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For a line structure(say a very long atomic chain) and a closed loop structure( connect the head and tail of this atomic chain). Does there exists a transformation between these two structures?

For example if we want to study the vibration mode of these two cases. If we already know all the modes of one case then are we able simultaneously know the information of the other modes without any further calculation?

Best Yen

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# Does there exist a transformation between a line and a closed loop ?

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