Condensed Matter Theory

Abstract:

We study shear flow in liquid crystal cells with elastic deformations using a lattice Boltzmann scheme that solves the full, three-dimensional Beris-Edwards equations of hydrodynamics. We consider first twisted and hybrid aligned nematic cells, in which the deformation is imposed by conflicting anchoring at the boundaries. We find that backflow renders the velocity profile non Newtonian, and that the director profile divides into two regions characterized by different director orientations. We next consider a cholesteric liquid crystal, in which a twist deformation is naturally present. We confirm the presence of secondary flow for small shear rates, and are able to follow the dynamical pathway of shear-induced unwinding, for higher shear rates. Finally, we analyze how the coupling between shear and elastic deformation can affect shear banding in an initially isotropic phase. We find that for a nematic liquid crystal, elastic distortions may cause an asymmetry in the dynamics of band formation, whereas for a cholesteric, shear can induce twist in an initially isotropic sample.

Abstract:

The buckling of multi-walled carbon nanotubes and rods was discussed. It was shown that electrostatic interactions exert a significant effect on the buckling instability of a rod. The threshold value of the compressional force needed to induce buckling was found to be independent of rod length for long charged rods. The critical buckling force crosses over from the classic inverse-square length dependence to asymptotic length-independent form with increasing rod length, in the case of rods of intermediate length. It was suggested that this effect leads to the possibility of electromechanical stiffening of nanotubes, which would allow relatively long segments of them to be used as atomic force probes.

Abstract:

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M dagger M where M is a complex matrix drawn from a normalized distribution P(M) approximately exp(-Tr [AMB M dagger]) with A and B positive definite (square) matrices of arbitrary dimensions. Such so-called correlated Wishart matrices occur in many fields ranging from information theory to multivariate analysis.