Numerical Calculations on Vortex Phenomena in Helium Superfluids

This thesis reports numerical calculations on quantized vortices in He and He superfluids. Vortices are of crucial importance in understanding many of the superfluid properties. All the calculations presented in the thesis have experimental relevance, either in understanding measured results or in predicting the outcome of planned experiments. Superfluid He has been observed to exhibit incomplete wetting on certain solid substrates. The variations in the thickness of the fluid layer are explained by a model with a nonuniform distribution of pinned vortices. Superfluid He under weak perturbations (due to container walls, flow and magnetic fields) is studied with the hydrostatic theory. Within this theory, the equilibrium properties of the superfluid are controlled by the distribution, i.e. the texture, of the order parameter describing the superfluid state. In the anisotropic A phase of He, vorticity usually appears in doubly-quantized continuous vortices, having no singular core. They can be created by applying a flow with a velocity exceeding an experimentally measurable threshold. The critical velocity can be theoretically identified with the instability of the underlying order-parameter distribution. The flow textures and critical velocities in He-A are calculated for different initial configurations in both one-dimensional and two-dimensional geometries. The full transverse NMR spectrum of He-B in a cylindrical container is calculated numerically. The effects of rotation, magnetic field and the number of vortices are included in the model. The results are used to determine the optimal sensitivity for observing changes in the number of vortices, the finite-size effect due to the end plates of the cylinder, and the change of absorption induced by the presence of a spin-mass vortex.