Numerical solution of two dimensional harmonic boundary problems containing singularities by conformal transformation methods

Numerical solutions to a class of two dimensional harmonic mixed boundary value problems defined on rectangular domains and containing singularities are obtained using conformal transformation methods. These map the original problems into similar ones containing no singularities, and to which analytic solutions are known. Although the mapping technique produces analytic solutions to the original problems, these involve elliptic functions and integrals which have to be evaluated numerically, so that in practice only approximations can be obtained. Results calculated in this manner for model problems compare favourably with those obtained previously by other methods. On this evidence, and because of the ease with which the method can be adapted to different individual problems, we strongly recommend the transformation technique for solving problems of this class. W

Cubic spline interpolation of harmonic functions

It is shown that for the two dimensional Laplace equation a univariate cubic spline approximation in either space direction together with a difference approximation in the other leads to the well-known nine-point finite-difference formula. For harmonic problems defined in rectangular regions this property provides a means of determining with ease accurate approximations at any point in the region

A cubic spline technique for the one dimensional heat conduction equation

A new method is developed for the numerical solution of the heat conduction equation in one space dimension by replacing the space derivative with a cubic spline approximation and the time derivative with a finite- difference approximation. The method is equivalent to a new finite-difference scheme and produces at each time level an interpolating spline function

Business Strategies for Transitions towards Sustainable Systems

This paper develops a strategic perspective for business to address persistent sustainability issues by contributing to the innovation of societal systems. Sustainability issues at the level of societal sectors or domains cannot be addressed by single organizations but require co-evolutionary changes in technology, economy, culture and organizational forms. We present the case of transition management in the Netherlands – an approach combining systems analysis with new modes of governance to influence the direction and speed of structural changes towards sustainability – and the activities of two firms working in this new context. From the two specific cases we conceptualize business strategies at different levels to advance sustainable development.transition management;sustainability;business development;systems

Giant Relaxation Oscillations in a Very Strongly Hysteretic SQUID ring-Tank Circuit System

In this paper we show that the radio frequency (rf) dynamical characteristics of a very strongly hysteretic SQUID ring, coupled to an rf tank circuit resonator, display relaxation oscillations. We demonstrate that the the overall form of these characteristics, together with the relaxation oscillations, can be modelled accurately by solving the quasi-classical non-linear equations of motion for the system. We suggest that in these very strongly hysteretic regimes SQUID ring-resonator systems may find application in novel logic and memory devices.Comment: 7 pages, 5 figures. Uploaded as implementing a policy of arXiving old paper

Pinch Resonances in a Radio Frequency Driven SQUID Ring-Resonator System

In this paper we present experimental data on the frequency domain response of a SQUID ring (a Josephson weak link enclosed by a thick superconducting ring) coupled to a radio frequency (rf) tank circuit resonator. We show that with the ring weakly hysteretic the resonance lineshape of this coupled system can display opposed fold bifurcations that appear to touch (pinch off). We demonstrate that for appropriate circuit parameters these pinch off lineshapes exist as solutions of the non-linear equations of motion for the system.Comment: 9 pages, 8 figures, Uploaded as implementing a policy of arXiving old paper