The motion of self-trapped vortices on a background vorticity gradient is examined numerically and analytically. The vortices act to level the local background vorticity gradient. Conservation of momentum dictates that positive vortices (“clumps”) and negative vortices (“holes”) react oppositely: clumps move up the gradient, whereas holes move down the gradient. A linear analysis gives the trajectory of small clumps and holes that rotate against the local shear. Prograde clumps and holes are always nonlinear, and move along the gradient at a slower rate. This rate vanishes when the background shear is sufficiently large.

Novel decay laws in three-dimensional incompressible magnetohydrodynamic turbulence are obtained by high-resolution numerical simulations with up to ${512}^3$ modes and explained by a simple theoretical model. For the typical case of finite magnetic helicity $H$ the energy decay is governed by the conservation of $H$ and the decay of the energy ratio $\Gamma {=E}^V/E^M$. One finds the relation $\left(E^{5/2}/\epsilon H\right){\Gamma }^{1/2}/(1+\Gamma {)}^{3/2}=\mathrm{const}$, where $\epsilon =-dE/\mathrm{dt}$. Use of the numerical result that $\Gamma \left(t\right)\propto E\left(t\right)$ gives the asymptotic law $E\sim t^{-0.5\mathrm{}}$ in good agreement with the numerical observations. For the special case $H=0\mathrm{}$ the energy decreases more rapidly $E\sim t^{-1\mathrm{}}$.

This paper demonstrates a mechanism of chaotic phase synchronization in which the transition from asynchronous to synchronous chaos is associated with the collision of the asynchronous chaotic attractor with an unstable periodic orbit. This gives rise to a hysteretic transition with the two chaotic regimes coexisting over a certain parameter interval.

In open-shield systems, we have derived current conditions that lead to remarkable magnetic-field confinement, which we call “supershielding.” The freedom to vary both primary and shield currents is important in solving the conditions. Solutions leading to very effective shielding are illustrated by the simple system of two parallel flat strips. Generalizations include other geometries, internal shielding, and electric-field confinement. An industrial coil design serves as a reference for practical issues. We discuss mathematical limits, via a “seesaw” approach, to “perfect shielding.”

We report the measurement of the third order susceptibility ${\chi }^{\left(3\right)}$ for doubly vibrationally enhanced four wave mixing in the model system, acetonitrile. Two resonances multiplicatively increase the mixing efficiency if there is mode coupling and provide an additional spectral dimension for vibrational spectroscopy that greatly improves its resolution. Such methods promise to have important applications for vibrational spectroscopy of complex materials.

We report on the observation of a new mechanism for self-trapping of optical beams: self-trapping that stems from spontaneous creation of ferroelectric crystalline clusters, seeded by a weak photorefractive diffusion field. This is an evident observation of the highly nonlinear aspects of propagation in a thermodynamically metastable system, including optically driven crystalline ordering in a medium undergoing a phase transition.

We present a new type of soliton, found in models characterized by opposing dispersions and competing nonlinearities at fundamental and second harmonics. They are isolated solitary waves, existing at discrete values of the propagation constant inside the system's continuous spectrum. We show analytically, and verify by simulations, that the fundamental solitons are linearly stable. They can be nonlinearly stable or unstable, depending on the sign of the energy perturbation, which could make these pulses useful for switching applications. Higher-order solitons are found, too, but they are linearly unstable.

We perform numerical simulations of the sandpile model for nonvanishing driving fields $h$ and dissipation rates $\epsilon$. Unlike simulations performed in the slow driving limit, the unique time scale present in our system allows us to measure unambiguously the response and correlation functions. We discuss the dynamic scaling of the model and show that fluctuation-dissipation relations are not obeyed in this system.

Surface waves interacting with a vertical vortex are studied both analytically and experimentally. There are similarities as well as differences with the Aharonov-Bohm effect: among the former, a dislocation in the wave fronts that is proportional to the vortex circulation, and among the latter, a significant change in the symmetry of the scattered wave.

The effect of coherence resonance can change the firing process in noise-driven excitable systems towards rather regular dynamics. For such stochastic oscillators, we study the synchronization in terms of locking of the peak frequencies in the power spectrum and also in terms of phase locking. Our investigations are based on numerical simulations of coupled Morris-Lecar neuron models and on full-scale experiments with coupled monovibrator electronic circuits.

