On a micropolar continuum approach to some problems of thermo- and electrodynamics

Abstract

A new nonlinear model of a micropolar continuum is suggested. The peculiarity of the model is that the constitutive equations depend only on the strain measures associated with rotational degrees of freedom, and at the same time, the stress tensor turns out to be different from zero. This mathematical model has been created with the view of its use for modeling various processes, including processes at the micro-scale level. Following the terminology of nineteenth-century scientists, we call our model the ether model, though in its mathematical content, it differs from the nineteenth-century ether models very significantly. There may be different points of view concerning the physical meaning of our model. On the one hand, one can suppose the same meaning that nineteenth-century scientists implied in their ether models. On the other hand, one can imagine a continuum consisting of quasi- or virtual particles. The choice of one of the aforementioned physical interpretations is not important for constructing the mathematical model. Our method of modeling thermo- and electrodynamic processes is as follows. In the framework of our model, we introduce mechanical analogies of physical quantities such as temperature, entropy, the electric field vector, the magnetic induction vector. We show that under certain simplifying assumptions the equations of our model coincide with well-known equations, in particular, with Maxwell’s equations. We explore the properties of our mathematical model in its most general form, investigate what processes can be described in the framework of our model, and suggest a possible interpretation of these processes.