Search results for "Tensor"
showing 10 items of 550 documents
Ricci Tensors on Some Infinite Dimensional Lie Algebras
1999
Abstract The Ricci tensor has been computed in several infinite dimensional situations. In this work, we shall be interested in the case of the central extension of loop groups and in the asymptotic behaviour of the Ricci tensor on free loop groups as the Riemannian metric varies.
Weak Levi-Civita Connection for the Damped Metric on the Riemannian Path Space and Vanishing of Ricci Tensor in Adapted Differential Geometry
2001
Abstract We shall establish in the context of adapted differential geometry on the path space P m o ( M ) a Weitzenbock formula which generalizes that in (A. B. Cruzeiro and P. Malliavin, J. Funct. Anal . 177 (2000), 219–253), without hypothesis on the Ricci tensor. The renormalized Ricci tensor will be vanished. The connection introduced in (A. B. Cruzeiro and S. Fang, 1997, J. Funct. Anal. 143 , 400–414) will play a central role.
Methods to Compute Pressure and Wall Tension in Fluids containing Hard Particles
2011
Colloidal systems are often modelled as fluids of hard particles (possibly with an additional soft attraction, e.g. caused by polymers also contained in the suspension). in simulations of such systems, the virial theorem cannot be straightforwardly applied to obtain the components of the pressure tensor. In systems confined by walls, it is hence also not straightforward to extract the excess energy due to the wall (the "wall tension") from the pressure tensor anisotropy. A comparative evaluation of several methods to circumvent this problem is presented, using as examples fluids of hard spheres and the Asakura-Oosawa model of colloid-polymer mixtures with a size ratio $q=0.15$ (for which th…
Magnetic exchange interaction in clusters of orbitally degenerate ions. II. Application of the irreducible tensor operator technique
2001
Abstract The irreducible tensor operator technique in R3 group is applied to the problem of kinetic exchange between transition metal ions possessing orbitally degenerate ground states in the local octahedral surrounding. Along with the effective exchange Hamiltonian, the related interactions (low-symmetry crystal field terms, Coulomb interaction between unfilled electronic shells, spin–orbit coupling and Zeeman interaction) are also taken into account within a unified computational scheme. Extension of this approach to high-nuclearity systems consisting of transition metal ions in the orbital triplet ground states is also demonstrated. As illustrative examples, the corner-shared D4h dimers…
Symmetry-adapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups
2004
International audience; We present a short review on the tensorial formalism developed by the Dijon group to solve molecular spectroscopy problems. This approach, originally devoted to the rovibrational spectroscopy of highly symmetrical species (spherical tops) has been recently extended in several directions: quasi-spherical tops, some symmetric and asymmetric tops, and rovibronic spectroscopy of spherical tops in a degenerate electronic state. Despite its apparent complexity (heavy notations, quite complex mathematical tools), these group theoretical tensorial methods have a great advantage of flexibility: a systematic expansion of effective terms for any rovib- rational/rovibronic probl…
High-resolution far-infrared synchrotron FTIR spectroscopy and analysis of the ν 7 , ν 19 and ν 20 bands of trioxane
2022
Rovibrational bands spectra of three ν20, ν7 and ν19 bands of 1, 3, 5 – trioxane (H2CO)3 were recorded in the 50–650 cm−1 range using a long path absorption cell coupled to a high resolution Fourier transform spectrometer and synchrotron radiation at the AILES beamline of the SOLEIL synchrotron. More than 16 000 lines were assigned with a dRMS better than 0.17 × 10−3 cm−1. Two different formalisms (tensorial and Watson) were used to derive accurate rotational and quartic parameters for the three bands and for the first time, a precise determination of Coriolis parameter and q+ l−doubling constant for both ν20 and ν19 perpendicular bands was obtained. Last, each set of spectroscopic paramete…
Modèle tensoriel pour l'entreposage et l'analyse des données des réseaux sociaux Application à l'étude de la viralité sur Twitter
2018
International audience; Dans cet article, nous montrons comment la notion de tenseur permet de construire un modèle multi-paradigmes pour l'entreposage des données sociales. D'un point de vue architecture , cette approche permet de lier différents systèmes de stockage (polystore) et de limiter l'impact des outils ETL réalisant les transformations de modèles pour alimenter différents al-gorithmes d'analyse. Ainsi, le modèle proposé permet d'assurer l'indépendance logique entre les données et les programmes implantant les algorithmes d'analyse. Avec un cas concret ex-trait d'une étude de la viralité sur Twitter durant la période de l'entre deux tours de l'élection présidentielle française de …
Etude des effets collisionnels dans les molécules tétraédriques. Applications au méthane perturbé par l'argon
1996
This thesis is devoted to the study of relaxational and collisional line-broadening processes in the first vibrational polyads of tetrahedral molecules. In a first part, the particular internal dynamics of such molecules is discussed. The second chapter reviews the literature on phenomena induced by intermolecular interactions involving this type of molecules. More theoretical aspects are developed in the second part. The so-called tetrahedral tensorial formalism adapted to the construction of Hamiltonians and transition moments of tetrahedral molecules is described. Main features of the infrared line-shapes theories and of semi-classical line-broadening and line-shifting calculations are a…
Adaptations neuromusculaires des muscles extenseurs du genou : contractions fatigantes uni- vs bi-latérales
2010
The aim of this work was to determine i) the influence of the level of absolute force on the duration of the endurance time, and subsequent neuromuscular alterations in same individual at the end of an exercise performed at the same relative intensity, with one or two legs, ii) the influence of central drive on the force capacity production of the knee extensor muscles during unilateral (UL) vs. bilateral (BL) contractions, iii) activation mechanisms evolution for a serie of submaximal evoked contractions by electrostimulation (EMS). The results of the first study confirm that the endurance limit depends on the level of absolute force for the same individual, contraction duration for UL is …
The Role of Differential Parameters in Beltrami's Work
1997
Abstract Differential parameters play a relevant role in Beltrami's mathematical work. They are employed in different contexts, in order to express some well-known results in a new way and to extend potential theory and the theory of elasticity to a Riemannian manifold. The author aims to show that differential parameters enabled Beltrami to solve many mathematical questions and that they constitute the first step toward the conception of tensor calculus. Les parametres differentiels jouent un role important dans l'oeuvre mathematique de Beltrami. Ils sont employes en contextes differents, pour exprimer dans une maniere nouvelle quelques resultats bien-connus et pour generaliser la theorie …