Second-harmonic generation as a minimal model of turbulence.

When two resonantly interacting modes are in contact with a thermostat, their statistics is exactly Gaussian and the modes are statistically independent despite strong interaction. Considering a noise-driven system, we show that when one mode is pumped and another dissipates, the statistics of such cascades is never close to Gaussian, no matter what is the relation between interaction and noise. One finds substantial phase correlation in the limit of strong interaction or weak noise. Surprisingly, the mutual information between modes increases and entropy decreases when interaction strength decreases. We use the model to elucidate the fundamental problem of far-from equilibrium physics: where the information, or entropy deficit, is encoded, and how singular measures form. For an instability-driven system, such as laser, even a small added noise leads to large fluctuations of the relative phase near the stability threshold, while far from the equilibrium the conversion into the second harmonic is weakly affected by noise.

Inelastic collapse and near-wall localization of randomly accelerated particles.

Inelastic collapse of stochastic trajectories of a randomly accelerated particle moving in half-space z>0 has been discovered by McKean [J. Math. Kyoto Univ. 2, 227 (1963)] and then independently rediscovered by Cornell et al. [Phys. Rev. Lett. 81, 1142 (1998)PRLTAO0031-900710.1103/PhysRevLett.81.1142]. The essence of this phenomenon is that the particle arrives at the wall at z=0 with zero velocity after an infinite number of inelastic collisions if the restitution coefficient ß of particle velocity is smaller than the critical value ß_{c}=exp(-π/sqrt[3]). We demonstrate that inelastic collapse takes place also in a wide class of models with spatially inhomogeneous random forcing and, what is more, that the critical value ß_{c} is universal. That class includes an important case of inertial particles in wall-bounded random flows. To establish how inelastic collapse influences the particle distribution, we derive the exact equilibrium probability density function ρ(z,v) for the particle position and velocity. The equilibrium distribution exists only at ß<ß_{c} and indicates that inelastic collapse does not necessarily imply near-wall localization.

Synchronization dynamics in diverse ensemble of noisy phase oscillators with asynchronous phase updates.

Decentralized control of autonomous phase oscillators integrated into networked systems is of great interest for many technological applications, from clock synchronization in sensor nets to coordinated motion in swarm robotics. In the simplest distributed synchronization scheme, each oscillator updates its phase from time to time to a new value equal to the average of its present phase and the phases of its neighbors. Here we describe the resulting synchronization dynamics within a mean-field model where the update actions of different oscillators are completely asynchronous. In particular, it is shown how the steady-state level of synchrony depends on noise intensity and frequency diversity for any given rate of updates. The central part of the analysis is devoted to the case when the correction rate positively correlates with the degree of macroscopic coherence. We demonstrate that depending on relation between correction rate and phase coherence the oscillators may exhibit both continuous and discontinuous transition from incoherence to synchrony upon the change of interaction constant. To illustrate our analytical results, numerical simulations have been performed for a large population of phase oscillators with the proposed type of coupling.

Localization-delocalization transitions in turbophoresis of inertial particles.

Small aerosols drift down a temperature or turbulence gradient since faster particles fly longer distances before equilibration. That fundamental phenomenon, called thermophoresis or turbophoresis, is widely encountered in nature and used in industry. It is universally believed that particles moving down the kinetic energy gradient must concentrate in minima (say, on walls in turbulence). Here, we show that this is incorrect: escaping minima is possible for inertial particles whose time of equilibration is longer than the time to reach the minimum. "The best way out is always through": particles escape by flying through minima or reflecting from walls. We solve the problem analytically and find the phase transition as a sign change of the mean velocity. That means separation: light particles concentrate in a minimum while heavy particles spread away from it (gravity can reverse the effect). That discovery changes our understanding of that fundamental phenomenon and may find numerous applications.

Adjustable subwavelength localization in a hybrid plasmonic waveguide.

The hybrid plasmonic waveguide consists of a high-permittivity dielectric nanofiber embedded in a low-permittivity dielectric near a metal surface. This architecture is considered as one of the most perspective candidates for long-range subwavelength guiding. We present qualitative analysis and numerical results which reveal advantages of the special waveguide design when dielectric constant of the cylinder is greater than the absolute value of the dielectric constant of the metal. In this case the arbitrary subwavelength mode size can be achieved by controlling the gap width. Our qualitative analysis is based on consideration of sandwich-like conductor-gap-dielectric system. The numerical solution is obtained by expansion of the hybrid plasmonic mode over single cylinder modes and the surface plasmon-polariton modes of the metal screen and matching the boundary conditions.

Magnetic resonance imaging in children receiving quinolones: no evidence of quinolone-induced arthropathy. A multicenter survey.

Twenty-nine children with cystic fibrosis (CF) were investigated for quinolone-induced arthropathy. Magnetic resonance imaging (MRI) was performed in 14/14 children treated with ofloxacin or ciprofloxacin and in 10/15 of those never treated with quinolones. The frequency of pathologic MRI findings, concerning cartilage thickness, careful analysis of the cartilage structure, presence of edema, cartilage-bone borderline and the presence of fluid in joints did not show any difference between both groups. Thus the presence of quinolone-induced arthrotoxicity cannot be confirmed in this study.