Construction Of Bundles Research Articles

Rim Slip and Bead Fitment of Tires: Analysis and Design

Abstract A tire slips circumferentially on the rim when subjected to a driving or braking torque greater than the maximum tire-rim frictional torque. The balance of the tire-rim assembly achieved with weight attachment at certain circumferential locations in tire mounting is then lost, and vibration or adverse effects on handling may result when the tire is rolled. Bead fitment refers to the fit between a tire and its rim, and in particular, to whether a gap exists between the two. Rim slip resistance, or the maximum tire-rim frictional torque, is the integral of the product of contact pressure, friction coefficient, and the distance to the wheel center over the entire tire-rim interface. Analytical solutions and finite element analyses were used to study the dependence of the contact pressure distribution on tire design and operating attributes such as mold ring profile, bead bundle construction and diameter, and inflation pressure, etc. The tire-rim contact pressure distribution consists of two parts. The pressure on the ledge and the flange, respectively, comes primarily from tire-rim interference and inflation. Relative contributions of the two to the total rim slip resistance vary with tire types, depending on the magnitudes of ledge interference and inflation pressure. Based on the analyses, general guidelines are established for bead design modification to improve rim slip resistance and mountability, and to reduce the sensitivity to manufacturing variability. An iterative design and analysis procedure is also developed to improve bead fitment.

Double-Bundle Posterior Cruciate Ligament Reconstruction With a Bifid Bone-Patellar Tendon-Bone Allograft

The treatment of posterior cruciate ligament (PCL) injuries remains controversial. The ideal choice of graft and reconstructive technique remains uncertain. A bifid bone-patellar tendon-bone allograft is described that is suitable for either arthroscopic transtibial tunnel or open tibial inlay reconstruction of the posterior cruciate ligament. This graft closely recreates the anatomic configuration and size of the native posterior cruciate ligament. Testing of this graft versus a single bundle construct showed improved biomechanical performance in a tibial inlay PCL reconstruction. When posterior cruciate ligament reconstruction is indicated, a double-bundle reconstruction effectively restores normal knee kinematics. We describe our clinical experience with this technique for PCL reconstruction with our active-duty military population.

Mortuary behaviour reconstruction through palaeoentomology: a case study from Chachapoya, Perú

This paper explores the contribution that applied forensic entomology can make to our understanding of prehistoric mortuary behaviour. Samples of insect remains were recovered from a mummy bundle that has been attributed to the Chachapoya people who occupied the northern highlands of Perú from ca. AD 800 to ca. AD 1532. The insects were identified to the family level and used to create a hypothetical timeline of post-mortem interval before the construction of the mummy bundle. The individual in question suffered from a number of blunt force insults to the head, followed by two and possibly three trepanation events. We speculate the initial insect colonisation to have taken place almost immediately following injury and subsequent surgery, occurring before the individual's death. Insect succession patterns and timing estimates for the appearance of periosteal reactive bone suggest that the individual was wrapped shortly following death. The application of such modern forensic techniques holds vast promise for addressing issues concerning Chachapoya mortuary behaviour and, further, these results can expand our understanding of mummy studies in general. Copyright © 2005 John Wiley & Sons, Ltd.

Bundle Constructions of Calibrated Submanifolds in $\mathbb R^7$ and $\mathbb R^8$

We construct calibrated submanifolds of R^7 and R^8 by viewing them as total spaces of vector bundles and taking appropriate sub-bundles which are naturally defined using certain surfaces in R^4. We construct examples of associative and coassociative submanifolds of R^7 and of Cayley submanifolds of R^8. This construction is a generalization of the Harvey-Lawson bundle construction of special Lagrangian submanifolds of R^{2n}.

Monopole bundles over fuzzy complex projective spaces

We give a construction of the monopole bundles over fuzzy complex projective spaces as projective modules. The corresponding Chern classes are calculated. They reduce to the monopole charges in the N → ∞ limit, where N labels the representation of the fuzzy algebra.

Enlargeability and index theory

Let M be a closed enlargeable spin manifold. We show non-triviality of the universal index obstruction in the K-theory of the maximal $C^*$-algebra of the fundamental group of M. Our proof is independent from the injectivity of the Baum-Connes assembly map for the fundamental group of M and relies on the construction of a certain infinite dimensional flat vector bundle out of a sequence of finite dimensional vector bundles on M whose curvatures tend to zero. Besides the well known fact that M does not carry a metric with positive scalar curvature, our results imply that the classifying map $M \to B \pi_1(M)$ sends the fundamental class of M to a nontrivial homology class in $H_n(B \pi_1(M) ; \Q)$. This answers a question of Burghelea (1983).

