Black hole solutions to the F4F_4-model and their orbits (I)

In this paper we continue the program of the classification of nilpotent orbits using the approach developed in arXiv:1107.5986, within the study of black hole solutions in D=4 supergravities. Our goal in this work is to classify static, single center black hole solutions to a specific N=2 four dimensional "magic" model, with special K\"ahler scalar manifold ${\rm Sp}(6,\mathbb{R})/{\rm U}(3)$, as orbits of geodesics on the pseudo-quaternionic manifold ${\rm F}_{4(4)}/[{\rm SL}(2,\mathbb{R})\times {\rm Sp}(6,\mathbb{R})]$ with respect to the action of the isometry group ${\rm F}_{4(4)}$. Our analysis amounts to the classification of the orbits of the geodesic "velocity" vector with respect to the isotropy group $H^*={\rm SL}(2,\mathbb{R})\times {\rm Sp}(6,\mathbb{R})$, which include a thorough classification of the \emph{nilpotent orbits} associated with extremal solutions and reveals a richer structure than the one predicted by the $\beta-\gamma$ labels alone, based on the Kostant Sekiguchi approach. We provide a general proof of the conjecture made in arXiv:0908.1742 which states that regular single center solutions belong to orbits with coinciding $\beta-\gamma$ labels. We also prove that the reverse is not true by finding distinct orbits with the same $\beta-\gamma$ labels, which are distinguished by suitably devised tensor classifiers. Only one of these is generated by regular solutions. Since regular static solutions only occur with nilpotent degree not exceeding 3, we only discuss representatives of these orbits in terms of black hole solutions. We prove that these representatives can be found in the form of a purely dilatonic four-charge solution (the generating solution in D=3) and this allows us to identify the orbit corresponding to the regular four-dimensional metrics.Comment: 81 pages, 24 tables, new section 4.4 about the fake superpotential added, typos corrected, references added, accepted in Nuclear Physics B.

Investigation of Heat Transfer From

The convective heat transfer from the surface of an ellipsoidal forebody of fineness ratio 3 and 20-inch maximum diameter was investigated in clear air for both stationary and rotating operation over a range of conditions including air speeds up to 240 knots, rotational speeds up to 1200 rpm, and angles of attack of 0 deg, 3 deg, and 6 deg. The results are presented in the form of heat-transfer coefficients and the correlation of Nusselt and Reynolds numbers. Both a uniform surface temperature and a uniform input heater density distribution were used. The experimental results agree well with theoretical predictions for uniform surface temperature distribution. Complete agreement was not obtained with uniform input heat density in the laminar-flow region because of conduction effects. No significant effects of rotation were obtained over the range of airstream and rotational speeds investigated. Operation at angle of attack had only minor effects on the local heat transfer. Transition from laminar to turbulent heat transfer occurred over a wide range of Reynolds numbers. The location of transition depended primarily on surface roughness and pressure and temperature gradients. Limited transient heating data indicate that the variation of surface temperature with time followed closely an exponential relation

Experimental Droplet Impingement on Four Bodies of Revolution

The rate and. area of cloud droplet impingement on four bodies of revolution were obtained experimentally in the NACA Lewis icing tunnel with a dye-tracer technique. The study included spheres, ellipsoidal forebodies of fineness ratios of 2.5 and 3.0, and a conical forebody of 300 included angle and covered a range of angles of attack from 0? to 60 and rotational speeds up to 1200 rpm. The data were obtained at an airspeed of 157 knots and are correlated by dimensionless impingement parameters. In general, the experimental data show that the local and total impingement rates and impingement limits of bodies of revolution are primarily functions of the modified inertia parameters, the body shape, and fineness ratio. Both the local impingement rate and impingement limits depend upon the angle of attack. Rotation of the bodies had a negligible effect on the impingement characteristics except for an averaging effect at angle of attack. For comparable diameters the bluffer bodies had the largest total impingement efficiency, but the finer and sharper bodies had the largest values of maximum local impingement efficiency and, in most cases, the largest limits of impingement. In most cases, the impingement characteristics were less than those calculated from theoretical trajectories; in general, however, fairly good agreement was obtained between the experimental and theoretical impingement characteristics

