25 research outputs found
Infinite Dimensional Lie Theory
The workshop focussed on recent developments in infinite-dimensional Lie theory. The talks covered a broad range of topics, such as structure and classification theory of infinite-dimensional Lie algebras, geometry of infinite-dimensional Lie groups and homogeneous spaces and representation theory of infinite-dimensional Lie groups, Lie algebras and Lie-superalgebras
Four-manifolds, geometries and knots
The goal of this book is to characterize algebraically the closed 4-manifolds
that fibre nontrivially or admit geometries in the sense of Thurston, or which
are obtained by surgery on 2-knots, and to provide a reference for the topology
of such manifolds and knots. The first chapter is purely algebraic. The rest of
the book may be divided into three parts: general results on homotopy and
surgery (Chapters 2-6), geometries and geometric decompositions (Chapters
7-13), and 2-knots (Chapters 14-18). In many cases the Euler characteristic,
fundamental group and Stiefel-Whitney classes together form a complete system
of invariants for the homotopy type of such manifolds, and the possible values
of the invariants can be described explicitly. The strongest results are
characterizations of manifolds which fibre homotopically over S^1 or an
aspherical surface (up to homotopy equivalence) and infrasolvmanifolds (up to
homeomorphism). As a consequence 2-knots whose groups are poly-Z are determined
up to Gluck reconstruction and change of orientations by their groups alone.
This book arose out of two earlier books "2-Knots and their Groups" and "The
Algebraic Characterization of Geometric 4-Manifolds", published by Cambridge
University Press for the Australian Mathematical Society and for the London
Mathematical Society, respectively. About a quarter of the present text has
been taken from these books, and I thank Cambridge University Press for their
permission to use this material. The book has been revised in March 2007. For
details see the end of the preface.Comment: This is the revised version published by Geometry & Topology
Monographs in March 200
Noncommutative Geometry of Quantized Coverings
This research is devoted to the noncommutative generalization of topological
coverings. Otherwise since topological coverings are related to the set of
geometric constructions one can obtain noncommutative generalizations of these
constructions. Here the generalizations of the universal covering space,
fundamental group, homotopy theory, Hurewicz homomorphism, covering of the
Riemannian manifold, flat connection are explained. The theory gives pure
algebraic proof well known results of the topology and the differential
geometry. Besides there are applications of the theory to (unbounded) operator
spaces and this theme is also discussed here.Comment: 686 pages, 134 reference
Morphodynamics of Barrier Island Systems
Barrier island systems, also referred to as multiple-inlet systems, are coastal environments with shallow, interconnected tidal basins that are fringed by a chain of elongated islands. Their geomorphology and tidal habitats encompass numerous transitional zones between the land and the sea that are rich in species specially adapted to the varying hydrodynamic conditions. Morphodynamics at mixed-energy barrier island coasts have been studied for several decades on the basis of aerial photographs, field observations and numerical or analytical models. A process-based understanding of the morphological response to the driving hydrodynamic forces, however, has still not been achieved. The aim of this study is to assess the system morphodynamics in response to the interaction of tidally- and wave-induced currents, wind stress and the availability of mobile sediments. The study area is the East Frisian Wadden Sea (Germany), a lagoon-type environment with intertidal flats that are sheltered by seven inhabited barrier islands; it belongs to the Wadden Sea extending along the southern North Sea coast. A state-of-the-art process-based model is applied as a hindcasting and experimental tool for the evaluation of relevant processes at short term (tidal cycle) to medium term (annual) time scales. The spatial scales encompass sand shoals (meso-scale) as typical morphological features at ebb-tidal deltas, to the entire system covering the upper shoreface, the barrier islands and the back-barrier basins (large-scale)
Quantum isometries and noncommutative geometry
The space has no free analogue, but we can talk instead about
the free sphere , as the manifold defined by the
equations . We discuss here the structure and
hierarchy of the submanifolds , with particular
attention to the manifolds having an integration functional .Comment: 400 pages. arXiv admin note: text overlap with arXiv:1909.0815
Adhesion and cohesion properties of diamond-like-carbon coatings deposited on biomaterials by saddle field neutral fast atom beam source: measurement and modelling
Diamond-like-carbon (DLC) has been shown to be strategically important in respect to biomedical applications due to its biocompatibility. Despite decades of work on film deposition there is an insufficient understanding in respect of the filmâs adhesion characteristics, particularly on biomaterial substrates. The central aim of this study is two pronged. A programme of work has been undertaken to set-up, study, understand and optimise the production technique for DLC deposition, while on the other hand diamond like carbon films have been characterised to investigate the strength of adhesion and cohesive strength with particular reference to biomedical applications.
