Mathematical Background

During the last two years of my first degree course in Philosophy, I attended postgraduate courses and seminars covering the foundations of Mathematics and the elementary results of Model Theory, Set Theory, Mathematical and Modal Logics.

Since the MSc course at Chelsea College was intended for mathematics graduates, I attended concurrently an intensive course in General Topology at LSE. The MSc course included: fundamental theorems of Mathematical Logic and first order arithmetic, Boolean Algebra, Set Theory, Model Theory, Proof Theory, Recursion Theory and Non-standard Analysis.

After gaining an MSc, I was awarded a Chelsea College Research Studentship for two years for research into the application of Category Theory to the foundations of Mathematics, unfortunately without any publishable results.

Before registering for a MPhil/PhD in Physics, amongst the courses I was required to attend was Mathematical Methods, covering those areas applicable to Physics such as analytic solutions of differential equations, partial differential equations, Fourier series and Gamma and Bessel functions. Other courses taken at this time included Electronics and Instrumentation, Heat and Thermodynamics, and the Three Phases of Matter.

Research

Research for my PhD thesis was carried out under the auspices of the Physics Department of the City of London Polytechnic, with advisers appointed from the Mathematics Department and the School of Navigation, in addition to a scientific consultant working in the field of marine cargoes.

For my PhD thesis, entitled "An experimental and theoretical investigation of the migration of moisture in cocoa beans", I carried out both theoretical and experimental research:

Theoretical: I wrote computer programs to yield numerical solutions of heat conduction and modified moisture diffusion equations, in order to model the temperature and moisture distribution in a ship's hold during a voyage. To this end, I investigated various mathematical methods for the numerical solution of non-linear parabolic partial differential equations, including implicit and explicit finite difference methods; the non-linearity of the equation to be solved, arising because of the investigation of diffusion occurring in a hygroscopic material as the result of a thermal gradient, did not allow the application of the Crank - Nicholson method. The use of finite element methods was also investigated, though not adopted as they were found unnecessarily complex for the problem under consideration.

Experimental: Because the research was carried out on a part time basis, I established a laboratory in my home office, and designed and constructed the experimental apparatuses with the associated control and measurement electronics myself.

Although primarily concerned with cocoa, the research for my PhD thesis also covered the bulk carriage of grain, such as wheat and maize, and convection currents in bulk and bagged (i.e. dunnaged) stows. For the latter, I applied an elaboration of Darcy's Law, appropriate to low velocity flows.

Other computer program applications developed in the course of my professional work include, for example, the calculation of the effect on the storage atmosphere of ethylene leakage in a vessel's ventilation system during the carriage of a cargo of bananas, using the Runge-Kutta method to solve the resulting set of differential equations, and a computer substitute for Hygrometric Tables, allowing chained calculations. While I have from choice used Pascal for most of these programs, I have also translated many programs and program fragments from the original Fortran source into Pascal. The platforms I have used range from an ancient DEC mainframe to IBM compatible, Macintosh and Acorn Risc PCs. In the past, I have also programmed in assembly language for the 1802 (proto-RISC), Z80 and 8086 microprocessors.

Although not published, I have carried out experimental research for particular legal cases, including patterns of condensation on cold bagged sugar and paper reels, and oxidative self-heating of baled wood pulp, using control and measurement equipment designed and constructed by me.