ABCD matrix for reflection and refraction of Gaussian beams at the surface of a parabola of revolution

We report the formulation of an ABCD matrix for reflection and refraction of Gaussian light beams at the surface of a parabola of revolution that separate media of different refractive indices based on optical phase matching. The equations for the spot sizes and wave-front radii of the beams are also obtained by using the ABCD matrix. With these matrices, we can more conveniently design and evaluate some special optical systems, including these kinds of elements. (c) 2005 Optical Society of America

Energy inequalities and error estimates for axisymmetric torsion of thin elastic shells of revolution

The problem motivating this investigation is that of pure axisymmetric torsion of an elastic shell of revolution. The analysis is carried out within the framework of the three-dimensional linear theory of elastic equilibrium for homogeneous, isotropic solids. The objective is the rigorous estimation of errors involved in the use of approximations based on thin shell theory.

The underlying boundary value problem is one of Neumann type for a second order elliptic operator. A systematic procedure for constructing pointwise estimates for the solution and its first derivatives is given for a general class of second-order elliptic boundary-value problems which includes the torsion problem as a special case.

The method used here rests on the construction of “energy inequalities” and on the subsequent deduction of pointwise estimates from the energy inequalities. This method removes certain drawbacks characteristic of pointwise estimates derived in some investigations of related areas.

Special interest is directed towards thin shells of constant thickness. The method enables us to estimate the error involved in a stress analysis in which the exact solution is replaced by an approximate one, and thus provides us with a means of assessing the quality of approximate solutions for axisymmetric torsion of thin shells.

Finally, the results of the present study are applied to the stress analysis of a circular cylindrical shell, and the quality of stress estimates derived here and those from a previous related publication are discussed.

Reconstruction of surfaces of revolution from single uncalibrated views

This paper addresses the problem of recovering the 3D shape of a surface of revolution from a single uncalibrated perspective view. The algorithm introduced here makes use of the invariant properties of a surface of revolution and its silhouette to locate the image of the revolution axis, and to calibrate the focal length of the camera. The image is then normalized and rectified such that the resulting silhouette exhibits bilateral symmetry. Such a rectification leads to a simpler differential analysis of the silhouette, and yields a simple equation for depth recovery. It is shown that under a general camera configuration, there will be a 2-parameter family of solutions for the reconstruction. The first parameter corresponds to an unknown scale, whereas the second one corresponds to an unknown attitude of the object. By identifying the image of a latitude circle, the ambiguity due to the unknown attitude can be resolved. Experimental results on real images are presented, which demonstrate the quality of the reconstruction. © 2004 Elsevier B.V. All rights reserved.

Ageing, Adaption and Accessibility: Time for the Inclusive Revolution!

Information and Communication Technology (ICT) is becoming increasingly central to many people’s lives, making it possible to be connected in any place at any time, be unceasingly and instantly informed, and benefit from greater economic and educational opportunities. With all the benefits afforded by these new-found capabilities, however, come potential drawbacks. A plethora of new PCs, laptops, tablets, smartphones, Bluetooth, the internet, Wi-Fi (the list goes on) expect us to know or be able to guess, what, where and when to connect, click, double-click, tap, flick, scroll, in order to realise these benefits, and to have the physical and cognitive capability to do all these things. One of the groups most affected by this increase in high-demand technology is older people. They do not understand and use technology in the same way that younger generations do, because they grew up in the simpler electro-mechanical era and embedded that particular model of the world in their minds. Any consequential difficulty in familiarising themselves with modern ICT and effectively applying it to their needs can also be exacerbated by age-related changes in vision, motor control and cognitive functioning. Such challenges lead to digital exclusion. Much has been written about this topic over the years, usually by academics from the area of inclusive product design. The issue is complex and it is fair to say that no one researcher has the whole picture. It is difficult to understand and adequately address the issue of digital exclusion among the older generation without looking across disciplines and at industry’s and government’s understanding, motivation and efforts toward resolving this important problem. To do otherwise is to risk misunderstanding the true impact that ICT has and could have on people’s lives across all generations. In this European year of Active Ageing and Solidarity between Generations and as the British government is moving forward with its Digital by Default initiative as part of a wider objective to make ICT accessible to as many people as possible by 2015, the Engineering Design Centre (EDC) at the University of Cambridge collaborated with BT to produce a book of thought pieces to address, and where appropriate redress, these important and long-standing issues. “Ageing, Adaption and Accessibility: Time for the Inclusive Revolution!” brings together opinions and insights from twenty one prominent thought leaders from government, industry and academia regarding the problems, opportunities and strategies for combating digital exclusion among senior citizens. The contributing experts were selected as individuals, rather than representatives of organisations, to provide the broadest possible range of perspectives. They are renowned in their respective fields and their opinions are formed not only from their own work, but also from the contributions of others in their area. Their views were elicited through conversations conducted by the editors of this book who then drafted the thought pieces to be edited and approved by the experts. We hope that this unique collection of thought pieces will give you a broader perspective on ageing, people’s adaption to the ever changing world of technology and insights into better ways of designing digital devices and services for the older population.

Family, Kinship and Revolution: The Russian Nobility, 1917-1923

Rendle, M. (2005). Family, Kinship and Revolution: The Russian Nobility, 1917-1923. Family and Community History. 8(1), pp.35-47. RAE2008