Langrangian finite element and finite difference methods for poisson problems

The use of Lagrangian finite element methods for solving a Poisson problem produces systems of linear equations, the global stiffness equations. The components of the vectors which are the solutions of these systems are approximations to the exact solution of the problem at nodal points in the region of definition. There is thus associated with each nodal point an equation which can be thought of as a difference equation. Difference equations resulting from the use of polynomial trial functions of various orders on regular meshes of square and isosceles right triangular elements are derived. The rival merits of this technique of setting up a standard difference equation, as distinct from the more usual practice with finite elements of the repeated use of local stiffness matrices, are considered

A numerical conformal transformation method for harmonic mixed boundary value problems in polygonal domains

A method is given for solving two dimensional harmonic mixed boundary value problems in simply-connected polygonal domains with re-entrant boundaries. The method consists of a numerical conformal mapping together with three other conformal transformations. The numerical mapping transforms the original domain onto the unit circle, which in turn is mapped onto a rectangle by means of two bilinear and one Schwarz-Christoffel transformations. The transformed problem in the rectangle is solved by inspection

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

Intraspecific Variation and Ecosystem Function: Implications for more effective Post-Restoration Monitoring

The effectiveness of stream restoration is often measured by the recolonization of certain focal species. However, important information regarding intraspecific variation (e.g. size structure) of these species is often ignored. Recent research suggests that intraspecific variation such as body size can have profound effects on food web dynamics and ecosystem functioning. Specifically, intraspecific predator size variation has been posited as a major determinant of a species’ ability to control lower trophic levels and even has the potential to alter trophic cascade intensity. The importance of predator feeding strategy (e.g. omnivory) and changes with body size may also be an important factor controlling the pervasiveness of top-down control. Therefore, considering factors such as size structure and how these factors interact with feeding strategy will enable better restoration planning and better predictions post restoration. We sought to identify the effects of size and size structure on top-down control by omnivorous Speckled Dace, Rhinichthys osculus, and how these effects scaled with density. Within our study system, R. osculus inhabit small isolated beaver ponds, the conditions of which we replicated in 1000L cattle tanks. Size, size structure, and density of R. osculus were then manipulated within these tanks and resulting changes in invertebrate and algal communities were monitored over 8 weeks. Benthic algal biomass was significantly lower in the fishless control and lowest fish density treatment, indicating that R. osculus may have caused a trophic cascade that varied in intensity by treatment. Invertebrate samples are currently being processed and should provide insight into the specific pathways of this potential trophic cascade. Once completed, this research will contribute to a growing body of knowledge regarding the role of intraspecific variation in maintaining the full suite of complex interactions that constitute healthy ecosystems. Additionally, this research highlights the importance of considering density and size structure in designing and assessing stream restorations

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