Ph.D. Theses

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On the classical solutions of field theoretical models
(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1984., 1984.) Kalaycı, Jan.; Hortaçsu, Mahmut.
Cononical structure and integrability of new-dimensional field theories
(Thesis (Ph.D.)- Bogazici University. Institute for Graduate Studies in Science and Engineering, 1984., 1984.) Neyzi, Fahrünisa.; Arık, Metin.
Signs and magnitudes of Lyapunov exponents in continuous time dynamical systems
(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Sciences and Engineering, 1997., 1997.) Birol, İnanç.; Hacinliyan, Avadis.
Methods for algebraically determining the signs and the magnitudes of Lyapunov exponents of a given dynamical system are studied.A number of Hamiltonian and dissipative systems are investigated.The existence of zero Lyapunov exponents for the Toda and Henon-Heiles systems are shown using the curvature of their potentials functions.For the Rossler system,the root bracketing criterion is used to show the existence of a zero Lyapunov exponent.The approximate Lyapunov spectra of Lorenz and Rossler systems are computed using the approximation schemes introduced.
Cosmology and spontaneous symmetry breaking
(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1998., 1998.) Saygılı, Kamuran.; Arık, Metin.
In the first problem we investigate a model which incorporates spontaneous symmetry breaking and gravitation in the context of scalar-tensor theory. Present day value of the gravitational constant is induced by the vacuum expectation value of the scalar field. Cosmology is dominated by the scalar field both in the early and the present universe and the scalar field supplies the critical density of the universe today. In the second problem we applied the long-wavelength approximation to low energy effective string action in the context of Hamilton-Jacobi theory. The Hamilton-Jacobi equation is explicitly invariant under scale factor duality. We present the leading order general solution near a singularity, which also contains the quasi-isotropic one. The duality transformation is written as a coordinate transformation in an abstract space of fields.
Frequency-resolved photoconductivity studies in amorphous chalcogenide films
(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2000., 2000.) Akat, Ercüment.; Aktaş, Gülen, 1951- .
Frequency-resolved photocurrent measurements (FRPC) were carried out on amorphous chalcogenide films such as AsSeSb AsSe and AsSeTe, by a method called frequency-resolved spectroscopy (FRS) as a function of temperature (between 230 K and 395 K), of excitation intensity (between 40 and 600 ) and in the frequency range of 10 Hz to 1.1x104 Hz, yielding the lifetime distribution directly. The results indicate that the recombination is through distant pairs, since the lifetime does depend on the excitation intensity, through ; as at 295 K and at 395 K, rather than by geminate (twin) pairs. It can also be concluded that there is a continuous distribution of states in the mobility gap implied by the value of the exponent 0.72 (in ), which is between 0.5 and 1.0, the figures that according to Rose (1978), correspond respectively to monomolecular and bimolecular recombination. The temperature exponent in the relationship has turned out to be between 7 and 10 for a frequency of some (=200 Hz); and 11 and 13 for (=3322 Hz); the value of the exponent showing a diminishing behaviour as the generation rate (intensity of excitation) is elevated. Finally, the exponent in the relationship is found to depend on both temperature and the generation rate in a manner such that the photocurrent will be more sensitive (inversely) to the frequency of excitation as either one of the above variables or both are lowered.
Normal forms, nonlocal chaotic behaviour in sportt and NMR systems
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2002., 2002.) Perdahçı, Nazım Ziya.; Oğuz, Ömer.; Hacinliyan, Avadis.
Poincaré's theory of normal forms is applied to a number of simple chaotic Sprott flows that have resonant eigenvalues. It is shown that the normal form expansion can give significant information not limited to the local properties of chaotic attractors, but also, on nonlocal properties such as positive and zero Liapunov exponents for systems that have the Hopf bifurcation property. Existence of a zero Liapunov exponent is indicated if the system has hyperbolic fixed points. The method is not directly applicable where an eigenvalue of the linearized part vanishes, because of the complexity of the normal form. Rational transformations that change the eigenvalue spectrum of the linearized parts are employed on the Sprott C and E systems to obtain simpler systems. A proposel on the possible use of fractal analysis methods on functional MRI data and preliminary results on possible source of chaotic behavior inherent in nuclear spin systems are presented.
