Hodge polynomials of the moduli spaces of pairs

Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. A holomorphic pair on $X$ is a couple $(E,\phi)$, where $E$ is a holomorphic bundle over $X$ of rank $n$ and degree $d$, and $\phi\in H^0(E)$ is a holomorphic section. In this paper, we determine the Hodge polynomials of the moduli spaces of rank 2 pairs, using the theory of mixed Hodge structures. We also deal with the case in which $E$ has fixed determinant.Comment: 23 pages, typos added, minor change

On the stability of Hamiltonian relative equilibria with non-trivial isotropy

We consider Hamiltonian systems with symmetry, and relative equilibria with isotropy subgroup of positive dimension. The stability of such relative equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In both papers the authors give sufficient conditions for stability which require first determining a splitting of a subspace of the Lie algebra of the symmetry group, with different splittings giving different criteria. In this note we remove this splitting construction and so provide a more general and more easily computed criterion for stability. The result is also extended to apply to systems whose momentum map is not coadjoint equivariant

Global Disk Oscillation Modes in Cataclysmic Variables and Other Newtonian Accretors

Diskoseismology, the theoretical study of small adiabatic hydrodynamical global perturbations of geometrically thin, optically thick accretion disks around black holes (and other compact objects), is a potentially powerful probe of the gravitational field. For instance, the frequencies of the normal mode oscillations can be used to determine the elusive angular momentum parameter of the black hole. The general formalism developed by diskoseismologists for relativistic systems can be readily applied to the Newtonian case of cataclysmic variables (CVs). Some of these systems (e.g., the dwarf nova SS Cygni) show rapid oscillations in the UV with periods of tens of seconds and high coherence. In this paper, we assess the possibility that these dwarf nova oscillations (DNOs) are diskoseismic modes. Besides its importance in investigating the physical origin of DNOs, the present work could help us to answer the following question. To what extent are the similarities in the oscillation phenomenology of CVs and X-ray binaries (XRBs) indicative of a common physical mechanism?Comment: 1 figur

On the Perturbations of Viscous Rotating Newtonian Fluids

The perturbations of weakly-viscous, barotropic, non-self-gravitating, Newtonian rotating fluids are analyzed via a single partial differential equation. The results are then used to find an expression for the viscosity-induced normal-mode complex eigenfrequency shift, with respect to the case of adiabatic perturbations. However, the effects of viscosity are assumed to have been incorporated in the unperturbed (equilibrium) model. This paper is an extension of the normal-mode formalism developed by Ipser & Lindblom for adiabatic pulsations of purely-rotating perfect fluids. The formulas derived are readily applicable to the perturbations of thin and thick accretion disks. We provide explicit expressions for thin disks, employing results from previous relativistic analyses of adiabatic normal modes of oscillation. In this case, we find that viscosity causes the fundamental p- and g- modes to grow while the fundamental c-mode could have either sign of the damping rate.Comment: Accepted for publication by The Astrophysical Journal. 11 pages, no figure

Quasi-normal modes, area spectra and multi-horizon spacetimes

We suggest an interpretation for the highly damped QNM frequencies of the spherically symmetric multi-horizon spacetimes (Reissner-Nordstrom, Schwarzschild-deSitter, Reissner-Nordstrom-deSitter) following Maggiore's proposal about the link between the asymptotic QNM frequencies and the black hole thermodynamics. We show that the behavior of the asymptotic frequencies is easy to understand if one assumes that all of the horizons have the same equispaced area spectra. The QNM analysis is then consistent with the choice of the area spectra to be the one originally proposed for the black hole's horizon by Bekenstein: A=8\pi n (in Planck units). The interpretation of the highly damped QNM frequencies in the multi-horizon case is based on the similar grounds as in the single horizon (Schwarzschild) case, but it has some new features that are discussed in the paper.Comment: 8 pages, v2: no physics changed, some references added, few sentences added in the discussion part

Stability of relative equilibria with singular momentum values in simple mechanical systems

A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group actions and singular momentum values. A normal form for the symplectic matrix at a relative equilibrium is also obtained.Comment: Partially rewritten. Some mistakes fixed. Exposition improve

Nitrogen Cycle And Ecosystem Services In The Brazilian La Plata Basin: Anthropogenic Influence And Climate Change.

The increasing human demand for food, raw material and energy has radically modified both the landscape and biogeochemical cycles in many river basins in the world. The interference of human activities on the Biosphere is so significant that it has doubled the amount of reactive nitrogen due to industrial fertiliser production (Haber-Bosch), fossil fuel burning and land-use change over the last century. In this context, the Brazilian La Plata Basin contributes to the alteration of the nitrogen cycle in South America because of its huge agricultural and grazing area that meets the demands of its large urban centres - Sao Paulo, for instance - and also external markets abroad. In this paper, we estimate the current inputs and outputs of anthropogenic nitrogen (in kg N.km(-2).yr(-1)) in the basin. In the results, we observe that soybean plays a very important role in the Brazilian La Plata, since it contributes with an annual entrance of about 1.8 TgN due to biological nitrogen fixation. Moreover, our estimate indicates that the export of soybean products accounts for roughly 1.0 TgN which is greater than the annual nitrogen riverine exports from Brazilian Parana, Paraguay and Uruguay rivers together. Complimentarily, we built future scenarios representing changes in the nitrogen cycle profile considering two scenarios of climate change for 2070-2100 (based on IPCC's A2 and B2) that will affect land-use, nitrogen inputs, and loss of such nutrients in the basin. Finally, we discuss how both scenarios will affect human well-being since there is a connection between nitrogen cycle and ecosystem services that affect local and global populations, such as food and fibre production and climate regulation.72691-70