is investigated in a material with a shear modulus $\mu$ and yield stress ${\sigma }_0$. Incompressible experiments are conducted with constant and impulsive acceleration histories $g\left(t\right)$ using a fully characterized material. Two dimensional (2D) perturbations are found to be stabilized for wave number $k>\mathrm{}\rho g/2\mathrm{}\mu$ and initial amplitude $h_0<{\sigma }_0/\rho g$, where $\rho$ is the density. The stability region is larger for 3D perturbations. Unstable modes are found to grow classically during the acceleration phase, but they can recover elastically while coasting.

We report long-time direct numerical simulations of two-dimensional Bénard-Marangoni convection at a low Prandtl number driven exclusively by surface tension gradients. At high Marangoni numbers we observe a turbulent flow characterized by a cycle of vorticity generation at the free surface and injection of surface vorticity into the layer. The energy dissipation obeys the Kolmogorov scaling. Our results differ from predictions of a scaling analysis by Pumir and Blumenfeld, but agree with a modified theory which takes the moderate Peclet numbers in the simulations into account.

A Comment on the Letter by G. L. J. A. Rikken and B. A. van Tiggelen, Phys. Rev. Lett. 78, 847 (1997). The authors of the Letter offer a Reply.

A Reply to the Comment by G. W. 't Hooft, G. Nienhuis, and J. C. J. Paasschens.

Scars have been mostly studied in the semiclassical limit. In this regime the density of states is high, and often the scarring effect gets dispersed among many states, complicating the understanding of scar formation. The systematics of scar formation at a very elementary level, uncluttered by other irrelevant effects, is studied by intentionally going to the edge of the chaotic region. The transition from chaos to order is induced by decreasing the value of $ħ$, and a series of broad avoided crossings marks the border between these two regions; scars then appear as mixing of the pairs of interacting wave functions.

A new regime in the transmission of waves through disordered waveguides is predicted, according to which ballistic, diffusive, and localized modes coexist within the same scale length, due to the surface-type disorder. This entangled regime is confirmed by the different behaviors of the transmitted intensities, obtained by means of numerical simulations based on invariant embedding equations for the reflection and transmission amplitudes. Also, an anomalous conductance crossover from quasiballistic transport to localization is encountered.

Second-harmonic generation from a subwavelength-thick Langmuir-Blodgett film forms an effective dipole oscillator with an essentially one-dimensional radiation pattern. A reflecting boundary is used to suppress $\left(\sim 80\%\right)$ and enhance $\left(\sim 70\%\right)$ the total rate of radiation from the system compared to its free-space value. The field amplitude between the dipole and the boundary is directly sampled and found to be constant in value, independent of the total rate of radiation. Hence, a nonvanishing field exists inside the system even during suppression of radiation, i.e., when the system loses no energy.

It is generally believed that long range periodic order is instrumental in the formation of a photonic band gap. Using a spectral method that scales linearly with the system size, we found that sizable spectral gaps for each polarization in 2D can be found in aperiodic arrangements of dielectrics that resemble quasicrystalline tiling. Since the aperiodic arrangement has many inequivalent sites, the defect properties of these systems are more complex and interesting than conventional photonic band gap systems.

We present a general analysis of the tunneling process through localized resonant states between one-dimensional continuums. We show that complete transfer can occur between the continuums by creating resonant states of different symmetry, and by forcing an accidental degeneracy between them. The degeneracy must exist in both the real and imaginary parts of the frequency. We illustrate the results of the analysis by performing computational simulations on the transport properties of electromagnetic waves in a two-dimensional photonic crystal.

We report experiments on convection driven by a radial electrical force in suspended annular smectic- $A$ liquid crystal films. In the absence of an externally imposed azimuthal shear, a stationary 1D pattern consisting of symmetric vortex pairs is formed via a supercritical transition at the onset of convection. Shearing reduces the symmetries of the base state and produces a traveling 1D pattern whose basic periodic unit is a pair of asymmetric vortices. For a sufficiently large shear, the primary bifurcation changes from supercritical to subcritical. We describe measurements of the resulting hysteresis as a function of the shear at radius ratio $\eta \sim 0.8$.

