Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

The second law of thermodynamics and the global climate system : A review of the maximum entropy production principle

The long-term mean properties of the global climate system and those of turbulent fluid systems are reviewed from a thermodynamic viewpoint. Two general expressions are derived for a rate of entropy production due to thermal and viscous dissipation (turbulent dissipation) in a fluid system. It is shown with these expressions that maximum entropy production in the Earth s climate system suggested by Paltridge, as well as maximum transport properties of heat or momentum in a turbulent system suggested by Malkus and Busse, correspond to a state in which the rate of entropy production due to the turbulent dissipation is at a maximum. Entropy production due to absorption of solar radiation in the climate system is found to be irrelevant to the maximized properties associated with turbulence. The hypothesis of maximum entropy production also seems to be applicable to the planetary atmospheres of Mars and Titan and perhaps to mantle convection. Lorenz s conjecture on maximum generation of available potential energy is shown to be akin to this hypothesis with a few minor approximations. A possible mechanism by which turbulent fluid systems adjust themselves to the states of maximum entropy production is presented as a selffeedback mechanism for the generation of available potential energy. These results tend to support the hypothesis of maximum entropy production that underlies a wide variety of nonlinear fluid systems, including our planet as well as other planets and stars

The Brauer group and the second Abel-Jacobi map for 0-cycles on algebraic varieties

This paper focuses on the connection between the Brauer group and the 0-cycles of an algebraic variety. We give an alternative construction of the second l-adic Abel-Jacobi map for such cycles, linked to the algebraic geometry of Severi-Brauer varieties on X. This allows us then to relate this Abel-Jacobi map to the standard pairing between 0-cycles and Brauer groups (see [M], [L]), completing results from [M] in this direction. Second, for surfaces, it allows us to present this map according to the more geometrical approach devised by M. Green in the framework of (arithmetic) mixed Hodge structures (see [G]). Needless to say, this paper owes much to the work of U. Jannsen and, especially, to his recently published older letter [J4] to B. Gross.

A numerical characterization of hypersurface singularities

In this note we give a numerical characterization of hypersurface singularities in terms of the normalized Hilbert-Samuel coefficients, and we interpret this result from the point of view of rigid polynomials.

What trees tell us: dendrochronological and statistical analysis of the data

Trees are a great bank of data, named sometimes for this reason as the "silentwitnesses" of the past. Due to annual formation of rings, which is normally influenced directly by of climate parameters (generally changes in temperature and moisture or precipitation) and other environmental factors; these changes, occurred in the past, are"written" in the tree "archives" and can be "decoded" in order to interpret what hadhappened before, mainly applied for the past climate reconstruction.Using dendrochronological methods for obtaining samples of Pinus nigra fromthe Catalonian PrePirineous region, the cores of 15 trees with total time spine of about 100 - 250 years were analyzed for the tree ring width (TRW) patterns and had quite high correlation between them (0.71 ¿ 0.84), corresponding to a common behaviour for the environmental changes in their annual growth.After different trials with raw TRW data for standardization in order to take outthe negative exponential growth curve dependency, the best method of doubledetrending (power transformation and smoothing line of 32 years) were selected for obtaining the indexes for further analysis.Analyzing the cross-correlations between obtained tree ring width indexes andclimate data, significant correlations (p<0.05) were observed in some lags, as forexample, annual precipitation in lag -1 (previous year) had negative correlation with TRW growth in the Pallars region. Significant correlation coefficients are between 0.27- 0.51 (with positive or negative signs) for many cases; as for recent (but very short period) climate data of Seu d¿Urgell meteorological station, some significant correlation coefficients were observed, of the order of 0.9.These results confirm the hypothesis of using dendrochronological data as aclimate signal for further analysis, such as reconstruction of climate in the past orprediction in the future for the same locality.

New horizons for black holes and branes

We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we uncover large classes of new black holes. These include helical black strings and black rings, black odd-spheres, for which the horizon is a product of a large and a small sphere, and non-uniform black cylinders. More exotic possibilities are also outlined. The blackfold description recovers correctly the ultraspinning Myers-Perry black holes as ellipsoidal even-ball configurations where the velocity field approaches the speed of light at the boundary of the ball. Helical black ring solutions provide the first instance of asymptotically flat black holes in more than four dimensions with a single spatial U(1) isometry. They also imply infinite rational non-uniqueness in ultraspinning regimes, where they maximize the entropy among all stationary single-horizon solutions. Moreover, static blackfolds are possible with the geometry of minimal surfaces. The absence of compact embedded minimal surfaces in Euclidean space is consistent with the uniqueness theorem of static black holes

La Geología de los Planetas: análisis estadístico de datos composicionales al servicio de la planetología

Anàlisi estadístic de dades composicionals dels planetes

New horizons for black holes and branes

We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we uncover large classes of new black holes. These include helical black strings and black rings, black odd-spheres, for which the horizon is a product of a large and a small sphere, and non-uniform black cylinders. More exotic possibilities are also outlined. The blackfold description recovers correctly the ultraspinning Myers-Perry black holes as ellipsoidal even-ball configurations where the velocity field approaches the speed of light at the boundary of the ball. Helical black ring solutions provide the first instance of asymptotically flat black holes in more than four dimensions with a single spatial U(1) isometry. They also imply infinite rational non-uniqueness in ultraspinning regimes, where they maximize the entropy among all stationary single-horizon solutions. Moreover, static blackfolds are possible with the geometry of minimal surfaces. The absence of compact embedded minimal surfaces in Euclidean space is consistent with the uniqueness theorem of static black holes

