General principles

By ‘modelling’ we shall understand the selection of some assumptions from which it is possible to calculate the properties of a system. Sometimes it is possible to obtain a close mathematical expression giving a property as a function of interesting variables. In this chapter and the following ones we shall mainly concern ourselves with such models. However, in many cases the model cannot be expressed in a closed mathematical form but results can also be obtained by numerical calculations using some iterative method. When the iteration in some way resembles the behaviour of a real physical system one talks about ‘simulation’. Such methods are becoming increasingly more powerful thanks to access to more and more powerful computers.

The purpose of modelling is two-fold. From a scientific point of view one likes to learn how nature functions. One way of gaining knowledge is to define some hypothesis resulting in a model and test it by comparing the predictions from the model with experimental information. Then, it does not matter much if the predictions are made by an analytical calculation or by some numerical method. From a more technological point of view one likes to predict the properties of a particular system in order to put it to efficient use in some practical construction or operation. Then it is often most convenient to have a model which yields an analytical expression.