Discontinuous deformation analysis (DDA) is a newly developed simulation method for discontinuous systems. It was designed to simulate systems with arbitrary shaped blocks with high efficiency while providing accurate solutions for energy dissipation. But DDA usually exhibits damping effects that are inconsistent with theoretical solutions. The deep reason for these artificial damping effects has been an open question, and it is hypothesized that these damping effects could result from the time integration scheme. In this thesis two time integration methods are investigated: the forward Euler method and the Newmark method. The work begins by combining the Newmark method and the DDA. An integrated Newmark method is also developed, where velocity and acceleration do not need to be updated. In simulations, two of the most widely used models are adopted to test the forward Euler method and the Newmark method. The first one is a sliding model, in which both the forward Euler method and the Newmark method give accurate solutions compared with analytical results. The second model is an impacting model, in which the Newmark method has much better accuracy than the forward Euler method, and there are minimal damping effects. / Master of Science

<p>This thesis is devoted to the study of neutrino physics in general and the study of neutrino mixing and oscillations in particular. In the standard model of particle physics, neutrinos are massless, and as a result, they do not mix or oscillate. However, many experimental results now seem to give evidence for neutrino oscillations, and thus, the standard model has to be extended in order to incorporate neutrino masses and mixing among different neutrino flavors.</p><p>When neutrinos propagate through matter, the neutrino mixing, and thus, also the neutrino oscillations, may be significantly altered. While the matter effects may be easily studied in a framework with only two neutrino flavors and constant matter density, we know that there exists (at least) three neutrino flavors and that the matter density of the Universe is far from constant. This thesis includes studies of three-flavor effects and a solution to the two-flavor neutrino oscillation problem in matter with an arbitrary density profile.</p><p>Furthermore, there have historically been attempts to describe the neutrino flavor transitions by other effects than neutrino oscillations. Even if these effects now seem to be disfavored as the leading mechanism, they may still give small corrections to the neutrino oscillation formulas. These effects may lead to erroneous determination of the fundamental neutrino oscillation parameters and are also studied in this thesis in form of damping factors.</p>

This thesis is devoted to the study of neutrino physics in general and the study of neutrino mixing and oscillations in particular. In the standard model of particle physics, neutrinos are massless, and as a result, they do not mix or oscillate. However, many experimental results now seem to give evidence for neutrino oscillations, and thus, the standard model has to be extended in order to incorporate neutrino masses and mixing among different neutrino flavors. When neutrinos propagate through matter, the neutrino mixing, and thus, also the neutrino oscillations, may be significantly altered. While the matter effects may be easily studied in a framework with only two neutrino flavors and constant matter density, we know that there exists (at least) three neutrino flavors and that the matter density of the Universe is far from constant. This thesis includes studies of three-flavor effects and a solution to the two-flavor neutrino oscillation problem in matter with an arbitrary density profile. Furthermore, there have historically been attempts to describe the neutrino flavor transitions by other effects than neutrino oscillations. Even if these effects now seem to be disfavored as the leading mechanism, they may still give small corrections to the neutrino oscillation formulas. These effects may lead to erroneous determination of the fundamental neutrino oscillation parameters and are also studied in this thesis in form of damping factors. / QC 20101124