Air injected into a two-dimensional porous medium displaced a flowing defending fluid. At low flow rates the invading air formed chains of fractal clusters similar to those observed in gradient percolation. The defending fluid was excluded from the invading region and moved around the invading clusters. Above a critical flow rate the invaded region fragmented into a plumelike structure that permitted the defending fluid to flow through the invaded region. Invasion percolation simulations, modified to include fragmentation and pressure gradients due to flow, describe the observations well.

The dynamics of water columns rising and falling in vertical glass capillaries are studied near the pinning threshold. In tubes with rough interior walls, the column height $h$ as a function of time $t$ exhibits stick-slip behavior. In tubes with smooth walls, falling experiments show no pinning effects, but rising experiments exhibit critical behavior with nonunique exponents. We argue that this is due to the fact that fluid has to be transported in a microscopic wetting film which does not have a stationary structure. Similar restrictions can affect avalanche dynamics in other systems.

We report experimental results of x-ray amplification of spontaneous emission in a Ni-like transient collisional excitation scheme. The Ni-like plasma formation, ionization, and collisional excitation requires irradiation of a slab target by two laser pulses: a formation beam with 5 J energy of 800 ps duration and a pump beam of 5 J energy in 1.1 ps. A gain of $35{\mathrm{cm}}^{-1\mathrm{}}$ and a $\mathrm{gL}$ product of 12.5 are measured on the $4d\to 4p$ $J=0\mathrm{}\to 1$ transition for Ni-like Pd at 147 Å with an 8 mm line focus. The high efficiency of this scheme at “table-top” laser energies is a direct consequence of the nonstationary population inversion produced by the high intensity picosecond pulse.

We introduce a new type of metallo-dielectric photonic band gap structure (PBG), intentionally incorporating very strong capacitive interactions between the periodic metallic islands. The band gaps become huge, with the lower band edge frequency being pushed down by the capacitive interaction between metallic islands, while the upper band edge frequency continues to depend primarily on the lattice constant, as in normal PBG's. With this new type of photonic crystal, the spatial periodicity can be much smaller than the corresponding electromagnetic wavelength, allowing PBG structures to play a role at radio frequencies.

Density waves of granular material (sand) flowing through a vertical pipe have been investigated. Clear density waves emerge when the cock attached to the bottom end of the pipe is closed. The FFT power spectra were found to show a stable power-law form $P\left(f\right)\sim f^{-\alpha }$. The value of the exponent was evaluated as $\alpha \cong 4/3$. We also introduce a simple one-dimensional model which reproduces $\alpha =4\mathrm{}/3$ from both simulation and theoretical analysis.

The dynamics of a thin Huygens front propagating through a turbulent medium is considered. A rigorous asymptotic expression for the effective velocity $v_F$ proportional to the front area is derived. The small-scale fluctuations of the front position are shown to be strongly intermittent. This intermittency plays a crucial role in establishing a steady state magnitude of the front velocity. The results are compared with experimental data.

A Comment on the Letter by M. A. Matias, et al., Phys. Rev. Lett. 78, 219 (1997). The authors of the Letter offer a Reply.

A Reply to the Comment by E. R. Hunt.

We examine the effect of short unstable periodic orbits on wave function statistics in a classically chaotic system, and find that the tail of the wave function intensity distribution in phase space is dominated by scarring associated with the least unstable periodic orbits. In an ensemble average over systems with classical orbits of different instabilities, a power-law tail is found, in sharp contrast to the exponential prediction of random matrix theory. The calculations are compared with numerical data, and quantitative agreement is obtained.

We demonstrate that interferometric imaging may be replaced by noninterferometric propagation-based techniques in many experiments. We explore propagation through the Poynting vector and find two classes of phase, one of which is topological in origin. Only this latter class may require interferometry to be determined, and even then only in specific well-defined circumstances. Our alternative definitions of phase are readily generalized to partially coherent radiation. Our analysis leads to an approach that is able to determine the absolute phase and the amplitude of a wave.

Analytic expressions are found for the index of refraction and attenuation length of an acoustic wave that propagates in a flow that can be modeled in terms of many slender vortices in three dimensions. This is done to second order in the Mach number, within a multiple scattering scheme and a Born approximation also carried to second order. As an example, their dependence on wavelength is explicitly computed in the case of the vortices being circular rings, uniformly distributed in space but randomly oriented.

The spatiotemporal dynamics of an excitable medium with multiple spiral defects is shown to vary smoothly with system size from short-lived transients for small systems to extensive chaos for large systems. A comparison of the Lyapunov dimension density with the average spiral defect density suggests an average dimension per spiral defect varying between 3 and 7. We discuss some implications of these results for experimental studies of excitable media.

We show that multimode incoherent spatial solitons are possible in logarithmically saturable nonlinear media. The mode-occupancy function associated with these soliton states is found to obey a Poisson distribution. Our analysis indicates that two approaches, i.e., the dynamic coherent density description as well as static self-consistent multimode method lead to exactly the same results. Closed form solutions are obtained for $(1+1)\mathrm{D}$ as well as for $(2+1)\mathrm{D}$ circular and elliptical incoherent solitons.

A new method is introduced to create artificial time sequences that fulfil given constraints but are random otherwise. Constraints are usually derived from a measured signal for which surrogate data are to be generated. They are fulfilled by minimizing a suitable cost function using simulated annealing. A wide variety of structures can be imposed on the surrogate series, including multivariate, nonlinear, and nonstationary properties. When the linear correlation structure is to be preserved, the new approach avoids certain artifacts generated by Fourier-based randomization schemes.

We show that many coupled oscillator array configurations considered in the literature can be put into a simple form so that determining the stability of the synchronous state can be done by a master stability function, which can be tailored to one's choice of stability requirement. This solves, once and for all, the problem of synchronous stability for any linear coupling of that oscillator.

Using exact time-dependent nonsingular solutions [Mineev-Weinstein and Dawson, Phys. Rev. E 50, R24 (1994); Dawson and Mineev-Weinstein, Physica (Amsterdam) 73D, 373 (1994)], we solve the Saffman-Taylor finger selection problem in the absence of surface tension. We show that a generic interface in a Hele-Shaw cell evolves to a nonlinearly stable single uniformly advancing finger occupying one-half of the channel width. This result contradicts the generally accepted belief that surface tension is indispensable for the selection of the $\frac{1}{2}$-width finger.

We investigate the dynamics of a pattern of liquid columns formed below a circular fountain. Traveling domains consisting of drifting asymmetrical cells are forced and quantitatively studied. We provide evidence of a unique propagation velocity of the domain walls, which increases with the flow rate but depends on neither the number of moving columns nor the fluid viscosity. Similar to the “printer's instability,” this velocity is proportional to a natural velocity formed from the static wavelength and the frequency of localized oscillations of the column position.

The probability density function (PDF) of passive scalar dissipation $P\left(\epsilon \right)$ is found analytically in the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime) in two dimensions. The tail of PDF at $\epsilon \gg 〈\epsilon 〉$ is shown to be stretched exponent $\ln P\left(\epsilon \right)\propto {\epsilon }^{1/3}$; at $\epsilon \ll 〈\epsilon 〉$, $P\propto 1/\sqrt{\epsilon }$.

The nonlinear dynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg–de Vries (KdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging from small harmonic oscillations (linearized model), to nonlinear oscillations, up through solitary waves. These non-axis-symmetric localized shapes are also described by a KdV Hamiltonian system. Recently such “rotons” were observed experimentally when the shape oscillations of a droplet became nonlinear. The results apply to droplike systems from cluster formation to stellar models, including hyperdeformed nuclei and fission.