On the Running of the Cosmological Constant in Quantum General Relativity

We present arguments that show what the running of the cosmological constant means when quantum general relativity is formulated following the prescription developed by Feynman.Comment: 5 page

Resummed Quantum Gravity

We present the current status of the a new approach to quantum general relativity based on the exact resummation of its perturbative series as that series was formulated by Feynman. We show that the resummed theory is UV finite and we present some phenomenological applications as well.Comment: 4 pages, 1 figure; presented at ICHEP0

On The Orbital Evolution of Jupiter Mass Protoplanet Embedded in A Self-Gravity Disk

We performed a series of hydro-dynamic simulations to investigate the orbital migration of a Jovian planet embedded in a proto-stellar disk. In order to take into account of the effect of the disk's self gravity, we developed and adopted an \textbf{Antares} code which is based on a 2-D Godunov scheme to obtain the exact Reimann solution for isothermal or polytropic gas, with non-reflecting boundary conditions. Our simulations indicate that in the study of the runaway (type III) migration, it is important to carry out a fully self consistent treatment of the gravitational interaction between the disk and the embedded planet. Through a series of convergence tests, we show that adequate numerical resolution, especially within the planet's Roche lobe, critically determines the outcome of the simulations. We consider a variety of initial conditions and show that isolated, non eccentric protoplanet planets do not undergo type III migration. We attribute the difference between our and previous simulations to the contribution of a self consistent representation of the disk's self gravity. Nevertheless, type III migration cannot be completely suppressed and its onset requires finite amplitude perturbations such as that induced by planet-planet interaction. We determine the radial extent of type III migration as a function of the disk's self gravity.Comment: 19 pages, 13 figure

Evolution of Migrating Planets Undergoing Gas Accretion

We analyze the orbital and mass evolution of planets that undergo run-away gas accretion by means of 2D and 3D hydrodynamic simulations. The disk torque distribution per unit disk mass as a function of radius provides an important diagnostic for the nature of the disk-planet interactions. We first consider torque distributions for nonmigrating planets of fixed mass and show that there is general agreement with the expectations of resonance theory. We then present results of simulations for mass-gaining, migrating planets. For planets with an initial mass of 5 Earth masses, which are embedded in disks with standard parameters and which undergo run-away gas accretion to one Jupiter mass (Mjup), the torque distributions per unit disk mass are largely unaffected by migration and accretion for a given planet mass. The migration rates for these planets are in agreement with the predictions of the standard theory for planet migration (Type I and Type II migration). The planet mass growth occurs through gas capture within the planet's Bondi radius at lower planet masses, the Hill radius at intermediate planet masses, and through reduced accretion at higher planet masses due to gap formation. During run-away mass growth, a planet migrates inwards by only about 20% in radius before achieving a mass of ~1 Mjup. For the above models, we find no evidence of fast migration driven by coorbital torques, known as Type III migration. We do find evidence of Type III migration for a fixed mass planet of Saturn's mass that is immersed in a cold and massive disk. In this case the planet migration is assumed to begin before gap formation completes. The migration is understood through a model in which the torque is due to an asymmetry in density between trapped gas on the leading side of the planet and ambient gas on the trailing side of the planet.Comment: 26 pages, 29 figures. To appear in The Astrophysical Journal vol.684 (September 20, 2008 issue

Sperm survival in the female reproductive tract in the fly Scathophaga stercoraria (L.)

While sperm competition risk favours males transferring many sperm to secure fertilizations, females of a variety of species actively reduce sperm numbers reaching their reproductive tract, e.g. by extrusion or killing. Potential benefits of spermicide to females include nutritional gains, influence over sperm storage and paternity, and the elimination of sperm bearing somatic mutations that would lower zygote fitness.We investigated changes in sperm viability after in vivo and in vitro exposure to the female tract in the polyandrous fly, Scathophaga stercoraria. Sperm viability was significantly lower in the females' spermathecae immediately after mating than in the experimental males' testes. Males also varied significantly in the proportion of live sperm found in storage in vivo. However, the exact mechanism of sperm degradation remains to be clarified. In vitro exposure to extracts of the female reproductive tract, including female accessory glands, failed to significantly lower sperm viability compared to controls. These results are consistent either with postcopulatory sperm mortality in vivo depending entirely on the male (with individual differences in sperm viability, motility or longevity) or with postcopulatory sperm mortality being subtly affected by female effects which were not detected by the in vitro experimental conditions. Importantly, we found no evidence in support of the hypothesis that female accessory glands contribute to sexual conflict via spermicide. Therefore, female muscular control remains to date the only ascertained mechanism of female influence on sperm storage in this species

k-Dirac operator and parabolic geometries

The principal group of a Klein geometry has canonical left action on the homogeneous space of the geometry and this action induces action on the spaces of sections of vector bundles over the homogeneous space. This paper is about construction of differential operators invariant with respect to the induced action of the principal group of a particular type of parabolic geometry. These operators form sequences which are related to the minimal resolutions of the k-Dirac operators studied in Clifford analysis