Emergent behaviour in electrodiffusion: Planck's other quanta

Bass, L. and Bracken, A. J. (2014) Emergent behaviour in electrodiffusion: Planck's other quanta. Reports On Mathematical Physics, 73 1: 65-75. doi:10.1016/S0034-4877(14)60032-X


Author Bass, L.
Bracken, A. J.
Title Emergent behaviour in electrodiffusion: Planck's other quanta
Journal name Reports On Mathematical Physics   Check publisher's open access policy
ISSN 0034-4877
1879-0674
Publication date 2014-02
Year available 2014
Sub-type Article (original research)
DOI 10.1016/S0034-4877(14)60032-X
Open Access Status
Volume 73
Issue 1
Start page 65
End page 75
Total pages 11
Place of publication Kidlington, Oxford, United Kingdom
Publisher Pergamon Press
Collection year 2015
Language eng
Abstract A well-established nonlinear continuum model of time-independent electrodiffusion describes the migrational and diffusional transport of two ionic species, with equal and opposite valences, across a liquid junction. The ionic charge densities provide the source for a static electric field, which in turn feeds back on the charges to contribute the migrational component of the ionic transport. Underpinning the model is a form of the second Painlevé ordinary differential equation (PII). When Bäcklund transformations, extended from those known in the context of PII, are applied to an exact solution of the model first found by Planck, a sequence of exact solutions emerges. These are characterized by corresponding ionic flux and current densities that are found to be quantized in a particularly simple way. It is argued here that this flux quantization reflects the underlying quantization of charge at the ionic level: the nonlinear continuum model ‘remembers’ its discrete roots, leading to this emergent phenomenon.
Keyword Emergent behaviour
Nonlinear electrodiffusion
Backlund transformations
Flux quantization
Painleve II equation
Painleve II model
Differential equations
Electrical structures
Steady electrolysis
Transformations
Interfaces
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
 
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