Toric K\"ahler metrics seen from infinity, quantization and compact tropical amoebas

We consider the metric space of all toric K\"ahler metrics on a compact toric manifold; when "looking at it from infinity" (following Gromov), we obtain the tangent cone at infinity, which is parametrized by equivalence classes of complete geodesics. In the present paper, we study the associated limit for the family of metrics on the toric variety, its quantization, and degeneration of generic divisors. The limits of the corresponding K\"ahler polarizations become degenerate along the Lagrangian fibration defined by the moment map. This allows us to interpolate continuously between geometric quantizations in the holomorphic and real polarizations and show that the monomial holomorphic sections of the prequantum bundle converge to Dirac delta distributions supported on Bohr-Sommerfeld fibers. In the second part, we use these families of toric metric degenerations to study the limit of compact hypersurface amoebas and show that in Legendre transformed variables they are described by tropical amoebas. We believe that our approach gives a different, complementary, perspective on the relation between complex algebraic geometry and tropical geometry.Comment: v1: 32 pages, 5 figures; v2: 1 figure added; v3: 1 reference added; v4: some reorganization, 1 theorem (now 1.1) added; v5: final version, to appear in JD

A Note on the Picard-Fuchs Equations for N=2 Seiberg-Witten Theories

A concise presentation of the PF equations for N=2 Seiberg-Witten theories for the classical groups of rank r with N_f massless hypermultiplets in the fundamental representation is provided. For N_f=0, all r PF equations can be given in a generic form. For certain cases with N_f\neq zero, not all equations are generic. However, in all cases there are at least r-2 generic PF equations. For these cases the classical part of the equations is generic, while the quantum part can be formulated using a method described in a previous paper by the authors, which is well suited to symbolic computer calculations.Comment: 25 pages, Latex; some new references adde

Estimating maintenance costs of a wind turbine pitch control system

Wind turbines are nowadays the principal source of wind energy production. However, the technical information publicly known about these machines is still very scarce. Indeed, information related to failure modes, unavailability and maintenance costs of these systems remains confidential and only is held by manufacturers. To be able to optimize the efficiency, to guarantee the security and to negotiate better warranty and maintenance contracts, it is necessary to know more information about the operation and maintenance and replacement costs of subsystems of a wind turbine. To this end, this paper presents a short literature review of what has been published so far about this issue, and, based on two years of operation, analyses an active power control system of 21 identical wind turbines, installed in a wind farm in Portugal. The emphasis of this study is on the operation, availability and maintenance, and replacement costs of the active pitch control device, which automatically manages the position and operation of blades according to wind direction and speed, thus maximizing the electrical power gathered from the natural forces. Moreover, the paper provides an estimation for the total maintenance cost of this device, one of the most important components of the wind turbine, thus allowing wind farm companies to carry out financial and economic analysis of maintenance contracts that probably will be the rationale for better contract negotiations with manufactures. The result and the analyses that have been reported may also contribute for further studies on the reliability and maintenance policies of wind turbines.This work was financed with FEDER Funds by Programa Operacional Fatores de Competitividade – COMPETE and by National Funds by FCT – Fundação para a Ciência e Tecnologia, Project: FCOMP-01-0124-FEDER-022674.info:eu-repo/semantics/publishedVersio

Brane Isotropisation in Extra-Dimensional Tolman-Bondi Universe

We consider the dynamics of a 3-brane embedded in an extra-dimensional Tolman-Bondi Universe where the origin of space plays a special role. The embedding is chosen such that the induced matter distribution on the brane respects the spherical symmetry of matter in the extra dimensional space. The mirage cosmology on the probe brane is studied, resulting in an inhomogeneous and anisotropic four dimensional cosmology where the origin of space is also special. We then focus on the spatial geometry around the origin and show that the induced geometry, which is initially inhomogeneous and anisotropic, converges to an isotropic and homogeneous Friedmann-Lemaitre 4d space-time. For instance, when a 3-brane is embedded in a 5d matter dominated model, the 4d dynamics around the origin converge to a Friedmann-Lemaitre Universe in a radiation dominated epoch. We analyse this isotropisation process and show that it is a late time attractor.Comment: 16 pages, 8 figures, one reference adde

Coherent state transforms and vector bundles on elliptic curves

AbstractWe extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k, rank n and genus one non-abelian theta functions with the unitarity of the CST transform being preserved. Furthermore, the shift in the level k→k+n appears in a natural way in this finite-dimensional framework