McPhedran, R. C. and Milton, G. W. (1987) Transport Properties of Touching Cylinder Pairs and of the Square Array of Touching Cylinders. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 411 (1841). pp. 313-326. ISSN 1364-5021. doi:10.1098/rspa.1987.0069. https://resolver.caltech.edu/CaltechAUTHORS:20150128-095535667
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Abstract
We consider the solution of the scalar transport problem for a pair of touching cylinders of high conductivity. We obtain a closed-form expression for the set of multipole coefficients characterizing the potential function in this problem. We show that this expression permits the estimation of truncation errors occurring in the matrix solution of the transport problem for the square array of touching cylinders. Consequently, we are able to study the array conductivity for arbitrarily high cylinder conductivities, and confirm an asymptotic expression due to O'Brien. We derive a perturbation formula giving the effect of small cylinder separations on array conductivity.
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| Additional Information: | © 1987 The Royal Society. Received 8 September 1986. Part of this work was undertaken while R. C. McP. was on study leave at Caltech. He thanks Associate Professor D. B. Rutledge for his hospitality during this period, and the University of Sydney for its support. He acknowledges the Science Foundation for Physics within the University of Sydney for the provision of facilities. G. W. M. is grateful for the support of the California Institute of Technology through the award of a Weingart fellowship. | ||||||||||||
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| Issue or Number: | 1841 | ||||||||||||
| DOI: | 10.1098/rspa.1987.0069 | ||||||||||||
| Record Number: | CaltechAUTHORS:20150128-095535667 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20150128-095535667 | ||||||||||||
| Official Citation: | Transport Properties of Touching Cylinder Pairs and of the Square Array of Touching Cylinders Author(s): R. C. McPhedran and G. W. Milton Source: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 411, No. 1841 (Jun. 8, 1987), pp. 313-326 Published by: The Royal Society Stable URL: http://www.jstor.org/stable/2398033 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 54175 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | INVALID USER | ||||||||||||
| Deposited On: | 28 Jan 2015 20:25 | ||||||||||||
| Last Modified: | 10 Nov 2021 20:30 |
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