In this article we study the spectral properties of the Schrödinger operator HV “ ́Δ ` V pxq, x P R, where the potential, V , is periodic and has honeycomb structure symmetry. For general periodic potentials the spectrum of HV , considered as an operator on LpRq, is the union of closed intervals of continuous spectrum called the spectral bands. Associated with each spectral band are a band dispe...

Super-hydrophobic surfaces which have been fabricated by various methods such as photolithography, chemical treatment, self-assembly, and imprinting have gained enormous attention in recent years. Especially 2D arrays of nano-needles have been shown to have super-hydrophobicity due to their sharp surface roughness. These arrays can be easily generated by removing the top portion of the honeycom...

The seed capsule of Delosperma nakurense is a remarkable example of a natural hygromorph, which unfolds its protecting valves upon wetting to expose its seeds. The beautiful mechanism responsible for this motion is generated by a specialized organ based on an anisotropic cellular tissue filled with a highly swelling material. Inspired by this system, we study the mechanics of a diamond honeycom...