Open AccessNon-stationary layered vector fields and their divergence functions
Author(s) -
B. M. Burakhanov
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1698/1/012025
Subject(s) - vector field , scalar (mathematics) , vector potential , vector valued function , scalar field , mathematics , divergence (linguistics) , vector laplacian , mathematical analysis , direction vector , convergence (economics) , pure mathematics , physics , geometry , mathematical physics , linguistics , philosophy , quantum mechanics , magnetic field , economics , economic growth
This paper discusses the general properties of non-stationary layered vector fields and their functions of divergence. According to the classification of vector fields proposed in [1], layered vector fields are vortex vector fields that require two scalar functions to be defined. The main attention is paid to the study of a class of non-stationary layered vector fields that have the property of convergence to a stationary layered vector field. This means that these stationary layered vector fields can be considered as the result of the convergence process of non-stationary layered vector fields. It is shown that the condition for convergence of some non-stationary layered vector fields to a stationary layered vector field is that one of the two scalar functions that must be set to define a layered vector field belongs to the set of so–called scalar T-functions. T–functions are divided into two classes and the general properties of T–functions belonging to each of these classes are considered. Scalar characteristics of the mentioned non-stationary layered vector fields with properties of the Lyapunov function [2] are established.