### Two-Mode
Rhomboidal States in Driven Surface Waves

H. Arbell and J. Fineberg

*The Racah
Institute of Physics, The Hebrew University
of Jerusalem, Jerusalem 91904,
Israel*

Received 19 May 1999

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 2*n*-fold quasipatterns
naturally arise from these states when the coupling angle between *k*→_{2}
and *k*→_{2}^{′} is 2π*/n*.