Transfer of extensities such as heat across sheared rough interfaces is considered, with particular attention to roughnesses characterized by a broad hierarchy of length scales. We analyze as a concrete example the corrections to the Nu-Ra dependence in high Rayleigh number convection cells induced when the thermal layer thickness $\lambda \sim L{\mathrm{Ra}}^{-\beta }$ is of the order of the conducting walls roughnesses $\xi$. We show that, provided $\frac{\ln \left(5\mathrm{Pr}\right)}{{\mathrm{Pr}}^{1/2}}\lesssim \frac{L}{\xi }{\mathrm{Ra}}^{1/2-2\beta }$, the increase of exchange surface area due to the covering of the rough surface by the thermal layer may significantly alter the transfer relationship in absolute value, and in law.

It is shown that in an ideal coupled magnetofluid, the equilibrium magnetic (velocity) field is described by a two-parameter, double curl $(▽\times ▽\times )$ system of equations. The new system allows, among others, a novel, fully diamagnetic, pressure confining, minimum $|B|$ configuration with velocity fields comparable (in appropriate units) to the magnetic fields.

We have found spatial decoherence (loss of phase coherence between distant points in space) of quantum states and chaotic behavior (“turbulence”) of quantum-mechanical currents for a nonlinear oscillator in a magnetic field. Use of quantum currents is dictated by the fact that they are simultaneously phase-sensitive and gauge-invariant measures. The theory is applicable to an electron in a quantum dot with soft confining potential in a magnetic field.

We present a new class of micro lasers based on nanoporous molecular sieve host-guest systems. Organic dye guest molecules of 1-ethyl-4-[4-( $p$-dimethylaminophenyl)-1,3-butadienyl]-pyridinium Perchlorat were inserted into the 0.73-nm-wide channel pores of a zeolite $\mathrm{AlPO}{}_4-5$ host. The zeolitic microcrystal compounds were hydrothermally synthesized according to a particular host-guest chemical process. The dye molecules are found not only to be aligned along the host channel axis, but to be oriented as well. Single mode laser emission at $687\mathrm{nm}$ was obtained from a whispering gallery mode oscillating in a $8-\mu \mathrm{m}-\mathrm{diameter}$ monolithic microresonator, in which the field is confined by total internal reflection at the natural hexagonal boundaries inside the zeolitic microcrystals.

We present analytical and numerical results related to partially coherent solitons (PCS) of a novel class. In effect, there is freedom to choose the shape of a PCS as it is governed by $2N-1$ parameters, where $N$ is the number of linear modes contributing to the soliton. In particular, we show that a PCS may have an asymmetric shape. The PCS shape becomes arbitrary in the limit of complete incoherence. Another remarkable new feature of a PCS is that collisions in Kerr-like media cause the PCS to change its shape, although each beam remains a stationary soliton after the collision.

The ratios of enstrophy and dissipation moments induced by localized vorticity are inferred to be finite. It follows that the scaling exponents for locally averaged dissipation and enstrophy are equal. However, enstrophy and dissipation exponents measured over finite ranges of scales may be different. The cylindrical vortex profile that yields maximal moment ratios is determined. The moment ratios for cylindrical vortices are used to interpret differences in scale dependence of enstrophy and dissipation previously found in numerical simulations.

The link between the level of chaos of the velocity and the saturation of the dynamo in $\mathrm{ABC}$ flows is examined numerically with the full MHD equations at magnetic Reynolds numbers up to $240$ and for scale separations up to four. In the latter case, a chaotic dynamo at small scale and a large-scale magnetic field develop together. Spatial modifications of the chaotic features of the resulting velocity measured by pdf of finite-time Lyapunov exponents occur in all cases because of both hydrodynamic and MHD instabilities. Saturation occurs as well with a weaker contrast in magnetic structures.

Lyapunov exponents, perhaps the most informative invariants of a complicated dynamical process, are also among the most difficult to determine from experimental data. In particular, when using embedding theory to build chaotic attractors in a reconstruction space, extra “spurious” Lyapunov exponents arise that are not Lyapunov exponents of the original system. The origin of these spurious exponents is discussed, and formulas for their determination in the low noise limit are given.

Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to stochasticity. Numerical results for partially surrogated time series and series derived from the stochastic Lorenz model illustrate the usefulness of the method proposed here. The method is shown to work also for high-dimensional systems.

We show that a recently proposed numerical technique for the calculation of unstable periodic orbits in chaotic attractors is capable of finding the least unstable periodic orbits of any given order. This is achieved by introducing a modified dynamical system which has the same set of periodic orbits as the original chaotic system, but with a tuning parameter which is used to stabilize the orbits selectively. This technique is central for calculations using the stability criterion for the truncation of cycle expansions, which provide highly improved convergence of calculations of dynamical averages in generic chaotic attractors. The approach is demonstrated for the Hénon attractor.