Multiparameter generalization of deformed particle algebras
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2004., 2004.) Arıkan, Ali Serdar.; Arık, Metin.
In this study, we generalize deformed boson and fermion algebras by considering as many deformation parameters as possible. The restriction on the number of deformation parameters emerges from the relations leaving the algebra consistent. In the bosonic part, we consider the Newton oscillator which is a one parameter generalization of the harmonic oscillator as a starting point. Then, we achieve the multiparameter generalization with d(d+1) parameters for d dimensional oscillator system. We also present the Fock representation of this oscillator. In the fermionic part, we first study the quantum group covariant two-parameter deformed fermion algebra. Then we show that if the quantum group symmetry is not preserved, then the number of deformation parameters in d dimension can be increased to 2(d-1). We study the limiting case where all deformation parameters go to zero such that the deformed fermionic oscillator reduces to the orthofermion algebra. Finally, we investigate the symmetry properties of this limiting case.
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.
Quantum group structures associated with invariances of some physical algebras
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2005., 2005.) Kayserilioğlu, Ufuk.; Arık, Metin.
In this study, the anticommuting spin algebra is introduced and it is shownto be invariant under the action of the quantum group SOq=-1(3). Furthermore, itsrepresentations and Hopf algebra structure are studied and found to be closely resemble the similar results for the angular momentum algebra. The invariance propertiesof the bosonic and fermionic oscillator algebras under inhomogeneous transformationsare also studied. The bosonic inhomogeneous symplectic group, BISp(2d,R) , andthe fermionic inhomogeneous orthogonal group, FIO(2d,R) , are defined as the inhomogeneous invariance quantum groups of these algebras. The sub(quantum)groupsand contractions of these quantum groups are studied as a source for new quantumgroups. Finally, the fermionic inhomogeneous orthogonal quantum group is defined forodd number of dimensions and its sub(quantum)groups and contractions are studied.
Chaotic structures in conductivity mechanisms
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2005., 2005.) Yıldırım, H. Ahmet.; Skarlatos, Yani.; Hacinliyan, Avadis.
Chaotic behavior in the transient current through thin Aluminum-PMMA-Alu-minum films has been analyzed for times ranging up to 30000s, in the temperaturerange 293-363 K for applied voltages in the range 10-80V. The general shape of the data suggests a slow decay to a steady state value superimposed with broadband os-cillations. The aperiodic and broadband behavior of the transient current remindsone of an underlying chaotic structure. Indeed time series analysis reveals a positiveLiapunov exponent consistently and reproducibly throughout this range which give sstrong evidence for chaoticity. Power law relaxation as refiected by the autocorrelationfunction and the positive Liapunov exponent show parallel behaviors as a function ofapplied electric field and temperature. The stretched exponential behavior of the data suggests that the process can beseen as random walk between random sites. The qualitative behavior of the data canbe understood in terms of a quenched disorder picture as first suggested by Erzan et.al.
Simulation of transient curret through polymethylmathacrylate thin films based on a charge density wave model
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2006., 2006.) Şahin, Gökhan.; Skarlatos, Yani.; Hacinliyan, Avadis.
A piecewise continuous, time dependent di®usive coupling in a classical onedimensional randomly pinned charge density wave model has been used for the analysisof experimentally observed transient current data for polymethylmethacrylate thin films. Satisfactory agreement has confirmed that this can be a dynamical model forthe behavior of the transient current. The analysis also suggests the presence of three different regimes in the decay of the transient current.
Effects of humidity and various gases on the electrical conductivity of polyethylene glycol
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2006., 2006.) Erdamar, Özgül.; Skarlatos, Yani.
