Valentin Lychagin

In this article, we explore thermodynamic processes and their controls usingthe geometry of jet spaces, instead of contact geometry. The equations ofstate are now defined by 1-jets of submanifolds of codimension one in thespace of intensive quantities, while thermodynamic processes are describedby vector fields in this space. This allows us to describe and study highorderphase transitions that occur in both thermodynamic processes andtheir controls.

We investigate various geometric structures associated with first-order linear differential operators acting on vector bundles, and use them to classify these operators with respect to a pseudogroup of the vector bundle automorphisms.

In this paper, thermodynamics of a moving medium is considered. Main goal of this paper is to describe thermodynamics state equations and equations of co-existence manifolds of media on two- and three-dimensional manifolds. To this end the phase space of a medium is extended with the deformation tensor and the stress tensor.

In this paper, recent results regarding generalized continuum mechanics on oriented Riemannian manifolds are reviewed and summarized. The mass, the momentum and the energy conservation laws are given. Thermodynamics arising in such media is also considered as a Lagrangian manifold endowed with a Riemannian structure. Thermodynamic model of moving media takes into account deformation and stress arising in a media in motion.

In this paper recent results regarding generalized continuum mechanics on oriented Riemannian manifolds are reviewed and summarized. The mass, the momentum and the energy conservation laws are given. Thermodynamics arising in such media is also considered as a Lagrangian manifold endowed with a Riemannian structure. Thermodynamic model of moving media takes into account deformation and stress arising in a media in motion.

In this paper we consider thermodynamics of a moving medium. We expand thermodynamic phase space with two additional quantities: deformation and stress. A geometrical interpretation of such thermodynamics as Lagrangian manifolds is given. With a pseudo-Riemannian structure arising on such manifolds, a co-existence curve of phases is found. An example regarding the van der Waals state equation is considered.