On the parallel lines for nondegenerate conics

Computation of parallel lines (envelopes) to parabolas, ellipses, and hyperbolas is of importance in structure engineering and theory of mechanisms. Homogeneous polynomials that implicitly define parallel lines for the given offset to a conic are found by computing Groebner bases for an elimination ideal of a suitably defined affine variety. Singularity of the lines is discussed and their singular points are explicitly found as functions of the offset and the parameters of the conic. Critical values of the offset are linked to the maximum curvature of each conic. Application to a finite element analysis is shown. Keywords: Affine variety, elimination ideal, Groebner basis, homogeneous polynomial, singularity, family of curves, envelope, pitch curve, undercutting, cam surfaceComment: 40 pages, 10 figures, TOC, 3 appendices, short version of this paper was presented at the 5th Annual Hawaii International Conference on Statistics, Mathematics and Related Fields, January 16 - 18, 2006, Honolulu Hawaii, US

Detecting and recognizing centerlines as parabolic sections of the steerable filter response

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The Relation Between Offset and Conchoid Constructions

The one-sided offset surface Fd of a given surface F is, roughly speaking, obtained by shifting the tangent planes of F in direction of its oriented normal vector. The conchoid surface Gd of a given surface G is roughly speaking obtained by increasing the distance of G to a fixed reference point O by d. Whereas the offset operation is well known and implemented in most CAD-software systems, the conchoid operation is less known, although already mentioned by the ancient Greeks, and recently studied by some authors. These two operations are algebraic and create new objects from given input objects. There is a surprisingly simple relation between the offset and the conchoid operation. As derived there exists a rational bijective quadratic map which transforms a given surface F and its offset surfaces Fd to a surface G and its conchoidal surface Gd, and vice versa. Geometric properties of this map are studied and illustrated at hand of some complete examples. Furthermore rational universal parameterizations for offsets and conchoid surfaces are provided

Development of a new Thomson parabola spectrometer for analysis of laser accelerated ions

This thesis details my work on developing a new Thomson parabola spectrometer for use at the SCARLET Laser Facility at The Ohio State University. The SCARLET laser facility is a 300 TW laser reaching peak intensities exceeding 10 21 W/cm 2 . The laser is used to study laser-matter interactions and plasma phenomena. The laser-matter interactions accelerate multiple types of particles and to understand the interactions it is necessary to have diagnostic tools to characterize the accelerated particles. In order to measure the charged particles a common device is a Thomson parabola spectrometer. A Thomson parabola spectrometer uses parallel electric and magnetic fields that are perpendicular to the incoming particles. This causes deflection of the particles based on their charge-to-mass ratio and energy. Therefore, the Thomson parabola spectrometer allows us to determine what particles are present and what their energy range is. I designed a new spectrometer to replace the existing Thomson parabola spectrometer which had problems during operation that reduced performance. Using a MATLAB code, I first modeled the performance of the new design to determine physical dimensions and field strengths that would allow for 1 MeV resolution of protons up to a maximum energy of 40 MeV. This resulted in a 5 cm long magnetic field with a field strength of 0.12 T and 10 cm electrodes with a voltage difference of 6 kV. These physical dimensions were used to create a SolidWorks model. As of this writing, the newly designed Thomson parabola spectrometer has been built and is currently being installed for use on future experiments.No embargoAcademic Major: Engineering Physic

Beam squint and Stokes V with off-axis feeds

Radio telescopes with off-axis feeds, such as the (E)VLA, suffer from "beam squint" in which the two orthogonal circular polarizations sampled have different pointing centers on the sky. Its effects are weak near the beam center but become increasingly important towards the edge of the antenna power pattern where gains in the two polarizations at a given sky position are significantly different. This effect has limited VLA measurements of circular polarization (Stokes V) and introduced dynamic range limiting, wide-field artifacts in images made in Stokes I. We present an adaptation of the visibility-based deconvolution CLEAN method that can correct this defect "on the fly" while imaging, correcting as well the associated self-calibration. We present two examples of this technique using the procedure "Squint" within the Obit package which allows wide-field imaging in Stokes V and reduced artifacts in Stokes I. We discuss the residual errors in these examples as well as a scheme for future correction of some of these errors. This technique can be generalized to implement temporally- and spatially-variable corrections, such as pointing and cross-polarization leakage errors.Comment: 9 pages, 6 figures (five of them double), to appear in Astronomy & Astrophysics (accepted: May 9, 2008). High-resolution versions of the figures (gzipped, tar,gzipped) can be downloaded from http://www.cv.nrao.edu/~juson/technical/squint/squint_figures.g