The Fourier transform of tubular densities
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 unres...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2012
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| _version_ | 1797093721646301184 |
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| author | Prior, C Goriely, A |
| author_facet | Prior, C Goriely, A |
| author_sort | Prior, C |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T04:04:19Z |
| format | Journal article |
| id | oxford-uuid:c5a11646-9f91-4300-9ebc-17687a139cae |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:04:19Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:c5a11646-9f91-4300-9ebc-17687a139cae2022-03-27T06:32:23ZThe Fourier transform of tubular densitiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c5a11646-9f91-4300-9ebc-17687a139caeEnglishSymplectic Elements at Oxford2012Prior, CGoriely, AWe 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. |
| spellingShingle | Prior, C Goriely, A The Fourier transform of tubular densities |
| title | The Fourier transform of tubular densities |
| title_full | The Fourier transform of tubular densities |
| title_fullStr | The Fourier transform of tubular densities |
| title_full_unstemmed | The Fourier transform of tubular densities |
| title_short | The Fourier transform of tubular densities |
| title_sort | fourier transform of tubular densities |
| work_keys_str_mv | AT priorc thefouriertransformoftubulardensities AT gorielya thefouriertransformoftubulardensities AT priorc fouriertransformoftubulardensities AT gorielya fouriertransformoftubulardensities |