We report numerical simulations of Bénard convection in infinite Prandtl number fluids driven by thermocapillary forces. At high Marangoni numbers a spectrum $E\left(k\right)\mathrm{}\sim k^{-3\mathrm{}}$ of surface temperature fluctuations is established due to the formation of discontinuities of the temperature gradient in the form of thermal ripples between contiguous convective cells. The results support the applicability of Sivashinsky's model equation beyond its mathematical limit of validity.

Exponential sensitivity and chaos can occur in quantum systems. An example is the propagation of spin-1/2 particles through a spin-precession apparatus consisting of a chain of magnetic field sections arranged spatially in a Fibonacci-like sequence. It is shown that the quantum propagation in this apparatus is as chaotic as Arnol'd's cat map.

We study analytically and numerically the corrections to scaling in turbulence which arise due to finite size effects as anisotropic forcing or boundary conditions at large scales. We find that the deviations δ${\mathrm{\zeta }}_{\mathit{m}}$ from the classical Kolmogorov scaling ${\mathrm{\zeta }}_{\mathit{m}}$=m/3 of the velocity moments 〈‖u(k)${\mathrm{\Vert }}^{\mathit{m}}$〉∝${\mathit{k}}^{\mathrm{-}\mathrm{\zeta }\mathit{m}}$ decrease like δ${\mathrm{\zeta }}_{\mathit{m}}$(Re)=${\mathit{c}}_{\mathit{m}}$${\mathrm{Re}}^{\mathrm{-}3/10}$. If, on the contrary, anomalous scaling in the inertial subrange can experimentally be verified in the large Re limit, this will support the suggestion that small scale structures should be responsible, originating form viscous effects either in the bulk (vortex tubes or sheets) or from the boundary layers (plumes or swirls), as both are underestimated in our reduced wave vector set approximation of the Navier-Stokes dynamics.

The series that arises from the semiclassical approximation for scattering amplitudes is studied when the scattering is chaotic. It is argued that the terms of the series decay with an exponent equal to $\frac{1}{2d}$, where $d$ is the capacity dimension of one of the classical scattering functions. The result applies to one-dimensional inelastic and two-dimensional elastic scattering, and it is verified numerically for a one-dimensional model. An estimate of how rapidly the semiclassical series converges is given.

We report the first theoretical and experimental study of the detailed frequency dependence of the "ionization" of excited H atoms by a two-frequency ($2f$) microwave field. Our 1D quantal and 1D classical calculations, in excellent agreement with each other, predict a new $2f$ ionization peak. The peak scales classically. We present a model which shows that the location and the width of the peak are determined by classical phase-space structures. The theoretical results are supported by experimental data with 3D atoms.

Motivated by the understanding of the turbulent mixing mechanisms at small scale, the time evolution of an initially regular passive scalar pattern in three-dimensional homogeneous turbulence is investigated in a line-dispresion experiment. The major observation is the increasing space-fillingness of the line as time elapses. It is shown that the evolution of the fractal dimension $d_f\mathrm{}\left(t\right)\mathrm{}$ of the support of the line can be related to the mean-field Kolmogorov scaling of velocity differences incorporating dissipative corrections and an expression for $d_f\mathrm{}\left(t\right)\mathrm{}$ is derived that compares very well with the experiments for several distinct Reynolds numbers. Following, a criterion of micromixing is discussed.

We present numerical evidence for the existence of two distinct universality classes characterizing driven interface roughening in the presence of quenched disorder. The evidence is based on the behavior of λ, the coefficient of the nonlinear term in the growth equation. Specifically, for three of the models studied, λ→∞ at the depinning transition, while for the two other models, λ→0.

Attractor reconstruction from interspike interval (ISI) data is described, in rough analogy with Taken’s theorem for attractor reconstruction from time series. Assuming a generic integrate-and-fire model coupling the dynamical system to the spike train, there is a one-to-one correspondence between the system states and interspike interval vectors of sufficiently large dimension. The correspondence has an important implication: interspike intervals can be forecast from past history. We show that deterministically driven ISI series can be distinguished from stochastically driven ISI series on the basis of prediction error.

We show experimentally that the quantum-limited linewidth of a laser can be smaller than the conventional Schawlow-Townes limit when the gain bandwidth is smaller than the cavity loss rate. Data obtained for a HeNe 3.39 μm laser confirm the theoretical result derived for the linewidth of a homogeneously broadened laser in the bad-cavity limit. We show how this result can be understood in terms of the group refractive index.

