Modeling the Black Hole Excision Problem

We analyze the excision strategy for simulating black holes. The problem is modeled by the propagation of quasi-linear waves in a 1-dimensional spatial region with timelike outer boundary, spacelike inner boundary and a horizon in between. Proofs of well-posed evolution and boundary algorithms for a second differential order treatment of the system are given for the separate pieces underlying the finite difference problem. These are implemented in a numerical code which gives accurate long term simulations of the quasi-linear excision problem. Excitation of long wavelength exponential modes, which are latent in the problem, are suppressed using conservation laws for the discretized system. The techniques are designed to apply directly to recent codes for the Einstein equations based upon the harmonic formulation.Comment: 21 pages, 14 postscript figures, minor contents updat

Perturbation theorems for Hele-Shaw flows and their applications

In this work, we give a perturbation theorem for strong polynomial solutions to the zero surface tension Hele-Shaw equation driven by injection or suction, so called the Polubarinova-Galin equation. This theorem enables us to explore properties of solutions with initial functions close to but are not polynomial. Applications of this theorem are given in the suction or injection case. In the former case, we show that if the initial domain is close to a disk, most of fluid will be sucked before the strong solution blows up. In the later case, we obtain precise large-time rescaling behaviors for large data to Hele-Shaw flows in terms of invariant Richardson complex moments. This rescaling behavior result generalizes a recent result regarding large-time rescaling behavior for small data in terms of moments. As a byproduct of a theorem in this paper, a short proof of existence and uniqueness of strong solutions to the Polubarinova-Galin equation is given.Comment: 25 page

On the exponential transform of lemniscates

It is known that the exponential transform of a quadrature domain is a rational function for which the denominator has a certain separable form. In the present paper we show that the exponential transform of lemniscate domains in general are not rational functions, of any form. Several examples are given to illustrate the general picture. The main tool used is that of polynomial and meromorphic resultants.Comment: 19 pages, to appear in the Julius Borcea Memorial Volume, (eds. Petter Branden, Mikael Passare and Mihai Putinar), Trends in Mathematics, Birkhauser Verla

Further Evidence of Narrow Baryonic Structures with Hadronic as Well as Leptonic Probes

Although extracted from several experiments using hadronic probes \cite{bor1}, narrow baryonic structures have been sometimes met with disbelief. New signatures are presented, which appear from already published data, obtained with hadronic probes as well as with leptonic probes. The authors of these results did not take into account the possibility to associate the discontinuities of their spectra with the topic of narrow baryonic low mass structures. The stability of the observed narrow structure masses, represents a confirmation of their genuine existence.Comment: 6 pages, 8 figures. Contribution XVII International Seminar on High Energy Physics Problems, Relativistic Nuclear Physics and Quantum Chromodynamics, Dubna, (Russia) Sept. 27- Oct 2, 200

Exotic low mass narrow baryons extracted from charge exchange reactions

This paper aims to give further evidence for the existence of low mass exotic baryons. Narrow structures in baryonic missing mass or baryonic invariant mass were observed during the last twelve years. Since their evidence is still under debate, various data, measured with incident hadrons, by different collaborations, are reanalyzed to bring evidence on these narrow exotic baryonic resonances excited in charge-exchange reactions. These structures are clearly exotic as there is no room for them in the $qqq$ configurations: their width is smaller than the widths of "classical" baryonic resonances, moreover some of the masses lie below the pion threshold mass.Comment: 21 pages, 27 figure

Generalized Du Fort-Frankel methods for parabolic initial boundary value problems

The Du Fort-Frankel difference scheme is generalized to difference operators of arbitrary high order accuracy in space and to arbitrary order of the parabolic differential operator. Spectral methods can also be used to approximate the spatial part of the differential operator. The scheme is explicit, and it is unconditionally stable for the initial value problem. Stable boundary conditions are given for two different fourth order accurate space approximations

On the Navier-Stokes equations with constant total temperature

For various applications in fluid dynamics, it is assumed that the total temperature is constant. Therefore, the energy equation can be replaced by an algebraic relation. The resulting set of equations in the inviscid case is analyzed. It is shown that the system is strictly hyperbolic and well posed for the initial value problems. Boundary conditions are described such that the linearized system is well posed. The Hopscotch method is investigated and numerical results are presented

The Calibration of Stromgren uvby-Hbeta Photometry for Late-Type Stars -- a Model Atmosphere Approach

We aim to test the power of theoretical calibrations based on a new generation of MARCS models by comparisons with observational photomteric data. We calculate synthetic uvby-Hbeta colour indices from synthetic spectra. A sample of 388 field stars as well as stars in globular clusters is used for a direct comparison of the synthetic indices versus empirical data and for scrutinizing the possibilities of theoretical calibrations for temperature, metallicity and gravity. We show that the temperature sensitivity of the synthetic (b-y) colour is very close to its empirical counterpart, whereas the temperature scale based upon Hbeta shows a slight offset. The theoretical metallicity sensitivity of the m1 index (and for G-type stars its combination with c1) is somewhat larger than the empirical one, based upon spectroscopic determinations. The gravity sensitivity of the synthetic c1 index shows a satisfactory behaviour when compared to obervations of F stars. For stars cooler than the sun a deviation is significant in the c1-(b-y) diagram. The theoretical calibrations of (b-y), (v-y) and c1 seem to work well for Pop II stars and lead to effective temperatures for globular cluster stars supporting recent claims by Korn et al. (2007) that atomic diffusion occurs in stars near the turnoff point of NGC 6397. Synthetic colours of stellar atmospheres can indeed be used, in many cases, to derive reliable fundamental stellar parameters. The deviations seen when compared to observational data could be due to incomplete linelists but are possibly also due to effects of assuming plane-parallell or spherical geometry and LTE

The Aging Heart: Mitophagy at the Center of Rejuvenation.

Aging is associated with structural and functional changes in the heart and is a major risk factor in developing cardiovascular disease. Many recent studies have focused on increasing our understanding of the basis of aging at the cellular and molecular levels in various tissues, including the heart. It is known that there is an age-related decline in cellular quality control pathways such as autophagy and mitophagy, which leads to accumulation of potentially harmful cellular components in cardiac myocytes. There is evidence that diminished autophagy and mitophagy accelerate the aging process, while enhancement preserves cardiac homeostasis and extends life span. Here, we review the current knowledge of autophagy and mitophagy in aging and discuss how age-associated alterations in these processes contribute to cardiac aging and age-related cardiovascular diseases