The co-divergence of vector valued currents

Reuven Segev, Lior Falach

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In the context of stress theory of the mechanics of continuous media, a generalization of the boundary operator for de Rham currents|the co-divergence operator - is introduced. While the boundary operator of de Rham's theory applies to real valued currents, the co-divergence operator acts on vector valued currents, i.e., functionals dual to differential forms valued in a vector bundle. From the point of view of continuum mechanics, the framework presented here allows for the formulation of the principal notions of continuum mechanics on a manifold that does not have a Riemannian metric or a connection while at the same time allowing irregular bodies and velocity fields.

Original languageEnglish
Pages (from-to)687-698
Number of pages12
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume17
Issue number2
DOIs
StatePublished - 1 Mar 2012

Keywords

  • Balance equations
  • Boundary operator
  • Con-tinuum mechanics
  • De Rham currents
  • Differential operators
  • Vector valued currents

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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