String structures and the path fibration of a group

We use the realisation of the universal bundle for the loop group as the path fibration of the group to investigate the string class, that is the obstruction to a loop group bundle lifting to a Kac-Moody group bundle. In the case that the loop group bundle is constructed by taking loops into a principal bundle we show that the classifying map is the holonomy around loops and give an explicit formula for the string class relating it to the Pontrjangin class of the principal bunble.     

Warps,grids and curvature in triple vector bundles

A triple vector bundle is a cube of vector bundle structures which commute in the (strict) categorical sense. A grid in a triple vector bundle is a collection of sections of each bundle structure with certain linearity properties. A grid provides two routes around each face of the triple vector bundle, and six routes from the base manifold to the total manifold; the warps measure the lack of commutativity of these routes. In this paper we first prove that the sum of the warps in a triple vector bundle is zero. The proof we give is intrinsic and, we believe, clearer than the proof using decompositions given earlier by one of us. We apply this result to the triple tangent bundle \(T^3M\) of a manifold and deduce (as earlier) the Jacobi identity. We further apply the result to the triple vector bundle \(T^2A\) for a vector bundle A using a connection in A to define a grid in \(T^2A\). In this case the curvature emerges from the warp theorem.

     

Nanotube bundle oscillators: Carbon and boron nitride nanostructures

In this paper, we investigate the oscillation of a fullerene that is moving within the centre of a bundle of nanotubes. In particular, certain fullerene–nanotube bundle oscillators, namely C₆₀-carbon nanotube bundle, C₆₀-boron nitride nanotube bundle, B₃₆N₃₆-carbon nanotube bundle and B₃₆N₃₆-boron nitride nanotube bundle are studied using the Lennard–Jones potential and the continuum approach which assumes a uniform distribution of atoms on the surface of each molecule. We address issues regarding the maximal suction energies of the fullerenes which lead to the generation of the maximum oscillation frequency. Since bundles are also found to comprise double-walled nanotubes, this paper also examines the oscillation of a fullerene inside a double-walled nanotube bundle. Our results show that the frequencies obtained for the oscillation within double-walled nanotube bundles are slightly higher compared to those of single-walled nanotube bundle oscillators. Our primary purpose here is to extend a number of established results for carbon to the boron nitride nanostructures.     

Spacetime tangent bundle with torsion

It is demonstrated explicitly that the bundle connection of the Finslerspacetime tangent bundle can be made compatible with Cartan's theory of Finsler space by the inclusion of bundle torsion, and without the restriction that the gauge curvature field be vanishing. A component of the contorsion is made to cancel the contribution of the gauge curvature field to the relevant component of the bundle connection. Also, it is shown that the bundle manifold remains almost complex, and that the almost complex structure can be made to have a vanishing covariant derivative if additional conditions on the torsion are satisfied. However, the Finsler-spacetime tangent bundle remains complex only if the gauge curvature field vanishes.     

BOILING HEAT TRANSFER MECHANISMS IN A HORIZONTAL TUBE BUNDLE

The effect of thermal environment on boiling heat transfer performance in a section of a horizontal tube bundle was investigated using R-113 as the working fluid. The in-line tube bundle has five columns and 27 rows with a pitch-to-diameter ratio of 1.3. Heal transfer coefficients obtained from the instrumented tube in the tube bundle with only one tube heated while the other tubes remained unhealed and with all the lubes in the bundle heated are reported for a range of heat flux, pressure, mass flow rate, and quality. The results showed that heat transfer coefficient of a tube in a heated bundle is slightly higher than that in an unhealed bundle, with the variation of heat transfer coefficient decreasing as heat flux, mass flow rate, or pressure increased. It was also found that higher quality would tend to improve the heat transfer. However, the effect of quality disappeared as heat flux, mass flow rate, and pressure increased. Based on the experimental data, the mechanism of the heat transfer augment due to thermal environment was analyzed. It was proposed that fluid agitation and thin liquid film formation are two main factors for a heated bundle to have better transfer performance than an unhealed bundle,     

基于单光纤对模型的光纤束调制函数的建模与仿真

基于单光纤对光强调制特性的函数表达式,建立了双束型光纤束的调制函数,并引入一个虚拟轴间距参量,建立了随机型光纤束的光强调制函数.同时又在视内圈光纤束为单根粗光纤的情况下,建立了同轴I型和同轴型光纤束的光调制函数.在随机型和同轴型光纤束模型的基础上建立了双圈型(DC)和同轴随机型(C-R)光纤束的光调制系数.最后对上述光纤束的调制特性函数进行了计算机仿真实验.     

