Extended Hodge Theory for Fibred Cusp Manifolds

For a particular class of pseudo manifolds, we show that the intersection cohomology groups for any perversity may be naturally represented by extended weighted $L^2$ harmonic forms for a complete metric on the regular stratum with respect to some weight determined by the perversity. Extended weighted $L^2$ harmonic forms are harmonic forms that are almost in the given weighted $L^2$ space for the metric in question, but not quite. This result is akin to the representation of absolute and relative cohomology groups for a manifold with boundary by extended harmonic forms on the associated manifold with cylindrical ends. As in that setting, in the unweighted $L^2$ case, the boundary values of the extended harmonic forms define a Lagrangian splitting of the boundary space in the long exact sequence relating upper and lower middle perversity intersection cohomology groups.Comment: 26 page

Study of the spectral properties of ELM precursors by means of wavelets

The high confinement regime (H-mode) in tokamaks is accompanied by the occurrence of bursts of MHD activity at the plasma edge, so-called edge localized modes (ELMs), lasting less than 1 ms. These modes are often preceded by coherent oscillations in the magnetic field, the ELM precursors, whose mode numbers along the toroidal and the poloidal directions can be measured from the phase shift between Mirnov pickup coils. When the ELM precursors have a lifetime shorter than a few milliseconds, their toroidal mode number and their nonlinear evolution before the ELM crash cannot be studied reliably with standard techniques based on Fourier analysis, since averaging in time is implicit in the computation of the Fourier coefficients. This work demonstrates significant advantages in studying spectral features of the short-lived ELM precursors by using Morlet wavelets. It is shown that the wavelet analysis is suitable for the identification of the toroidal mode numbers of ELM precursors with the shortest lifetime, as well as for studying their nonlinear evolution with a time resolution comparable to the acquisition rate of the Mirnov coils

CONCENTRATION ISSUES IN THE U.S. BEEF SUBSECTOR

Industrial Organization, Livestock Production/Industries,

Cooling in the X-ray halo of the rotating, massive early-type galaxy NGC 7049

The relative importance of the physical processes shaping the thermodynamics of the hot gas permeating rotating, massive early-type galaxies is expected to be different from that in non-rotating systems. Here, we report the results of the analysis of XMM-Newton data for the massive, lenticular galaxy NGC 7049. The galaxy harbours a dusty disc of cool gas and is surrounded by an extended hot X-ray emitting gaseous atmosphere with unusually high central entropy. The hot gas in the plane of rotation of the cool dusty disc has a multi-temperature structure, consistent with ongoing cooling. We conclude that the rotational support of the hot gas is likely capable of altering the multiphase condensation regardless of the $t_{\rm cool}/t_{\rm ff}$ ratio, which is here relatively high, $\sim 40$. However, the measured ratio of cooling time and eddy turnover time around unity ($C$-ratio $\approx 1$) implies significant condensation, and at the same time, the constrained ratio of rotational velocity and the velocity dispersion (turbulent Taylor number) ${\rm Ta_t} > 1$ indicates that the condensing gas should follow non-radial orbits forming a disc instead of filaments. This is in agreement with hydrodynamical simulations of massive rotating galaxies predicting a similarly extended multiphase disc.Comment: 11 pages, 12 figures, accepted for publication in MNRA

Total Synthesis of (±)-Actinophyllic Acid

During a search for new natural product structures as potential leads for developing agents for treating cardiovascular disorders, Quinn, Carroll, and co-workers reported in 2005 the isolation and relative configuration of actinophyllic acid (1).1 This structurally unique indole alkaloid was obtained from the leaves of the tree Alstonia actinophylla collected on the Cape York Peninsula, Far North Queensland, Australia. It was identified in a coupled CPU/ hippuricase assay as an inhibitor of carboxypeptidase U (CPU), an endogenous inhibitor of the process the body uses to clear fibrin clots (fibrinolysis).2 The structure of actinophyllic acid (1) is unique becausethe1-azabicyclo[4.4.2]dodecaneand1-azabicyclo[4.2.1]nonane fragments that define its structure are found in no other indole alkaloid. We report herein the first total synthesis of (()-actinophyllic acid (1) by a route that is sufficiently concise that it would be suitable for production of gram quantities of the natura

Suppression of turbulence and subcritical fluctuations in differentially rotating gyrokinetic plasmas

Differential rotation is known to suppress linear instabilities in fusion plasmas. However, even in the absence of growing eigenmodes, subcritical fluctuations that grow transiently can lead to sustained turbulence. Here transient growth of electrostatic fluctuations driven by the parallel velocity gradient (PVG) and the ion temperature gradient (ITG) in the presence of a perpendicular ExB velocity shear is considered. The maximally simplified case of zero magnetic shear is treated in the framework of a local shearing box. There are no linearly growing eigenmodes, so all excitations are transient. The maximal amplification factor of initial perturbations and the corresponding wavenumbers are calculated as functions of q/\epsilon (=safety factor/aspect ratio), temperature gradient and velocity shear. Analytical results are corroborated and supplemented by linear gyrokinetic numerical tests. For sufficiently low values of q/\epsilon (<7 in our model), regimes with fully suppressed ion-scale turbulence are possible. For cases when turbulence is not suppressed, an elementary heuristic theory of subcritical PVG turbulence leading to a scaling of the associated ion heat flux with q, \epsilon, velocity shear and temperature gradient is proposed; it is argued that the transport is much less stiff than in the ITG regime.Comment: 36 pages in IOP latex style; 12 figures; submitted to PPC