Elastic Spin Hall effect in Mechanical Graphene

We show that spin-orbit interaction and elastic spin-Hall effect can exist in a classical mechanical system consisting of a two-dimensional honeycomb lattice of masses and springs. The band structure shows the presence of splitting at K point induced by the difference of longitudinal and transverse elastic constant, and this splitting can be regarded as an effective Dresselhaus-type spin-orbit coupling. Interestingly, as an initial displacement away from the equilibrium is applied, the time evolution simulation shows that waves of different spin polarization propagates along different directions at the Gamma and K point, which is characteristic of spin-Hall effect. Several cases for spin-Hall effect are also discussed.Comment: 15 pages, 5 figures, and 3395 word

Skew Cyclic codes over \F_q+u\F_q+v\F_q+uv\F_q

In this paper, we study skew cyclic codes over the ring R=\F_q+u\F_q+v\F_q+uv\F_q, where $u^{2}=u,v^{2}=v,uv=vu$, $q=p^{m}$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $R$ through a decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length $n$ over $R.