A four-dimensional Walker geometry is a four-dimensional manifold M with a neutral metric g and a parallel distribution of totally null two-planes. This distribution has a natural characterization as a projective spinor field subject to a certain constraint. Spinors therefore provide a natural tool for studying Walker geometry, which we exploit to draw together several themes in recent explicit...

Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group operation is a one-to-one map acting on the manifold, whereas a point-group operation is a linear map acting between two tangent spaces of the...

Geometry is an important part of mathematics. Described is a Scalable Vector Graphics (SVG) based system for teaching and learning geometry and mathematics. The work is part of the WME project for enhancing mathematics education using Web technologies. An SVG library for diagramming and interactive geometry learning is created. Building on this library, a Web-based authoring tool GeoSVG that ma...

In this work, a comparative study on different drill point geometries and feed rate for composite laminates drilling is presented. For this goal, thrust force monitoring during drilling, hole wall roughness measurement and delamination extension assessment after drilling is accomplished. Delamination is evaluated using enhanced radiography combined with a dedicated computational platform that i...

The cost of tooling in sheet metal industries contributes a considerable part to the overall cost of manufacturing a component. It is therefore imperative to keep down this cost by ensuring that the tool works for a long period in production without interruption. One way of achieving this objective is to reduce the stress on the tool during punching/blanking. This paper deals with the study of ...

This work proposes a process planning for machining of a Floor which is the most prominent elemental machining feature in a 21⁄2D pocket. Traditionally, the process planning of 21⁄2D pocket machining is posed as stand-alone problem involving either tool selection, tool path generation or machining parameter selection, resulting in sub-optimal plans. For this reason, the tool path generation and...

Abstract Machining abrasive carbon fibre reinforced polymers (CFRP) is characterised by extensive mechanical wear. In consequence, the cutting edge micro-geometry and thus tool/material contact situation are continuously changing, which affects process forces machining quality. As a conclusion, fundamental understanding of tool wear behaviour its influencing factors crucial in order to improve ...

1. Introduction Many natural structures cannot be described by conventional methods, because they are complex and irregular. Relatively a new approach is the application of fractal geometry [1]–[3]. This geometry is successfully used in science, but an application in industry is sporadic and experimental only. However, the fractal geometry can be used as a useful tool for an explicit, objective...