Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram

The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from the Satake diagram, in a way that is suited for the use with computer algebra systems. As an example application, the totally geodesic submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified. The submission also contains an example implementation of the algorithms and formulas of the paper as a package for Maple 10, the technical documentation for this implementation, and a worksheet carrying out the computations for the space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical documentatio

Exact General Relativistic Thick Disks

A method to construct exact general relativistic thick disks that is a simple generalization of the ``displace, cut and reflect'' method commonly used in Newtonian, as well as, in Einstein theory of gravitation is presented. This generalization consists in the addition of a new step in the above mentioned method. The new method can be pictured as a ``displace, cut, {\it fill} and reflect'' method. In the Newtonian case, the method is illustrated in some detail with the Kuzmin-Toomre disk. We obtain a thick disk with acceptable physical properties. In the relativistic case two solutions of the Weyl equations, the Weyl gamma metric (also known as Zipoy-Voorhees metric) and the Chazy-Curzon metric are used to construct thick disks. Also the Schwarzschild metric in isotropic coordinates is employed to construct another family of thick disks. In all the considered cases we have non trivial ranges of the involved parameter that yield thick disks in which all the energy conditions are satisfied.Comment: 11 pages, RevTex, 9 eps figs. Accepted for publication in PR

Microscopic Conductivity of Lattice Fermions at Equilibrium - Part I: Non-Interacting Particles

We consider free lattice fermions subjected to a static bounded potential and a time- and space-dependent electric field. For any bounded convex region $\mathcal{R}\subset \mathbb{R}^{d}$ ($d\geq 1$) of space, electric fields $\mathcal{E}$ within $\mathcal{R}$ drive currents. At leading order, uniformly with respect to the volume $\left| \mathcal{R}\right|$ of $\mathcal{R}$ and the particular choice of the static potential, the dependency on $\mathcal{E}$ of the current is linear and described by a conductivity distribution. Because of the positivity of the heat production, the real part of its Fourier transform is a positive measure, named here (microscopic) conductivity measure of $\mathcal{R}$, in accordance with Ohm's law in Fourier space. This finite measure is the Fourier transform of a time-correlation function of current fluctuations, i.e., the conductivity distribution satisfies Green-Kubo relations. We additionally show that this measure can also be seen as the boundary value of the Laplace-Fourier transform of a so-called quantum current viscosity. The real and imaginary parts of conductivity distributions satisfy Kramers-Kronig relations. At leading order, uniformly with respect to parameters, the heat production is the classical work performed by electric fields on the system in presence of currents. The conductivity measure is uniformly bounded with respect to parameters of the system and it is never the trivial measure $0\,\mathrm{d}\nu$. Therefore, electric fields generally produce heat in such systems. In fact, the conductivity measure defines a quadratic form in the space of Schwartz functions, the Legendre-Fenchel transform of which describes the resistivity of the system. This leads to Joule's law, i.e., the heat produced by currents is proportional to the resistivity and the square of currents

Geometrization of the Gauge Connection within a Kaluza-Klein Theory

Within the framework of a Kaluza-Klein theory, we provide the geometrization of a generic (Abelian and non-Abelian) gauge coupling, which comes out by choosing a suitable matter fields dependence on the extra-coordinates. We start by the extension of the Nother theorem to a multidimensional spacetime being the direct sum of a 4-dimensional Minkowski space and of a compact homogeneous manifold (whose isometries reflect the gauge symmetry); we show, how on such a ``vacuum'' configuration, the extra-dimensional components of the field momentum correspond to the gauge charges. Then we analyze the structure of a Dirac algebra as referred to a spacetime with the Kaluza-Klein restrictions and, by splitting the corresponding free-field Lagrangian, we show how the gauge coupling terms outcome.Comment: 10 pages, no figure, to appear on Int. Journ. Theor. Phy

The MESANGE model: re-estimation on National Accounts base 2000 - Part 1 Version with fixed-base volumes

