Distribution functions for a family of axially symmetric galaxy models

We present the derivation of distribution functions for the first four members of a family of disks, previously obtained in (MNRAS, 371, 1873, 2006), which represent a family of axially symmetric galaxy models with finite radius and well behaved surface mass density. In order to do this we employ several approaches that have been developed starting from the potential-density pair and, essentially using the method introduced by Kalnajs (Ap. J., 205, 751, 1976) we obtain some distribution functions that depend on the Jacobi integral. Now, as this method demands that the mass density can be properly expressed as a function of the gravitational potential, we can do this only for the first four discs of the family. We also find another kind of distribution functions by starting with the even part of the previous distribution functions and using the maximum entropy principle in order to find the odd part and so a new distribution function, as it was pointed out by Dejonghe (Phys. Rep., 133, 217, 1986). The result is a wide variety of equilibrium states corresponding to several self-consistent finite flat galaxy models.Comment: 12 pages, 7 figures, updated version, accepted for publication in Rev. Acad. Colomb. Cienc. Ex. Fis. Na

Geometric Aspects of Holographic Bit Threads

We revisit the recent reformulation of the holographic prescription to compute entanglement entropy in terms of a convex optimization problem, introduced by Freedman and Headrick. According to it, the holographic entanglement entropy associated to a boundary region is given by the maximum flux of a bounded, divergenceless vector field, through the corresponding region. Our work leads to two main results: (i) We present a general algorithm that allows the construction of explicit thread configurations in cases where the minimal surface is known. We illustrate the method with simple examples: spheres and strips in vacuum AdS, and strips in a black brane geometry. Studying more generic bulk metrics, we uncover a sufficient set of conditions on the geometry and matter fields that must hold to be able to use our prescription. (ii) Based on the nesting property of holographic entanglement entropy, we develop a method to construct bit threads that maximize the flux through a given bulk region. As a byproduct, we are able to construct more general thread configurations by combining (i) and (ii) in multiple patches. We apply our methods to study bit threads which simultaneously compute the entanglement entropy and the entanglement of purification of mixed states and comment on their interpretation in terms of entanglement distillation. We also consider the case of disjoint regions for which we can explicitly construct the so-called multi-commodity flows and show that the monogamy property of mutual information can be easily illustrated from our constructions.Comment: 48 pages, multiple figures. v3: matches published versio

QCD resummation for the fully differential Drell-Yan cross section

We study an extension of resummation to the fully differential cross section in the Drell-Yan process. This new method extends the Collins-Soper-Sterman formalism to the longitudinal WL and double delta helicity structure function WDeltaDelta, recovering the next-to-leading-order predictions. The new extension also modifies the transverse structure function WT obtained in previous extensions.;The angular coefficients, lambda and nu, used for parametrization of the angular distribution, were studied with the new structure functions. No violation of the Lam-Tung relation was found. A possible solution to explain the difference between theoretical and experimental results is proposed. This solution may also explain the existence of the azimuthal asymmetry.;For completeness, leading-order and next-to-leading-order results are presented. The Collins-Soper-Sterman formalism is also reviewed

Effects of quintessence on scattering and absorption sections of black holes

Basing on the ideas used by Kiselev, we study three black holes surrounded by quintessence and the effects of quintessence on the classical and semiclassical scattering cross-sections. In contrast, the absorption section is studied with the sinc approximation in the eikonal limit. For Schwarzschild, Reissner-Nordstr\"{o}m and Bardeen black holes surrounded by quintessence, the values critical of charges and the normalization factor are obtained. We also described the horizons and the extremal condition of the black holes surrounded by quintessence. By setting for the quintessence state parameter in two the particular cases w=-2/3 and w=-1/2

Quasinormal modes of the Schwarzchild black hole with a deficit solid angle and quintessence-like matter: Scalar and electromagnetic perturbations

We study the quasinormal modes (QNM) for scalar, and electromagnetic perturbations in the Schwarzchild black hole with a deficit solid angle and quintessence-like matter. Using the sixth--order WKB approximation and the improved asymptotic iteration method (AIM) we can determine the dependence of the quasinormal modes on the parameters of the black hole and the parameters on the test fields. The values of the real part and imaginary parts of the quasi--normal modes increase with the decrease of the values of the deficit solid angle and density of quintessence-like matter. The quasinormal modes gotten by these two methods are in good agreement. Using the finite difference method, we obtain the time evolution profile of such perturbations in this Black Hole

Transverse momentum dependence of the angular distribution of the Drell-Yan process

