Sequential dual sided SPIF using low order geometry reconstruction

Harmonic decomposition is an analytical technique that is able to express a manifold surface as the sum of a number of simple surface harmonic components. By reconstructing the initial geometry using a reduced number of components, a similar surface is obtained with a lower level of geometric detail. Because small features are filtered out and the resulting surface lies equal parts above and below the original surface, a tailored multi-step SPIF (Single Point Incremental Forming) processing strategy can be devised. This sequential SPIF strategy uses three processing passes to form a workpiece. The first step is a regular SPIF operation using a conventional toolpath strategy to form the reduced geometry. Two finishing steps are then needed, one from the same side to form the smaller features that lies deeper than the reduced geometry and one backwards pass from the other side of the sheet. To add features that need to be shallower than the reduced geometry, the part is flipped around. The used sequence of these finishing steps and the toolpath strategy used significantly influence the final part accuracy and surface quality. The advantages and disadvantages of four of these combined strategies are examined and compared to regular SPIF.

Diatonic Illusions and Chromatic Waterwheels

In a 1915 article for the Westminster Gazette, Edward Elgar described chromatic major-third cycles as waterwheels, which are adjuncts to a house. If this metaphor is read tonally, then the ‘house’ in question might be thought of as a tonic. Chromaticism – the ‘waterwheel’ – serves to power this tonic, in much the same way that actual waterwheels power mechanical processes in the buildings to which they are affixed. Contrary to modern neo-Riemannian theories, then, which stress the origin of chromatic progressions in ‘non-tonal’ syntaxes, I argue that Elgar experienced tertiary chromaticism as being tonally grounded. The ‘Romance’ from Elgar’s Violin Sonata, Op. 82, might be taken as a practical elucidation of this waterwheel theory if the same qualities ascribed by Elgar to foreground chromatic-third cycles are projected onto background structures too (i.e. progressions which present surface harmonic content in massive rhythmic augmentation). However, the Romance’s structural chromaticism only becomes apparent when it is demonstrated that the movement’s background is sometimes dissimulated by diatonic foreground illusions. The ‘house’ Elgar’s ‘waterwheel’ powers, then, cannot be assumed to be a particular diatonic collection. In this case, it is a single chord, which can be set off as a tonal centre in a number of ways, both diatonic and chromatic.

Fast Simulation of Lipid Vesicle Deformation Using Spherical Harmonic Approximation

Lipid vesicles appear ubiquitously in biological systems. Understanding how the mechanical and intermolecular interactions deform vesicle membranes is a fundamental question in biophysics. In this article we develop a fast algorithm to compute the surface configurations of lipid vesicles by introducing surface harmonic functions to approximate themembrane surface. This parameterization allows an analytical computation of the membrane curvature energy and its gradient for the efficient minimization of the curvature energy using a nonlinear conjugate gradient method. Our approach drastically reduces the degrees of freedom for approximating the membrane surfaces compared to the previously developed finite element and finite difference methods. Vesicle deformations with a reduced volume larger than 0.65 can be well approximated by using as small as 49 surface harmonic functions. The method thus has a great potential to reduce the computational expense of tracking multiple vesicles which deform for their interaction with external fields.