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Mathematical Physics

arXiv:1407.8245 (math-ph)
[Submitted on 31 Jul 2014]

Title:Transport of Charged Particles: Entropy Production and Maximum Dissipation Principle

Authors:Chia-Yu Hsieh, YunKyong Hyon, Hijin Lee, Tai-Chia Lin, Chun Liu
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Abstract:In order to describe the dynamics of crowded ions (charged particles), we use an energetic variation approach to derive a modified Poisson-Nernst-Planck (PNP) system which includes an extra dissipation due to the effective velocity differences between ion species. Such a system is more complicated than the original PNP system but with the same equilibrium states. Using Schauder's fixed-point theorem, we develop a local existence theorem of classical solutions for the modified PNP system. Different dynamics (but same equilibrium states) between the original and modified PNP systems can be represented by numerical simulations using finite element method techniques.
Comments: 28 pages,8 figures
Subjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
Cite as: arXiv:1407.8245 [math-ph]
  (or arXiv:1407.8245v1 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1407.8245

Submission history

From: Tai-Chia Lin [view email]
[v1] Thu, 31 Jul 2014 00:36:50 UTC (46 KB)
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