DLC films have been deposited on to substrates of 316L stainless steel, cobalt chrome (CoCr) and Ti6AI4V alloy using a saddle field neutral beam deposition system (Microvac 1200DB, Ion Tech Ltd) with acetylene and acetyleneargon mixture as the process gas. It is noted that numerous parameters influence coating adhesion including the stress in the film, contamination and chemical bonding between the film and the substrate, and the physical properties and roughness of the substrate. Discharge current vs. discharge voltage characteristics were investigated with different pressure and process gas. Uv absorption spectra were used to measure the photon energy and optical band gap of the films. The optical band gap was found in the range of -0.85 and 0.85 -0.97 eV for lower and higher deposition current respectively. The adhesion of the films has been measured as a function of the duration of in-situ etching by a neutral argon beam and also as a function of source current, system pressure and process gas (pure C2H2 and C2H2+Ar gas mixture). The studies were performed on DLC films with thickness -0 .4 |im. The adhesion of the film was measured using pull-off and Rockwell C tests whereas four point bend (FPB) test was used to measure the cohesive strength of the films. Argon pre etching for 15 minutes is recommended to guarantee an optimal adhesion. The etching process also influenced the film structure in terms of the sp3/sp2 ratio and stress. It was also found that this optimisation of the adhesion is correlated with a change in the structure and thickness of the native oxide layer on the steel surface of the substrates. Substrate surface temperature during etching and deposition also influenced film structure and adhesion. Correlation between the residual stress and the adhesion of the films has also been established which helped to identify optimum process parameters for substrate-film adhesion properties. No significant change with deposition pressure has been observed but high anode currents may lead to higher sp3 content. The adhesion strength has been found to be inversely proportional to residual stress and to increase at low deposition pressures. At source anode current of 0.6A, the adhesion is a monotonic function of pressure in the range examined where as with 1.0A source current the behaviour is more complex. The relationship between the stress and the sp3 content of the films measured by analysis of Raman signature has also been investigated.
The experimental work of FPB has been used to support and develop a numerical (Finite Element) model for the determination and prediction of the film's cohesive strength. The model takes into account the film hardness, Youngâs modulus and thickness and has been shown to be capable of predicting the filmâs cohesive strength when combined with a theoretical formulation for brittle fracture. It has been observed that maximum stress developed at the outer surface of film during the bend test, which influenced the initiation of cracks at the outer surface of the film and their propagation through the film-substrate interface. This result has only been valid for films with higher Young's modulus compared with the substrate
Influence of cavity flow on turbine aerodynamics
In order to deal with high temperatures faced by the components downstream
of the combustion chamber, some relatively cold air is bled at the compressor.
This air feeds the cavities under the turbine main annulus and cool down the rotor
disks ensuring a proper and safe operation of the turbine. This thesis manuscript
introduces a numerical study of the effect of the cavity flow close to the turbine
hub on its aerodynamic performance. The interaction phenomena between the cavity
and main annulus flow are not currently fully understood. The study of these
phenomena is performed based on different numerical approaches (RANS, LES and
LES-LBM) applied to two configurations for which experimental results are available.
A linear cascade configuration with an upstream cavity and various rim seal
geometries (interface between rotor and stator platform) and cavity flow rate available.
A rotating configuration that is a two stage turbine including cavities close
to realistic industrial configurations. Additional losses incurred by the cavity flow
are measured and studied using a method based on exergy (energy balance in the
purpose to generate work)