Transport of muonic hydrogen and deuterium atoms in gaseous hydrogen and deuterium is studied in the diffusion approximation and by means of the multiple collision expansion. The diffusion coefficient is derived. Scattering kernels are computed from the kinematics of an inelastic binary collision. The effect of rotations of the target molecules is treated by defining and computing an effective inelastic energy transfer Q_eff. The Doppler effect is taken into account by averaging the cross sections over the Maxwellian velocity distribution of the target molecules. Numerical results of the time-dependent problem in slab geometry are presented. In part two we construct a candidate for a realistic four generation Calabi-Yau manifold by dividing an algebraic variety in CP₄ x CP₄ with the Z₂ x Z₂ symmetry. A nontrivial embedding of Z₂ x Z₂ in E(6) allows the physically interesting intermediate symmetry, based on Pati-Salam SU(2)_L x SU(2)_R x SU(4)_C group. The group of honest symmetries G_H of the manifold is identified and the transformations properties of quark and lepton fields under G_H are given. / Ph. D.