Duality of conservation laws and their role in the processes of emergence of physical structures and formations

Abstract

As it is known, the conservation laws for material media are conservationlaws for energy, linear momentum, angular momentum, and mass. Such conser-vation laws are described by differential equations. And the conservation laws forphysical fields are conservation laws that state the presence of conservative physicalquantities or objects (structures). Such conservation laws are described by closedexterior skew-symmetric forms. It can be seen that conservation laws possess dual-ity. The conservation laws for material media and the conservation laws for physicalfields are different. A peculiarity consists in the fact that there exists a connectionbetween the conservation laws for material media and those for physical fields. Thisconnection is realized discretely in the evolutionary process. It describes the emer-gence of physical structures and the observed formations, such as waves, vortices,turbulent pulsations.