In this article, three new green's functions are presented for a narrow strip line (not a thin wire) inside or on a homogeneous dielectric, supposing quasi-TEM dominant mode. These functions have no singularity in contrast to so far presented ones, so that they can be used easily to determine the capacitance matrix of multi-layer and single-layer homogeneous coupled microstrip lines. To obtain ...

The escape of Brownian motion through a narrow absorbing window in an otherwise reflecting boundary of a domain is a rare event. In the presence of a deep potential well, there are two long time scales, the mean escape time from the well and the mean time to reach the absorbing window. We derive a generalized Kramers formula for the mean escape time through the narrow window.

We describe initial work on a system for augmenting video sequences with 3-D graphics so that they appear to be present within the scene. Our aim is to do this in realtime for sequences captured by uncalibrated ‘live’ cameras, such as a hand-held or wearable. The paper focuses on obtaining 3-D camera motion and depth estimates for these types of sequences using sparse feature tracking and the r...

Flexural wave speeds on beams or plates depend upon the bending stiffnesses which differ by the well-known factor (1 - nu2). A quantitative analysis of a plate of finite lateral width displays the plate-to-beam transition, and permits asymptotic analysis that shows the leading order dependence on the width. Orthotropic plates are analyzed using both the Kirchhoff and Kirchhoff-Rayleigh theories...

A Brownian particle with diffusion coefficientD is confined to a bounded domain of volume V in R by a reflecting boundary, except for a small absorbing window. The mean time to absorption diverges as the window shrinks, thus rendering the calculation of the mean escape time a singular perturbation problem. We construct an asymptotic approximation for the case of an elliptical window of large se...

A simple and general description of the dynamics of a narrow-eccentric ring is presented. We view an eccentric ring which precesses uniformly at a slow rate as exhibiting a global m = 1 mode, which can be seen as originating from a standing wave superposed on an axisymmetric background. We adopt a continuum description using the language of fluid dynamics which gives equivalent results for the ...