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Macroscopic Internal Variables and Mesoscopic Theory: A Comparison considering Liquid Crystals

This version is not peer-reviewed.

  ‡ These authors contributed equally to this work.

Submitted:

26 December 2017

Posted:

27 December 2017

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Abstract
Internal and mesoscopic variables differ from each other fundamentally: both are state space variables, but mesoscopic variables are additional equipped with a distribution function introducing a statistical item into consideration which is missing in connection with internal variables. Thus, the alignment tensor of liquid crystal theory can be introduced as an internal variable or as one generated by a mesoscopic background using the microscopic director as mesoscopic variable. Because the mesoscopic variable is part of the state space, the corresponding balance equations change into mesoscopic balances, and additionally an evolution equation of the mesoscopic distribution function appears. The flexibility of the mesoscopic concept is not only demonstrated for liquid crystals, but is also discussed for dipolar media and flexible fibers.
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Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

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