On Hermitian-Holomorphic Classes Related to Uniformization, the Dilogarithm, and the Liouville Action

Metrics of constant negative curvature on a compact Riemann surface are critical points of the Liouville action functional, which in recent constructions is rigorously defined as a class in a Cech-de Rham complex with respect to a suitable covering of the surface. We show that this class is the square of the metrized holomorphic tangent bundle in hermitian-holomorphic Deligne cohomology. We achieve this by introducing a different version of the hermitian-holomorphic Deligne complex which is nevertheless quasi-isomorphic to the one introduced by Brylinski in his construction of Quillen line bundles. We reprove the relation with the determinant of cohomology construction. Furthermore, if we specialize the covering to the one provided by a Kleinian uniformization (thereby allowing possibly disconnected surfaces) the same class can be reinterpreted as the transgression of the regulator class expressed by the Bloch-Wigner dilogarithm.

Characterizing the hydrogeology of a complex clay-rich aquitard system using detailed vertical profiles of the stable isotopes of water

High-resolution 1D profiles of the stable isotopes of porewater (δ2H and δ18O) obtained by direct porewater-equilibration of core samples were used to identify hydrogeologic zones in a thick, complex, till aquitard system in Saskatchewan, Canada. Detailed 1D isotope profiles revealed the presence of three distinct hydrogeological zones: an upper (5–10 m), an intermediate (10–30 m), and a lower (30–62.5 m) till zone. The upper hydrogeological zone was controlled by a sand layer having a high hydraulic conductivity (K). The lack of vertical variability in the stable isotope data in the intermediate zone suggested groundwater flow and solute transport was controlled by a system of interconnected vertical fractures and lateral sand layers. The curved shape of the isotope profile in the lower till zone suggested that solute transport in this zone was controlled mainly by molecular diffusion. We show that high-resolution vertical stable isotope profiles of porewater obtained from core samples and direct equilibration yield cost-effective and invaluable hydrogeologic information on groundwater flow in aquitard systems that cannot be realistically obtained by construction of costly conventional piezometer bundles (i.e. δ2H and δ18O analyses of water samples and K determinations). Further, the direct equilibration approach overcomes the problem of piezometer leakage in low K aquitards.

Characterizing the hydrogeology of a complex clay-rich aquitard system using detailed vertical profiles of the stable isotopes of water

High-resolution 1D profiles of the stable isotopes of porewater (δ 2H and δ 18O) obtained by direct porewater-equilibration of core samples were used to identify hydrogeologic zones in a thick, complex, till aquitard system in Saskatchewan, Canada. Detailed 1D isotope profiles revealed the presence of three distinct hydrogeological zones: an upper (5–10 m), an intermediate (10–30 m), and a lower (30–62.5 m) till zone. The upper hydrogeological zone was controlled by a sand layer having a high hydraulic conductivity ( K). The lack of vertical variability in the stable isotope data in the intermediate zone suggested groundwater flow and solute transport was controlled by a system of interconnected vertical fractures and lateral sand layers. The curved shape of the isotope profile in the lower till zone suggested that solute transport in this zone was controlled mainly by molecular diffusion. We show that high-resolution vertical stable isotope profiles of porewater obtained from core samples and direct equilibration yield cost-effective and invaluable hydrogeologic information on groundwater flow in aquitard systems that cannot be realistically obtained by construction of costly conventional piezometer bundles (i.e. δ 2H and δ 18O analyses of water samples and K determinations). Further, the direct equilibration approach overcomes the problem of piezometer leakage in low K aquitards.

A geometric construction of Tango bundle on $\p^5$

The Tango bundle T over P 5 is proved to be the pull-back of the twisted Cayley bundle C(1) via a map f : P 5 ! Q5 existing only in character- istic 2. The Frobenius morphism ' factorizes via such f.

A construction of stable vector bundles on Calabi–Yau manifolds

In this paper we present a construction of stable bundles on a Calabi–Yau manifold using elementary transformation. As an application, we give examples of stable bundles on certain Calabi–Yau threefolds.

Cohomology of Complex Torus Bundles Associated to Cocycles

AbstractEquivariant holomorphic maps of Hermitian symmetric domains into Siegel upper half spaces can be used to construct families of abelian varieties parametrized by locally symmetric spaces, which can be regarded as complex torus bundles over the parameter spaces. We extend the construction of such torus bundles using 2-cocycles of discrete subgroups of the semisimple Lie groups associated to the given symmetric domains and investigate some of their properties. In particular, we determine their cohomology along the fibers.

Collective Coordinates of the Skyrme Model Coupled with Fermions

The problem of construction of fiber bundle over the moduli space of the Skyrme model is considered. We analyse an extension of the original Skyrme model which includes the minimal interaction with fermions. An analogy with modili space of the fermion–monopole system is used to construct a fiber bundle structure over the skyrmion moduli space. The possibility of the non-trivial holonomy appearance is considered. It is shown that the effect of the fermion interaction turns the n-skyrmion moduli space into a real vector bundle with natural SO(2n + 1) connection.

