Explain the differing Fourier wavenumbers of the simulated and experimental SSS-I patterns

Determine why the numerically obtained SSS-I-like pattern contains secondary hexagonal modes with wavenumber \(\sqrt{3}k_c/2\) and a secondary subharmonic mode with wavenumber \(\sqrt{3}k_c/4\), whereas the experimentally observed SSS-I pattern contains primary hexagonal modes with wavenumber \(k_c\) and a primary subharmonic mode with wavenumber \(k_c/2\).

Background

The simulations reproduce the overall DNA-like geometry and temporal behavior of the experimentally observed SSS-I superlattice, but their dominant Fourier modes are located on a different hexagonal scale. In the simulations described in Section 3.1, the superlattice is formed from secondary hexagonal modes at 3kc/2\sqrt{3}k_c/2 and a secondary spatially subharmonic mode at 3kc/4\sqrt{3}k_c/4.

By contrast, Arbell and Fineberg’s experimental SSS-I state is described as consisting of primary hexagonal modes at kck_c and a primary subharmonic mode at kc/2k_c/2. The paper explicitly identifies the reason for this discrepancy as unknown, making the relationship between the two observed SSS-I realizations an unresolved problem.

References

The modes present in the SSS-I of are the three primary hexagonal modes ($k=k_c$) and one primary subharmonic mode ($k=k_c/2$), whereas those in figure \ref{fig:SL-B}(c) are the secondary hexagonal ($k=\sqrt{3}k_c/2$) and secondary subharmonic ($k=\sqrt{3}k_c/4$) modes. We do not know the reason for this difference.

— Numerical simulation of a two-frequency-driven superlattice Faraday-wave pattern  (2608.31141 - Panda et al., 31 Aug 2026) in Section 3.1, “Simulation starting from hexagonal equilibrium at F = F_h”; revisited in Section 4, “Concluding remarks”