Forces de Casimir i les seves aplicacions

Report for the scientific sojourn carried out at the Darmouth College, from august 2007 until february 2008. It has been very successful, from different viewpoints: scientific, philosophical, human. We have definitely advanced, during the past six months, towards the comprehension of the behaviour of the fluctuations of the quantum vacuum in the presence of boundaries, moving and non-moving, and also in situations where the topology of space-time changes: the dynamical Casimir effect, regularization problems, particle creation statistics, according to different BC, etc. We have solved some longstanding problems and got in this subject quite remarkable results (as we will explain in more detail below). We also pursued a general approach towards a viable modified f(R) gravity in both the Jordan and the Einstein frames (which are known to be mathematically equivalent, but physically not so). A class of exponential, realistic modified gravities has been introduced by us and investigated with care. Special focus was made on step-class models, most promising from the phenomenological viewpoint and which provide a natural way to classify all viable modified gravities. One- and two-steps models were considered, but the analysis is extensible to N-step models. Both inflation in the early universe and the onset of recent accelerated expansion arise in these models in a natural, unified way, what makes them very promising. Moreover, it is monstrated in our work that models in this category easily pass all local tests, including stability of spherical body solution, non-violation of Newton's law, and generation of a very heavy positive mass for the additional scalar degree of freedom.

Issue of time in generally covariant theories and the Komar-Bergmann approach to observables in general relativity

Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants of the motion. Time-dependent invariants arise through the choice of an intrinsic time, or equivalently through the imposition of time-dependent gauge fixation conditions. One example of such a time-dependent gauge fixing is the Komar-Bergmann use of Weyl curvature scalars in general relativity. An analogous gauge fixing is also imposed for the relativistic free particle and the resulting complete set time-dependent invariants for this exactly solvable model are displayed. In contrast with the free particle case, we show that gauge invariants that are simultaneously constants of motion cannot exist in general relativity. They vary with intrinsic time.

The Role of the Delay Time in the Modeling of Biological Range Expansions

The time interval between successive migrations of biological species causes a delay time in the reaction-diffusion equations describing their space-time dynamics. This lowers the predicted speed of the waves of advance, as compared to classical models. It has been shown that this delay-time effect improves the modeling of human range expansions. Here, we demonstrate that it can also be important for other species. We present two new examples where the predictions of the time-delayed and the classical (Fisher) approaches are compared to experimental data. No free or adjustable parameters are used. We show that the importance of the delay effect depends on the dimensionless product of the initial growth rate and the delay time. We argue that the delay effect should be taken into account in the modeling of range expansions for biological species

Espacio y tiempo en el imaginario digital. La construcción técnico estética de la espacio-temporalidad contemporánea.

Partiendo de la idea ampliamente aceptada de que las TIC (Tecnologías de Información y Comunicación) han tenido una profunda influencia en los modos en que la sociedad contemporánea experimenta y concibe las nociones de espacio y tiempo, y sustentándose en el contexto de la importancia adquirida por dichas nociones en la comprensión de los procesos sociales en general y estéticos en particular, esta investigación ha tenido por objetivo analizar la espacio-temporalidad en el contexto específico de la era digital. Poniendo en relación la fenomenología de los dispositivos tecnológicos con las nuevas estrategias de representación y puesta en imagen del espacio y el tiempo, nuestro propósito ha sido mostrar no sólo cómo a través de las prácticas artísticas digitales puede identificarse y analizarse el imaginario espacio-temporal de la era digital, sino también cómo éstas –basadas en una larga trayectoria estética de intersecciones entre arte y tecnología- han revestido al espacio y al tiempo de nuevas fenomenologías posibles, dando lugar a nuevas formas de percibirlos y cumpliendo, por tanto, un papel activo en la configuración de dicho imaginario y sus sucesivas transformaciones. La perspectiva teórica adoptada para esta investigación parte de las teorías postmodernas del espacio y el tiempo –considerando autores como Harvey o Jameson-, recurriendo a la sociología del Imaginario Social desarrollada por Castoriadis, Castro-Nogueira o J. L. Pintos para comprender cómo el espacio y el tiempo adquieren significaciones particulares. Combinando estas bases teóricas con los estudios visuales y los trabajos de teóricos de los medios como McLuhan, De Kerckhove o Lev Manovich, se establecerían las posibles relaciones entre las tecnologías, las representaciones sociales del espacio y el tiempo – analizadas a partir de metáforas como “compresión espacio-temporal”, “espacio de los flujos” o “tiempo atemporal” y sus relaciones con el Ciberespacio- y la fenomenología espacio-temporal de las prácticas artísticas y sus estrategias de representación visual –tomando como objeto de estudio tipologías artísticas que van desde el Hipercine a la Realidad Virtual y Aumentada, los Medios Locativos o la Telepresencia. La conclusión que hemos podido extraer de este estudio es que si bien distintos tipos de tecnologías afectan operacional y perceptivamente a la construcción social de la espacio-temporalidad, los modos en que estas tecnologías han estetizado la propia realidad y los modos en que condicionan la construcción estética de las nociones de espacio y tiempo, tanto a partir de la propia fenomenología del dispositivo como de la experimentación creativa con el mismo, ejercen una profunda influencia sobre el imaginario social y espacio-temporal propios de la era digital.

