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The Ratcheting States
Ratcheting states result from secondary bifurcations of ordered states in which symmetry is broken by small spatial inhomogeneities. In the ratcheting states, one or more rings drift (~1 deg/sec) in a circular path, speeding up and slowing down in a characteristic manner.
The ratcheting states differ from the uniformly rotating states in at least four significant ways: the spatiotemporal symmetries are more complicated; the motions are not uniform; the types of motion are more varied; and the magnitude of the average angular velocity is smaller by a factor of 100.
12/5
Movie (.97M) Motion: outer ring ratchets around a stationary inner ring. |
12/6/1 Movie (.99M) Motion: two outer rings ratchet together, speeding up and slowing down in a jerky motion. |
13/6/1
Movie (.97M) Motion: outer ring moves clockwise with the inner ring locked to it through an angle of approximately sixteen degrees. The inner ring unlocks and snaps back to its original position. |
13/6
Movie (.97M) Motion: rings ratchet in an irregular motion. |
Related Paper
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Ratcheting motion of concentric rings in cellular flames
M. Gorman, M. el-Hamdi and K. A. Robbins,
Physical Review Letters 76 (1996) pp. 228-231.