Finite time singularities in a class of hydrodynamic models

Models of inviscid incompressible fluid are considered, with the kinetic energy (i.e., the Lagrangian functional) taking the form ${\cal L}\sim\int k^\alpha|{\bf v_k}|^2d^3{\bf k}$ in 3D Fourier representation, where $\alpha$ is a constant, $0<\alpha< 1$. Unlike the case $\alpha=0$ (the usual Eulerian hydrodynamics), a finite value of $\alpha$ results in a finite energy for a singular, frozen-in vortex filament. This property allows us to study the dynamics of such filaments without the necessity of a regularization procedure for short length scales. The linear analysis of small symmetrical deviations from a stationary solution is performed for a pair of anti-parallel vortex filaments and an analog of the Crow instability is found at small wave-numbers. A local approximate Hamiltonian is obtained for the nonlinear long-scale dynamics of this system. Self-similar solutions of the corresponding equations are found analytically. They describe the formation of a finite time singularity, with all length scales decreasing like $(t^*-t)^{1/(2-\alpha)}$, where $t^*$ is the singularity time.Comment: LaTeX, 17 pages, 3 eps figures. This version is close to the journal pape

Generation of Large-Scale Vorticity in a Homogeneous Turbulence with a Mean Velocity Shear

An effect of a mean velocity shear on a turbulence and on the effective force which is determined by the gradient of Reynolds stresses is studied. Generation of a mean vorticity in a homogeneous incompressible turbulent flow with an imposed mean velocity shear due to an excitation of a large-scale instability is found. The instability is caused by a combined effect of the large-scale shear motions (''skew-induced" deflection of equilibrium mean vorticity) and ''Reynolds stress-induced" generation of perturbations of mean vorticity. Spatial characteristics, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This instability and the dynamics of the mean vorticity are associated with the Prandtl's turbulent secondary flows. This instability is similar to the mean-field magnetic dynamo instability. Astrophysical applications of the obtained results are discussed.Comment: 8 pages, 3 figures, REVTEX4, submitted to Phys. Rev.

On the Potts model partition function in an external field

We study the partition function of Potts model in an external (magnetic) field, and its connections with the zero-field Potts model partition function. Using a deletion-contraction formulation for the partition function Z for this model, we show that it can be expanded in terms of the zero-field partition function. We also show that Z can be written as a sum over the spanning trees, and the spanning forests, of a graph G. Our results extend to Z the well-known spanning tree expansion for the zero-field partition function that arises though its connections with the Tutte polynomial

Demonstration of surface electron rejection with interleaved germanium detectors for dark matter searches

The SuperCDMS experiment in the Soudan Underground Laboratory searches for dark matter with a 9-kg array of cryogenic germanium detectors. Symmetric sensors on opposite sides measure both charge and phonons from each particle interaction, providing excellent discrimination between electron and nuclear recoils, and between surface and interior events. Surface event rejection capabilities were tested with two 210 Pb sources producing ∼130 beta decays/hr. In ∼800 live hours, no events leaked into the 8–115 keV signal region, giving upper limit leakage fraction 1.7 × 10−5 at 90% C.L., corresponding to < 0.6 surface event background in the future 200-kg SuperCDMS SNOLAB experiment

A 330 bp region of the spinach nitrite reductase gene promoter directs nitrate-inducible tissue-specific expression in transgenic tobacco.

Nitrite reductase is an enzyme in the nitrate assimilatory pathway whose expression is induced upon the addition of nitrate. Furthermore, it is known to be located in chloroplasts in leaves and plastids in roots. A 3.1 kb 5&prime; upstream region of the spinach nitrite reductase (NiR) gene promoter was shown previously to confer nitrate inducibility on the &beta;-glucuronidase (GUS) reporter gene expression in both the leaves and the roots of transgenic tobacco plants. In the present study, this 3.1 kb promoter fragment as well as a series of promoter deletion constructs, fused to a GUS gene, were utilized to delineate the region of NiR promoter involved in nitrate regulation of NiR expression by studying the cellular localization of NiR-GUS expression as well as its regulation by nitrate. In plants carrying the longest promoter fragment (-3100 from the transcription start site) and promoter sequences progressively deleted to -330 bp, the expression of GUS was markedly increased in the presence of nitrate, and this expression was found to occur in mesophyll cells in leaves and in the vascular tissues of stem and roots. When nitrate was added to NiR-GUS plants grown in the absence of nitrate, significant levels of GUS activity could be seen in the roots after 2 h and in the leaves after 6 h. Furthers 5&prime; deletion of the promoter to -200 bp abolished the nitrate induction of GUS expression, indicating that the 130 bp region of the nitrite reductase promoter located between -330 and -200 is required for full nitrate-inducible tissue-specific expression