Wells Computer Consultants Ltd

Prior to entry into commercial computing, twenty one years ago, Dr Williams was engaged in research projects which required use of computers to analyse and forecast results.

'Curve Fitting' comes under the heading of 'Numerical Analysis' and is an application of Taylor's theorem. There are now many packages available for the fitting of many mathematical functions to find the best fit to data generated from measurements. In those early days of computing the code required for the matrix algebra computations was written by many researchers to meet their individual requirements. Modified versions of curve fitting routines were used by Dr Williams to fit the real and imaginary parts of complex number mathematical functions to data generated from experiments.

'Simulation' is a mathematical modelling technique that attempts to model the 'real world' in terms of the underlying mechanisms. The techniques are used to aid our development and understanding of the mechanisms and concepts that control the way in which the 'real world' appears to us human beings. Mathematical modelling techniques are equally applicable in other disciplines.

In this instance Dr Williams took the mathematical models of water molecules developed by J.A.Pople (in 1954) and allowed a set of model water molecules to interact near a surface. The interaction between the molecules is electronic and the forces between them cause them to move and rotate. The computer calculated the forces, speeds and the rotation of the molecules and then allowed the molecules to move for a very small increment in time (a Pico second - one million millionth of a second) and recalculated the new position and orientation of each molecule before repeating the calculation cycle many times. The objective of these computations was to determine the energy of this model representing the microscopic world and compare the values it generated with measurements made on real water at a surface to develop a better understanding of how molecules of water interact near to a surface.

Consult with WCCL for real world modelling info@wccl.co.uk