Apparent horizons in D-dimensional Robinson-Trautman spacetime

We derive the higher dimensional generalization of Penrose-Tod equation describing apparent horizons in Robinson-Trautman spacetimes. New results concerning the existence and uniqueness of its solutions in four dimensions are proven. Namely, previous results of Tod are generalized to nonvanishing cosmological constant.Comment: 4 pages, 1 figure, to appear in ERE 2008 conference proceedings, to be published by AI

From speech to song: an interdisciplinary investigation of rhythm in English and Spanish

The general theoretical frame of this dissertation has to do with the study, from an interdisciplinary and interlinguistic point of view, of the typological dichotomy between stress-timed and syllable-timed languages, inasmuch as this distinction is valid at all. As a preliminary step, I carry out a comparative examination of the basic prosodic characteristics of English and Spanish, in order to then analyse the standard versification systems of these two languages. In the central part of my dissertation, I explore the most important text-setting Optimality Theory constraints as applied to a corpus of English and Spanish folk and art songs.My main objective in carrying out these three-level analyses is to check whether the actual setting of verse to music responds to some kind of underlying rhythmic constraints common to language prosody, verse prosody and music, and whether those constraints are ranked differently from language to language.The conclusions have to do with a correspondence between the timing typologies of language and the rhythmic typologies of music. I find clear inconsistencies or mismatches between speech prosody, on the one hand, and verse and music rhythm, on the other. These inconsistencies work differently in a syllabletimed language like Spanish than in a stress-timed language like English. While in the first type of languages I find a natural counterpoint or dialogue between speech prosody and musical rhythm, in the second type this counterpoint tends to be considered arhythmic. In other words, I establish a difference in kind in relation to the dialogue between prosody and music for each of the two types of languages. In English, the level of agreement between the two stress-patterns is really high, while in Spanish the counterpoint between the two patterns is used as an expressive device

The wave equation on axisymmetric stationary black hole backgrounds

Understanding the behaviour of linear waves on black hole backgrounds is a central problem in general relativity, intimately connected with the nonlinear stability of the black hole spacetimes themselves as solutions to the Einstein equations--a major open question in the subject. Nonetheless, it is only very recently that even the most basic boundedness and quantitative decay properties of linear waves have been proven in a suitably general class of black hole exterior spacetimes. This talk will review our current mathematical understanding of waves on black hole backgrounds, beginning with the classical boundedness theorem of Kay and Wald on exactly Schwarzschild exteriors and ending with very recent boundedness and decay theorems (proven in collaboration with Igor Rodnianski) on a wider class of spacetimes. This class of spacetimes includes in particular slowly rotating Kerr spacetimes, but in the case of the boundedness theorem is in fact much larger, encompassing general axisymmetric stationary spacetimes whose geometry is sufficiently close to Schwarzschild and whose Killing fields span the null generator of the horizon.Comment: 20 pages, 6 pages, to appear in the proceedings of the Spanish Relativity Meeting, Salamanca 200

How do compounds released by the green tide alga Ulvaria obscura affect development on invertebrate larvae?

Green tides are vast accumulations of green macroalgae that, in the last decade, have become a common nuisance worldwide. Due to compounds the algae release, the blooms may negatively affect other organisms. Ulvaria obscura, a dominant contributor to green tides along the Pacific coast of the United States, produces, among other compounds, dopamine, a catecholamine and neurotransmitter known to affect settlement and metamorphosis of marine invertebrates. We tested the effects of U. obscura exudates and commercially purchased dopamine on fertilization, early development, and larval survival and morphology of the sand dollar Dendraster excentricus and Pacific oyster Crassostrea gigas. The exudate and dopamine treatments did not strongly affect fertilization success of D. excentricus or C. gigas, but they did affect early development and larval morphology of D. excentricus and C. gigas. We found significant differences in archenteron length of D. excentricus gastrulae and shell morphology of C. gigas veligers exposed to the exudates or dopamine. Morphology of D. excentricus plutei also varied significantly among the exudate treatments with larval arm lengths being affected. Our data indicate that compounds released by U. obscura can impact development and, presumably, survival of embryos and larvae, but that the effects differ between species. The impacts could affect development rates, larval dispersal, recruitment and population dynamics of invertebrate species

Accelerated expansion through interaction

Interactions between dark matter and dark energy with a given equation of state are known to modify the cosmic dynamics. On the other hand, the strength of these interactions is subject to strong observational constraints. Here we discuss a model in which the transition from decelerated to accelerated expansion of the Universe arises as a pure interaction phenomenon. Various cosmological scenarios that describe a present stage of accelerated expansion, like the LCDM model or a (generalized) Chaplygin gas, follow as special cases for different interaction rates. This unifying view on the homogeneous and isotropic background level is accompanied by a non-adiabatic perturbation dynamics which can be seen as a consequence of a fluctuating interaction rate.Comment: 4 pages, to appear in the Proceedings of the Spanish Relativity Meeting ERE2008 in Salamanca, September 200