Reconeixement de gestos de la mà amb el sensor Kinect

El reconeixement dels gestos de la mà (HGR, Hand Gesture Recognition) és actualment un camp important de recerca degut a la varietat de situacions en les quals és necessari comunicar-se mitjançant signes, com pot ser la comunicació entre persones que utilitzen la llengua de signes i les que no. En aquest projecte es presenta un mètode de reconeixement de gestos de la mà a temps real utilitzant el sensor Kinect per Microsoft Xbox, implementat en un entorn Linux (Ubuntu) amb llenguatge de programació Python i utilitzant la llibreria de visió artifical OpenCV per a processar les dades sobre un ordinador portàtil convencional. Gràcies a la capacitat del sensor Kinect de capturar dades de profunditat d’una escena es poden determinar les posicions i trajectòries dels objectes en 3 dimensions, el que implica poder realitzar una anàlisi complerta a temps real d’una imatge o d’una seqüencia d’imatges. El procediment de reconeixement que es planteja es basa en la segmentació de la imatge per poder treballar únicament amb la mà, en la detecció dels contorns, per després obtenir l’envolupant convexa i els defectes convexos, que finalment han de servir per determinar el nombre de dits i concloure en la interpretació del gest; el resultat final és la transcripció del seu significat en una finestra que serveix d’interfície amb l’interlocutor. L’aplicació permet reconèixer els números del 0 al 5, ja que s’analitza únicament una mà, alguns gestos populars i algunes de les lletres de l’alfabet dactilològic de la llengua de signes catalana. El projecte és doncs, la porta d’entrada al camp del reconeixement de gestos i la base d’un futur sistema de reconeixement de la llengua de signes capaç de transcriure tant els signes dinàmics com l’alfabet dactilològic.

Nonideal particle distributions from kinetic freeze-out models

In fluid dynamical models the freeze-out of particles across a three-dimensional space-time hypersurface is discussed. The calculation of final momentum distribution of emitted particles is described for freeze-out surfaces, with both spacelike and timelike normals, taking into account conservation laws across the freeze-out discontinuity.

On the zeta-function regularization of a two-dimensional series of epsten-Hurwitz type

For a few years now, the study of quantum field theories in partially compactified space-time manifolds has acquired increasing importance in several domains of quantum physics. Let me just mention the issues of dimensional reduction and spontaneous compactification, and the multiple questions associated with the study of quantum field theories in the presence of boundaries (like the Casimir effect) and on curved space-time (manifolds with curvature and nontrivial topology), a step towards quantum gravity.

Invariant decomposition of the retarded electromagnetic field.

The integral representation of the electromagnetic two-form, defined on Minkowski space-time, is studied from a new point of view. The aim of the paper is to obtain an invariant criteria in order to define the radiative field. This criteria generalizes the well-known structureless charge case. We begin with the curvature two-form, because its field equations incorporate the motion of the sources. The gauge theory methods (connection one-forms) are not suited because their field equations do not incorporate the motion of the sources. We obtain an integral solution of the Maxwell equations in the case of a flow of charges in irrotational motion. This solution induces us to propose a new method of solving the problem of the nature of the retarded radiative field. This method is based on a projection tensor operator which, being local, is suited to being implemented on general relativity. We propose the field equations for the pair {electromagnetic field, projection tensor J. These field equations are an algebraic differential first-order system of oneforms, which verifies automatically the integrability conditions.

