Backlund flux quantization in a model of electrodiffusion based on Painlevé II

Bracken, A. J., Bass, L. and Rogers, C. (2012) Backlund flux quantization in a model of electrodiffusion based on Painlevé II. Journal of Physics A: Mathematical and Theoretical, 45 10: .

Author Bracken, A. J.
Bass, L.
Rogers, C.
Title Backlund flux quantization in a model of electrodiffusion based on Painlevé II
Journal name Journal of Physics A: Mathematical and Theoretical   Check publisher's open access policy
ISSN 1751-8113
Publication date 2012-03
Sub-type Article (original research)
DOI 10.1088/1751-8113/45/10/105204
Volume 45
Issue 10
Total pages 20
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2013
Language eng
Abstract A previously established model of steady one-dimensional two-ion electrodiffusion across a liquid junction is reconsidered. It involves three coupled first-order nonlinear ordinary differential equations and has the second-order Painlevé II equation at its core. Solutions are now grouped by Bäcklund transformations into infinite sequences, partially labelled by two Bäcklund invariants. Each sequence is characterized by evenly-spaced quantized fluxes of the two ionic species, and hence evenly-spaced quantization of the electric current density. Finite subsequences of exact solutions are identified, with positive ionic concentrations and quantized fluxes, starting from a solution with zero electric field found by Planck, and suggesting an interpretation as a ground state plus excited states of the system. Positivity of ionic concentrations is established whenever Planck's charge-neutral boundary conditions apply. Exact solutions are obtained for the electric field and ionic concentrations in well-stirred reservoirs outside each face of the junction, enabling the formulation of more realistic boundary conditions. In an approximate form, these lead to radiation boundary conditions for Painlevé II. Illustrative numerical solutions are presented, and the problem of establishing compatibility of boundary conditions with the structure of flux-quantizing sequences is discussed.
Keyword Electrical structures
Steady electrolysis
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article number 105204

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2013 Collection
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