Bundle gerbes and moduli spaces

In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes with a natural connection and curving, and show that it is isomorphic to the analytically constructed index bundle gerbe. We apply these constructions to certain moduli spaces associated to compact Riemann surfaces, constructing on these moduli spaces, natural bundle gerbes with connection and curving, whose 3-curvature represent Dixmier-Douady classes that are generators of the third de Rham cohomology groups of these moduli spaces.     

Translation map in quantum principal bundles

The notion of a translation map in a quantum principal bundle is introduced. A translation map is then used to prove that the cross sections of a quantum fibre bundle E((B, V, A) associated to a quantum principal bundle P (B, A) are in bijective correspondence with equivariant maps V → P, and that a quantum principal bundle is trivial if it admits a cross section which is an algebra map. The vertical automorphisms and gauge transformations of a quantum principal bundle are discussed. In particular it is shown that vertical automorphisms are in bijective correspondence with Ad_R-covariant maps A → P.     

A generalized second-order frame bundle for Fréchet manifolds

Working within the framework of Fréchet modelled infinite-dimensional manifolds, we propose a generalized notion of second-order frame bundle. We revise in this way the classical notion of bundles of linear frames of order 2, the direct definition and study of which is problematic due to intrinsic difficulties of the space models. However, this new structure keeps all the fundamental characteristics of a frame bundle. It is a principal Fréchet bundle associated (differentially and geometrically) with the corresponding second-order tangent bundle.     

Curvature on determinant bundles and first Chern forms

The Quillen–Bismut–Freed construction associates a determinant line bundle with connection to an infinite dimensional super vector bundle with a family of Dirac-type operators. We define the regularized first Chern form of the infinite dimensional bundle, and relate it to the curvature of the Bismut–Freed connection on the determinant bundle. In finite dimensions, these forms agree (up to sign), but in infinite dimensions there is a correction term, which we express in terms of Wodzicki residues.

We illustrate these results with a string theory computation. There is a natural super vector bundle over the manifold of smooth almost complex structures on a Riemannian surface. The Bismut–Freed superconnection is identified with classical Teichmüller theory connections, and its curvature and regularized first Chern form are computed.     

Non-holonomic and semi-holonomic frames in terms of Stiefel and Grassmann tangent bundles

We prove that the bundles of non-holonomic and semi-holonomic second-order frames of a real or complex manifold M can be obtained as extensions of the bundle F²(M) of second-order jets of (holomorphic) diffeomorphisms of into M, where or . If and is the bundle of -linear frames of M we will associate to the tangent bundle two new bundles and with fibers of type the Stiefel manifold and the Grassmann manifold , respectively, where . The natural projection of onto defines a -principal bundle. We have found that the subset of given by the horizontal n-planes is an open sub-bundle isomorphic to the bundle of semi-holonomic frames of second-order of M. Analogously, the subset of given by the horizontal n-bases is an open sub-bundle which is isomorphic to the bundle of non-holonomic frames of second-order of M. Moreover the restriction of the former projection still defines a -principal bundle. Since a linear connection is a horizontal distribution of n-planes invariant under the action of it therefore determines a -reduction of the bundle , in a bijective way. This is a new proof of a theorem of Libermann.     

Finsler-spacetime tangent bundle

The Levi-Civita connection coefficients of the spacetime tangent bundle, for the case of a Finsler spacetime, are reduced to the form given by Yano and Davies for a generic tangent bundle of a Finsler manifold. A useful expression is also obtained for the Riemann curvature scalar of a Finsler-spacetime tangent bundle.     

