Institute for Mathematics and Its Applications
Paul Umbanhowar, University of Pennsylvania
Experiments on vertically vibrated granular layers reveal, at a critical acceleration amplitude (about 2.5 g's), a well-defined hysteretic transition from a flat surface to standing wave patterns oscillating at half the drive frequency. At low frequencies, the hysteresis is large and the patterns are squares, while at high frequencies, the hysteresis is small and the patterns are stripes. For frequencies in the middle of this transition regime, and at acceleration amplitudes below the onset of planar wave patterns, highly localized, non-propagating, standing waves appear. These localized excitations, which we term "oscillons", come in two ``flavors''. Like oscillons repel, while opposites attract and bind to form diatoms, tetramers, and polymer-like chains. Near onset, planar patterns of squares and hexagons can be interpreted as oscillon composites.