A quantum graph approach to metamaterial design

The initial fired element model illustrates the dispersion curves for the short legs, represented by the Graph Model. This model displays the relationship between wave number and frequency. Our finite element model closely aligns with this representation.

For longer lengths, the dispersion characteristics appear compressed, resulting in a second band. Although the curves are similar, deviations become evident at higher frequencies or shorter wavelengths. The consistency observed in the lower frequencies further supports the validity of our pipe model as an effective representation of our graphs.