The geometry of unstented and stented pig common carotid artery bypass grafts

The long-term success of arterial bypass grafting with autologous saphenous veins is limited by neointimal hyperplasia (NIH), which seemingly develops preferentially at sites where hydrodynamic wall shear is low. Placement of a loose-fitting, porous stent around end-to-end, or end-to-side, autologous saphenous vein grafts on the porcine common carotid artery has been found significantly to reduce NIH, but the mechanism is unclear. In a preliminary study, we implanted autologous saphenous vein grafts bilaterally on the common carotid arteries of pigs, placing a stent around one graft and leaving the contralateral graft unstented. At sacrifice 1 month post implantation, the grafts were pressure fixed in situ and resin casts were made. Unstented graft geometry was highly irregular, with non-uniform dilatation, substantial axial lengthening, curvature, kinking, and possible long-pitch helical distortion. In contrast, stented grafts showed no major dilatation, lengthening or curvature, but there was commonly fine corrugation, occasional slight kinking or narrowing of segments, and possible long-pitch helical distortion. Axial growth of grafts against effectively tethered anastomoses could account for these changes. CFD studies are planned, using 3D MR reconstructions, on the effects of graft geometry on the flow. Abnormality of the flow could favour the development of vascular pathology, including NIH.

Implementation of a non-orthogonal model for the finite element simulation of textile composite draping

In the pursuit of producing high quality, low-cost composite aircraft structures, out-of-autoclave manufacturing processes for textile reinforcements are being simulated with increasing accuracy. This paper focuses on the continuum-based, finite element modelling of textile composites as they deform during the draping process. A non-orthogonal constitutive model tracks yarn orientations within a material subroutine developed for Abaqus/Explicit, resulting in the realistic determination of fabric shearing and material draw-in. Supplementary material characterisation was experimentally performed in order to define the tensile and non-linear shear behaviour accurately. The validity of the finite element model has been studied through comparison with similar research in the field and the experimental lay-up of carbon fibre textile reinforcement over a tool with double curvature geometry, showing good agreement.

A Numerical Study of Inlet Geometry for a Low Inertia Mixed Flow Turbocharger Turbine

Mixed flow turbines can offer improvements over typical radial turbines used in automotive turbochargers, with regards to transient performance and low velocity ratio efficiency. Turbine rotor mass dominates the rotating inertia of the turbocharger, and any reductions of mass in the outer radii of the wheel, including the rotor back-disk, can significantly reduce this inertia and improve the acceleration of the assembly. Off-design, low velocity ratio conditions are typified by highly tangential flow at the rotor inlet and a non-zero inlet blade angle is preferred for such operating conditions. This is achievable in a Mixed Flow Turbine without increasing bending stresses within the rotor blade, which is beneficial in high speed and high inlet temperature turbine design. A range of mixed flow turbine rotors was designed with varying cone angle and inlet blade angle and each was assessed at a number of operating points. These rotors were based on an existing radial flow turbine, and both the hub and shroud contours and exducer geometry were maintained. The inertia of each rotor was also considered. The results indicated that there was a trade-off between efficiency and inertia for the rotors and certain designs may be beneficial for the transient performance of downsized, turbocharged engines.

A numerical study of trailing edge geometry for low inertia automotive mixed flow turbines

Abstract. Mixed flow turbines can offer improvements over typical radial turbines used in automotive turbochargers, with respect to transient performance and low velocity ratio efficiency. Turbine rotor mass dominates the rotating inertia of the turbocharger’s rotating assembly, and any reductions of mass in the outer radii of the wheel, including the rotor back-disk, can significantly reduce this inertia and improve the acceleration of the assembly. Off-design, low velocity ratio conditions are typified by highly tangential flow at the rotor inlet and a non-zero inlet blade angle is desirable for such operating conditions. This is achievable in a Mixed Flow Turbine without increasing bending stresses within the rotor blade, which is beneficial in high speed and high inlet temperature turbine designs.
This study considers the meridional geometry of Mixed Flow Turbines using a multi-disciplinary study to assess both the structural and aerodynamic performance of each rotor, incorporating both CFD and FEA. Variations of rotor trailing edge were investigated at different operating conditions representing both on- and off-design operation within the constraints of existing hardware geometries. In all cases, the performance is benchmarked against an existing state-of-the-art radial turbocharger turbine with consideration of rotor inertia and its benefit for engine transient performance. The results indicate the influence of these parameters and this report details their benefits with respect to turbocharging a downsized, automotive engine.

