| Topological Constraints on the Charge Distributions for the Thomson Problem (2006) | |||||||||
Abstract | |||||||||
| The method of Morse theory is used to analyze the distributions of unit charges interacting through a repulsive force and constrained to move on the surface of a sphere -- the Thomson problem. We find that, due to topological reasons, the system may organize itself in the form of pentagonal structures. This gives a qualitative account for the interesting ``pentagonal buttons'' discovered in recent numerical work.. Comment: 10 pages; dedicated to Rafael Sorkin on his 60th birthday | |||||||||
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