Search results for "Fiber bundle"
showing 10 items of 51 documents
Lie algebra on the transverse bundle of a decreasing family of foliations
2010
Abstract J. Lehmann-Lejeune in [J. Lehmann-Lejeune, Cohomologies sur le fibre transverse a un feuilletage, C.R.A.S. Paris 295 (1982), 495–498] defined on the transverse bundle V to a foliation on a manifold M, a zero-deformable structure J such that J 2 = 0 and for every pair of vector fields X , Y on M: [ J X , J Y ] − J [ J X , Y ] − J [ X , J Y ] + J 2 [ X , Y ] = 0 . For every open set Ω of V, J. Lehmann-Lejeune studied the Lie Algebra L J ( Ω ) of vector fields X defined on Ω such that the Lie derivative L ( X ) J is equal to zero i.e., for each vector field Y on Ω : [ X , J Y ] = J [ X , Y ] and showed that for every vector field X on Ω such that X ∈ K e r J , we can write X = ∑ [ Y ,…
A Statistical Approach to Permeability of Clustered Fibre Reinforcements
2004
The focus is set on mesoscale modelling of permeability of real fabrics used in composite manufacturing. Of particular interest is the effect of expected perturbations from perfect geometries, such as fibre bundle crimp, on the permeability. To start with, variational methods are used to calculate the permeability of individual gaps between fibre bundles. Based on this study a network of unit cells is formed enabling studies of two-and three-dimensional flow through the structure. From such an analysis the overall permeability of an arbitrary distribution of unit cell permeabilities can be calculated. Here random and controlled distributions are simulated. The former is an approximate repr…
Glass fibre strength distribution determined by common experimental methods
2002
The tensile strength of brittle fibres is routinely described by the Weibull distribution. The parameters of the distribution can be obtained from tests on single fibres and fibre bundles or from model composite tests. However, there is growing evidence that the distribution parameters obtained by different experimental techniques differ systematically. In order to investigate the possible causes of such discrepancies, single-fibre tension, fibre bundle, and single-fibre fragmentation tests are employed in this study to obtain strength distribution of commercial E-glass fibres. The results reveal parameter dependence on the approach used to extract the distribution parameters from experimen…
An index formula on manifolds with fibered cusp ends
2002
We consider a compact manifold whose boundary is a locally trivial fiber bundle and an associated pseudodifferential algebra that models fibered cusps at infinity. Using trace-like functionals that generate the 0-dimensional Hochschild cohomology groups, we express the index of a fully elliptic fibered cusp operator as the sum of a local contribution from the interior and a term that comes from the boundary. This answers the index problem formulated by Mazzeo and Melrose. We give a more precise answer in the case where the base of the boundary fiber bundle is the circle. In particular, for Dirac operators associated to a "product fibered cusp metric", the index is given by the integral of t…
Kähler Tubes of Constant Radial Holomorphic Sectional Curvature
1997
We determine (up to holomorphic isometries) the family of Kahler tubes, around totally geodesic complex submanifolds, of constant radial holomorphic sectional curvature when the centreP of the tube is either simply connected or a complex hypersurface withH1 (P, R)=0. In the last case, these tubes have the topology of tubular neighbourhoods of the zero section of the complex lines bundles over symplectic manifolds (when they are Kahler) of the Kostant-Souriau prequantization.
Quasi *-Algebras of Operators in Rigged Hilbert Spaces
2002
In this chapter, we will study families of operators acting on a rigged Hilbert space, with a particular interest in their partial algebraic structure. In Section 10.1 the notion of rigged Hilbert space D[t] ↪ H ↪ D × [t ×] is introduced and some examples are presented. In Section 10.2, we consider the space.L(D, D ×) of all continuous linear maps from D[t] into D × [t ×] and look for conditions under which (L(D, D ×), L +(D)) is a (topological) quasi *-algebra. Moreover the general problem of introducing in L(D, D ×) a partial multiplication is considered. In Section 10.3 representations of abstract quasi *-algebras into quasi*-algebras of operators are studied and the GNS-construction is …
Uniform fibre Bragg gratings with an embedded perturbed section for multiple applications
1999
The interest in fibre Bragg gratings has been increased with the development of flexible fabrication techniques which are able to make gratings with any non-uniform characteristic (chirped, apodised, sampled, phase-shifted, etc.) required for an specific application [1].
Presymplectic manifolds and conservation laws
2008
In this paper we make use of a new structure called seeded fibre bundle. This allows us to combine the symplectic formalism and general relativity. A theorem of existence is obtained and some examples and properties are studied.
One-Loop Effective Lagrangian in QED
2020
Our main goal in this section is the derivation of an expression for the effective Lagrangian in one-loop approximation. So let’s start with the vacuum persistence amplitude in presence of an external field: $$\displaystyle \langle 0_+\vert 0_-\rangle ^A = e^{ iW^{(1)}[A]} = e^{i \int d^4x\mathcal {L}^{(1)}(x)} $$
A field theoretic realization of a universal bundle for gravity
1992
Abstract Based upon a local vector supersymmetry algebra, we discuss the general structure of the quantum action for topological gravity theories in arbitrary dimensions. The precise form of the action depends on the particular dimension, and also on the moduli space of interest. We describe the general features by examining a theory of topological gravity in two dimensions, with a moduli space specified by vanishing curvature two-form. It is shown that these topological gravity models together with their observables provide a field theoretic realization of a universal bundle for gravity.