Cohomology of the space of commuting n-tuples in a compact Lie group

Consider the space Hom(Z^n,G) of pairwise commuting n-tuples of elements in a compact Lie group G. This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingularization of the generic component of Hom(Z^n,G), which allows us to derive formulas for its ordinary and equivariant cohomology in terms of the Lie algebra of a maximal torus in G and the action of the Weyl group. This is an application of a general theorem concerning G-spaces for which every element is fixed by a maximal torus.Comment: 11 pages Changes made: Implemented referee recommendations, in particular to use the Vietoris mapping theorem to generalize results and simplify argument

Topology of generalized complex quotients

Consider the Hamiltonian action of a torus on a compact twisted generalized complex manifold $M$. We first observe that Kirwan injectivity and surjectivity hold for ordinary equivariant cohomology in this setting. Then we prove that these two results hold for the twisted equivariant cohomology as well.Comment: 33 pages, substantial changes made, expositions on twisted equivariant cohomology improve

Micro-Nano : des comportements différents, des procédés à adapter

6 pagesL'arrivée de nanomatériaux parmi les différents matériaux utilisés en pyrotechnie pose de nombreux problèmes de mise en œuvre. En effet, leurs propriétés texturales particulières ne permettent pas de les utiliser comme des matériaux classiques. Il est impératif d'adapter les procédés de mise en œuvre habituels. Pour obtenir l'adéquation de ces nouveaux matériaux et de nos procédés, des études spécifiques du comportement des nanomatériaux au cours des procédés de mise en œuvre par coulée ont été réalisés. L'observation des écarts de comportement des nanomatériaux par rapport aux "micro-matériaux" pour une même nature chimique et des conditions identiques de mise en œuvre permet d'établir des lois de comportement spécifiques, fonction de la taille des particules manipulées. Les mentalités, comme les procédés, doivent évoluer et prendre en compte l'élévation de surface spécifique qu'offre le passage à l'échelle nanométrique. Ainsi un chargement moindre en nanomatériaux ne sera pas forcement synonyme de lacunes sur les caractéristiques du produit fini (propriétés mécaniques ou pyrotechniques). Deux questions peuvent alors se poser : faut-il adapter les formulations aux procédés, en prenant en compte les caractéristiques des matières premières ou bien adapter des procédés devant supporter des taux de chargement élevés en nanomatériaux ? Le manque de connaissance et le recul sur le comportement des nanomatériaux sont un frein à leur intégration dans des composés pyrotechniques mais les propriétés exhibées laissent présagées d'un grand intérêt en vue de l'optimisation des propriétés des composés fabriqués

A Flow Time Model for Melt-Cast Insensitive Explosive Process

International audienceDiphasic flows of concentrated suspensions of melt-cast insensitive explosives exhibit specific rheological properties. In order to limit the handling of pyrotechnical products presenting a risk with respect to the mechanical and thermal shocks, a lot of work has been undertaken for many years in the civil engineering sector. The objective of this study is to propose a predictive model of the flow time of a concentrated suspension through a nozzle located at the bottom of a tank. Similar to our industrial process, the suspension is made out of insensitive energetic materials and flows under gravity. Experimental results are compared to three models (Quemada, Krieger-Dougherty, and Mooney) predicting the viscosity μ of a suspension as a function of the solid volume fraction ϕ, the maximum packing density ϕm and the viscosity μ0 of the interstitial liquid. De Larrard's model is used to calculate ϕm. The value of viscosity measured for the pure liquid is close to the one predicted by the Bernoulli theorem, where liquids are considered as incompressible and inviscid. Finally, it was found that the Quemada's model gives a fair agreement between predictions and experiments

Development of a new mixing rheometer for studying rheological behaviour of concentrated energetic suspensions

International audienceThe overall objective is to present a procedure based on a Couette analogy to quantitatively analyse torque/rotor speed data and extract viscosity/shear-rate curves using a non-conventional geometry. Diphasic flows of energetic concentrated suspensions of melt-cast insensitive explosives exhibit particular rheological properties. The characterization of these complex fluids may be a challenging task when conventional rheometers are used. Placing these tense suspensions in a classic cylindrical geometry may lead to a partial destruction of the internal fluid structure. To prevent that, a "RheoXF" a mixer-type rheometer has been developed : it consists of a mixing device with quite a complex geometry rotating in a cylindrical tank

Application d'un modèle de viscosité à la coulée d'explosifs : Modélisation du temps de coulée.

