2007/04/19 by Л. И. Петрова, Petrova, L. I.
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Earth Systems and Cosmic Evolution #FOS: Physical sciences #LaTex 2e #Mathematical Physics (math-ph) #Modeling, Simulation, and Optimization
paper · pdf · doi:10.48550/arxiv.0704.2473
openalex publication_date 2007/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the paper the role of conservation laws in evolutionary processes, which proceed in material systems (in material media) and lead to generation of physical fields, is shown using skew-symmetric differential forms. In present paper the skew-symmetric differential forms on deforming (nondifferentiable) manifolds were used in addition to exterior forms, which have differentiable manifolds as a basis. Such skew-symmetric forms (which were named evolutionary ones since they possess evolutionary properties), as well as the closed exterior forms, describe the conservation laws. But in contrast to exterior forms, which describe conservation laws for physical fields, the evolutionary forms correspond to conservation laws for material systems. The evolutionary forms possess an unique peculiarity, namely, the closed exterior forms are obtained from these forms. It is just this that enables one to describe the process of generation of physical fields, to disclose connection between physical fields and material systems and to resolve many problems of existing field theories.