A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics

This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical phenomenon, collected temperature data along the rod, then referenced the demonstration for purposes in and out of the classroom. Here, we discuss the experimental setup, how the demonstration informed practices in the classroom and a project based on the collected data, including analytical and computational components

Mode-matching analysis of a shielded rectangular dielectric-rod waveguide

Rectangular cross-section dielectric waveguides are widely used at millimeter wavelengths. In addition, shielded dielectric resonators having a square cross-section are often used as filter elements, however there is almost no information available on the effect of the shield. Rectangular or square dielectric waveguide is notoriously difficult to analyze, because of the singular behaviour of the fields at the corners. Most published analyses are for materials with a low dielectric constant, and do not include the effects of a shield. This paper describes a numerically efficient mode matching method for the analysis of shielded dielectric rod waveguide, which is applicable to both low and high dielectric constant materials. The effect of the shield on the propagation behaviour is studied. The shield dimensions may be selected such that the shield has a negligible effect, so that results can be compared with free space data. The results are verified by comparison with several sets of published data, and have been confirmed by measurement for a nominal 'e' r of 37.4

Kernel-based high-dimensional histogram estimation for visual tracking

©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.Presented at the 15th IEEE International Conference on Image Processing, October 12–15, 2008, San Diego, California, U.S.A.DOI: 10.1109/ICIP.2008.4711862We propose an approach for non-rigid tracking that represents objects by their set of distribution parameters. Compared to joint histogram representations, a set of parameters such as mixed moments provides a significantly reduced size representation. The discriminating power is comparable to that of the corresponding full high dimensional histogram yet at far less spatial and computational complexity. The proposed method is robust in the presence of noise and illumination changes, and provides a natural extension to the use of mixture models. Experiments demonstrate that the proposed method outperforms both full color mean-shift and global covariance searches

A new perspective on metformin therapy in type 1 diabetes

Metformin is quite frequently used off-label in type 1 diabetes to limit insulin dose requirement. Guidelines recommend that it can improve glucose control in those who are overweight and obese but evidence in support of this is limited. Recently-published findings from the REducing with MetfOrmin Vascular Adverse Lesions (REMOVAL) trial suggest that metformin therapy in type 1 diabetes can reduce atherosclerosis progression, weight and LDL-cholesterol levels. This provides a new perspective on metformin therapy in type 1 diabetes and suggests a potential role for reducing the long-term risk of cardiovascular disease