Investigation of Heat Transfer from a Stationary and Rotating Conical Forebody

The convective heat transfer from the surface of a conical forebody having a hemispherical nose, an included angle of approximately 30 deg, and. a maximum diameter of 18.9 inches was investigated in a wind tunnel for both stationary and. rotating operation. The range of test conditions included free-stream velocities up to 400 feet per second, rotational speeds up to 1200 rpm, and. angles of attack of 0 deg and 6 deg. Both a uniform surface temperature and a uniform heater input power density were used. The Nusselt-Reynolds number relations provided good correlation of the heat-transfer data for the complete operating range at 0 deg angle of attack with and without spinner rotation, and for 6deg angle of attack with rotation. Rotational speeds up to 1200 rpm had no apparent effect on the heat-transfer characteristics of the spinner. The results obtained at 6 deg angle of attack with rotation were essentially the same as those obtained at 0 deg angle of attack without rotation. The experimental heat-transfer characteristics in the turbulent flow region were consistently in closer agreement with the results predicted for a two-dimensional body than with those predicted. for a cone. For stationary operation at 60 angle of attack, the measured heat-transfer coefficients in the turbulent flow region were from 6 to 13 percent greater on the lower surface (windward. side) than on the upper surface (sheltered side) for corresponding surface locations. The spinner-nose geometry appeared to cause early boundary-layer transition. Transition was initiated at a fairly constant Reynolds number (based on surface distance from nose) of 8.0 x 10(exp 4). Transition was completed at Reynolds numbers less than 5.0 x 10(exp 5) for all conditions investigated

Pre-implantation mouse embryos cultured In vitro under different oxygen concentrations show altered ultrastructures

Abstract Assisted Reproductive Technologies routinely utilize different culture media and oxygen (O2) concentrations to culture human embryos. Overall, embryos cultured under physiological O2 tension (5%) have improved development compared to embryos cultured under atmospheric O2 conditions (20%). The mechanisms responsible for this remain unclear. This study aimed to evaluate the effect of physiologic (5%) or atmospheric O2 (20%) tension on the microscopic ultrastructure of pre-implantation mouse embryos using Transmission Electron Microscopy (TEM). Embryos flushed out of the uterus after natural mating were used as the control. For use as the control, 2-cells, 4-cells, morulae, and blastocysts were flushed out of the uterus after natural fertilization. In vitro fertilization (IVF) was performed using potassium simplex optimized medium (KSOM) under different O2 tensions (5% and 20%) until the blastocyst stage. After collection, embryos were subjected to the standard preparative for light microscopy (LM) and TEM. We found that culture in vitro under 5% and 20% O2 results in an increase of vacuolated shaped mitochondria, cytoplasmic vacuolization and presence of multi-vesicular bodies at every embryonic stage. In addition, blastocysts generated by IVF under 5% and 20% O2 showed a lower content of heterochromatin, an interruption of the trophectodermal and inner cell mass cell membranes, an increased density of residual bodies, and high levels of glycogen granules in the cytoplasm. In conclusion, this study suggests that in vitro culture, particularly under atmospheric O2 tension, causes stage-specific changes in preimplantation embryo ultrastructure. In addition, atmospheric (20%) O2 is associated with increased alterations in embryonic ultrastructure; these changes may explain the reduced embryonic development of embryos cultured with 20% O2

Experimental Investigation of Supercooled Water Droplet Breakup near the Leading Edge of an Airfoil

This paper presents the results of an experimental study on supercooled droplet deformation and breakup near the leading edge of an airfoil. The results are compared to prior room-temperature droplet deformation results to explore the effects of droplet supercooling. The experiments were conducted in the Adverse Environment Rotor Test Stand at The Pennsylvania State University. An airfoil model placed at the end of the rotor blades mounted onto the hub in the Adverse Environment Rotor Test Stand chamber was moved at speeds ranging between 50 and 80 ms. The temperature of the chamber was 20C. A monotonic droplet generator was used to produce droplets that fell perpendicular to the airfoil path. High-speed imaging was employed to observe the interaction between the droplets and the airfoil. Cases with equal slip and initial velocity were selected for the two environmental conditions. The airfoil velocity was 60 ms, and the slip velocity for both sets of data was 40 ms. The deformation of the weakly supercooled and warm droplets did not present different trends. The similar behavior for both conditions indicates that water supercooling has no effect on particle deformation for the range of supercooling of the droplets tested and the selected impact velocity

Cost Effectiveness Analysis of A Vaccine To Prevent Herpes Zoster and Postherpetic Neuralgia in Italy

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From The Minimum Clinically Important Difference To The Minimum Cost Effective Difference For Eq-5d In Patients With Chronic Widespread Pain

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The saturation assumption yields optimal convergence of two-level adaptive BEM

We consider the convergence of adaptive BEM for weakly-singular and hypersingular integral equations associated with the Laplacian and the Helmholtz operator in 2D and 3D. The local mesh-refinement is driven by some two-level error estimator. We show that the adaptive algorithm drives the underlying error estimates to zero. Moreover, we prove that the saturation assumption already implies linear convergence of the error with optimal algebraic rates