Ph.D. Theses
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Browsing Ph.D. Theses by Subject "Boundary value problems."
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Item A ramond-nevu schwarz string one end fixed(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2005., 2005.) Arapoğlu, A. Savaş.; Turgut, Osman Teoman.; Saçlıoğlu, Cihan,We study an open string with one end free and the other fixed on a D0-brane as a qualitative guide to the spectrum of hadrons containing one very heavy quark. We first consider the bosonic degrees of freedom, then introduce the fermionic degrees offreedom through the world sheet supersymmetry. The mixed boundary conditions break half of the world sheet supersymmetry and allow only odd-moded a and even-moded d oscillators in the Ramond sector, while the Neveu-Schwarz oscillators b's become odd-integer moded. Boson-fermion masses can still be matched if space-time is 9 dimensional; thus SO(8) triality still plays a role in the spectrum, although full space-time supersymmetry does not survive. We quantize the system in a temporal-like gauge where X^0 ~ t. Although the gauge choice eliminates negative-norm states at the outset, there are still even-moded Virasoro and even(odd) moded super-Virasoro constraints to be imposed in the NS(R) sectors. The Casimir energy is now positive in both sectors; there are no tachyons. States for a' M^2 b 13/4 are explicitly constructed and found to be organized into SO(8) irreps by (super)constraints, which include a novel ``" operator in the NS and I in the R-sectors. GSO projections are not allowed. The pre-constraint states above the ground state have matching multiplicities, indicating spacetime supersymmetry is broken by the (super)constraints. A distinctive physical feature of the system is a slope twice that of the open RNS string. When both ends are fixed, all leading and subleading trajectories are eliminated, resulting in a spectrum qualitatively similar to the J/ and particles.Item Adiabatic solutions in general relativity and boundary symmetries(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2020., 2020.) Kutluk, Emine Şeyma.; Bleeken, Dieter Van den.We investigate adiabatic solutions to general relativity for a spacetime with spatial slices with boundary, by Manton approximation. This approximation tells us for a theory with a Lagrangian in the natural form, a motion that is described as a slow motion on the space of vacua-static solutions that minimize the energy- is a good approximate solution. To apply this to the case of general relativity we rst bring it to the natural form by splitting space and time and choosing Gaussian normal coordinates, where a spacetime is described by the metric on its spatial slices. Then following Manton we propose slow solutions such that each slice is a slowly changing di eomorphism of a reference slice, and thus each solution is described by a vector eld on the spatial slice. These solutions will have the property that the action will become a functional of the vector elds on the boundaries of the spatial slices. Moreover using the Hodge- Morrey-Friedrichs decomposition we will show that the constraints of general relativity will identify a unique solution for a given boundary value. Then we comment on the structure of the space of vacua which we show to be a (pseudo)-Riemannian homogeneous space. We illustrate our procedure for a speci c reference slice we choose: the 3d Euclidean round ball.