Abelian subgroups of Garside groups

In this paper, we show that for every abelian subgroup $H$ of a Garside group, some conjugate $g^{-1}Hg$ consists of ultra summit elements and the centralizer of $H$ is a finite index subgroup of the normalizer of $H$. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems concerning abelian subgroups of Garside groups.Comment: This article replaces our earlier preprint "Stable super summit sets in Garside groups", arXiv:math.GT/060258

On the Plants Leaves Boundary, "Jupe \`a Godets" and Conformal Embeddings

The stable profile of the boundary of a plant's leaf fluctuating in the direction transversal to the leaf's surface is described in the framework of a model called a "surface \`a godets". It is shown that the information on the profile is encoded in the Jacobian of a conformal mapping (the coefficient of deformation) corresponding to an isometric embedding of a uniform Cayley tree into the 3D Euclidean space. The geometric characteristics of the leaf's boundary (like the perimeter and the height) are calculated. In addition a symbolic language allowing to investigate statistical properties of a "surface \`a godets" with annealed random defects of curvature of density $q$ is developed. It is found that at $q=1$ the surface exhibits a phase transition with critical exponent $\alpha=1/2$ from the exponentially growing to the flat structure.Comment: 17 pages (revtex), 8 eps-figures, to appear in Journal of Physics

Optical activity induced by curvature in a gravitational pp-wave background

We study optical activity induced by curvature. The optical activity model we present has two phenomenological gyration parameters, within which we analyze three model cases, namely, an exactly integrable model, the Landau-Lifshitz model and the Fedorov model, these latter two are solved in the short wavelength approximation. The model background is a gravitational pp-wave. The solutions show that the optical activity induced by curvature leads to Faraday rotation.Comment: 16 pages, late

Effect of rejection on electrophysiologic function of canine intestinal grafts: Correlation with histopathology and na-k-ATPase activity

To investigate whether electrophysiologic changes can detect the early onset and progress of intestinal rejection, changes in in vitro electrophysiologic function, intestinal histopathology, and Na-K-ATPase activity were studied in dogs. Adult mongrel dogs of both sexes, weighing 18-24 kg, were used for auto and allo small bowel transplantation. The entire small bowels, except for short segments at the proximal and distal ends, were snitched between a pair of dogs (allograft). Animals receiving intestinal autotransplantation were used as controls. AIIograji recipients were sacrificed 3, 4, 5, 7, or 9 days after transplantation, and autograft recipients were sacrificed 3, 7, or 14 days afier transplantation. Immunosuppression was not used. Electrophysiologic measurements were done with an Ussing chamber. Histological analysis was performed blindly using whole thickness sections. Na-K-ATPase activity in the mucosal tissue, which is said to regulate the potential difference, was also measured. Potential difference, resistance, and Na-K-ATPase activity of the allografi intestine decreased with time and were significantly lower 7 and 9 days after transplantation compared to host intestine, normul intestine, and graft intestine of controls (autograft). Potential difference, resistance, and Na-K-ATPase activity of the native intestinal tissue and the autografts did not decrease with time. Detection of histologically mild rejection of the intestine, which is important for appropriate immunosup-pressive treatment in clinical cases, could not be achieved based on electrophysiology or Na-K-ATPase activity. Deterioration of electrophysiologic function during rejection correlated with the histological rejection process and Na-K-ATPase activity; however, electrophysiology my not be a reliable tool for monitoring grafrs, since it cannot detect early intestinal rejection. © 1995 Informa UK Ltd All rights reserved: reproduction in whole or part not permitted

Measurement of the electron electric dipole moment using GdIG

A new method for the detection of the electron edm using a solid is described. The method involves the measurement of a voltage induced across the solid by the alignment of the samples magnetic dipoles in an applied magnetic field, H. A first application of the method to GdIG has resulted in a limit on the electron edm of 5E-24 e-cm, which is a factor of 40 below the limit obtained from the only previous solid-state edm experiment. The result is limited by the imperfect discrimination of an unexpectedly large voltage that is even upon the reversal of the sample magnetization.Comment: 10 pages, 5 figures, v2:references corrected, submitted to PRL, v3:added labels to figure

Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t = -1

We prove that the hyperelliptic Torelli group is generated by Dehn twists about separating curves that are preserved by the hyperelliptic involution. This verifies a conjecture of Hain. The hyperelliptic Torelli group can be identified with the kernel of the Burau representation evaluated at t = −1 and also the fundamental group of the branch locus of the period mapping, and so we obtain analogous generating sets for those. One application is that each component in Torelli space of the locus of hyperelliptic curves becomes simply connected when curves of compact type are added

Generation and Structure of Solitary Rossby Vortices in Rotating Fluids

The formation of zonal flows and vortices in the generalized Charney-Hasegawa-Mima equation is studied. We focus on the regime when the size of structures is comparable to or larger than the deformation (Rossby) radius. Numerical simulations show the formation of anticyclonic vortices in unstable shear flows and ring-like vortices with quiescent cores and vorticity concentrated in a ring. Physical mechanisms that lead to these phenomena and their relevance to turbulence in planetary atmospheres are discussed.Comment: 3 pages in REVTeX, 5 postscript figures separately, submitted to Phys. Rev.

Quasi-Two-Dimensional Dynamics of Plasmas and Fluids

In the lowest order of approximation quasi-twa-dimensional dynamics of planetary atmospheres and of plasmas in a magnetic field can be described by a common convective vortex equation, the Charney and Hasegawa-Mirna (CHM) equation. In contrast to the two-dimensional Navier-Stokes equation, the CHM equation admits "shielded vortex solutions" in a homogeneous limit and linear waves ("Rossby waves" in the planetary atmosphere and "drift waves" in plasmas) in the presence of inhomogeneity. Because of these properties, the nonlinear dynamics described by the CHM equation provide rich solutions which involve turbulent, coherent and wave behaviors. Bringing in non ideal effects such as resistivity makes the plasma equation significantly different from the atmospheric equation with such new effects as instability of the drift wave driven by the resistivity and density gradient. The model equation deviates from the CHM equation and becomes coupled with Maxwell equations. This article reviews the linear and nonlinear dynamics of the quasi-two-dimensional aspect of plasmas and planetary atmosphere starting from the introduction of the ideal model equation (CHM equation) and extending into the most recent progress in plasma turbulence.U. S. Department of Energy DE-FG05-80ET-53088Ministry of Education, Science and Culture of JapanFusion Research Cente

Turbulent spectrum of the Earth's ozone field

The Total Ozone Mapping Spectrometer (TOMS) database is subjected to an analysis in terms of the Karhunen-Loeve (KL) empirical eigenfunctions. The concentration variance spectrum is transformed into a wavenumber spectrum, $E_c(k)$. In terms of wavenumber $E_c(k)$ is shown to be $O(k^{-2/3})$ in the inverse cascade regime, $O(k^{-2})$ in the enstrophy cascade regime with the spectral {\it knee} at the wavenumber of barotropic instability.The spectrum is related to known geophysical phenomena and shown to be consistent with physical dimensional reasoning for the problem. The appropriate Reynolds number for the phenomena is $Re\approx 10^{10}$.Comment: RevTeX file, 4 pages, 4 postscript figures available upon request from Richard Everson <[email protected]

Active Amplification of the Terrestrial Albedo to Mitigate Climate Change: An Exploratory Study

This study explores the potential to enhance the reflectance of solar insolation by the human settlement and grassland components of the Earth's terrestrial surface as a climate change mitigation measure. Preliminary estimates derived using a static radiative transfer model indicate that such efforts could amplify the planetary albedo enough to offset the current global annual average level of radiative forcing caused by anthropogenic greenhouse gases by as much as 30 percent or 0.76 W/m2. Terrestrial albedo amplification may thus extend, by about 25 years, the time available to advance the development and use of low-emission energy conversion technologies which ultimately remain essential to mitigate long-term climate change. However, additional study is needed to confirm the estimates reported here and to assess the economic and environmental impacts of active land-surface albedo amplification as a climate change mitigation measure.Comment: 21 pages, 3 figures. In press with Mitigation and Adaptation Strategies for Global Change, Springer, N