Introduction to Formal Graphs, a new approach to the classical formalism

Abstract

The creation of a purely graphic language called Formal Graphs for modelling many physical and physico-chemical systems is described. It represents an improvement over traditional equivalent circuits used for modelling systems made of individual components and over bond graphs used mainly in physico-chemistry. In contradistinction with these graphs, which represent graphically only mounting equations and maintain algebraic equations for describing components behaviour, a formal graph is an oriented graph incorporating all the information contained in a usual algebraic model. Combination of paths considerably extends use to domains that were not accessible to quantitative graphs, such as relaxation processes, chemical reactivity or mass-transfer. Moreover, inclusion of space derivation allows representing graphically every physical law describing a process involving energy conservation or dissipation, such as particle diffusion. Physical meaning can be deduced from paths in a graph that can be followed by processes, as illustrated by the exponent of fractional derivation, which appears as bearing the information on the proportion of conserved versus dissipated energy. The numerous examples given in this introduction address several domains, electrodynamics, mechanics, thermodynamics, and physico-chemistry. They show common graph structures that reveal a striking unity of our classical formalism, bringing transversal insight and opening a new route towards unification. Differences also appear that are subjects of interrogation.