2013/12/30 by Lior Falach, Falach, Lior, Reuven Segev +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1312.7671
openalex publication_date 2013/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Reynolds transport theorem for the rate of change of an integral over an\nevolving domain is generalized. For a manifold B, a differentiable motion m\nof B in the manifold \S, an r-current T in B, and the\nsequence of images m(t) sharpT of the current under the motion, we\nconsider the rate of change of the action of the images on a smooth r-form in\n\S. The essence of the resulting computations is that the derivative\noperator is represented by the dual of the Lie derivative operation on smooth\nforms.\n