Mesange is a quarterly macro-econometric model of the French economy. This model has been developed and is used jointly by INSEE and the French Treasury. This working paper presents the new version of the model. The data used in the re-estimation process are those of the National Accounts base 2000 with fixed-base volumes. The paper contains a set of standard simulations giving some examples of the results used in the evaluation of economic policy measures and in the study of standard macroeconomic shocks. A second version of the model, re-estimated on National-Account data with chained volumes to better suit forecasting and short-term analysis, will be presented in a forthcoming INSEE working paper. The structure of the model is not very different from the initial version (Allard-Prigent et al., 2002). The French economy is represented as a small-open economy where the rest of the world is treated as exogenous. The economy is divided into three sectors: the manufacturing, non-manufacturing and non-market sectors. The model describes short-term Keynesian dynamics and its long-term equilibrium is driven by supply-side determinants. The re-estimation of the model has enabled us to take into account the structural evolutions of the French economy that have occurred since the last estimation (notably in terms of changes in labour productivity growth, the long-term elasticity of unemployment rate to real wage and the elasticity of substitution between labour and capital). Some extensions have been achieved, such as the creation of an energy block and the improvement of the fiscal block.macroeconometric model, estimation, simulation, macroeconomic policy

Five-Dimensional Unification of the Cosmological Constant and the Photon Mass

Using a non-Riemannian geometry that is adapted to the 4+1 decomposition of space-time in Kaluza-Klein theory, the translational part of the connection form is related to the electromagnetic vector potential and a Stueckelberg scalar. The consideration of a five-dimensional gravitational action functional that shares the symmetries of the chosen geometry leads to a unification of the four-dimensional cosmological term and a mass term for the vector potential.Comment: 8 pages, LaTe

On forward and inverse uncertainty quantification for models involving hysteresis operators

Parameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied. Results of forward UQ for a play operator with a stochastic yield limit are presented. Moreover, inverse UQ is performed to identify the parameters in the weight function in a Prandtl-Ishlinskiĭ operator and the uncertainties of these parameters

Evolution of replication efficiency following infection with a molecularly cloned feline immunodeficiency virus of low virulence

The development of an effective vaccine against human immunodeficiency virus is considered to be the most practicable means of controlling the advancing global AIDS epidemic. Studies with the domestic cat have demonstrated that vaccinal immunity to infection can be induced against feline immunodeficiency virus (FIV); however, protection is largely restricted to laboratory strains of FIV and does not extend to primary strains of the virus. We compared the pathogenicity of two prototypic vaccine challenge strains of FIV derived from molecular clones; the laboratory strain PET<sub>F14</sub> and the primary strain GL8<sub>414</sub>. PET<sub>F14</sub> established a low viral load and had no effect on CD4<sup>+</sup>- or CD8<sup>+</sup>- lymphocyte subsets. In contrast, GL8<sub>414</sub> established a high viral load and induced a significant reduction in the ratio of CD4<sup>+</sup> to CD8<sup>+</sup> lymphocytes by 15 weeks postinfection, suggesting that PET<sub>F14</sub> may be a low-virulence-challenge virus. However, during long-term monitoring of the PET<sub>F14</sub>-infected cats, we observed the emergence of variant viruses in two of three cats. Concomitant with the appearance of the variant viruses, designated 627<sub>W135</sub> and 628<sub>W135</sub>, we observed an expansion of CD8<sup>+</sup>-lymphocyte subpopulations expressing reduced CD8 ß-chain, a phenotype consistent with activation. The variant viruses both carried mutations that reduced the net charge of the V3 loop (K409Q and K409E), giving rise to a reduced ability of the Env proteins to both induce fusion and to establish productive infection in CXCR4-expressing cells. Further, following subsequent challenge of naïve cats with the mutant viruses, the viruses established higher viral loads and induced more marked alterations in CD8<sup>+</sup>-lymphocyte subpopulations than did the parent F14 strain of virus, suggesting that the E409K mutation in the PET<sub>F14</sub> strain contributes to the attenuation of the virus

Geodesic Deviation in Kaluza-Klein Theories

We study in detail the equations of the geodesic deviation in multidimensional theories of Kaluza-Klein type. We show that their 4-dimensional space-time projections are identical with the equations obtained by direct variation of the usual geodesic equation in the presence of the Lorentz force, provided that the fifth component of the deviation vector satisfies an extra constraint derived here.Comment: 5 pages, Revtex, 1 figure. To appear in Phys. Rev. D (Brief Report