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Bodmann, B.E.J., Vilhena, M.T., Zabadal, J.R. and Beck, D. (2011) On a New Definition of the Reynolds Number from the Interplay of Macroscopic and Microscopic Phenomenology. In: Constanda, C. and Harris, P.J. (Eds.), Integral Methods in Science and Engineering: Computational and Analytic Aspects, Springer, London, 7-14. https://doi.org/10.1007/978-0-8176-8238-5_2
https://link.springer.com/chapter/10.1007/978-0-8176-8238-5_2

has been cited by the following article:

• TITLE: Fundamental Connections in Differential Geometry: Quantum Field Theory, Electromagnetism, Chemistry and Fluid Mechanics

  AUTHORS: Jorge Zabadal, Ederson Staudt, Ádnei Marinho, Vinícius Ribeiro

  KEYWORDS: Commutation Relations, Extended Navier-Stokes Equations, Extended Helmholtz Equations, Interaction Terms, Quantum Behavior

  JOURNAL NAME: Open Access Library Journal, Vol.10 No.9, September 7, 2023

  ABSTRACT: This work presents novel hydrodynamic formulations that reconcile the continuum hypothesis with the emergence of electromagnetic interactions among molecules from fundamental principles. Two models are proposed: a relativistic version of the Navier-Stokes equations derived from commutation relations, and a Helmholtz-like system obtained by applying the Hodge operator to the extended Navier-Stokes equations. Preliminary analysis suggests that the second model, with its nonlinear terms serving as a generalized current, can reproduce microscopic quantum effects. It shows promise for generating self-consistent field equations via B?cklund transformations, remaining valid across all scales despite the breakdown of the continuum hypothesis.