Magneto-Solid Mechanics and the Aleph Tensor

Michael Grinfeld^1, and Pavel Grinfeld²

¹The US Army Research Laboratory, Aberdeen Proving Ground, USA

²Department of Mathematics, Drexel University, Philadelphia, USA

Cite this paper:
Michael Grinfeld and Pavel Grinfeld. Magneto-Solid Mechanics and the Aleph Tensor. Applied Mathematics and Physics. 2020; 8(1):8-13. doi: 10.12691/amp-8-1-2

Abstract

In Reference [1], a new master system was formulated allowing to the analyze polarizable and/or magnetizable solids. The central distinction of the suggested approach consists in the systematic usage of the Cardinal Aleph tensor. By choosing different thermodynamic potentials, the suggested approach can be recommended for the analysis of a wide variety of static or dynamic engineering systems. Given the variety of possible applications, the system is relatively simple and can be analyzed not only computationally but also analytically. However, in order to make the analytical and computational results simpler and more transparent it makes sense to adjust the general system for different applications. Using our approach, we formulate the exact nonlinear system for dynamics of magnetizable fluid and solids. Then, we apply our exact nonlinear general system to ferrofluids and its linearized version to piezo-magnetic solids.

Keywords:
magnetizable substances the Cardinal tensors partial differential equations

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References:

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