Relative Geodesics in the Special Euclidean Group

We propose a notion of distance between two parametrized planar curves, called their discrepancy, and defined intuitively as the minimal amount of deformation needed to deform the source curve into the target curve. A precise definition of discrepancy is given as follows. A curve of transformations in the special Euclidean group SE(2) is said to be admissible if it maps the source curve to the target curve under the point-wise action of SE(2) on the plane. After endowing the group SE(2) with a left-invariant metric, we define a relative geodesic in SE(2) to be a critical point of the energy functional associated to the metric, over all admissible curves. The discrepancy is then defined as the value of the energy of the minimizing relative geodesic. In the first part of the paper, we derive a scalar ODE which is a necessary condition for a curve in SE(2) to be a relative geodesic, and we discuss some of the properties of the discrepancy. In the second part of the paper, we consider discrete curves, and by means of a variational principle, we derive a system of discrete equations for the relative geodesics. We finish with several examples

Geospatial Authentication

A software package that has been designed to allow authentication for determining if the rover(s) is/are within a set of boundaries or a specific area to access critical geospatial information by using GPS signal structures as a means to authenticate mobile devices into a network wirelessly and in real-time has been developed. The advantage lies in that the system only allows those with designated geospatial boundaries or areas into the server. The Geospatial Authentication software has two parts Server and Client. The server software is a virtual private network (VPN) developed in Linux operating system using Perl programming language. The server can be a stand-alone VPN server or can be combined with other applications and services. The client software is a GUI Windows CE software, or Mobile Graphical Software, that allows users to authenticate into a network. The purpose of the client software is to pass the needed satellite information to the server for authentication

Predicted and measured strain responses of isotropic panels to base excitation

The accuracy of classical linear theory for predicting acceleration and strain for cantilevered and Clamped-Free-Clamped-Free (C-F-C-F) panels excited through the base is studied. Aluminum, steel and titanium plates of various dimensions and thicknessess were vibration tested, using a broadband random signal applied through a shaker mounting fixture. The strains were measured at 9 locations on the cantilevered panels and at 5 locations on the C-F-C-F panels. Predictions were based on the Ritz method. The measured accelerations of the base were input to the analysis for the forcing function. Comparisons between predicted and measured strain acceleration spectra were within an average error of 20 percent for both the cantilevered and C-F-C-F panels

Prediction of forces and moments for hypersonic flight vehicle control effectors

This research project includes three distinct phases. For completeness, all three phases of the work are briefly described in this report. The goal was to develop methods of predicting flight control forces and moments for hypersonic vehicles which could be used in a preliminary design environment. The first phase included a preliminary assessment of subsonic/supersonic panel methods and hypersonic local flow inclination methods for such predictions. While these findings clearly indicated the usefulness of such methods for conceptual design activities, deficiencies exist in some areas. Thus, a second phase of research was conducted in which a better understanding was sought for the reasons behind the successes and failures of the methods considered, particularly for the cases at hypersonic Mach numbers. This second phase involved using computational fluid dynamics methods to examine the flow fields in detail. Through these detailed predictions, the deficiencies in the simple surface inclination methods were determined. In the third phase of this work, an improvement to the surface inclination methods was developed. This used a novel method for including viscous effects by modifying the geometry to include the viscous/shock layer

Method of identifying clusters representing statistical dependencies in multivariate data

Approach is first to cluster and then to compute spatial boundaries for resulting clusters. Next step is to compute, from set of Monte Carlo samples obtained from scrambled data, estimates of probabilities of obtaining at least as many points within boundaries as were actually observed in original data

Longitudinal elastic velocities in MgO to 360 kbar

Numerical descriptions of shock wave induced flows obtained with a two-dimensional Lagrangian finite difference code are compared in detail with experimental data obtained via the lateral relaxation method for polycrystalline magnesium oxide (MgO) to a pressure of 360 kbar. The equation of state used for MgO was assumed to be of the Mie-Grüneisen form, and detailed comparison of experimental and calculated data was used to obtain refined values of the shear strength and shear modulus of MgO at high pressures. The best fitting rheological model for MgO was characterized by a shear strength which decreased from a value of 26 kbar at 16.5-kbar mean stress to 13.5 kbar at 360-kbar mean stress along the principal Hugoniot curve. The first and second pressure derivatives of the shear modulus, when the shear modulus is evaluated as a quadratic function of pressure, yield (∂μ/∂P) = 2.44 and μ(∂^2μ/∂P^2) = 1.7±3.0. The uncertainties in the determination of μ(∂^2μ/∂P^2) have been reduced by a factor of 5 over previous estimates

