Density perturbations in hybrid inflation

Thesis: S.M., Massachusetts Institute of Technology, Department of Physics, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (page 35).Inflation is a substantial modification to the big bang theory, and supernatural inflation is a hybrid inflation motivated from supersymmetry. In this thesis we carry out a one dimensional numerical simulation to verify the untested analytic approximation of Radall et al. The results show a good agreement for a wide range of parameters. We also propose a new method for calculating density perturbations in hybrid inflation, which shows an excellent agreement with the simulation in one dimension.by Nguyen Thanh Son.S.M

Interpolation Based Parametric Model Order Reduction

In this thesis, we consider model order reduction of parameter-dependent large-scale dynamical systems. The objective is to develop a methodology to reduce the order of the model and simultaneously preserve the dependence of the model on parameters. We use the balanced truncation method together with spline interpolation to solve the problem. The core of this method is to interpolate the reduced transfer function, based on the pre-computed transfer function at a sample in the parameter domain. Linear splines and cubic splines are employed here. The use of the latter, as expected, reduces the error of the method. The combination is proven to inherit the advantages of balanced truncation such as stability preservation and, based on a novel bound for the infinity norm of the matrix inverse, the derivation of error bounds. Model order reduction can be formulated in the projection framework. In the case of a parameter-dependent system, the projection subspace also depends on parameters. One cannot compute this parameter-dependent projection subspace, but has to approximate it by interpolation based on a set of pre-computed subspaces. It turns out that this is the problem of interpolation on Grassmann manifolds. The interpolation process is actually performed on tangent spaces to the underlying manifold. To do that, one has to invoke the exponential and logarithmic mappings which involve some singular value decompositions. The whole procedure is then divided into the offline and online stage. The computation time in the online stage is a crucial point. By investigating the formulation of exponential and logarithmic mappings and analyzing the structure of sums of singular value decompositions, we succeed to reduce the computational complexity of the online stage and therefore enable the use of this algorithm in real time

耐環境用途に向けた複合酸化物およびその複合材料の材料設計と創製に関する研究

国立大学法人長岡技術科学大

Multi-directional Bicycle Robot for Steel Bridge Inspection

In contrast to the current climbing robots, this research presents a new design and implementation of a roller chain-based climbing robot to provide a practical solution for steel structure inspection (bridges, poles, pipes, etc.) The proposed roller chain-like robot has 12 joints for moving and 3 pairs of joints for turning, which makes the robot very flexible. This setup allows the robot to traverse areas of complex geometry on steel bridges. The robot utilizes permanent magnets to be able to well adhere on steel structures while moving