We propose a mechanism for the origin of non-Gaussian tails in the probability distribution functions of local variables in nonlinear, diffusive, dynamical systems including passive scalars advected by chaotic velocity fields: Intermittent fluctuations on appropriate time scales in the amplitude of the (chaotic) noise can lead to exponential tails in certain regimes. We provide numerical evidence for such behavior in deterministic, discrete-time passive scalar models. Different possibilities for probability distribution functions are also outlined.

Irradiating glass by intense light at frequencies ω and 2ω generates a semipermanent dc electric field in the glass that transforms the glass into a phase-method optical-frequency doubler. We map out this dc electric field over a wide variety of experimental conditions. We show that its symmetries are predicted by a theory based on the interference of competing multiphoton ionization channels.

A linear chain of atoms, interacting with anharmonic forces, one of whose end atoms is forced to vibrate harmonically, is studied as a simple model for kinetic friction between ideal crystalline solids. It is found that there is a transition, as a function of chain length and driving frequency between a regime in which there is dissipation (i.e., the internal energy increases as a function of time on the average) and one in which there is practically no dissipation. This suggests that there can be dissipationless sliding fro sufficiently small solids.

A critical analysis of the conformal approach to the theory of 2D turbulence is delivered. It is shown, in particular, that conformal minimal models cannot give a general turbulent solution, which should provide for constant fluxes of all vorticity integrals of motion.

We consider the viscous motion of an axisymmetric column of fluid with a free surface. The Navier-Stokes equation forms a singularity as the height of the fluid neck goes to zero. Close to pinchoff, the solutions have a scaling form characterized by a set of universal exponents. The shape of the neck and its velocity field is described by scaling functions, which we predict without adjustable parameters.

We find the self-similar scaling behavior x∼${\mathit{t}}^{3/5}$,y∼${\mathit{t}}^{2/5}$ for the arms which form in radial Hele-Shaw flow with anisotropic surface energy, where x is the longitudinal and y is the transverse coordinate of each primary finger. We first obseve this by direct numerical simulation using a boundary-integral method. Then we analytically derive the scaling law and the full asymptotic shape, by combining a simple boundary-layer analysis with previous results on velocity selection.

The dynamical behavior of the surface tension of two initially immiscible phases on raising the temperature to a value greater than or equal to the critical temperature is studied using analytic techniques, mean field dynamical equations, Monte Carlo simulations, and molecular dynamics simulations. Distinct behavior is predicted in situations with a conserved order parameter and when no conservation law is operative. A novel scaling form is obtained for a system evolving to equilibrium at its critical temperature.

The vortex street behind a ring of circular cross section and large aspect ratio is investigated experimentally. Different modes of annular and helical vortex shedding are identified by phase and frequency measurements. Their stability domains overlap in a large interval in Reynolds number where mode selection depends on initial conditions only. A new instability of the vortex shedding process involving characteristic mode transitions has been observed. This instability can be explained in the context of a Ginzburg-Landau model by a mechanism resembling formally the Eckhaus instability of spatially periodic patterns.

The acceleration of a material interface by a shock wave generates an interface instability known as the Richtmyer-Meshkov instability. Previous attempts to model the growth rate of the instability have produced values that are almost twice that of the experimental measurements. This Letter presents numerical simulations using front tracking that for the first time are in quantitative agreement with experiments of a shocked air-${\mathrm{SF}}_6$ interface. Moreover, the failure of the impulsive model, and the linear theory from which it is derived, to model experiments correctly is understood in terms of time limits on the validity of the linear model.

A new type of optical soliton is presented for two-wave interactions in quadratic nonlinear media. Unlike the conventional soliton in cubic nonlinear media, the most unique feature of the present solitons is found in the feasibility of multidimensional confinement. A compact analytical expression for the new solitons with arbitrary transverse dimension is derived through the self-consistent-field approximation. With available nonlinear materials in mind, a specific method for observing the multidimensional solitons is investigated.

Wavelet cross spectra and cross scalograms are used to analyze the time-scale structure of bivariate turbulence data from the boundary layer over the ocean. The cross scalogram for the streamwise and vertical turbulent velocity components shows a highly intermittent pattern with significant contributions of opposite signs appearing at two specific scales, ∼60 m and ∼2 km, believed to be related to small-scale turbulent mixing and large-scale secondary flow in the boundary layer.

