Kinematically restricted phonon transmission in partly-unzipped tubes of square and triangular lattices

An analysis of the transmission of `scalar' phonons across partially unzipped square and triangular lattice tubes, assuming nearest neighbor interactions between particles, is presented. The phonon transport is assumed to involve the out-of-plane phonons in the unzipped portion and the radial phonons in the tubular portion. An exact expression of reflectance and transmittance for the waves incident from either portions of the waveguide are provided explicitly, in terms of the Chebyshev polynomials, which leads to the provision of a simple expression for the ballistic conductance.