Measurement of fibre fracture toughness using an alternative specimen geometry

This paper presents an experimental and numerical study focused on the tensile fibre fracture toughness characterisation of hybrid plain weave composite laminates using non-standardized Overheight Compact Tension (OCT) specimens. The position as well as the strain field ahead of the crack tip in the specimens was determined using a digital speckle photogrammetry system. The limitation on the applicability of standard data reduction schemes for the determination of the intralaminar fibre fracture toughness of composites is presented and discussed. A methodology based on the numerical evaluation of the strain energy release rate using the J-integral method is proposed to derive new geometric correction functions for the determination of stress intensity factor for alternative composite specimen geometries. A comparison between different methods currently available to compute the intralaminar fracture toughness in composites is also presented and discussed. Good agreement between numerical and experimental results using the proposed methodology was obtained.

First-principles electronic theory of non-collinear magnetic order in transition-metal nanowires

The structural, electronic and magnetic properties of one-dimensional 3d transition-metal (TM) monoatomic chains having linear, zigzag and ladder geometries are investigated in the frame-work of first-principles density-functional theory. The stability of long-range magnetic order along the nanowires is determined by computing the corresponding frozen-magnon dispersion relations as a function of the 'spin-wave' vector q. First, we show that the ground-state magnetic orders of V, Mn and Fe linear chains at the equilibrium interatomic distances are non-collinear (NC) spin-density waves (SDWs) with characteristic equilibrium wave vectors q that depend on the composition and interatomic distance. The electronic and magnetic properties of these novel spin-spiral structures are discussed from a local perspective by analyzing the spin-polarized electronic densities of states, the local magnetic moments and the spin-density distributions for representative values q. Second, we investigate the stability of NC spin arrangements in Fe zigzag chains and ladders. We find that the non-collinear SDWs are remarkably stable in the biatomic chains (square ladder), whereas ferromagnetic order (q =0) dominates in zigzag chains (triangular ladders). The different magnetic structures are interpreted in terms of the corresponding effective exchange interactions J(ij) between the local magnetic moments μ(i) and μ(j) at atoms i and j. The effective couplings are derived by fitting a classical Heisenberg model to the ab initio magnon dispersion relations. In addition they are analyzed in the framework of general magnetic phase diagrams having arbitrary first, second, and third nearest-neighbor (NN) interactions J(ij). The effect of external electric fields (EFs) on the stability of NC magnetic order has been quantified for representative monoatomic free-standing and deposited chains. We find that an external EF, which is applied perpendicular to the chains, favors non-collinear order in V chains, whereas it stabilizes the ferromagnetic (FM) order in Fe chains. Moreover, our calculations reveal a change in the magnetic order of V chains deposited on the Cu(110) surface in the presence of external EFs. In this case the NC spiral order, which was unstable in the absence of EF, becomes the most favorable one when perpendicular fields of the order of 0.1 V/Å are applied. As a final application of the theory we study the magnetic interactions within monoatomic TM chains deposited on graphene sheets. One observes that even weak chain substrate hybridizations can modify the magnetic order. Mn and Fe chains show incommensurable NC spin configurations. Remarkably, V chains show a transition from a spiral magnetic order in the freestanding geometry to FM order when they are deposited on a graphene sheet. Some TM-terminated zigzag graphene-nanoribbons, for example V and Fe terminated nanoribbons, also show NC spin configurations. Finally, the magnetic anisotropy energies (MAEs) of TM chains on graphene are investigated. It is shown that Co and Fe chains exhibit significant MAEs and orbital magnetic moments with in-plane easy magnetization axis. The remarkable changes in the magnetic properties of chains on graphene are correlated to charge transfers from the TMs to NN carbon atoms. Goals and limitations of this study and the resulting perspectives of future investigations are discussed.

A numerical scheme for two-dimensional, open channel flows with non-rectangular geometries

An algorithm based on flux difference splitting is presented for the solution of two-dimensional, open channel flows. A transformation maps a non-rectangular, physical domain into a rectangular one. The governing equations are then the shallow water equations, including terms of slope and friction, in a generalized coordinate system. A regular mesh on a rectangular computational domain can then be employed. The resulting scheme has good jump capturing properties and the advantage of using boundary/body-fitted meshes. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

Adsorption and dissociation of benzene on bimetallic surfaces - the influence of surface geometry and electronic structure

This topical review discusses the influence of the surface geometry (e.g. lattice parameters and termination) and electronic structure of well-defined bimetallic surfaces on the adsorption and dissociation of benzene. The available data can be divided into two categories with combinations of non-transition metals and transition metals on the one side and combinations of two transition metals on the other. The main effect of non-transition metals in surface alloys is site blocking which can suppress chemisorption and dissociation of the molecules completely. When two transition metals are combined, the effects are less dramatic. They mainly affect the strength of the chemisorption bond and the degree of dissociation due to electronic and template effects.