The inverse cascade of the mean square potential $A$ in a 2D magnetofluid randomly forced at small scales is studied by numerical simulations. One finds the spectrum $A_k\simeq 2.6{\epsilon }_A^{\frac{2}{3}}{k}^{\frac{-7\mathrm{}}{3}}$. The cascade proceeds by coalescence of current filaments, which is a fast reconnection process owing to high turbulent resistivity. Statistics of $\delta {\nu }_l$ and $\delta B_l$ are strictly Gaussian, also in the condensation phase of $A_k$ at $k=1\mathrm{}$. Only when the coherent magnetic field intensity exceeds that of the fluctuations, non-Gaussian statistics in $\delta B_l$ occur, which are, however, entirely due to the static magnetic structure and not associated with intermittency of the small-scale turbulence, the latter remaining Gaussian.

We show that exponential instabilities and quantum chaos occur in a system with a mixed classical-quantum description. This type of chaos is of general importance and may occur in any quantum system which divides in a natural way into a fast (quantum) and a slow (classical) subsystem.

On-off intermittency is an aperiodic switching between static, or laminar, behavior and bursts of oscillations. It has been recently investigated in a class of one-dimensional maps that are multiplicatively coupled to either random or chaotic signals. The addition of noise to the system results in a fundamental change in the nature of the intermittency. The critical onset parameter changes discontinously, and the distribution of the laminar phases is modified. These contrasts are examined in terms of random walks.

We experimentally demonstrate that two chaotic passive Q-switched lasers can be synchronized by modulating the saturable absorber in the cavity of one laser with the output of the other laser. The entrainment of the chaotic motion takes place when the slave system has a slightly different strange attractor from that of the master system. The observed synchronized pulsation of the two lasers is well reproduced by the computer simulation based on our rate-equation model.

The field of the one-atom maser, or micromaser, shows strong variations in certain parameter regions usually identified as phase transitions. In this paper the time development of the field in the vicinity of those regions is investigated. Depending on the parameters, spontaneous jumps or slow transitions between two metastable field values can be observed. Hystersis behavior also occurs. The results are explained by means of a quantum Monte Carlo simulation of the maser field as well as a Fokker-Planck description used earlier in micromaser theory.

Noise driven transients in single mode semiconductor, solid state, and molecular gas lasers after they are ‘‘switched on’’ have strong (nearly linear) correlations between the time at which the laser intensity becomes significantly different from zero and the peak intensity of the first large pulse emitted by laser. We present evidence of a clear difference in the signs of the slopes of the linear correlations for these lasers for transients resulting from gain switching and loss switching and demonstrate the physical origin for this difference.

Tracers convected through porous media disperse irreversibly. We studied the reversibility of a tracer line across a channel, dispersing in creeping (low Reynolds number) high Péclet number flow around a cylinder. Flow reversal at a time t returned the line to start at 2t. At the midchannel position of this ‘‘echo,’’ we measured an effective dispersion exceeding molecular diffusion by 2 orders of magnitude. A new lattice Boltzmann model adapted to the experiments described them accurately. This first test of lattice Boltzmann simulations on dispersion experiments yields excellent agreement.

The assumption of the existence of an asymptotic shape when t→∞ for the probability density function (PDF) of an inert scalar field undergoing turbulent convection and molecular transport [Y. G. Sinai and V. Yakhot, Phys. Rev. Lett. 63, 1962 (1989)] is generalized to include the time evolution. Statistically quasistationary PDFs and conditional scalar dissipation rates compare surprisingly well with direct numerical simulation data at different times. Closed form PDFs are parametrized in terms of the flatness factor solely.

In this work we study deterministic, turbulent partial differential equations (the Kuramoto-Sivashinsky equation and generalizations) with initial conditions which are nonzero only in a small region. We demonstrate that the asymptotic state has a well-defined growth shape, which can be determined by the combination of nonlinear growth velocities, and front propagation governed by the linear instabilities. We show that the growth shapes are, in general, singular and that a new type of instability occurs when the growth shape becomes discontinuous.

We consider generation of an electrical pulse by an optical pulse in the ‘‘virtual excitation’’ regime. The electronic system, which is any electro-optic material including a quantum well structure biased by a dc electric field, is assumed to be coupled to an external circuit. It is found that the photon frequency is subject to an extra redshift in addition to the usual self-phase modulation, whereas the photon number is conserved. The Joule energy consumed in the external circuit is supplied only from the extra redshift.

We investigate pattern formation in the immiscible displacement of foam from a confining geometry. The dominant length scales with the driving pressure gradient as for a Newtonian fluid, but depends surprisingly on the ratio of plate separation to bubble diameter. The pattern morphology exhibits a transition from a jagged, presumably elastic, character to a smooth, viscous character as the shear strain rate rises far above the natural internal relaxation time scale of the foam. These features may result from the two-dimensional nature of the flows and the unusual rheology of foams.