On Modelling Physical Phenomena

Abstract

Our use of the term “mathematical model” or “model” will refer to a set of consistent equations intended to describe the particular features or behavior of a physical system which we seek to understand. Thus, we can have different models of the system dependent on the questions of interest and on the features relevant to those questions. To derive an adequate mathematical description with a consistent set of equations and relevant conditions, we clearly must have in mind a purpose or objective and limit the problem to exclude factors irrelevant to our specific interest. We begin by considering the pertinent physical principles which govern the phenomena of interest along with the constitutive properties of material with which the phenomena may interact.