Among the very rich range of possibilities for the dynamics of one dimensional fronts, this article presents, in a film draining experiment, the first observation of a continuous transition from solitary waves to a static spatially periodic pattern. Between these two extreme situations, a regime of colliding solitary waves exhibiting chaos with spatiotemporal intermittency is observed. These observations suggest the description of the static periodic pattern as being the result of a dense packing of propagating solitary waves, and its destabilization to spatiotemporal intermittency as the attempt of some solitary waves to propagate.

A pattern of standing surface waves in the form of equilateral triangles is observed in the Faraday experiment with two-frequency forcing. By perturbing with a third frequency the dynamics of a ‘‘phason mode’’ is under external control and transitions between triangles and hexagons can be enforced. The experiment is understood in terms of a three-mode amplitude equation model.

Experimental studies of the source dynamics of counterpropagating waves in a convecting binary fluid are presented. The source motion is controlled by side heating. There exists a locking band inside which the source is pinned by the underlying roll structure. Outside this band the source commences to move abruptly by steps of half a wavelength. A distortion of the phase field and the resulting nonlinear flow are essential ingredients responsible for the abrupt transition to the sliding state. Strong similarity to switching charge density waves dynamics is discussed.

A new route is described for eliminating chaos in nonlinear oscillators by changing only the shape of a weak nonlinear periodic perturbation and illustrated with the example of the Duffing-Holmes oscillator forced with the Jacobian elliptic function sn. Two techniques are used in the illustration: applying the Melnikov-Holmes analysis, and studying the behavior of the Lyapunov exponent from a simple recursion relation which models an unstable limit cycle. The connection with related previously described routes is also discussed in a general setting.

The measured mass distributions of fragments from 26 fractured objects of gypsum, soap, stearic paraffin, and potato show evidence of obeying scaling laws; this suggests the possibility of self-organized criticality in fragmenting. The probability of finding a fragment scales inversely to a power of the mass; the power, or scaling exponent, was found to depend on the shape of the object rather than on the material. For objects of different shapes (balls, cubes, half cubes, plates, and bars) scaling was found for fragment sizes smaller than the smallest dimension of the object undergoing fragmentation.

Nonlinear mode interactions and pattern formation occurring along the primary stability boundary for counterrotating eccentric cylinders have been studied experimentally. Counterrotating concentric cylinders produce either Taylor vortex flow or spiral vortices with various azimuthal wave numbers. Eccentric cylinders break the rotational symmetry of the base flow, introducing a delay of the onset of the primary instability and changes in the locations of the bicritical points separating patterns with differing azimuthal wave number. A theoretical model for this system is in qualitative agreement with the observations.

I develop a general approach for computing random-function solutions of the periodic Korteweg–de Vries (KdV) equation using the inverse scattering transform (IST) in the hyperelliptic function representation. I exploit IST to construct realizations of KdV random processes which have power-law spectra, ${\mathit{k}}^{\mathrm{-}\gamma }$ (k the wave number, γ a constant), and uniformly distributed random IST phases on (-π,π). IST characterizes these realizations in terms of solitons moving in a sea of background radiation and is thus able to extract solitons, by nonlinear filtering techniques, from complex, random motions described by the KdV equation.

The transfer operator developed recently by Bogomolny is used to calculate approximate semiclassical energy eigenvalues for a chaotic system, the wedge billiard. Only four classical trajectories, starting and ending on the Poincaré surface of section and crossing it once in between, are required to calculate an element of the T matrix. A 100×100T matrix is shown to give excellent results for the first 20 energy eigenvalues. It is also shown how the actions of the shortest periodic orbits of the 49° wedge can be obtained by calculating the Fourier transforms of Tr(${\mathit{T}}^{\mathit{m}}$).

We study how weak broadband noise affects 30.36 GHz 10%-‘‘ionization’’ thresholds F(10%) of ${\mathit{n}}_0$=54,...,72 H atoms. Calculations confirm that increased noise lowers F(10%) for most ${\mathit{n}}_0$’s raises some, but affects others little. We show noise to be a useful spectroscopic tool for uncovering novel quantal phenomena such as scarred states, which we link semiclassically to approximately adiabatic evolution near the separatrix of a nonlinear resonance island. Our results apply generally to the quantal behavior of classical mixed phase space systems.