An investigation into the use of conformal transformations in two-dimensional field theory.

Smith, Michael Alexander

Abstract

The object of this thesis is to investigate the use of Conformal Transformations in solving Laplace's equation for two-dimensional field problems. Conformal Transformations is one of several analytical methods available for this purpose and its usefulness is generally limited to those problems in which the transformation integral is solvable. The theory of Conformal Transformations and the various methods of solution are given along with two examples which illustrate the different boundary conditions. Various field problems that can be obtained from the transformation equation are also included. This provides the information necessary to tackle specific problems. The main section of the thesis involves the investigation of several corner configurations which illustrate the use of the different methods of solution and also the degree of manipulation often required in some of the problems. In some cases a field plot is made of the area around the corner while others contain a graph of the field strength variations along with conductor surface. In conclusion an outline of two non-analytical methods is given. The study provides a step by step account of the procedure involved in solving, from first principles, the required field properties of particular problems, most which have not previously been investigated.

Citation

SMITH, M.A. 1975. An investigation into the use of conformal transformations in two-dimensional field theory. Robert Gordon's Institute of Technology, MPhil thesis. Hosted on OpenAIR [online]. Available from: https://doi.org/10.48526/rgu-wt-1993262

• Thesis Type: Thesis
• Deposit Date: Oct 22, 2024
• Publicly Available Date: Oct 22, 2024
• DOI: https://doi.org/10.48526/rgu-wt-1993262
• Public URL: https://rgu-repository.worktribe.com/output/1993262
• Award Date: Aug 31, 1975