Heat conduction in a 1D harmonic chain with three dimensional vibrations
  We study vibrational energy transport in a quasi 1-D harmonic chain with both longitudinal and transverse vibrations. We demonstrate via both numerical simulation and theoretic analysis that for 1-D atomic chain connected by 3D harmonic springs, the coefficient of heat conduction changes it continuously with its lattice constant, indicating the qualitative difference from the corresponding 1-D case where the coefficient is independent of the lattice constant. 
Zonghua Liu and Baowen Li