Effective degrees of nonlinearity in a family of generalized models of two-dimensional turbulence

We study the small-scale behavior of generalized two-dimensional turbulence governed by a family of model equations, in which the active scalar $\theta=(-\Delta)^{\alpha/2}\psi$ is advected by the incompressible flow $\u=(-\psi_y,\psi_x)$. The dynamics of this family are characterized by the material conservation of $\theta$, whose variance is preferentially transferred to high wave numbers. As this transfer proceeds to ever-smaller scales, the gradient $\nabla\theta$ grows without bound. This growth is due to the stretching term $(\nabla\theta\cdot\nabla)\u$ whose ``effective degree of nonlinearity'' differs from one member of the family to another. This degree depends on the relation between the advecting flow $\u$ and the active scalar $\theta$ and is wide ranging, from approximately linear to highly superlinear. Linear dynamics are realized when $\nabla\u$ is a quantity of no smaller scales than $\theta$, so that it is insensitive to the direct transfer of the variance of $\theta$, which is nearly passively advected. This case corresponds to $\alpha\ge2$, for which the growth of $\nabla\theta$ is approximately exponential in time and non-accelerated. For $\alpha<2$, superlinear dynamics are realized as the direct transfer of entails a growth in \nabla\u, thereby enhancing the production of $\nabla\theta$. This superlinearity reaches the familiar quadratic nonlinearity of three-dimensional turbulence at $\alpha=1$ and surpasses that for $\alpha<1$. The usual vorticity equation ($\alpha=2$) is the border line, where \nabla\u and $\theta$ are of the same scale, separating the linear and nonlinear regimes of the small-scale dynamics. We discuss these regimes in detail, with an emphasis on the locality of the direct transfer.Comment: 6 journal pages, to appear in Physical Review

The Gut Microbiome Is Altered in a Letrozole-Induced Mouse Model of Polycystic Ovary Syndrome.

Women with polycystic ovary syndrome (PCOS) have reproductive and metabolic abnormalities that result in an increased risk of infertility, diabetes and cardiovascular disease. The large intestine contains a complex community of microorganisms (the gut microbiome) that is dysregulated in humans with obesity and type 2 diabetes. Using a letrozole-induced PCOS mouse model, we demonstrated significant diet-independent changes in the gut microbial community, suggesting that gut microbiome dysbiosis may also occur in PCOS women. Letrozole treatment was associated with a time-dependent shift in the gut microbiome and a substantial reduction in overall species and phylogenetic richness. Letrozole treatment also correlated with significant changes in the abundance of specific Bacteroidetes and Firmicutes previously implicated in other mouse models of metabolic disease in a time-dependent manner. Our results suggest that the hyperandrogenemia observed in PCOS may significantly alter the gut microbiome independently of diet

Quantum signatures of breather-breather interactions

The spectrum of the Quantum Discrete Nonlinear Schr\"odinger equation on a periodic 1D lattice shows some interesting detailed band structure which may be interpreted as the quantum signature of a two-breather interaction in the classical case. We show that this fine structure can be interpreted using degenerate perturbation theory.Comment: 4 pages, 4 fig

Isochoric thermal conductivity of solid nitrogen

The isochoric thermal conductivity of solid nitrogen has been investigated on four samples of different densities in the temperature interval from 20 K to the onset of melting. In alfa-N2 the isochoric thermal conductivity exhibits a dependence weaker than 1/T; in beta-N2 it increases slightly with temperature. The experimental results are discussed within a model in which the heat is transported by low-frequency phonons or by "diffusive" modes above the mobility boundary. The growth of the thermal conductivity in beta-N2 is attributed to the decreasing "rotational" component of the total thermal resistance, which occurs as the rotational correlations between the neighboring molecules become weaker.Comment: Postscript 12 pages, 3 figures, 1 table. To be published in 200

Wind turbine generator interaction with conventional diesel generators on Block Island, Rhode Island. Volume 2: Data analysis

Assessing the performance of a MOD-OA horizontal axis wind turbine connected to an isolated diesel utility, a comprehensive data measurement program was conducted on the Block Island Power Company installation on Block Island, Rhode Island. The detailed results of that program focusing on three principal areas of (1) fuel displacement (savings), (2) dynamic interaction between the diesel utility and the wind turbine, (3) effects of three models of wind turbine reactive power control are presented. The approximate two month duration of the data acquisition program conducted in the winter months (February into April 1982) revealed performance during periods of highest wind energy penetration and hence severity of operation. Even under such conditions fuel savings were significant resulting in a fuel reduction of 6.7% while the MOD-OA was generating 10.7% of the total electrical energy. Also, electrical disturbance and interactive effects were of an acceptable level

Wind turbine generator interaction with conventional diesel generators on Block Island, Rhode Island. Volume 1: Executive summary

Primary results are summarized for a three-part study involving the effects of connecting a MOD-OA wind turbine generator to an isolated diesel power system. The MOD-OA installation considered was the third of four experimental nominal 200 kW wind turbines connected to various utilities under the Federal Wind Energy Program and was characterized by the highest wind energy penetration levels of four sites. The study analyses address: fuel displacement, dynamic interaction, and three modes of reactive power control. These analyses all have as their basis the results of the data acquisition program conducted on Block Island, Rhode Island

Looking at a soliton through the prism of optical supercontinuum

A traditional view on solitons in optical fibers as robust particle-like structures suited for informa- tion transmission has been significantly altered and broadened over the past decade, when solitons have been found to play the major role in generation of octave broad supercontinuum spectra in photonic-crystal and other types of optical fibers. This remarkable spectral broadening is achieved through complex processes of dispersive radiation being scattered from, emitted and transformed by solitons. Thus solitons have emerged as the major players in nonlinear frequency conversion in optical fibers. Unexpected analogies of these processes have been found with dynamics of ultracold atoms and ocean waves. This colloquium focuses on recent understanding and new insights into physics of soliton-radiation interaction and supercontinuum generation.Comment: http://rmp.aps.org/abstract/RMP/v82/i2/p1287_1 (some figures have been deleted due to space limits imposed by archive

Negative Differential Resistivity and Positive Temperature Coefficient of Resistivity effect in the diffusion limited current of ferroelectric thin film capacitors

We present a model for the leakage current in ferroelectric thin- film capacitors which explains two of the observed phenomena that have escaped satisfactory explanation, i.e. the occurrence of either a plateau or negative differential resistivity at low voltages, and the observation of a Positive Temperature Coefficient of Resistivity (PTCR) effect in certain samples in the high-voltage regime. The leakage current is modelled by considering a diffusion-limited current process, which in the high-voltage regime recovers the diffusion-limited Schottky relationship of Simmons already shown to be applicable in these systems