It was noted that microscopic defects in a crystalline structure affected phonon transport and, at the macroscopic scale, heat propagation. Among these defects, disclinations changed the topology by breaking the rotational symmetry of the material. Considering the Katanaev-Volovich metric for such defect description, a new phonon motion equation was derived near to a disclination. Then, using the Boltzmann formalism to model phonon transport, a modified radiative transfer equation was introduced which involved an effective refraction index that took account of the disclination.

Multiscale Heat Conduction Near a Disclination. S.Fumeron, D.Lacroix: EPL, 2008, 82, 66003