In this dissertation, regularization of simultaneous binary collision, existence of a Schubart-like periodic orbit, existence of a planar symmetric periodic orbit with multiple simultaneous binary collisions, and their linear stabilities are studied. The detailed background of those problems is introduced in chapter 1. The singularities of simultaneous binary collision in the collinear four-body problem is regularized in chapter 2. We use canonical transformations to collectively analytically continue the singularities of the simultaneous binary collision solutions in both the decoupled case and the coupled case. All the solutions are found and more importantly, we find a crucial first integral which describes the relationship between the decoupled solutions and the coupled solutions. In chapter 3, we show the existence of a Schubart-like orbit, a periodic orbit with singularities in the symmetric collinear four-body problem. In each period of the orbit, there is a binary collision (BC) between the inner two bodies and a simultaneous binary collision (SBC) of the two clusters on both sides of the origin. The system is regularized and the existence is proven by using a "turning point" technique and a continuity argument on differential equations of the regularized Hamiltonian. Analytical methods are used in chapter 4 to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method can be extended to any even number of bodies. Multiple simultaneous binary collisions are a key feature of the orbits generated. In chapter 5, we apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four body problem with masses 1, m, m , 1, and also in a symmetric planar four-body problem with equal masses. For the collinear problem, this verifies the earlier numerical results of Sweatman for linear stability.

We investigate the existence of a symmetric singular periodic brake orbit in the equal mass, fully symmetric planar four body problem. Using regularized coordinates, we remove the singularity of binary collision for each symmetric pair. We use topological and symmetry tools in our investigation.

This diploma thesis deals with comparison of experimental and simulated low energy ion scattering spectra. There is a theoretical description of basic principles of low energy ion scattering and description of the spectrometer, which is situated at Institute of physical engineering. It is shown, how to prepare samples using the colloidal gold solution. The deposition of gold nanoparticles is characterized. The usage and meaning of time and energy spectra of low energy ion scattering is explained. There is also shown the effect of channeling in Si substrate.

二体衝突近似法を、粒子－物質相互作用に関する様々な現象に応用した。特に二体衝突近似法と動的モンテカルロ法の接続によるBCA-kMCハイブリッドシミュレーションにより、従来の二体衝突近似法と拡散方程式を合わせた手法が抱える問題を克服することで、材料内での不純物拡散挙動をより詳細に解析することに成功した。本論文は将来的な二体衝突近似法の幅広い分野への応用の足がかりになることが期待される。 / 博士(工学) / Doctor of Philosophy in Engineering / 同志社大学 / Doshisha University