Fig. 3.

Spatial distributions of modes. The spatial distributions of the modes at ω/ω _b = 0.44 a, 1.0 b, 2.63 c, and 8.96 d. The participation ratios are p(ω _n) = 0.44 a, 0.3 b, 0.244 c, and 0.00499 d. Here $p\left({\omega }_n\right)\equiv \frac{{\left({\sum }_i{m}_i{∣e_{n,i}∣}^2\right)}^2}{\left(N{\sum }_i{m}_i^2{∣e_{n,i}∣}^4\right)}$, where e _n,i is the polarization vector of the particle i in the nth mode (see, e.g., ref. ⁸). Note that the magnitudes of the polarization vectors in different modes are shown at different scales