The foliation operator in history quantum field theory

As a preliminary to discussing the quantization of the foliation in a history form of general relativity, we show how the discussion in an earlier work [J. Math. Phys. 43, 3053 (2002)] of a history version of free, scalar quantum field theory can be augmented in such a way as to include the quantization of the unit-length, timelike vector that determines a Lorentzian foliation of Minkowski space–time. We employ a Hilbert bundle construction that is motivated by (i) discussing the role of the external Lorentz group in the existing history quantum field theory [J. Math. Phys. 43, 3053 (2002)] and (ii) considering a specific representation of the extended history algebra obtained from the multi-symplectic representation of scalar field theory.

Cohomogeneity one manifolds with positive Ricci curvature

One of the central problems in Riemannian geometry is to determine how large the classes of manifolds with positive/nonnegative sectional -, Ricci or scalar curvature are (see [Gr]). For scalar curvature the situation is fairly well understood by comparison. Special surgery constructions as in [SY, Wr] and bundle constructions as in [Na] have resulted in a large number of interesting manifolds with positive Ricci curvature. So far the only known obstructions to have positive Ricci curvature come from obstructions to have positive scalar curvature, (see [Li] and [RS]), and from the classical Bonnet-Myers Theorem, which implies that a closed manifold with positive Ricci curvature must have finite fundamental group. It is well known that among homogeneous manifolds G/H this is also a sufficient condition (see e.g. the proof of Corollary 3.5 or [Br]). In this paper we prove that this is true as well when the manifold admits an action by a compact Lie group G with orbits of codimension one.

Transverse group actions on bundles

An action of a Lie group G on a bundle π :E→M is said to be transverse if it is projectable and if the orbits of G on E are diffeomorphic under π to the orbits of G on M. Transverse group actions on bundles are completely classified in terms of the pullback bundle construction for G-invariant maps. This classification result is used to give a full characterization of the G invariant sections of E for projectable group actions.

Construction of low rank vector bundles on 𝐏⁴ and 𝐏⁵

We describe a technique which permits a uniform construction of a number of low rank bundles, both known and new. In characteristic two, we obtain rank two bundles on P 5 \mathbf {P}^{5} . In characteristic p p , we obtain rank two bundles on P 4 \mathbf {P}^4 and rank three bundles on P 5 \mathbf {P}^5 . In arbitrary characteristic, we obtain rank three bundles on P 4 \mathbf {P}^4 and rank two bundles on the quadric S 5 S_5 in P 6 \mathbf {P}^6 .

Cohomologie équivariante de [formula omitted] et application de Kirwan

Let X be a holomorphic curve of genus g and m the moduli space of rank n degree k stable holomorphic bundles on X with fixed determinant, n⩾2, (n,k)=1 . We generalize the construction given in [4], when n=2, k=1 , of a universal bundle on X× m . The space m can be seen as a quasi-Hamiltonian reduction of the quasi-Hamiltonian space SU (n) 2g . Using our construction of the universal bundle, we give some results about the image of the equivalent of the Kirwan map for quasi-Hamiltonian spaces, the strongest results being when n=2.

Logarithmic jet bundles and applications

We generalize Demailly's construction of projective jet bundles and strictly negatively curved pseudometrics on them to the logarithmic case. We establish this logarithmic generalization explicitly via coordinates, just as Noguchi's generalization of the jets used by Green-Griffiths. As a first application, we give a metric proof for the logarithmic version of Lang's conjecture concerning the hyperbolicity of complements of divisors in a semi-abelian variety as well as for the corresponding big Picard theorem.

Symplectic Reduction and the Homogeneous Complex Monge–Ampère Equation

A Riemannian manifold (\(\mathcal{M}^n \)n, g) is said to be the center of thecomplex manifold \(\mathcal{X}^n \)n if \(\mathcal{M}\) is the zero set of a smooth strictly plurisubharmonic exhaustion function ν2 on \(\mathcal{X}\) such that ν is plurisubharmonic and solves theMonge–Ampere equation (∂\(\bar \partial \)ν)n = 0 off \(\mathcal{M}\), and g is induced by the canonical Kahler metric withfundamental two-form \( - \sqrt { - 1} \) ∂\(\bar \partial \)ν2. Insisting that ν be unbounded puts severe restrictions on \(\mathcal{X}\) as acomplex manifold as well as on (\(\mathcal{M}\), g). It is an open problemto determine the class Riemannian manifolds that are centers of complexmanifolds with unbounded ν. Before the present work, the list of knownexamples of manifolds in that class was small. In the main result of thispaper we show, by means of the moment map corresponding to isometric actionsand the associated bundle construction, that such class is larger than originally thought and contains many metrically and diffeomorphically`exotic' examples.