Toughening of BIS maleimide resins: Synthesis and characterization of maleimide terminated poly(arylene ether) oligomers and polymers

Amine functional poly(arylene ether) sulfones were previously reported. Herein, the chemistry was extended to amorphous poly(arylene ether) ketones because of their higher fracture toughness values, relative to the polysulfones. It was demonstrated that the amino functional oligomers undergo a self-crosslinking reaction at temperatures above about 220 C. This produces an insoluble, but ductile network that has excellent resistance. A ketamine structure hypothesis was proposed and verified using solid state magic angle NMR. In most cases, the water generated upon ketamine formation is too low to produce porosity and solid networks are obtained. The stability of the ketamine networks towards hydrolysis is excellent. The chemistry was further demonstrated to be able to crosslink preformed nonfunctional poly(arylene ether) ketones if a difunctional amine was utilized. This concept has the possibility of greatly improving the creep resistance of thermoplastics. Also, a new technique was developed for converting the amine functional oligomers cleanly into maleimide structures. This method involves reacting maleic anhydride with monomeric aminophenols in the presence of solvent mixtures

Aerial Videography From Locally Launched Rockets

A method of quickly collecting digital imagery of ground areas from video cameras carried aboard locally launched rockets has been developed. The method can be used, for example, to record rare or episodic events or to gather image data to guide decisions regarding treatment of agricultural fields or fighting wildfires. The method involves acquisition and digitization of a video frame at a known time along with information on the position and orientation of the rocket and camera at that time. The position and orientation data are obtained by use of a Global Positioning System receiver and a digital magnetic compass carried aboard the rocket. These data are radioed to a ground station, where they are processed, by a real-time algorithm, into georeferenced position and orientation data. The algorithm also generates a file of transformation parameters that account for the variation of image magnification and distortion associated with the position and orientation of the camera relative to the ground scene depicted in the image. As the altitude, horizontal position, and orientation of the rocket change between image frames, the algorithm calculates the corresponding new georeferenced position and orientation data and the associated transformation parameters. The output imagery can be rendered in any of a variety of formats. The figure presents an example of one such format

Factors affecting sperm recovery rates and survival after centrifugation of equine semen

Conventional centrifugation protocols result in important sperm losses during removal of the supernatant. In this study, the effect of centrifugation force (400 or 900 × g), duration (5 or 10 min), and column height (20 or 40 mL; Experiment 1); sperm concentration (25, 50, and 100 × 10[superscript 6]/mL; Experiment 2), and centrifugation medium (EZ-Mixin CST [Animal Reproduction Systems, Chino, CA, USA], INRA96 [IMV Technologies, Maple Grove, MN, USA], or VMDZ [Partnar Animal Health, Port Huron, MI, USA]; Experiment 3) on sperm recovery and survival after centrifugation and cooling and storage were evaluated. Overall, sperm survival was not affected by the combination of centrifugation protocol and cooling. Total sperm yield was highest after centrifugation for 10 min at 400 × g in 20-mL columns (95.6 ± 5%, mean ± SD) or 900 × g in 20-mL (99.2 ± 0.8%) or 40-mL (91.4 ± 4.5%) columns, and at 900 × g for 5 min in 20-mL columns (93.8 ± 8.9%; P < 0.0001). Total (TMY) and progressively motile sperm yield followed a similar pattern (P < 0.0001). Sperm yields were not significantly different among samples centrifuged at various sperm concentrations. However, centrifugation at 100 × 10[superscript 6]/mL resulted in significantly lower total sperm yield (83.8 ± 10.7%) and TMY (81.7 ± 6.8%) compared with noncentrifuged semen. Centrifugation in VMDZ resulted in significantly lower TMY (69.3 ± 22.6%), progressively motile sperm yield (63.5 ± 18.2%), viable yield (60.9 ± 36.5%), and survival of progressively motile sperm after cooling (21 ± 10.8%) compared with noncentrifuged semen. In conclusion, centrifuging volumes of ≤ 20 mL minimized sperm losses with conventional protocols. With 40-mL columns, it may be recommended to increase the centrifugal force to 900 × g for 10 min and dilute the semen to a sperm concentration of 25 to 50 × 10[superscript 6]/mL in a milk- or fractionated milk-based medium. The semen extender VMDZ did not seem well suited for centrifugation of equine semen