Open AccessThe evolution equation: An application of groupoids to material evolution
Author(s) -
Víctor Manuel Jiménez,
Manuel de León
Publication year - 2022
Publication title -
journal of geometric mechanics
Language(s) - English
Resource type - Journals
eISSN - 1941-4897
pISSN - 1941-4889
DOI - 10.3934/jgm.2022001
Subject(s) - evolution equation , construct (python library) , point (geometry) , encoding (memory) , time evolution , computer science , mathematics , mathematical analysis , geometry , physics , artificial intelligence , programming language , quantum mechanics
The aim of this paper is to study the evolution of a material point of a body by itself, and not the body as a whole. To do this, we construct a groupoid encoding all the intrinsic properties of the material point and its characteristic foliations, which permits us to define the evolution equation. We also discuss phenomena like remodeling and aging.