14 pagesLa rhéologie des coulées d'explosifs est décrite par la dynamique des écoulements diphasiques de suspensions concentrées. Afin d'améliorer la manipulation de produits présentant par nature un risque vis-à-vis des agressions mécaniques et thermiques, des avancées issues des travaux de recherche menés depuis de nombreuses années dans le secteur du génie civil permettent de développer de nouveaux procédés pyrotechniques. L'objectif de ces travaux est de proposer un modèle prédictif des temps d'écoulement des suspensions concentrées en matériaux énergétiques dans une configuration similaire au procédé de mise en oeuvre développé en production. Les résultats expérimentaux sont comparés à trois modèles (Quémada, Krieger-Dougherty, Mooney) représentant la viscosité dynamique comme étant fonction de la fraction volumique solide , de l'empilement compact maximal et de la viscosité du fluide interstitiel . Le modèle de De Larrard est utilisé pour le calcul de . Les hypothèses d'un fluide parfait et incompressible, pour le calcul du temps de coulée du fluide interstitiel , aboutissent à la relation de Bernoulli et satisfont à l'expérience. Nous montrons que le modèle de Quémada conduit à des valeurs théoriques du temps de coulée de la suspension en bon accord avec les valeurs expérimentales

Emptying time of a tank filled up with explosive paste. Comparison between experimental measurements and predictions based on rheological characterization of the paste

International audienceOne industrial process used by Nexter Munitions to manufacture pyrotechnical materials consists in preparing an emulsion of wax in TNT (2,4,6-trinitrotoluene) and adding Aluminium and ONTA (3-nitro-1,2,4-triazole-5-one) particles. When the suspension is homogeneous, it is allowed to flow by gravity through a pipe located at the bottom of the tank and to fill up a shell body. The suspension is characterized by a solid volume fraction of 53.4%, which leads to high viscosities. In some circumstances, the emptying time is prohibitively long and the economic profitability is reduced. This study has been performed to make the emptying time lower with the constraint of unchanged volume fractions and grains mean diameter. So, we investigated the influence of the grain size distribution on the suspension viscosity. Different samples of Aluminium and ONTA have been used, with rather small differences in grain size distributions. The suspensions have been prepared in the industrial tank and the flow cast times measured. It has been observed that they differ by one order of magnitude. To avoid situations with too high emptying times, a procedure has been implemented to make prior characterization of the suspension rheology. Because of particles sedimentation and emulsion destabilisation, the classical Couette rheometer is not adapted. So, we designed and built a small size tank (113 cm3), where the suspension is continuously stirred and kept homogeneous. The measurement of the torque and rotational speed together with the use of the Couette analogy allowed us to observe an Ostwald fluid behaviour (flow consistency index k, flow behaviour index n). To gain in prediction, we established a correlation between the measured (k, n) values and the grain size distributions. We characterized each suspension by the ratio of to , where is the solid volume fraction (imposed by the commercial specifications) and is the maximum packing fraction. Because of the strong analogy between concrete and energetic paste, we chose the widely used De Larrard model to compute . A linear dependance between the ratio and the indices k and n was observed. The second step was to provide an analytical expression for the flow cast time of a power-law suspension from a tank with a given geometry. Considering the large difference between the industrial inner tank diameter and the evacuation pipe diameter, we assumed that all the pressure drop was located in the evacuation pipe. Then, extending the Hagen-Poiseuille equation to Ostwald fluid, we were able to predict the emptying time with the knowledge of k and n. Experimental and predicted emptying time are in very good agreement. This work helped the industrial manufacturer to divide the emptying time by a factor 12

Refined Analytic Torsion as an Element of the Determinant Line

We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray-Singer norm of the refined analytic torsion. In particular, if there exists a flat Hermitian metric on E, we show that this norm is equal to 1. We prove a duality theorem, establishing a relationship between the refined analytic torsions corresponding to a flat connection and its dual.Comment: A sign in the definition (4.2) is changed (we are grateful to Guangxiang Su for this correction). Some minor misprints are also correcte

A semiclassical approach to the Dirac equation

We derive a semiclassical time evolution kernel and a trace formula for the Dirac equation. The classical trajectories that enter the expressions are determined by the dynamics of relativistic point particles. We carefully investigate the transport of the spin degrees of freedom along the trajectories which can be understood geometrically as parallel transport in a vector bundle with SU(2) holonomy. Furthermore, we give an interpretation in terms of a classical spin vector that is transported along the trajectories and whose dynamics, dictated by the equation of Thomas precession, gives rise to dynamical and geometric phases every orbit is weighted by. We also present an analogous approach to the Pauli equation which we analyse in two different limits