We represent explicitly the excluded volume V-e{B-1, B-2} of two generic cylindrically symmetric, convex rigid bodies, B-1 and B-2, in terms of a family of shape functionals evaluated separately on B-1 and B-2. We show that V-e{B-1, B-2} fails systematically to feature a dipolar component, thus making illusory the assignment of any shape dipole to a tapered body in this class. The method proposed here is applied to cones and validated by a shape-reconstruction algorithm. It is further applied to spheroids (ellipsoids of revolution), for which it shows how some analytic estimates already regarded as classics should indeed be emended.
Explicit excluded volume of cylindrically symmetric convex bodies
PIASTRA, MARCO;VIRGA, EPIFANIO GUIDO GIOVANNI
2015-01-01
Abstract
We represent explicitly the excluded volume V-e{B-1, B-2} of two generic cylindrically symmetric, convex rigid bodies, B-1 and B-2, in terms of a family of shape functionals evaluated separately on B-1 and B-2. We show that V-e{B-1, B-2} fails systematically to feature a dipolar component, thus making illusory the assignment of any shape dipole to a tapered body in this class. The method proposed here is applied to cones and validated by a shape-reconstruction algorithm. It is further applied to spheroids (ellipsoids of revolution), for which it shows how some analytic estimates already regarded as classics should indeed be emended.File in questo prodotto:
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