Contact Structures in Continuous Media Theory
Alexei Kushner, Svetlana Mukhina, Vladislav Gavrilov · 2024
This paper is devoted to two applications of contact geometry to problems arising in the theory of continuous media control: control of the thermodynamic state of a van der Waals gas and control of liquid crystals. The first problem is reduced to constructing vector fields on a two-dimensional Lagrangian manifold, which is determined by the equations of the thermodynamic states of the gas. The second one is devoted to the method of solving the Cauchy problem for the Hunter-Saxton equation, which describes the dynamics of liquid-crystal structures.