TY - JOUR
T1 - Nonlinear competition between small and large hexagonal patterns
AU - Silber, Mary
AU - Proctor, Michael R E
PY - 1998/9/21
Y1 - 1998/9/21
N2 - Recent experiments by Kudrolli, Pier, and Gollub [Physica D (to be published)] on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular “superlattice” pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.
AB - Recent experiments by Kudrolli, Pier, and Gollub [Physica D (to be published)] on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular “superlattice” pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.
UR - http://www.scopus.com/inward/record.url?scp=0000649887&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000649887&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.81.2450
DO - 10.1103/PhysRevLett.81.2450
M3 - Article
AN - SCOPUS:0000649887
SN - 0031-9007
VL - 81
SP - 2450
EP - 2453
JO - Physical review letters
JF - Physical review letters
IS - 12
ER -