Prior, C. and Goriely, A. (2012) The Fourier transform of tubular densities. Journal of Physics A: Mathematical and General . (Submitted)
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 minimise 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 ODE’S.
|Subjects:||D - G > General|
|Research Groups:||Oxford Centre for Collaborative Applied Mathematics|
|Deposited By:||Peter Hudston|
|Deposited On:||02 Mar 2012 07:48|
|Last Modified:||29 May 2015 19:10|
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