Coisotropic Variational Problems

In this article we study constrained variational problems in one independent variable defined on the space of integral curves of a Frenet system in a homogeneous space G/H. We prove that if the Lagrangian is G-invariant and coisotropic then the extremal curves can be found by quadratures. Our proof is constructive and relies on the reduction theory for coisotropic optimal control problems. This gives a unified explanation of the integrability of several classical variational problems such as the total squared curvature functional, the projective, conformal and pseudo-conformal arc-length functionals, the Delaunay and the Poincar{\'e} variational problems

Diversity-induced resonance in a system of globally coupled linear oscillators

The purpose of this paper to analyze in some detail the arguably simplest case of diversity-induced reseonance: that of a system of globally-coupled linear oscillators subjected to a periodic forcing. Diversity appears as the parameters characterizing each oscillator, namely its mass, internal frequency and damping coefficient are drawn from a probability distribution. The main ingredients for the diversity-induced-resonance phenomenon are present in this system as the oscillators display a variability in the individual responses but are induced, by the coupling, to synchronize their responses. A steady state solution for this model is obtained. We also determine the conditions under which it is possible to find a resonance effect.Comment: Reported at the XI International Workshop "Instabilities and Nonequilibrium Structures" Vina del Mar (Chile

Intrinsic point defects and volume swelling in ZrSiO4 under irradiation

The effects of high concentration of point defects in crystalline ZrSiO4 as originated by exposure to radiation, have been simulated using first principles density functional calculations. Structural relaxation and vibrational studies were performed for a catalogue of intrinsic point defects, with different charge states and concentrations. The experimental evidence of a large anisotropic volume swelling in natural and artificially irradiated samples is used to select the subset of defects that give similar lattice swelling for the concentrations studied, namely interstitials of O and Si, and the anti-site Zr(Si), Calculated vibrational spectra for the interstitials show additional evidence for the presence of high concentrations of some of these defects in irradiated zircon.Comment: 9 pages, 7 (color) figure

Microlensing of the Lensed Quasar SDSS0924+0219

We analyze V, I and H band HST images and two seasons of R-band monitoring data for the gravitationally lensed quasar SDSS0924+0219. We clearly see that image D is a point-source image of the quasar at the center of its host galaxy. We can easily track the host galaxy of the quasar close to image D because microlensing has provided a natural coronograph that suppresses the flux of the quasar image by roughly an order of magnitude. We observe low amplitude, uncorrelated variability between the four quasar images due to microlensing, but no correlated variations that could be used to measure a time delay. Monte Carlo models of the microlensing variability provide estimates of the mean stellar mass in the lens galaxy (0.02 Msun < M < 1.0 Msun), the accretion disk size (the disk temperature is 5 x 10^4 K at 3.0 x 10^14 cm < rs < 1.4 x 10^15 cm), and the black hole mass (2.0 x 10^7 Msun < MBH \eta_{0.1}^{-1/2} (L/LE)^{1/2} < 3.3 x 10^8 Msun), all at 68% confidence. The black hole mass estimate based on microlensing is consistent with an estimate of MBH = 7.3 +- 2.4 x 10^7 Msun from the MgII emission line width. If we extrapolate the best-fitting light curve models into the future, we expect the the flux of images A and B to remain relatively stable and images C and D to brighten. In particular, we estimate that image D has a roughly 12% probability of brightening by a factor of two during the next year and a 45% probability of brightening by an order of magnitude over the next decade.Comment: v.2 incorporates referee's comments and corrects two errors in the original manuscript. 28 pages, 10 figures, published in Ap

Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem

Dark energy cosmology is considered in a modified Gauss-Bonnet (GB) model of gravity where an arbitrary function of the GB invariant, $f(G)$, is added to the General Relativity action. We show that such theory is endowed with a quite rich cosmological structure: it may naturally lead to an effective cosmological constant, quintessence or phantom cosmic acceleration, with a possible transition from deceleration to acceleration. It is demonstrated in the paper that this theory is perfectly viable, since it is compliant with Solar System constraints. Specific properties of $f(G)$ gravity in a de Sitter universe, such as dS and SdS solutions, their entropy and its explicit one-loop quantization are studied. The issue of a possible solution of the hierarchy problem in modified gravities is addressed too.Comment: LaTeX file 20 pages, new subsections are adde

Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect

Zeta regularization has proven to be a powerful and reliable tool for the regularization of the vacuum energy density in ideal situations. With the Hadamard complement, it has been shown to provide finite (and meaningful) answers too in more involved cases, as when imposing physical boundary conditions (BCs) in two-- and higher--dimensional surfaces (being able to mimic, in a very convenient way, other {\it ad hoc} cut-offs, as non-zero depths). What we have considered is the {\it additional} contribution to the cc coming from the non-trivial topology of space or from specific boundary conditions imposed on braneworld models (kind of cosmological Casimir effects). Assuming someone will be able to prove (some day) that the ground value of the cc is zero, as many had suspected until very recently, we will then be left with this incremental value coming from the topology or BCs. We show that this value can have the correct order of magnitude in a number of quite reasonable models involving small and large compactified scales and/or brane BCs, and supergravitons.Comment: 9 pages, 1 figure, Talk given at the Seventh International Workshop Quantum Field Theory under the Influence of External Conditions, QFEXT'05, Barcelona, September 5-9, 200

Developments in perfect simulation of Gibbs measures through a new result for the extinction of Galton-Watson-like processes

This paper deals with the problem of perfect sampling from a Gibbs measure with infinite range interactions. We present some sufficient conditions for the extinction of processes which are like supermartingales when large values are taken. This result has deep consequences on perfect simulation, showing that local modifications on the interactions of a model do not affect simulability. We also pose the question to optimize over a class of sequences of sets that influence the sufficient condition for the perfect simulation of the Gibbs measure. We completely solve this question both for the long range Ising models and for the spin models with finite range interactions.Comment: 28 page

Kinematic studies of transport across an island wake, with application to the Canary islands

Transport from nutrient-rich coastal upwellings is a key factor influencing biological activity in surrounding waters and even in the open ocean. The rich upwelling in the North-Western African coast is known to interact strongly with the wake of the Canary islands, giving rise to filaments and other mesoscale structures of increased productivity. Motivated by this scenario, we introduce a simplified two-dimensional kinematic flow describing the wake of an island in a stream, and study the conditions under which there is a net transport of substances across the wake. For small vorticity values in the wake, it acts as a barrier, but there is a transition when increasing vorticity so that for values appropriate to the Canary area, it entrains fluid and enhances cross-wake transport.Comment: 28 pages, 13 figure