111,305 research outputs found
Hierarchical fiber bundle strength statistics
No full textMulti-scale modeling is currently one of the most active research topics in a wide range of disciplines. In this thesis we develop innovative hierarchical multi-scale models to analyze the probabilistic strength of fiber bundle structures. The Fiber Bundle Model (FBM) was developed initially by Daniels (1945), and then expanded, modified and generalized by many authors. Daniels considered a bundle of N fibers with identical elastic properties under uniform tensile stress. When a fiber breaks, the load from the broken fiber is distributed equally over all the remaining fibers (global load sharing). The strength of fibers is assigned randomly most often according to the Weibull probability distribution. In chapter 2, we develop for the first time an ad hoc hierarchical theory designed to tackle hierarchical architectures, thus allowing the determination of the strength of macroscopic hierarchical materials from the properties of their constituents at the nanoscale. The results show that the mean strength of the fiber bundle is reduced when scaling up from a fiber bundle to bundles of bundles. The hierarchical model developed in this study enables the prediction of strength values in good agreement with existing experimental results. This new ad hoc extension of the fiber bundle model is used for evaluating the role of hierarchy on structural strength. Different hierarchical architectures of fiber bundles have been investigated through analytical multiscale calculations based on a fiber bundle model at each hierarchical level. In general, we find that an increase in the number of hierarchical levels leads to a decrease in the strength of material. On a more abstract level, the hierarchical fiber bundle model (HFBM), an extension of the fiber bundle model (FBM) presented in this thesis, can be applied to any hierarchical system. FBMs are an established method helpful to understand hierarchical strength. Another extension of Daniels‘ theory for bimodal statistical strength has been implemented to model flaws in carbon nanotube fibers such as joints between carbon nanotubes, where careful analysis is necessary to assess the true mean strength. This model provides a more realistic description of the microscopic structure constituted by a nanotube-nanotube joint than a simple fiber bundle model. We demonstrate that the disorder distribution and the relative importance of the two failure modes have a substantial effect on mean strength of the structure. As mentioned, the fiber bundle model describes a collection of elastic fibers under load. The fibers fail successively and for each failure, the load is redistributed among the surviving fibers. In the fiber bundle model, the survival probability is defined as a ratio between number of surviving fibers and the total number of fibers in the bundle. We find that this classical relation is no longer suitable for a bundle with a small number of fibers, so that it is necessary to implement a modification into the probability function. It is possible to predict snap-back instabilities by inserting this modification in the theoretical expression of the load-strain (F-ε) relationship for the bundle, as discussed in chapter 4. Scrutiny into the composition of natural, or biological materials convincingly reveals that high material and structural efficiency can be attained, even with moderate-quality constituents, by hierarchical topologies, i.e., successively organized material levels. This is shown in chapter 5, where a composite bundle with two different types of fibers is considered, and an improvement in the mean strength is obtained for some specific hierarchical architectures, indicating that both hierarchy and material ―mixing‖ are necessary ingredients to obtain improved mechanical properties. In Chapter 6, we consider a novel modeling approach, namely we introduce self healing in a fiber bundle model. Here, we further assume that faile
Full-field optical coherence tomography using a fibre imaging bundle
No full textAn imaging fibre bundle is demonstrated for spatially-multiplexed probe beam
delivery in OCT, with the aim of eliminating the mechanical scanning currently
required at the probe tip in endoscopic systems. Each fibre in the bundle
addresses a Fizeau interferometer formed between the bundle end and the sample,
allowing acquisition of information across a plane with a single measurement.
