Second fundamental form of the Prym map in the ramified case

In this paper we study the second fundamental form of the Prym map $P_{g,r}: R_{g,r} \rightarrow {\mathcal A}^{\delta}_{g-1+r}$ in the ramified case $r>0$. We give an expression of it in terms of the second fundamental form of the Torelli map of the covering curves. We use this expression to give an upper bound for the dimension of a germ of a totally geodesic submanifold, and hence of a Shimura subvariety of ${\mathcal A}^{\delta}_{g-1+r}$, contained in the Prym locus.Comment: To appear in Galois Covers, Grothendieck-Teichmueller Theory and Dessins d'Enfants - Interactions between Geometry, Topology, Number Theory and Algebra. Springer Proceedings in Mathematics & Statistics. arXiv admin note: text overlap with arXiv:1711.0342

Analytical and Experimental Studies of a Divided-flow Ram-jet Combustor

Results of a theoretical and experimental study of the total pressure losses and combustion efficiencies associated with the divided-flow combustor are presented and comparisons made with the nondivided-flow combustor. The theoretical treatment indicated the range of primary-zone size, primary-zone air flow, and flame-holder pressure-loss coefficients over which the total-pressure loss through the divided-flow combustor was less than that through the nondivided-flow combustor. The experimental work indicated the range of fuel-air ratios, for a given size primary zone, over which the combustion efficiency in the divided-flow combustor was higher than that in the nondivided-flow combustor

Palatini Variational Principle for an Extended Einstein-Hilbert Action

We consider a Palatini variation on a generalized Einstein-Hilbert action. We find that the Hilbert constraint, that the connection equals the Christoffel symbol, arises only as a special case of this general action, while for particular values of the coefficients of this generalized action, the connection is completely unconstrained. We discuss the relationship between this situation and that usually encountered in the Palatini formulation.Comment: 14 pages, LaTe

Plasma Panel Sensors for Particle and Beam Detection

The plasma panel sensor (PPS) is an inherently digital, high gain, novel variant of micropattern gas detectors inspired by many operational and fabrication principles common to plasma display panels (PDPs). The PPS is comprised of a dense array of small, plasma discharge, gas cells within a hermetically-sealed glass panel, and is assembled from non-reactive, intrinsically radiation-hard materials such as glass substrates, metal electrodes and mostly inert gas mixtures. We are developing the technology to fabricate these devices with very low mass and small thickness, using gas gaps of at least a few hundred micrometers. Our tests with these devices demonstrate a spatial resolution of about 1 mm. We intend to make PPS devices with much smaller cells and the potential for much finer position resolutions. Our PPS tests also show response times of several nanoseconds. We report here our results in detecting betas, cosmic-ray muons, and our first proton beam tests.Comment: 2012 IEEE NS

Relativistic Diskoseismology. I. Analytical Results for 'Gravity Modes'

We generalize previous calculations to a fully relativistic treatment of adiabatic oscillations which are trapped in the inner regions of accretion disks by non-Newtonian gravitational effects of a black hole. We employ the Kerr geometry within the scalar potential formalism of Ipser and Lindblom, neglecting the gravitational field of the disk. This approach treats perturbations of arbitrary stationary, axisymmetric, perfect fluid models. It is applied here to thin accretion disks. Approximate analytic eigenfunctions and eigenfrequencies are obtained for the most robust and observable class of modes, which corresponds roughly to the gravity (internal) oscillations of stars. The dependence of the oscillation frequencies on the mass and angular momentum of the black hole is exhibited. These trapped modes do not exist in Newtonian gravity, and thus provide a signature and probe of the strong-field structure of black holes. Our predictions are relevant to observations which could detect modulation of the X-ray luminosity from stellar mass black holes in our galaxy and the UV and optical luminosity from supermassive black holes in active galactic nuclei.Comment: 31 pages, 6 figures, uses style file aaspp4.sty, prepared with the AAS LATEX macros v4.0, significant revision of earlier submission to include modes with axial index m>