A procedure is introduced for deriving a coarse-grained dissipative particle dynamics from molecular dynamics. The rules of the dissipative particle dynamics are derived from the underlying molecular interactions, and a Langevin equation is obtained that describes the forces experienced by the dissipative particles and specifies the associated canonical Gibbs distribution for the system.

Intense rapidly tunable picosecond laser pulses have been generated in the far infrared from 30 to 250 μm, a range not well covered by other sources. The transform-limited, diffraction-limited pulses have energies of up to 17 μJ, peak powers of more than 1 MW, a length of only 18 optical periods, and focused intensities of 0.1 $\mathrm{GW}/{\mathrm{cm}}^2$. Measurements of both the optical field amplitude and the phase have been performed at 150 μm with a rapid-scanning cross-correlation technique probing the field-induced birefringence in ZnTe with a 10-fs Ti:sapphire laser. The far-infrared laser opens up the exciting possibility of performing nonlinear experiments in a relatively unexplored spectral range.

We report observations of a new optical memory effect in Sm-doped ZnS nanocrystals and elucidate its mechanism. One of the salient properties of this effect is that the incident angle as well as the wavelength of incoming light is memorized with high resolution. We show that this effect is not based upon spectral selection of homogeneous absorption lines as in the persistent spectral hole-burning effect but upon recording of interference patterns of multiple-scattered light in disordered media.

The evolution and relaxation of an initial shear flow subject to the Kelvin-Helmholtz instability are investigated via two-dimensional compressible hydrodynamic simulations and the calculus of variations. During the instability evolution the total kinetic energy remains almost constant, but the enstrophy decays rapidly by the selective dissipation with the artificial viscosity. The successive vortex pairings lead to the emergence of an isolated vortex and the initial shear flow relaxes toward a self-organized state, i.e., a nearly minimum enstrophy state in the incompressible fluid.

We show that diffusionlike transport of a spherical sorbate molecule through a zeolite crystal can be driven by deterministic chaos instead of thermal stochastic noise when the sorbate and crystal do not equilibrate. Using a random-phase approximation for the resulting Arnold diffusion and a boundary-layer analysis of the quasisteady Fokker-Planck equation, we estimate the effective diffusivity to scale as $\sqrt{T}$ for an axisymmetric, single-pore zeolite with a harmonic radial potential, in contrast to the Arrhenius temperature dependence of high-barrier, noise-driven transport of near-equilibrium diffusion.

A Comment on the Letter by Ali Reza Mehrabi and Muhammad Sahimi, Phys. Rev. Lett. 82, 735 (1999). The authors of the Letter offer a Reply.

A Reply to the Comment by Michael W. Deem.

We study the dynamical localization in a pendulum with slowly modulated amplitude. Because of the phenomenon of separatrix crossing, the classical model shows a diffusive ergodic motion inside a confined phase space region even in the adiabatic limit. We present numerical results on the quantum dynamics which show a gradually increasing localization with decreasing modulation frequency, leading eventually towards quantum adiabaticity in the classical ergodic region.

Methods for the determination of local dynamical linearization information from experimental time series data are subject to computational artifacts. We investigate the artifacts due to observational noise in the data, and give formulas for the expected values of the reconstructed Jacobian in some simple cases. The formulas we derive in the case of realistic noise amplitudes are quite different from those for the noiseless case. In turn, spurious Lyapunov exponents in the noisy case are correspondingly different from the noiseless case.

We consider a Sinai billiard where the usual hard disk scatterer is replaced by a repulsive potential with $V\left(r\right)\sim \lambda r^{-\alpha }$ close to the origin. Using periodic orbit theory and numerical evidence we show that its spectral statistics tends to Poisson statistics for large energies when $\alpha <2\mathrm{}$ and to Wigner-Dyson statistics when $\alpha >2\mathrm{}$, while for $\alpha =2\mathrm{}$ it is independent of energy, but depends on $\lambda$. We apply the approach of Altshuler and Levitov [Phys. Rep. 288, 487 (1997)] to show that the transition in the spectral statistics is accompanied by a dynamical localization-delocalization transition. This behavior is reminiscent of a metal-insulator transition in disordered electronic systems.