Depth scanning components are now contained within a processing interferometer
external to the completely passive endoscope probe. The technique has been
evaluated in our laboratory for non-biological samples. Images acquired using
the bundle-based system are presented. The potential of the system is assessed,
with reference to SNR performance and acquisition speed
Equivariant cohomology of the skyrmion bundle
No full textsummary:The author constructs the gauged Skyrme model by introducing the skyrmion bundle as follows: instead of considering maps he thinks of the meson fields as of global sections in a bundle . For calculations within the skyrmion bundle the author introduces by means of the so-called equivariant cohomology an analogue of the topological charge and the Wess-Zumino term. The final result of this paper is the following Theorem. For the skyrmion bundle with , one has where is the universal bundle for the Lie group and is the Lie algebra of
Fiber bundle fluorescence endomicroscopy
No full textAn improved design for fiber bundle fluorescence endomicroscopy is demonstrated. Scanned illumination and detection using coherent fiber bundles with 30,000 elements with 3 μm resolution enables high speed imaging with reduced pixel cross talk
Tangent bundle of hypersurfaces in G/P
No full textLet G be a simple linear algebraic group defined over an algebraically closed field k of characteristic p≥ 0, and let P be a maximal proper parabolic subgroup of G. If p > 0, then we will assume that dim G/P ≤ p. Let L : H →G/P be a reduced smooth hypersurface in G/P of degree d. We will assume that the pullback homomorphism Z = Pic(G/P) →i* Pic(H) is an isomorphism (this assumption is automatically satisfied when dimH ≥3). We prove that the tangent bundle of H is stable if the two conditions τ (G/P) ≠ d and d > τ (G/P)(n-1)/ 2n-1 ( hold; here n = dimH, and T (G/P)∈ N is the index of G/P which is defined by the identity K-1G/P= L ⊗τG/P where L is the ample generator of Pic(G/P) and K-1 G/P is the anti-canonical line bundle of G/P. If d = τ (G/P), then the tangent bundle TH is proved to be semistable. If ρ > 0, and τG/P > d > τ(G/P)(n-1)/ 2n-1, then TH is strongly stable. If p > 0, and d = τ(G/P), then TH is strongly semistable
HORIZONTAL LAPLACIAN ON TANGENT BUNDLE OF FINSLER MANIFOLD WITH g-NATURAL METRIC
No full textRecently the third author studied horizontal Laplacians in real Finsler vector bundles and complex Finsler manifolds. In this paper, we introduce a class of g-natural metrics G(a,b) on the tangent bundle of a Finsler manifold (M, F) which generalizes the associated Sasaki-Matsumoto metric and Miron metric. We obtain the Weitzenbock formula of the horizontal Laplacian associated to G(a, b), which is a second-order differential operator for general forms on tangent bundle. Using the horizontal Laplacian associated to G(a,b), we give some characterizations of certain objects which are geometric interest (e.g. scalar and vector fields which are horizontal covariant constant) on the tangent bundle. Furthermore, Killing vector fields associated to G(a,b) are investigated
Modeling Sudden Ice Shedding from Conductor Bundles
No full textSudden ice shedding from conductor bundles was modeled numerically and experimentally by improving the approaches proposed formerly for a single cable. The experimental study was carried out on a small-scale laboratory model of one span of a twin bundle. A numerical model of the experimental setup was developed using the commercial finite-element software ADINA. This model was validated by simulating: 1) the vertical cable vibration during former load shedding tests on a full-scale line of single conductors; 2) the bundle rotation on a full-scale twin bundle during former static torsional tests; and 3) the vertical cable vibration and bundle rotation at midspan during the present load shedding tests on a small-scale twin bundle. The coincidence of calculated and measured tendencies justified the applicability of the numerical model to simulate the vibration following ice shedding from bundled conductors in most cases. The model was finally applied to simulate sudden ice shedding from a full-scale span with a twin bundle. Simulation results showed that the application of spacers reduces the cable jump height during this vibration; however, a higher number of spacers in the same span does not decrease the angle of bundle rotation
Imaging fibre bundles for Fizeau-based optical coherence tomography
No full textAn OCT system incorporating a coherent fibre imaging bundle is described. Fibres
are accessed sequentially by a beam focused onto the input face of the bundle,
allowing 2D or 3D images to be acquired using point detection. A Fizeau
interferometer configuration is used, in which light from the distal end of a
fibre in the bundle (forming the reference arm) mixes with light reflected by
the sample itself (forming the sample arm). The use of coherent imaging bundles
for OCT beam delivery allows mechanical scanning parts to be removed from the
sample arm, resulting in a passive probe. Such a configuration can form a
compact, robust and "downlead insensitive" OCT system. In the common-path
configuration used, an inherent path-length difference is present in the Fizeau
sample interferometer, so an additional processing interferometer is required to
ensure path-length matching. The depth scanning mechanism is confined within the
processing interferometer, external to the sample probe
Computational experience with a bundle approach for semidenfinite cutting plane relaxations of max-cut and equipartition.
No full textOn the Picard bundle
No full textAbstractFix a holomorphic line bundle ξ over a compact connected Riemann surface X of genus g, with g⩾2, and also fix an integer r such that degree(ξ)>r(2g−1). Let Mξ(r) denote the moduli space of stable vector bundles over X of rank r and determinant ξ. The Fourier–Mukai transform, with respect to a Poincaré line bundle on X×J(X), of any F∈Mξ(r) is a stable vector bundle on J(X). This gives an injective map of Mξ(r) in a moduli space associated to J(X). If g=2, then Mξ(r) becomes a Lagrangian subscheme
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