Influence of disorder on the rupture process of fibrous materials

Based on computational modelling the influence of disorder on the rupture process of fibrous materials have been evaluated. This has been done by simulating a bundle of parallel fibers under a constant uniaxial force. The disorder process was introduced by randomly assigning a strength threshold to each fiber of the bundle according to the Weibull distribution. The results indicate that the rupture process is extremely sensitive to the disorder level. In particular, we demonstrated that the load necessary to break a fiber bundle with large disorder is smaller than that necessary to break a fiber bundle with small disorder.     

New geometrical approach to Rainich-Misner-Wheeler theory

We introduce a new principal fiber bundle, the bundle of biframes, associated with the geometry of bivectors on spacetime. It is shown that the biframe bundle is a natural geometric arena for modeling the already unified theory of Rainich, Misner, and Wheeler (RMW). The structure equations for the bitorsion inherent in the biframe bundle lead to a generalization of Rainich's algebraic conditions for electromagnetic-type stress tensors which includes sources in a natural way. Besides the usual complexion vector of the RMW theory, an additional new complexion-type vector is found. The generalized algebraic conditions reduce to the usual RMW conditions in the special case of no sources.     

Spacetimeb-boundaries

It is shown that Schmidt'sb-boundary for a spacetime can be analyzed using a submanifold of the tangent bundle, rather than the principal bundle or the bundle of orthogonal frames.     

温州蜜柑和椪柑橘络主要矿质元素含量的比较分析

橘络是位于柑橘果实中果皮与内果皮之间的维管束系统,主要起着营养物质和水分在果肉与果皮间转运的功能。橘络不仅在柑橘果实采前发育和采后枯水病发生过程中起重要作用,还是一种重要的中药资源,具有多种功效。本研究对温州蜜柑和椪柑橘络的外观形态与含水量进行分析,并利用火焰原子吸收光谱法对橘络的主要矿质元素(钾、钙、镁、铜、锌)含量进行测定,经过初步讨论,结果表明：(1)椪柑中橘络的含水量(63.57%±1.53%)显著低于温州蜜柑70.25%±0.24%,果肉含水量也呈现类似趋势。(2)橘络富含钾、钙、镁元素,浓度分别为：3 525～6 495,6 866～9 430,3 94～632 mg·kg-1干重;铜、锌元素含量分别为1.5～2.3和8.5～14.7 mg·kg-1干重。(3)橘络钾、钙、镁、锌元素含量在椪柑中明显高于温州蜜柑。本研究首次揭示了橘络矿质元素的含量特征,并发现矿质元素的含量变化与果实含水量具有相关性,为进一步研究枯水病的发生机理提供了重要借鉴;同时也为开发橘络这一宝贵的中药资源奠定了理论基础。     

Miniaturized two-photon microscope based on a flexible coherent fiber bundle and a gradient-index lens objective

We present a miniature, flexible two-photon microscope consisting of a fused coherent optical fiber bundle with 30,000 cores and a gradient-index lens objective. The laser focus of a standard two-photon laser-scanning microscope was scanned over the entrance surface of the fiber bundle, resulting in sequential coupling into individual cores. Fluorescent light was detected through the fiber bundle. Micrometer-sized fluorescent beads and pollen grains were readily resolved. In addition, fluorescently labeled blood vessels were imaged through the fiber bundle in rat brain in vivo.     

Covariant derivative on non-linear fiber bundles

A gauge field is usually described as a connection on a principal bundle. It induces a covariant derivative on associated vector bundles, sections of which represent matter fields. In general, however, it is not possible to define a covariant derivative on non-linear fiber bundles, i.e. on those which are not vector bundles. We definelogarithmic covariant derivatives acting on two special non-linear fiber bundles — on the principal bundle and on the local gauge group bundle. The logarithmic derivatives map from sections of these bundles to the sections of the local gauge algebra bundle. Some properties of the logarithmic derivatives are formulated.     

Cracks in random brittle solids:

Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.