Quasi-classical approximation in vortex filament dynamics. Integrable systems, gradient catastrophe and flutter

Quasiclassical approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this approximation the governing equations are given by elliptic system of quasi-linear PDEs of the first order. Dispersionless Da Rios system and dispersionless Hirota equation are among them. They describe motion of vortex filament with slow varying curvature and torsion without or with axial flow. Gradient catastrophe for governing equations is studied. It is shown that geometrically this catastrophe manifests as a fast oscillation of a filament curve around the rectifying plane which resembles the flutter of airfoils. Analytically it is the elliptic umbilic singularity in the terminology of the catastrophe theory. It is demonstrated that its double scaling regularization is governed by the Painleve' I equation.Comment: 25 pages, 5 figures, minor typos correcte

Constraining the Nature of Dark Energy using the SKA

We investigate the potential of the Square Kilometer Array Telescope (SKA) to constrain the sound speed of dark energy. The Integrated Sachs Wolfe (ISW) effect results in a significant power spectrum signal when CMB temperature anisotropies are cross-correlated with galaxies detectable with the SKA in HI. We consider using this measurement, the autocorrelation of HI galaxies and the CMB temperature power spectrum to derive constraints on the sound speed. We study the contributions to the cross-correlation signal made by galaxies at different redshifts and use redshift tomography to improve the signal-to-noise. We use a chi-square analysis to estimate the significance of detecting a sound speed different from that expected in quintessence models, finding that there is potential to distinguish very low sound speeds from the quintessence value.Comment: 8 pages, 8 figures; updated references for publication MNRA

Cellular magnesium acquisition : an anomaly in embryonic cation homeostasis

Author Posting. © The Author(s), 2007. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Experimental and Molecular Pathology 83 (2007): 224-240, doi:10.1016/j.yexmp.2007.03.007.The intracellular dominance of magnesium ion makes clinical assessment difficult despite the critical role of Mg++ in many key functions of cells and enzymes. There is general consensus that serum Mg++ levels are not representative of the growing number of conditions for which magnesium is known to be important. There is no consensus method or sample source for testing for clinical purposes. High intracellular Mg++ in vertebrate embryos results in part from interactions of cations which influence cell membrane transport systems. These are functionally competent from the earliest stages, at least transiently held over from the unfertilized ovum. Kinetic studies with radiotracer cations, osmolar variations, media lacking one or more of the four biological cations, Na+, Mg++, K+, and Ca++, and metabolic poison 0.05 mEq/L NaF, demonstrated: (1) all four cations influence the behavior of the others, and (2) energy is required for uptake and efflux on different time scales, some against gradient. Na+ uptake is energy dependent against an efflux gradient. The rate of K+ loss is equal with or without fluoride, suggesting a lack of an energy requirement at these stages. Ca++ efflux took twice as long in the presence of fluoride, likely due in part to intracellular binding. Mg++ is anomalous in that early teleost vertebrate embryos have an intracellular content exceeding the surrounding sea water, an isolated unaffected yolk compartment, and a clear requirement for energy for both uptake and efflux. The physiological, pathological, and therapeutic roles of magnesium are poorly understood. This will change: (1) when 28Mg is once again generally available at a reasonable cost for both basic research and clinical assessment, and (2) when serum or plasma levels are determined simultaneously with intracellular values, preferably as part of complete four cation profiles. Atomic absorption spectrophotometry, energy-dispersive x-ray analysis, and inductively coupled plasma emission spectroscopy on sublingual mucosal and peripheral blood samples are potential methods of value for coordinated assessments.AEC Grant No. 134