We report the observation of three-dimensional spiraling collision of interacting two-dimensional spatial solitons. The solitons are photorefractive screening solitons and are phase incoherent to each other at all times. The collision provides the solitons with angular momentum which is manifested in a centrifugal repulsion force. When it is balanced by attraction, the solitons spiral about each other in a DNA-like structure.

A new class of propagating fronts is proposed in which a spreading instability evolves through a singular configuration before saturating. As an example, we examine the viscous Rayleigh instability of a stationary fluid column, using the marginal stability criterion to estimate the front velocity, front width, and the selected wavelength in terms of the surface tension and viscosity contrast. Systems that may display this phenomenon include droplets elongated in extensional flows, capillary bridges, liquid crystal tethers, and viscoelastic jets. The related problem of propagation in Rayleigh-like systems that do not fission is also considered.

We show that at high Reynolds number, smooth, Lagrangian chaotic flows are typically linearly unstable. Numerical integration of the relevant linear partial differential equations with Reynolds number $R$ up to ${10}^6$ shows that the wave number power spectrum of the perturbed vorticity has a power-law behavior and that the norm of the perturbed vorticity is a multifractal. These properties are theoretically predicted at short scales by a wave packet model, whereby vorticity wave packets are evolved according to ordinary differential equations.

General turbulent mean statistics are shown to be characterized by a variational principle. The variational functionals, or “effective actions,” have experimental consequences for turbulence fluctuations and are subject to realizability conditions of positivity and convexity. An efficient Rayleigh-Ritz algorithm is available to calculate approximate effective actions within probability density function (PDF) closures. Examples are given for Navier-Stokes and for a three-mode system of Lorenz. The new realizability conditions succeed at detecting a priori the poor predictions of PDF closures even when the classical second-order moment realizability conditions are satisfied.

The three-dimensional stability problem of a stretched stationary vortex is addressed in this Letter. More specifically, we prove that the discrete part of the temporal spectrum is associated only with two-dimensional perturbations.

We present a technique to estimate the information flow in dynamical systems. The information flow characterizes the underlying dynamics which can be stochastic, deterministic chaotic, or deterministic nonchaotic. For chaos our approach offers a method for calculating the Kolmogorov-Sinai (KS) entropy from continuous probability density functions. These density functions are approximated by neural networks. For stochastic processes (noisy chaos, autoregressive models) our approach yields the rate of memory loss of the dynamics.

Wholesale symmetry breaking of the $-1/r$ potential opens all of configuration space for motion. Despite this, recent experimental studies of atomic versions of such systems can be explained by planar motion alone. We show how the nucleus selects two dimensional motion, and predict how photoabsorption spectra for a hydrogen atom in crossed electric and magnetic fields can be selectively tuned between 2D and 3D.

We theoretically predict and experimentally demonstrate the phenomenon of frequency entrainment in optically injected semiconductor lasers. The laser exhibits nonlinear subharmonic and ultraharmonic resonances for appropriate values of its frequency detuning from the externally injected signal.

We present an analytic expression for the onset of the Faraday instability, which is applicable to a wide frequency range covering both shallow gravity and deep capillary waves. For sufficiently thin fluid layers, the surface oscillates in harmonic rather than subharmonic resonance with the forcing. An experimental confirmation of this result is reported.

An exact two-dimensional solution of a viscous flow generated by two point vortices is obtained. The viscosity $\nu$ is introduced as a Brownian motion in the Hamiltonian dynamics of two point vortices. The derived exact solution describes in particular the merging process of two Lamb vortices. In the limit $\nu \to 0$, the apparition of a spiral structure in the topology of the vorticity distribution is observed. This solution also describes the selection by viscosity of a particular solution among the infinity of patterns satisfying the Euler equation.

We analyze the collective behavior of a set of coupled damped driven pendula with finite (large) inertia, and show that the synchronization of the oscillators exhibits a first order phase transition synchronization onset, substantially different from the second order transition obtained in the case of no inertia. There is hysteresis between two macroscopic states, a weakly and a strongly coherent synchronized state, depending on the coupling and the initial state of the oscillators. A self-consistent theory is shown to determine these cooperative phenomena and to predict the observed numerical data in specific examples.

We present an experimental and theoretical study of the decay of high order optical vortices in media with an anisotropic nonlocal nonlinearity. Vortices with charge $n$ decay into an aligned array of $n$ vortices of unit charge.

We show that any generic nonadiabatic slow flow of ideal compressible fluid develops a significant vorticity. As an example, an initially irrotational conductive cooling flow (CF) is considered. A perturbation theory for the vorticity generation is developed that employs, as a zero order solution, a novel two-dimensional similarity solution. Full gasdynamic simulations of this CF demonstrate the vorticity generation and support the theory. The relevance of this problem to the experiments with the “hot channels” is discussed.

Molecular dynamics simulations are used to compute the flow of both a simple atomistic liquid and a model polymer melt through a channel with a reentrant corner. In the Newtonian case, the shear stress near the corner is found to agree with the Stokes flow prediction of Moffatt [J. Fluid Mech. 18, 1 (1964)]. In the non-Newtonian case, the shear stress has a stronger apparent power-law divergence but the exponent appears to saturate at an integrable value of approximately 0.8 for all chain lengths. The molecular origin of the stress enhancement is that the extensional flow near the reentrant corner flow tends to elongate the molecules.

A new, containerless method for measuring viscosity variations, as a function, e.g., of temperature or concentration, is described. Relative viscosities are extracted from the resonance quality factor near eigenfrequencies of deformation modes of gas-film levitated liquid drops. Both the geometrical aspect of the drop and the resonance profile are dissymmetric in general. This can be understood in terms of a parametric instability against nonlinear oscillations. The method could be useful for viscosity measurements under conditions where contact with walls should be avoided—in particular at high temperatures, in order to avoid corrosion or chemical contamination.

We discuss a topological property which we believe provides a useful conceptual characterization of a variety of strange sets occurring in nonlinear dynamics (e.g., strange attractors, fractal basin boundaries, and stable and unstable manifolds of chaotic saddles). Sets with this topological property are known as indecomposable continua. As an example, we give detailed results for the case of an indecomposable continuum that arises from the entrainment of dye advected by a fluid flowing past a cylinder. We show for this case that the indecomposable continuum persists in the presence of small noise.

We numerically study heat conduction in chains of nonlinear oscillators with time-reversible thermostats. A nontrivial temperature profile is found to set in, which obeys a simple scaling relation for increasing the number $N$ of particles. The thermal conductivity diverges approximately as $N^{1/2}$, indicating that chaotic behavior is not enough to ensure the Fourier law. Finally, we show that the microscopic dynamics ensures fulfillment of a macroscopic balance equation for the entropy production.

We examine the stability of flows which are the sum of a linear flow with elliptic streamlines and a transverse standing wave. Such flows are exact solutions of the 3D Euler equations for an inviscid incompressible fluid. We examine the stability of such flows under local 3D high frequency perturbations, which can be viewed as secondary perturbations of the elliptic flow itself. We find that these flows are unstable to such perturbations and compute growth rate in several cases.

We propose a new approach for the analysis of stationary correlation functions of the 1D Burgers equation driven by a random force. We use this to study the asymptotic behavior of the probability distribution of velocity gradients and velocity increments.

We derive the exact equation of motion for a vortex in two- and three-dimensional nonrelativistic systems governed by the Ginzburg-Landau equation with complex coefficients. The velocity is given in terms of local gradients of the magnitude and phase of the complex field and is exact also for arbitrarily small intervortex distances. The results for vortices in a superfluid or a superconductor are recovered.