We prove that the excluded volume of convex shapes A and A(v) with equal volumes attains its minimum only if A(v) coincides with the inversion A* of A relative to its centroid. It follows that if A is a cylindrically symmetric shape, and A' is a replica of A rotated in space, then the excluded volume of A and A' attains its minimum when A and A' are in the antiparallel configuration. This suggests that ensembles of such hard particles may experience the same geometric frustration as spins in the Ising model for antiferromagnetism on certain lattices.
The minimum excluded volume of convex shapes
VIRGA, EPIFANIO GUIDO GIOVANNI
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2014-01-01
Abstract
We prove that the excluded volume of convex shapes A and A(v) with equal volumes attains its minimum only if A(v) coincides with the inversion A* of A relative to its centroid. It follows that if A is a cylindrically symmetric shape, and A' is a replica of A rotated in space, then the excluded volume of A and A' attains its minimum when A and A' are in the antiparallel configuration. This suggests that ensembles of such hard particles may experience the same geometric frustration as spins in the Ising model for antiferromagnetism on certain lattices.File in questo prodotto:
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