The surface geometry of carbon monoxide and oxygen co-adsorbed on Ni{111}

Low energy electron diffraction (LEED) structure determinations have been performed for the p(2 x 2) structures of pure oxygen and oxygen co-adsorbed with CO on Ni{111}. Optimisation of the non-geometric parameters led to very good agreement between experimental and theoretical IV-curves and hence to a high accuracy in the structural parameters. In agreement with earlier work atomic oxygen is found to adsorb on fee sites in both structures. In the co-adsorbed phase CO occupies atop sites. The positions of the substrate atoms are almost identical, within 0.02 Angstrom, in both structures, implying that the interaction with oxygen dominates the arrangement of Ni atoms at the surface.

Pseudoclassical description of scalar particle in non-abelian background and path-integral representations

Path-integral representations for a scalar particle propagator in non-Abelian external backgrounds are derived. To this aim, we generalize the procedure proposed by Gitman and Schvartsman of path-integral construction to any representation of SU(N) given in terms of antisymmetric generators. And for arbitrary representations of SU(N), we present an alternative construction by means of fermionic coherent states. From the path-integral representations we derive pseudoclassical actions for a scalar particle placed in non-Abelian backgrounds. These actions are classically analyzed and then quantized to prove their consistency.

An algorithm for automatic checking of exercises in a dynamic geometry system: iGeom

One of the key issues in e-learning environments is the possibility of creating and evaluating exercises. However, the lack of tools supporting the authoring and automatic checking of exercises for specifics topics (e.g., geometry) drastically reduces advantages in the use of e-learning environments on a larger scale, as usually happens in Brazil. This paper describes an algorithm, and a tool based on it, designed for the authoring and automatic checking of geometry exercises. The algorithm dynamically compares the distances between the geometric objects of the student`s solution and the template`s solution, provided by the author of the exercise. Each solution is a geometric construction which is considered a function receiving geometric objects (input) and returning other geometric objects (output). Thus, for a given problem, if we know one function (construction) that solves the problem, we can compare it to any other function to check whether they are equivalent or not. Two functions are equivalent if, and only if, they have the same output when the same input is applied. If the student`s solution is equivalent to the template`s solution, then we consider the student`s solution as a correct solution. Our software utility provides both authoring and checking tools to work directly on the Internet, together with learning management systems. These tools are implemented using the dynamic geometry software, iGeom, which has been used in a geometry course since 2004 and has a successful track record in the classroom. Empowered with these new features, iGeom simplifies teachers` tasks, solves non-trivial problems in student solutions and helps to increase student motivation by providing feedback in real time. (c) 2008 Elsevier Ltd. All rights reserved.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

COMMUTATIVE FINITE-DIMENSIONAL ALGEBRAS SATISFYING x(x(xy))=0 ARE NILPOTENT

We investigate the structure of commutative non-associative algebras satisfying the identity x(x(xy)) = 0. Recently, Correa and Hentzel proved that every commutative algebra satisfying above identity over a field of characteristic not equal 2 is solvable. We prove that every commutative finite-dimensional algebra u over a field F of characteristic not equal 2, 3 which satisfies the identity x(x(xy)) = 0 is nilpotent. Furthermore, we obtain new identities and properties for this class of algebras.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

Studies in non-Gaussian analysis

This thesis presents general methods in non-Gaussian analysis in infinite dimensional spaces. As main applications we study Poisson and compound Poisson spaces. Given a probability measure μ on a co-nuclear space, we develop an abstract theory based on the generalized Appell systems which are bi-orthogonal. We study its properties as well as the generated Gelfand triples. As an example we consider the important case of Poisson measures. The product and Wick calculus are developed on this context. We provide formulas for the change of the generalized Appell system under a transformation of the measure. The L² structure for the Poisson measure, compound Poisson and Gamma measures are elaborated. We exhibit the chaos decomposition using the Fock isomorphism. We obtain the representation of the creation, annihilation operators. We construct two types of differential geometry on the configuration space over a differentiable manifold. These two geometries are related through the Dirichlet forms for Poisson measures as well as for its perturbations. Finally, we construct the internal geometry on the compound configurations space. In particular, the intrinsic gradient, the divergence and the Laplace-Beltrami operator. As a result, we may define the Dirichlet forms which are associated to a diffusion process. Consequently, we obtain the representation of the Lie algebra of vector fields with compact support. All these results extends directly for the marked Poisson spaces.