Energy formulation for electronic, optical and acoustical applications including interfacial properties and irreversible processes

Abstract

A non-integrable energy formulation lying in the framework of continuum physics with electromagnetic interactions and including interfacial properties is presented. Non-integrability is required in a number of physical applications and particularly when irreversible processes occur. The central concept is that of duality between geometrical and dynamical fields; it allows the distinction between virtual and real states, as well as the use of invariance principles. Here, three invariance principles are basic to the theory: scale-change invariance related to the extension of continuous functions to discontinuous ones, then gauge and rotational invariances associated with electromagnetism and mechanical systems, respectively. The need for such an approach is shown on physical examples where the classical energy and vectorial formulations cease to apply. In brief, after providing a systematic construction of the method in a Galilean and then a Lorentzian framework, the formulation is extended to electromagnetomechanical interactions including interfacial properties and irreversible processes.