A new construction of homogeneous quaternionic manifolds and related geometric structures

Let V be the pseudo-Euclidean vector space of signature (p,q), p>2 and W a module over the even Clifford algebra Cl^0 (V). A homogeneous quaternionic manifold (M,Q) is constructed for any spin(V)-equivariant linear map \Pi : \wedge^2 W \to V. If the skew symmetric vector valued bilinear form \Pi is nondegenerate then (M,Q) is endowed with a canonical pseudo-Riemannian metric g such that (M,Q,g) is a homogeneous quaternionic pseudo-K\"ahler manifold. The construction is shown to have a natural mirror in the category of supermanifolds. In fact, for any spin(V)-equivariant linear map \Pi : Sym^2 W \to V a homogeneous quaternionic supermanifold (M,Q) is constructed and, moreover, a homogeneous quaternionic pseudo-K\"ahler supermanifold (M,Q,g) if the symmetric vector valued bilinear form \Pi is nondegenerate.Comment: to appear in the Memoirs of the AMS, 81 pages, Latex source fil

Special Kaehler manifolds: a survey

This is a survey of recent contributions to the area of special Kaehler geometry. It is based on lectures given at the 21st Winter School on Geometry and Physics held in Srni in January 2001

Abelian simply transitive affine groups of symplectic type

We construct a model space C(\gsp(\bR^{2n})) for the variety of Abelian simply transitive groups of affine transformations of type {\rm Sp}(\bR^{2n}). The model is stratified and its principal stratum is a Zariski-open subbundle of a natural vector bundle over the Grassmannian of Lagrangian subspaces in \bR^{2n}. \noindent Next we show that every flat special K\"ahler manifold may be constructed locally from a holomorphic function whose third derivatives satisfy some algebraic constraint. In particular global models for flat special K\"ahler manifolds with constant cubic form correspond to a subvariety of C(\gsp(\bR^{2n})).Comment: corrected typos, updated reference

Evaluating the Rheological and Tribological Behaviors of Coconut Oil Modified with Nanoparticles as Lubricant Additives

In metal-forming processes, the use of lubricants for providing desirable tribological conditions at the tool–workpiece interface is critical to increase the material formability and prolonging tool life. Nowadays, the depletion of crude oil reserves in the world and the global concern in protecting the environment from contamination have renewed interest in developing environmentally-friendly lubricants derived from alternative sources such as vegetable oils. In the present study, the rheological and tribological behavior of coconut oil modified with nanoparticle additives was experimentally evaluated. Two different nanoparticle additives were investigated: Silicon dioxide (SiO2) and copper oxide (CuO). For the two conditions, nanoparticles were dispersed at different concentrations within the coconut oil. The effects of concentration and shear rate on the viscosity were evaluated and the experimental data was compared with conventional models. A custom-made tribotester was used to evaluate the effect of concentration on the tribological performance of the nano-lubricants. The experimental results showed that wear volume loss was lowered by 37% and 33% using SiO2 and CuO nanoparticles, respectively. Furthermore, the addition of SiO2 and CuO nanoparticles decreased the coefficient of friction (COF) by 93.75% and 93.25%, respectively, as compared to coconut oil without nanoparticles

Development of Vegetable Oil Based Nano-lubricants

Nowadays, the depletion of crude oil reserves in the world and the global concern in protecting the environment from contamination have renewed interest in developing environment friendly lubricants derived from alternative sources such as vegetable oils. Mineral oil is the most common lubricant, however, it also has poor biodegradable properties. Vegetable oils exhibit good viscosity index, flash point, pour point, tribological properties, and are biodegradable. Furthermore, the use of nanoparticles as additives has shown to improve anti wear and anti-friction properties of the base lubricant. The present research project will evaluate experimentally the rheological and tribological behavior of coconut oil, sunflower oil, and grapeseed oil modified with nanoparticle additives. Three different nanoparticle additives are investigated: silicon dioxide (SiO2), copper oxide (CuO), and titanium dioxide (TiO2). For the three conditions, nanoparticles were dispersed at different concentrations within the vegetable oil. The effects of concentration and shear rate on the viscosity were evaluated and the experimental data was compared with conventional models. Wear scars were analyzed using SEM, EDS, and roughness to identify nanoparticle effect. From the experimental results, it was found that wear volume loss and coefficient of friction were lowered. The developed modified vegetable oil nano-lubricants show potential as possible replacements to conventional mineral oils

The Performance of SiO2 and TiO2 Nanoparticles as Lubricant Additives in Sunflower Oil

In recent years, there has been growing concern regarding the use of petroleum-based lubricants. This concern has generated interest in readily biodegradable fluids such as vegetable oils. The present work evaluated the rheological and tribological characteristics of sunflower oil modified with silicon dioxide (SiO2) and titanium dioxide (TiO2) nanoparticles as lubricant additives at different concentrations. A parallel plate rheometer was used to evaluate the eects of concentration and shear rate on the shear viscosity, and the experimental data was compared with conventional models. The wear protection and friction characteristics of the oil-formulations were evaluated by conducting block-on-ring sliding tests. Surface analysis-based instruments, including scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS), and profilometry, were used to characterize the morphology and structure of the worn surfaces. The experimental results showed that the coeffcient of friction decreased with the addition of SiO2 and TiO2 nanoparticles by 77.7% and 93.7%, respectively when compared to base sunflower oil. Furthermore, the volume loss was lowered by 74.1% and 70.1%, with the addition of SiO2 and TiO2 nanoparticles, respectively. Based on the experimental results, the authors conclude that modified sunflower oil enhanced with nanoparticles has the potential for use as a good biodegradable lubricant

Multidirectional Pin-on-Disk Testing Device to Evaluate the Cross-shear Effect on the Wear of Biocompatible Materials

One of the main causes of hip prostheses failure is the premature wear of their components. Multi-directional motion or “cross-shear” motion has been identified as one of the most significant factors affecting the wear rate of UHMWPE in total hip joint replacement prostheses. To better evaluate the effect of this cross-shear motion on the tribological behavior of different biomaterials, a new wear testing device has been designed and developed. This new instrument is capable to reproduce the “cross-shear” effect with bidirectional motion on bearing materials and to determine coefficient of friction (COF) between surfaces during testing. To validate the functionality of this new testing platform, alumina balls were articulated against Ti-6Al-4V ELI alloy disks in Ringer’s solution. Four different articulation patterns, all with identical path lengths per cycle, were tested. Gravimetric weight loss was converted to volumetric wear data in order to determine the effects of motion patterns on the wear. Worn surfaces were analyzed by scanning electron microscopy. This scientific approach to quantifying the tribological effects of cross-shear provides fundamental data that are crucial in evaluating potential biomaterials for use in knee and hip joint replacements

ASK/PSK-correspondence and the r-map

We formulate a correspondence between affine and projective special K\"ahler manifolds of the same dimension. As an application, we show that, under this correspondence, the affine special K\"ahler manifolds in the image of the rigid r-map are mapped to one-parameter deformations of projective special K\"ahler manifolds in the image of the supergravity r-map. The above one-parameter deformations are interpreted as perturbative $\alpha'$-corrections in heterotic and type-II string compactifications with $N=2$ supersymmetry. Also affine special K\"ahler manifolds with quadratic prepotential are mapped to one-parameter families of projective special K\"ahler manifolds with quadratic prepotential. We show that the completeness of the deformed supergravity r-map metric depends solely on the (well-understood) completeness of the undeformed metric and the sign of the deformation parameter.Comment: 30 page