The shape complexity of irregular surfaces is quantified by a dimensionless area-volume measure. A joint distribution of shape complexity and size is found for level-set islands and lakes in two-dimensional slices of the scalar field of liquid-phase turbulent jets, with complexity values increasing with size. A well-defined power law, over 3 decades in size (6 decades in area), is found for the shape complexity distribution. Such properties are important in various phenomena that rely on large area-volume ratios of surfaces or interfaces, such as turbulent mixing and combustion.

The variational principle of V. I. Arnold [J. Appl. Math. Mech. 29, 1002 (1965)] is extended to general ideal magnetohydrodynamics (MHD). This is done using the trick of “superdynamics,” or the replacement of certain terms in the equations of motion by arbitrary functions. The variational constraint thus introduced leads to a sufficient, and likely necessary, Lyapunov stability criterion. All ideal MHD equilibria with fluid flow, except those with parallel sub-Alfvénic flow, are unstable according to this criterion. The method of superdynamics is extensible to other Hamiltonian systems.

We study the largest Lyapunov exponent $\lambda$ and the finite size effects of a system of $N$ fully coupled classical particles, which shows a second order phase transition. Slightly below the critical energy density $U_c$, $\lambda$ shows a peak which persists for very large $N$ values $(N=20\mathrm{}000)$. We show, both numerically and analytically, that chaoticity is strongly related to kinetic energy fluctuations. In the limit of small energy, $\lambda$ goes to zero with an $N$-independent power law: $\lambda \sim \sqrt{U}$. In the continuum limit the system is integrable in the whole high temperature phase. More precisely, the behavior $\lambda \sim N^{-1/3\mathrm{}}$ is found numerically for $U>\mathrm{}{U}_c$ and justified on the basis of a random matrix approximation.

A new transition mechanism into spatiotemporal chaos is reported. In a system with hysteresis we consider a steady wave that is unstable due to a saddle node. If it is taken as a carrier wave one can find a new steady wave combined by the carrier and a nonlinear structure trapped in it. The trapped wave can also become chaotic. Crisis occurs when the chaotic attractor collides with the unstable saddle orbit. After crisis the orbit is attracted to a new created large attractor and the temporally chaotic motion transits to spatiotemporal chaos.

In dynamical systems, as a parameter is varied past a critical value, a chaotic attractor may be destroyed by a crisis. This attractor is replaced by a chaotic transient, which eventually leads to a different attractor. We present a method for maintaining chaotic dynamics after the crisis. The model, formulated for arbitrary dimensions, directs the phase space trajectory toward a target region near the periodic saddle orbit that mediates the crisis. It is used to maintain chaos numerically in the Ikeda map and experimentally in a magnetoelastic ribbon.

We study how an axisymmetric drop of inviscid fluid breaks under the action of surface tension. The evolution of various initial shapes is calculated numerically using a boundary-element method, and finite-time breakage is observed in detail. The pinchoff region is shown to have lengths scaling as ${\tau }^{2/3}$, where $\tau$ is the time remaining until pinchoff, and is found to adopt a unique shape with two cones of angles $18.1°$ and $112.8°$, independent of the initial conditions. The velocity potential in the intermediate region between the small pinchoff region and the large bulk of the drops is shown to take the form ${\mathrm{Ar}}^{1/2}{P}_{1/2}\left(\cos \theta \right)+B\tau /r+\dots$ .

We introduce a formalism that allows us to study space-scale correlations in multiscale processes. This method, based on the wavelet transform, is particularly well suited to study multiplicative random cascade processes for which the correlation functions take a very simple expression. This two-point space-scale statistical analysis is illustrated on some pedagogical examples and then applied to fully developed turbulence data.

We describe a new constitutive theory for two-phase flow models of chaotic mixing layers, which form as two incompressible fluids interpenetrate. This theory is compatible with arbitrary velocities of the edges of a mixing layer, and it gives analytic solutions for the distribution of fluid variables across the layer in terms of these velocities. Our results are in agreement with all available data from planar Rayleigh-Taylor instability experiments. The model that we discuss can be embedded in a larger system of two-phase flow equations in order to predict other important physical quantities, such as the fluid pressures and internal energies in compressible mixing.