Certain dynamical systems exhibit a phenomenon called bubbling, whereby small perturbations induce intermittent bursting. In this Letter we show that, as a parameter is varied through a critical value, the transition to bubbling can be “hard” (the bursts appear abruptly with large amplitude) or “soft” (the maximum burst amplitude increases continuously from zero), and that the presence or absence of symmetry in the unperturbed system has a fundamental effect on these transitions. These results are confirmed by numerical and physical experiments.

A light induced frequency shift of the 0-0 line was measured in two-photon excitation spectra of single diphenyloctatetraene molecules doped in a crystal matrix. The shifts were proportional to the laser power with a slope of about 600 MHz/W when the laser beam of about 300 mW power was focused to a diameter of 2 μm. Significantly, the observed line broadenings were an order of magnitude smaller than the shifts. The effect is ascribed mainly to a “fast” energy exchange between a local vibration and thermal phonons created by the third harmonic C-H band absorption in the matrix, and partially to an ac Stark shift.

Developed Navier-Stokes turbulence is simulated with varying wave-vector mode reductions. The flatness and the skewness of the velocity derivative depend on the degree of mode reduction. They show a crossover towards the value of the full numerical simulation when the viscous subrange starts to be resolved. The intermittency corrections of the scaling exponents ${\zeta }_p$ of the $p\mathrm{th}$ order velocity structure functions seem to depend mainly on the proper resolution of the inertial subrange. Universal scaling properties (i.e., independent of the degree of mode reduction) are found for the relative scaling exponents ${\rho }_{p,q}=({\zeta }_p-{\zeta }_{3}p/3\mathrm{})/({\zeta }_q-{\zeta }_{3}q/3\mathrm{})$.

A mechanism for intermittency in spatial distribution of small inertial particles advected by a turbulent incompressible fluid flow is discussed. The mechanism is related to self-excitation (i.e., exponential growth without an external source) of fluctuations of concentration of small particles in a turbulent fluid flow. The effect is caused by the inertia of particles which results in a divergent velocity field of particles. An equation for the high-order correlation functions of concentration of small inertial particles is derived. It is shown that the growth rates of the higher moments of particle concentration are higher than those of the lower moments, i.e., particle spatial distribution is intermittent. Similar phenomena occur for noninertial admixtures advected by divergent turbulent velocity field.

A Comment on the Letter by Hsueh-Chia Chang, Evgeny A. Demekhin, and Dmitry I. Kopelevich, Phys. Rev. Lett. 75, 1747 (1995).

Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analog in which some tori in phase space are associated with a symmetry which the classical Hamiltonian does not share. A local analysis in the vicinity of these special tori reveals a neighborhood of phase space foliated by tori. This clarifies the suppression of classical chaos associated with partial dynamical symmetry. The results are used to divide the states of a mixed system into “chaotic” and “regular” classes.

Soft x-ray lasing with a gain length $\mathrm{GL}\approx 5.5$ was demonstrated in hydrogenlike Li III at 13.5 nm (2-1 transition) in a 5 mm long LiF microcapillary using a 50 mJ, 250 fs UV laser beam at a 2 Hz repetition rate. The initial plasma was created in the 0.3 mm diameter microcapillary by a low power Nd/YAG laser. The strongly nonlinear increase of the 13.5 nm line intensity with increasing microcapillary length was compared with a linear increase of the Li III 11.4 nm (3-1 transition) line intensity.

A family of two-parameter solitary waves due to three-wave mixing in a diffractive quadratic medium (which includes type II second-harmonic generation) is found. A novel type of analytical stability criterion for the vector solitons is derived and also verified numerically.

Strange nonchaotic attractors are attractors that are geometrically strange, but have nonpositive Lyapunov exponents. We show that for dynamical systems with an invariant subspace in which there is a quasiperiodic torus, the loss of the transverse stability of the torus can lead to the birth of a strange nonchaotic attractor. A physical phenomenon accompanying this route to strange nonchaotic attractors is an extreme type of intermittency.

The susceptibility of chaotic Hamiltonian systems with 2 degrees of freedom to a perturbation of harmonical time dependence is studied. The dispersion relation for the susceptibility that includes the Lyapunov exponent is established. The equations that connect the parameters of the susceptibility with those of the power spectrum of the coordinate and the density of states are derived from the equivalence of quantum and classical susceptibilities in the limit $\hslash \to 0$. The susceptibility of the Pullen-Edmonds nonlinear oscillator is calculated as an example.

Recent works have considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. We show that riddling can be induced by arbitrarily small random noise even if the attractor is transversely unstable, and we obtain universal scaling laws for noise-induced riddling. Our results imply that the phenomenon of riddling can be more prevalent than expected before, as noise is practically inevitable in dynamical systems.

We present a mechanism to explain spiral wave formation in excitable optical systems. We show the forming geometry of the spirals to be unique to nonlinear diffractive (optical) interactions. This is explained through a new velocity-curvature relation of the truncated wave fronts from which they evolve.

We present the first experimental evidence of chaotic scattering in a fluid wake. Measurements of tracer particles and dye in the stratified wake of a moving cylinder are shown to be consistent with four predictions based on simple models and direct numerical simulation: unstable periodic orbits were shadowed by tracer particles; streaklines marked by wake-delayed dye are shown to be fractal; early time-delay statistics of fluid elements interacting with the wake decayed exponentially; and finally, the fractal dimension of the wake is consistent with the dynamics of the wake, as measured by characteristic time delays and Lyapunov exponents.

In this paper a new type of crisis in random maps is studied. The trigger of this new crisis is the tunnel effect induced by a backward tangent bifurcation. This is different from the formerly reported crises caused by the collision of the chaotic attractor with an unstable orbit. The reasons why the characteristic time of this new crisis is super long are given. Another case of crisis triggered by the random collision of the attractor with the system's trapping region boundary can also be found in this model. The two cases of crisis can transform into each other by continuously varying the control parameter.

According to classical theories, the frequencies of internal-gravity waves in stratified rotating fluids must lie between the Brunt-Väisälä frequency (a measure of the vertical density stratification) and the Coriolis frequency (equal to twice the rotation rate about the vertical axis). It is shown here that, in the case of the Earth's rotation where the pole-to-pole axis of rotation is almost everywhere not parallel to the local vertical, the range of realizable frequencies is broader. New formulas are derived for the lower and upper bounds of the frequencies.

A Comment on the Letter by Yujiang Qu, Surendra Singh, and Cyrus D. Cantrell, Phys. Rev. Lett. 76, 1236 (96). The authors of the Letter offer a Reply.

A Reply to the Comment by S. Chopra.

We present a general method for preserving chaos in nonchaotic parameter regions by using the natural dynamics of the system, and apply it to a ${\mathrm{CO}}_2$-laser model. Chaos is preserved by redirecting the flow towards the chaotic region along unstable manifolds of basin boundary saddles, with the use of small infrequent parameter perturbations.

We study analytically and numerically the classical diffusive process which takes place in a chaotic billiard. This allows one to estimate the conditions under which the statistical properties of eigenvalues and eigenfunctions can be described by random matrix theory. In particular, the phenomenon of quantum dynamical localization should be observable in real experiments.

It is shown that normal and anomalous chaotic diffusion can be totally suppressed by the presence of quenched disorder in the equations of motion. In special cases the problem can be mapped to random walks in random environments, where this effect is known as the Golosov phenomenon.