Brane-world creation and black holes

An inflating brane world can be created from ``nothing'' together with its anti-de Sitter (AdS) bulk. The resulting space-time has compact spatial sections bounded by the brane. During inflation, the continuum of KK modes is separated from the massless zero mode by the gap m=(3/2)H, where H is the Hubble rate. We consider the analogue of the Nariai solution and argue that it describes the pair production of ``black cigars'' attached to the inflating brane. In the case when the size of the instantons is much larger than the AdS radius, the 5-dimensional action agrees with the 4-dimensional one. Hence, the 5D and 4D gravitational entropies are the same in this limit. We also consider thermal instantons with an AdS black hole in the bulk. These may be interpreted as describing the creation of a hot universe from nothing or the production of AdS black holes in the vicinity of a pre-existing inflating brane world. The Lorentzian evolution of the brane world after creation is briefly discussed. An additional ``integration constant'' in the Friedmann equation-accompanying a term which dilutes like radiation-describes the tidal force in the fifth direction and arises from the mass of a spherical object inside the bulk. In general, this could be a 5-dimensional black hole or a ``parallel'' brane world of negative tension concentrical with our brane-world. In the case of thermal solutions, and in the spirit of the AdS/CFT correspondence, one may attribute the additional term to thermal radiation in the boundary theory. Then, for temperatures well below the AdS scale, the entropy of this radiation agrees with the entropy of the black hole in the AdS bulk.

Large N phases, gravitational instantons and the nuts and bolts of AdS holography

Recent results in the literature concerning holography indicate that the thermodynamics of quantum gravity (at least with a negative cosmological constant) can be modeled by the large N thermodynamics of quantum field theory. We emphasize that this suggests a completely unitary evolution of processes in quantum gravity, including black hole formation and decay, and even more extreme examples involving topology change. As concrete examples which show that this correspondence holds even when the space-time is only locally asymptotically AdS, we compute the thermodynamical phase structure of the AdS-Taub-NUT and AdS-Taub-bolt spacetimes, and compare them to a (2+1)-dimensional conformal field theory (at large N) compactified on a squashed three-sphere and on the twisted plane.

Charged AdS black holes and catastrophic holography

We compute the properties of a class of charged black holes in antide Sitter space-time, in diverse dimensions. These black holes are solutions of consistent Einstein-Maxwell truncations of gauged supergravities, which are shown to arise from the inclusion of rotation in the transverse space. We uncover rich thermodynamic phase structures for these systems, which display classic critical phenomena, including structures isomorphic to the van der WaalsMaxwell liquid-gas system. In that case, the phases are controlled by the universal cusp and swallowtail shapes familiar from catastrophe theory. All of the thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can sometimes be found on the world volumes of coincident rotating branes.

Radiative isotropic cosmologies with extra dimensions

We solve Einsteins equations in an n-dimensional vacuum with the simplest ansatz leading to a Friedmann-Robertson-Walker (FRW) four-dimensional space time. We show that the FRW model must be of radiation. For the open models the extra dimensions contract as a result of cosmological evolution. For flat and closed models they contract only when there is one extra dimension.

Particle and string fluid interpretation for the scalar sector of Kaluza-Klein theories

The scalar sector of the effective low-energy six-dimensional Kaluza-Klein theory is seen to represent an anisotropic fluid composed of two perfect fluids if the extra space metric has a Euclidean signature, or a perfect fluid of geometric strings if it has an indefinite signature. The Einstein field equations with such fluids can be explicitly integrated when the four-dimensional space-time has two commuting Killing vectors.

Anisotropic fluid with SU(2) type structure in general relativity: A model of localized matter

A model of anisotropic fluid with three perfect fluid components in interaction is studied. Each fluid component obeys the stiff matter equation of state and is irrotational. The interaction is chosen to reproduce an integrable system of equations similar to the one associated to self-dual SU(2) gauge fields. An extension of the BelinskyZakharov version of the inverse scattering transform is presented and used to find soliton solutions to the coupled Einstein equations. A particular class of solutions that can be interpreted as lumps of matter propagating in empty space-time is examined.

A family of inhomogeneous cosmological Einstein - Rosen metrics

Some generalized soliton solutions of the cosmological EinsteinRosen type defined in the space-time region t2=z2 in terms of canonical coordinates are considered. Vacuum solutions are studied and interpreted as cosmological models. Fluid solutions are also considered and are seen to represent inhomogeneous cosmological models that become homogeneous at t?8. A subset of them evolve toward isotropic FriedmannRobertsonWalker metrics.