Reynolds transport theorem for smooth deformations of currents on manifolds. (July 2015)

• Record Type: Journal Article
• Authors: Falach, Lior; Segev, Reuven
• Other Names: Destrade Michel guest-editor.; Dorfmann Luis guest-editor.
• Is Part Of: Mathematics and mechanics of solids. Volume 20:Number 6(2015:Jul.)
• Page Start: 770
• Page End: 786
• Publication Date: 2015-07
• Subjects: Reynolds transport theorem -- differentiable manifolds -- de Rham currents -- homotopy formula -- Lie derivative; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286514551503
• Languages: English
• ISSNs: 1081-2865

Abstract

The Reynolds transport theorem for the rate of change of an integral over an evolving domain is generalized. For a manifold B, a differentiable motion m of B in the manifoldS, an r -current T in B, and the sequence of images m ( t ) ♯ T of the current under the motion, we consider the rate of change of the action of the images on a smooth r -form inS . The essence of the resulting computations is that the derivative operator is represented by the dual of the Lie derivative operation on smooth forms.