This dissertation presents a Nuclear Magnetic Resonance (NMR) study of a novel anisotropic superconductor, HgBa$_{2}$CuO$_{4+\delta}$ (Hg1201) and unconventional strain dependence of the mean free path of silica aerogel. Hg1201 is one of the most structurally simple cuprates known. Therefore, it is an ideal compound in investigation of various phases in...