The stability of two-parameter families of walking vector solitons of coupled nonlinear Schrödinger equations in investigated. It is shown that all known, lowest-order soliton types, namely, slow, fast, vector in phase, and vector out of phase are dynamically stable in certain regions of the parameter space. The condition of linear marginal stability of the solitons is not necessarily given by an explicit geometric criterion, because soliton instability mediated by the existence of complex eigenvalues of the corresponding Lyapunov operator is found to occur also.

It is shown that stable, large amplitude, spatially coherent solutions of the nonlinear Schrödinger equation can be excited by a weak forcing composed of an oscillation and a standing wave with a slowly varying frequency. The excitation involves autoresonant transition from a growing amplitude, uniform state to spatially modulated solution approaching the soliton, as the frequency increases in time.

Structural alterations induced by “thermal poling” in $v-{\mathrm{SiO}}_2$, a treatment which enables the glass to double the frequency of impinging infrared light, are revealed by neutron diffraction to be a breakdown of macroscopic isotropy. This leads to concomitant changes in the vibrational density of states measured by inelastic neutron scattering. The observations are consistent with emergence of partial ordering within the glassy matrix along the direction of an electrostatic field applied during the poling treatment.

Large grains are well known to rise to the top of granular beds. In this Letter, we report to the contrary on a shaking regime in which large, heavy grains rise, but equally large, light grains sink in a granular bed. This behavior occurs in deep beds with high amplitude vibrations—precisely the regime encountered during transportation of industrial solids mixtures. We examine a simple one-dimensional model that captures some aspects of this effect. The central observation underlying this model is that inertia causes heavy objects to lift off the bed, permitting smaller particles to infiltrate beneath; the motion of light objects, by contrast, can fluctuate wildly, preventing this infiltration.

Steady state dynamics of clustering, long-range order, and inelastic collapse are experimentally observed in vertically shaken granular monolayers. At large vibration amplitudes, particle correlations show only short-range order like equilibrium 2D hard sphere gases. Lowering the amplitude “cools” the system, resulting in a dramatic increase in correlations leading to either clustering or an ordered state. Further cooling forms a collapse: a condensate of motionless balls coexisting with a less dense gas. Measured velocity distributions are non-Gaussian, showing nearly exponential tails.

We present theoretical predictions and wind tunnel measurements of the 3-point correlator of fluctuating temperature in preheated turbulent flow. The dependence of this passive scalar correlator on the point configuration is calculated on the basis of a model Hopf operator describing its time evolution but can be understood in terms of the underlying frontlike structure of the temperature field. Model predictions reproduce the main features observed in experiment. The geometric insight into the structure of the fluctuating field provided by multipoint correlators suggests new approaches to the study of turbulence itself.

We present a pseudospectral study of the randomly forced Navier-Stokes equation (RFNSE) stirred by a stochastic force with zero mean and a variance $\sim k^{4-d-y}$, with $k$ the wave vector and the dimension $d=3\mathrm{}$. We provide the first evidence for multiscaling of velocity structure functions for $y\ge 4$. We extract the multiscaling exponent ratios ${\zeta }_p/{\zeta }_2$ by using extended self-similarity, examine their dependence on $y$, and show that, if $y=4\mathrm{}$, they are in agreement with those obtained for the Navier-Stokes equation forced at large spatial scales (3DNSE). Also well-defined vortex filaments, which appear clearly in studies of the 3DNSE, are absent in the RFNSE.

We address the fundamental problem of dissipation of kinetic energy in superfluid turbulence at temperatures low enough that friction against the normal fluid is negligible. We find that the kinetic energy of a turbulent vortex tangle, transformed into compressional energy, can result in a significant heating of the fluid. We suggest that vortex heating can be used to investigate turbulence at these low temperatures, where the traditional second-sound technique fails.

Nonlinear waves with basic wave numbers, $k_1$ and $k_2$, are simultaneously excited via two-frequency parametric excitation of a fluid surface. Three new multiwave states are observed: (1) A superlattice state composed of $k_1$ and $k_2$ whose relative orientation is governed by a temporal resonance condition, (2) a superlattice built entirely of wave numbers $k_1$ and $k_1/2$, and (3) a state composed of wave numbers of lengths $k_1$ and $k_2$ that are uncorrelated in both space and time. The three states exhibit interesting temporal as well as spatial behavior and are observed in a variety of frequency combinations.

A Comment on the Letter by Mark Mineev-Weinstein, Phys. Rev. Lett. 80, 2113 (1998). The authors of the Letter offer a Reply.