Excited states of a string in a time dependent orbifold
  We present analytical results on the propagation of a classical string in non-zero modes through the singularity of the compactified Milne space. We restrict our analysis to a string winding around the compact dimension of spacetime. The compact dimension undergoes contraction to a point followed by re-expansion. We demonstrate that the classical dynamics of the string in excited states is non-singular in the entire spacetime. 
Przemyslaw Malkiewicz and Wlodzimierz Piechocki