title: Two-mode rhomboidal states in driven surface waves
abstract: Two-mode rhomboid patterns are generated experimentally via two-frequency parametric forcing of surface waves. These patterns are formed by the simple nonlinear resonance: k-->'2-k-->(2) = k-->(1) where k(1) and k(2)( = k(')(2)) are concurrently excited eigenmodes. The state possesses a direction-dependent time dependence described by a superposition of the two modes, and a dimensionless scaling delineating the state's region of existence is presented. We also show that 2n-fold quasipatterns naturally arise from these states when the coupling angle between k-->(2) and k-->'2 is 2pi/n.
authors.affiliation: The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.initials: H
authors.lastname: Arbell
authors.initials: J
authors.lastname: Fineberg