Unsteady analytical solutions to the Poisson-Nernst-Planck equations
It is shown that the Poisson-Nernst-Planck equations for a single ion species can be formulated as one equation in terms of the electric field. This previously not analyzed equation shows similarities to the vector Burgers equation and is identical with it in the one dimensional case. Several unstea...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
29 October 2012
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| In: |
Journal of physics. A, Mathematical and theoretical
Year: 2012, Jahrgang: 45, Heft: 45 |
| ISSN: | 1751-8121 |
| DOI: | 10.1088/1751-8113/45/45/455204 |
| Online-Zugang: | Verlag, Volltext: http://dx.doi.org/10.1088/1751-8113/45/45/455204 Verlag, Volltext: http://stacks.iop.org/1751-8121/45/i=45/a=455204 
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| Verfasserangaben: | Johannes Schönke |
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| 520 | |a It is shown that the Poisson-Nernst-Planck equations for a single ion species can be formulated as one equation in terms of the electric field. This previously not analyzed equation shows similarities to the vector Burgers equation and is identical with it in the one dimensional case. Several unsteady exact solutions for one and multidimensional cases are presented. Besides new mathematical insights which these first known unsteady solutions give, they can serve as test cases in computer simulations to analyze numerical algorithms and to verify code. | ||
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