A class of shell models for turbulent energy transfer at varying the intershell separation, λ, is investigated. Although in the continuum limit $(\lambda \to 1)$ the model becomes nonintermittent, we found universal aspects of the velocity statistics which can be interpreted in the framework of log-Poisson distributions, as proposed by She and Waymire [Phys. Rev. Lett. 74, 262 (1995)]. Universal properties of the free parameters entering log-Poisson description and connections with similar results reported in other shell models investigations and in real turbulent flows are discussed.

The dynamics of velocity fluctuations governed by the Burgers equation, driven by the white-in-time random forcing function with $\overline{\left[f\right(x+r,t)-f({x,t}^{\prime }){]}^2}\propto r^{\xi }\delta \left({t-t}^{\prime }\right)$ is considered on the interval $0<x<L$. The properties of the probability density function of velocity differences $P(\Delta u,r)$ are investigated for the three cases $\xi =\{0;1/2;2\}$. It is shown that the tail of the probability density function in the interval $\Delta u/r^z\ll -1\mathrm{}$; $|\Delta u|\ll u_{\mathrm{rms}}$ and $r\ll L$ is accurately described by the asymptotic algebraic relation $P(\Delta u,r)\propto r/(\Delta u{)}^{\gamma }$ with $\gamma =1+1\mathrm{}/z$, where $z=(\xi +1\mathrm{})/3$. A detailed numerical investigation, performed in this work, supports this result.

This paper is devoted to the experimental study and theoretical modeling of the coupled wakes of a pair of cylinders placed side by side in a constant flow. We propose here a dynamical system which models the behavior of these two coupled wakes. This model is constituted by two coupled Landau equations whose coefficients are estimated from experimental observations. A stability diagram is analytically and numerically computed. Finally, we present some new experiments which complete previous observations of locked and unlocked wakes.

Rayleigh-Bénard convection is investigated for Prandtl numbers $\sigma$ from 0.3 to 1.0 by using various pure gases and binary gas mixtures. The onset of spiral-defect chaos (SDC) moves to smaller values of $\epsilon \equiv R/R_c-1\mathrm{}$ ( $R$ is the Rayleigh number and $R_c$ its critical value) as $\sigma$ decreases. The measurements suggest that large-scale mean flows, which are expected to be stronger at smaller $\sigma$, play an important role in the spontaneous generation of SDC. SDC can occur and fully develop in the regime dominated by the Soret effect.

It is shown that “perfect” control of a system along a desired trajectory is the control analog of the different techniques of synchronization of chaos. Analysis of this control problem leads to a general framework for synchronization of chaotic systems. Numerical examples are presented to illustrate the connection between synchronization and perfect control. Modifications of the control scheme are carried out to make the control technique useful in practical situations.

Numerical computations of Lyapunov exponents for a class of three- and four-dimensional billiards whose boundary consists of flat and spherical components illustrate that such billiards are chaotic due to a defocusing mechanism similar to the one which produces chaos in two-dimensional billiards (e.g., in the stadium). These results demonstrate that recently established rigorous results or higher dimensional defocusing billiards are valid under substantially weaker assumptions.

The concept of the conditional probability density is used to define a specific entropy for open dynamical systems exhibiting transient chaos. The production of entropy turns out to be proportional to the difference of the escape rate and the sum of all averaged Lyapunov exponents on the saddle governing the dynamics. The single-particle transport properties do not depend on the microscopic details provided the dynamical systems produce the same entropy. The dimension of the unstable foliation of the saddle is shown to be identical in all microscopic single-particle models of the same transport process.

Absolute photonic band gaps in two-dimensional square and honeycomb lattices of circular cross-section rods can be increased by reducing the structure symmetry. The addition of a smaller diameter rod into the center of each lattice unit cell lifts band degeneracies to create significantly larger band gaps. Symmetry breaking is most effective at filling fractions near those which produce absolute band gaps for the original lattice. Rod diameter ratios in the range 0.1–0.2 yield the greatest improvement in absolute gap size. Crystal symmetry reduction opens up new ways for engineering photonic gaps.

Finding a parameter whose threshold controls the onset of breaking in nonlinear modulating surface gravity wave trains has been an elusive problem. Our numerical study of the fully nonlinear two-dimensional inviscid problem on a periodic spatial domain for a range of wave group structures examined the behavior of dimensionless relative growth rates of the local mean wave energy and momentum densities. We found that these growth rates at the envelope maxima of the wave group oscillate on a fast time scale with a significant dynamic range and that a universal threshold exists for the maximum of either of these growth rates that determines whether breaking will occur.

A Comment on the Letter by T. O. de Carvalho and M. A. M. de Aguiar, Phys. Rev. Let. 76, 2690 (1996). The authors of the Letter offer a Reply.

A Reply to the Comment by Joshua Wilkie and Paul Brumer.

We present a new method for the semiclassical quantization of classically integrable as well as nonintegrable systems. The method is based on the semiclassical approximation of the equilibrium density matrix, using classical trajectories on the upside down potential surface. Periodic orbits do not play any special role. Explicit results are given for the case of the classically chaotic potential ${\mathrm{kx}}^2{y}^2/2$.

This Letter discusses the question of how the white noise of radiative corrections affects the chaotic properties of an original quantum system. It is shown, by an explicit mathematical analysis, that the radiative corrections, in effect, remove the original chaos in the system.

We report the first observation of a full photonic band gap for surface modes. An experimental study has been made of the propagation of surface plasmon polaritons on a silver surface that is textured with a hexagonal array of dots with a periodicity of 300 nm. We find that propagation is prohibited in all directions for modes with energies between 1.91 and 2.00 eV.

We establish by exact, nonperturbative methods a universality for the correlation functions in Kraichnan's “rapid-change” model of a passively advected scalar field. We show that the solutions for separated points in the convective range of scales are unique and independent of the particular mechanism of the scalar dissipation. Any nonuniversal dependences therefore must arise from the large length-scale features. The main step in the proof is to show that solutions of the model equations are unique when square integrable, even in the idealized case of zero diffusivity.

Spatiotemporal disorder is studied in traveling-wave convection in an ethanol-water mixture. A technique for calculating the complex order parameter of the pattern is described, and the identification of phase defects is demonstrated. Point defects, domain boundaries, and standing wave patterns are shown to produce unique defect structures. The transition from a disordered state to a more ordered pattern is described in terms of the dynamics of defects and their statistics.

Experiments compare long-range chaotic mixing of miscible and immiscible impurities in a time-periodic flow. For the miscible case, the transport is enhanced diffusion with an effective diffusion constant determined by lobes (turnstiles) that carry impurities between vortices. For the immiscible case, the impurity is broken into a distribution of droplets. If the characteristic droplet size is appreciably smaller than the lobe size, the transport is equivalent to that from the miscible case. Otherwise, interfacial tension results in reduction (and possibly extinction) of the transport.

A Comment on the Letter by Ali Oksasogla and Tayfun Akgul, Phys. Rev. Lett. 75, 4595 (1995). The authors of the Letter offer a reply.

A Reply to the Comment by H.-Y. Sun and L. Wang.

We directly combine ideas of the quasiclassical approximation with random matrix theory and apply them to the study of the spectrum, in particular, to the two-level correlator. Bogomolny's transfer operator T, quasiclassically an $N\times N$ unitary matrix, is considered to be a random matrix. Rather than rejecting all knowledge of the system, except for its symmetry (as with Dyson's circular unitary ensemble), we choose an ensemble which incorporates the knowledge of the shortest periodic orbits, the prime quasiclassical information bearing on the spectrum. The results largely agree with expectations but contain novel features differing from other recent theories.