Handle URI:
http://hdl.handle.net/10754/599915
Title:
The Fourier transform of tubular densities
Authors:
Prior, C B; Goriely, A
Abstract:
We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. © 2012 IOP Publishing Ltd.
Citation:
Prior CB, Goriely A (2012) The Fourier transform of tubular densities. J Phys A: Math Theor 45: 225208. Available: http://dx.doi.org/10.1088/1751-8113/45/22/225208.
Publisher:
IOP Publishing
Journal:
Journal of Physics A: Mathematical and Theoretical
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
18-May-2012
DOI:
10.1088/1751-8113/45/22/225208
Type:
Article
ISSN:
1751-8113; 1751-8121
Sponsors:
This publication is based on work supported by award number KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). AG is a Wolfson Royal Society Merit Holder. CP also would like to thank Cameron Hall for a discussion on approximations.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorPrior, C Ben
dc.contributor.authorGoriely, Aen
dc.date.accessioned2016-02-28T06:32:21Zen
dc.date.available2016-02-28T06:32:21Zen
dc.date.issued2012-05-18en
dc.identifier.citationPrior CB, Goriely A (2012) The Fourier transform of tubular densities. J Phys A: Math Theor 45: 225208. Available: http://dx.doi.org/10.1088/1751-8113/45/22/225208.en
dc.identifier.issn1751-8113en
dc.identifier.issn1751-8121en
dc.identifier.doi10.1088/1751-8113/45/22/225208en
dc.identifier.urihttp://hdl.handle.net/10754/599915en
dc.description.abstractWe consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. © 2012 IOP Publishing Ltd.en
dc.description.sponsorshipThis publication is based on work supported by award number KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). AG is a Wolfson Royal Society Merit Holder. CP also would like to thank Cameron Hall for a discussion on approximations.en
dc.publisherIOP Publishingen
dc.titleThe Fourier transform of tubular densitiesen
dc.typeArticleen
dc.identifier.journalJournal of Physics A: Mathematical and Theoreticalen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.