Higher-dimensional rotating charged black holes

Using the blackfold approach, we study new classes of higher-dimensional rotating black holes with electric charges and string dipoles, in theories of gravity coupled to a 2-form or 3-form field strength and to a dilaton with arbitrary coupling. The method allows to describe not only black holes with large angular momenta, but also other regimes that include charged black holes near extremality with slow rotation. We construct explicit examples of electric rotating black holes of dilatonic and non-dilatonic Einstein-Maxwell theory, with horizons of spherical and non-spherical topology. We also find new families of solutions with string dipoles, including a new class of prolate black rings. Whenever there are exact solutions that we can compare to, their properties in the appropriate regime are reproduced precisely by our solutions. The analysis of blackfolds with string charges requires the formulation of the dynamics of anisotropic fluids with conserved string-number currents, which is new, and is carried out in detail for perfect fluids. Finally, our results indicate new instabilities of near-extremal, slowly rotating charged black holes, and motivate conjectures about topological constraints on dipole hair.

Growth and functionalization of carbon nanotubes on quartz filter for environmental applications

Background: Air pollution has become an important issue worldwide due to its adverse health effects. Among the different air contaminants, volatile organic compounds (VOCs) are liquids or solids with a high vapor pressure at room temperature that are extremely dangerous for human health. Removal of these compounds can be achieved using nanomaterials with tailored properties such as carbon nanotubes. Methods: Vertically-aligned multiwall carbon nanotubes (CNTs) were successfully grown on quartz filters by means of plasma enhanced chemical vapor deposition (PECVD). Furthermore, a plasma treatment was performed in order to modify the surface properties of the CNTs. The adsorption/desorption processes of three chlorinated compounds (trichloroethylene, 1,2-dichlorobenzene and chloroform) on the CNTs were studied using mass spectrometry measurements with a residual gas analyzer. Results: The adsorption capability of the CNTs increased after functionalization of their surface with a water plasma treatment. In addition, it was found that the presence of aromatic rings, water solubility and polarity of the VOCs play an important role on the adsorption/desorption kinetics at the CNTs surface. Conclusions: This study demonstrates the applicability of CNTs deposited on quartz filters for the removal or selective detection of volatile organic compounds (VOCs). The presence of aromatic rings in VOCs results in π -stacking interactions with a significant increase of their adsorption. On the other hand, it was found that CNTs surface interactions increase with water solubility and polarity of the VOC.

Evolución del crecimiento radial en un rodal adulto de Pinus nigra Arn. de la provincia de Lleida

Se ha estudiado un rodal adulto (edad media = 139 años) de Pinus nigra ssp. salzmannii var. pyrenaica en el W de la comarca del Solsonès (Lérida). Se han medido y extraído testigos de madera de 97 árboles adultos, a partir de los cuales se han medido e interdatado 13.340 anillos anuales, construyendo una cronología de crecimientos que abarca desde 1818 a 1996. Se han analizado las relaciones entre diversos parámetros dendrométricos medidos y los crecimientos observados, encontrándose en general muy bajas correlaciones. Se han construido tres series medias de crecimiento (cronología media, estandarizada, y en función de la edad) a partir de las cuales se ha analizado la evolución del rodal. Se ha observado un prolongado período de ralentización y estancamiento del crecimiento que se mantiene cerca de ochenta años, seguido de una fuerte corta a la que la masa reacciona con un notable incremento del crecimiento radial en un momento en que la edad media era ya de 101 años.

Spatiotemporal variability in radial growth of trees in the Central Pyrenees: climatic and site influences.

To understand how tree growth has responded to recent climate warming, an understanding of the tree-climate-site complex is necessary. To achieve this, radial growth variability among 204 trees established before 1850 was studied in relation to both climatic and site factors. Seventeen forest stands were sampled in the Spanish Central Pyrenees. Three species were studied: Pinus uncinata, Abies alba, and Pinus sylvestris. For each tree, a ring-width residual chronology was built. All trees cross-dated well, indicating a common influence of the regional climate. For the 1952-1993 period, the radial growth of all species, especially P. uncinata, was positively correlated with warm Novembers during the year before ring formation and warm Mays of the year the annual ring formed. Differences in species-stand elevation modulated the growth-climate associations. Radial growth in P. uncinata at high elevation sites was reduced when May temperatures were colder and May precipitation more abundant. In the 20th century, two contrasting periods in radial growth were observed: one (1900-1949) with low frequency of narrow and wide rings, low mean annual sensitivity, and low common growth variation; and another (1950-1994) with the reverse characteristics. The increased variability in radial growth since the 1950s was observed for all species and sites, which suggests a climatic cause. The low shared variance among tree chronologies during the first half of the 20th century may result from a"relaxation" of the elevation gradient, allowing local site conditions to dominate macroclimatic influence. These temporal trends may be related to the recently reported increase of climatic variability and warmer conditions. This study emphasizes the need to carefully assess the relationships between radial growth and site conditions along ecological gradients to improve dendroclimatic reconstructions.