We calculate the transverse momentum Q_{\perp} dependence of the helicity structure functions for the hadroproduction of a massive pair of leptons with pair invariant mass Q. These structure functions determine the angular distribution of the leptons in the pair rest frame. Unphysical behavior in the region Q_{\perp} --> 0 is seen in the results of calculations done at fixed-order in QCD perturbation theory. We use current conservation to demonstrate that the unphysical inverse-power and \ln(Q/Q_{\perp}) logarithmic divergences in three of the four independent helicity structure functions share the same origin as the divergent terms in fixed-order calculations of the angular-integrated cross section. We show that the resummation of these divergences to all orders in the strong coupling strength \alpha_s can be reduced to the solved problem of the resummation of the divergences in the angular-integrated cross section, resulting in well-behaved predictions in the small Q_{\perp} region. Among other results, we show the resummed part of the helicity structure functions preserves the Lam-Tung relation between the longitudinal and double spin-flip structure functions as a function of Q_{\perp} to all orders in \alpha_s.Comment: 18 pages, 4 figures; typos corrected, references updated, a few clarifications recommended by the referee. Paper accepted for publication in Physical Review

Cumulant expansion framework for internal gradient distributions tensors

Magnetic resonance imaging is a powerful, non invasive tool for medical diagnosis. The low sensitivity for detecting the nuclear spin signals, typically limits the image resolution to several tens of micrometers in preclinical systems and millimeters in clinical scanners. Other sources of information, derived from diffusion processes of intrinsic molecules as water in the tissues, allow getting morphological information at micrometric and submicrometric scales as potential biomarkers of several pathologies. Here we consider extracting this morphological information by probing the distribution of internal magnetic field gradients induced by the heterogeneous magnetic susceptibility of the medium. We use a cumulant expansion to derive the dephasing on the spin signal induced by the molecules that explore these internal gradients while diffuse. Based on the cumulant expansion, we define internal gradient distributions tensors (IGDT) and propose modulating gradient spin echo sequences to probe them. These IGDT contain microstructural morphological information that characterize porous media and biological tissues. We evaluate the IGDT effects on the magnetization decay with typical conditions of brain tissue and show their effects can be experimentally observed. Our results thus provide a framework for exploiting IGDT as quantitative diagnostic tools

Efectos de la discretización en la simulación de escorrentía urbana

La urbanización produce un fuerte impacto sobre las respuestas hidrológicas de las cuencas. El incremento de la impermeabilidad aumenta notablemente los escurrimientos superficiales. Para evacuar los excedentes pluviales urbanos, se diseñan y construyen sistemas de drenaje, utilizando modelos matemáticos que permiten realizar los cálculos de diseño, operación y planificación de tales sistemas. El avance de la informática ha generalizado la aplicación de la modelación distribuida, lo que supone una mejora de la descripción de los fenómenos que participan en la transformación lluvia-escorrentía. Sin embargo, incorpora una incertidumbre relacionada con la elección del tamaño de la discretización superficial apropiada para la simulación. Este trabajo examina los efectos de la discretización espacial sobre la simulación del escurrimiento en una red de conductos pluviales, analiza la variación del parámetro de calibración W para diferentes escalas espaciales de una cuenca urbana y propone criterios para elegir la mayor escala espacial que satisfaga una precisión deseada en los resultados. Para ello se realizaron ensayos numéricos con el modelo SWMM sobre una cuenca urbana teórica y sobre una cuenca urbana experimental. A partir de los resultados obtenidos, se observa que la escala espacial influye en los resultados de la simulación con el modelo SWMM. La red de drenaje adiciona almacenamiento al sistema, atenuando y retardando los caudales pico. A medida que aumenta la escala una parte de la red es removida y en consecuencia se empuntan los hidrogramas y se anticipan los picos. Para que el modelo represente, a una escala mayor, una función de respuesta similar a la obtenida con la escala de detalle, es necesario compensar la pérdida de almacenamiento. Para ello, se debe reducir el ancho total de la cuenca, es decir, aumentar la longitud de escurrimiento. Para aplicaciones del modelo SWMM en cuencas similares a la del estudio, una vez discretizada la cuenca y si no se dispone de información pluvio-hidrométrica, se puede estimar el valor medio del parámetro W a partir de la relación ancho medio de escorrentía - área media de subcuencas. Para la cuenca experimental estudiada la escala espacial más grande que conserva la precisión admisible de los hidrogramas a la salida y de niveles de agua en nodos de interés es la meso escala.Peer Reviewe