Characterization of the electrical properties of covalently linked pure, hydrogenated and hydrophobically modified poly{ethylene glycol} (PEG) thin films under a changing relative humidity is examined by dc measurements. Perfluoroalkylethylalcohol is used as the hydrophobic additive. At low humidity levels, electronic conduction takes place while the absorbed water contributes to this mechanism and increases the current. At around 70% relative humidity, as a result of the water clusters formed, the polymer melts from the semicrystalline form and the current shows a steeper increase. The water vapor condenses and conduction takes an ionic nature. For the pure PEG samples, after 75%, the conductivity shows irregularities with respect to increase in the relative humidity. The irregularities subside in the hydrogenated as well as the hydrophobically modified PEG samples, while in the latter the steep increase in conductivity shifts to higher values of relative humidity with increase of perfluoroalkylethylalcohol concentration in the film. There is a hysterisis between the absorption and desorption of water as the film cannot reach its semicrystalline form in the time interval of desorption. The polymer film could get its pre-absorption form after annealing. The response of PEG thin films to the exposure to acetone and methanol vapor at changing pressures are observed by dc measurements under vacuum. The conductivity of the polymer increases with the increasing pressure of vapor while this increase reaches a significant value at 1100 Pa. Acetone causes an augmentation in current 10 times greater than methanol due to the difference between their dielectric constants.
Cylindrically symmetric spacetimes with pure rediation
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2006., 2006.) Delice, Özgür.; Arık, Metin.
In this thesis we have investigated some solutions of Einstein's field equations having cylindrical symmetry. The corresponding energy momentum tensor of most of these solutions has pure radiation equation of state. First, the static Levi-Civita solution has been generalized to a Kasner type time dependent solution. Using this solution, we have presented a time dependent Vaidya type solution representing pure and gravitational radiation emitted from a nonstatic cylindrical source. As an application, we have analyzed a radiating nonstatic cosmic string like object. Next, we have presented cylindrically symmetric, static solutions of the Einstein field equations around a line singularity such that the energy momentum tensor corresponds to infinitely thin photonic shells composed of counter propagating pure radiation in certain directions. Positivity of the energy density of the thin shell and the line singularity is discussed. Among these solutions, a particular solution corresponding to a photonic shell whose interior and exterior is flat is interesting since the cylinder becomes a plane for an outside observer. We have also investigated the generalization of these solutions to multiple thin shells and found that line singularities including cosmic strings may be screened by photonic shells until they all appear as a planar wall. Lastly we have investigated solutions corresponding to circulating or counter circulating pure radiation around the axis. The first solution we have studied was an approximate thin shell solution corresponding to counter rotating photons with small contribution from an anisotropic fluid. Next, we study a cylindrical circulating beam of light. The gravitational field of a counter rotating pure radiation field is presented as a last solution for this thesis. These solutions can smoothly match to the corresponding vacuum solutions from either interior or exterior.
Primordial and late-time inflation in Brans-Dicke cosmology
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2006., 2006.) Çalık, Mehmet.; Arık, Metin.
The basic motivation of this work is to attempt to explain the rapid primordial inflation and the observed slow late-time inflation by using the Brans-Dicke theory of gravity. We show that the ratio of primordial and late-time inflation parameters is proportional to the square root of the Brans-Dicke parameter w(). We also calculate the Hubble parameter H and the time variation of the time dependent Newtonian gravitational constant G for both regimes. The variation of the Hubble parameter predicted by Brans-Dicke cosmology is shown to be consistent with recent measurements: The value of H in the late-time future is predicted as 0.86 times the present value of H0. By using a linearized non-vacuum late time solution in Brans-Dicke cosmology we account for the seventy five percent dark energy contribution but not for approximately twenty-three percent dark matter contribution to the present day energy density of the universe. In the context of Brans-Dicke scalar tensor theory of gravitation, the cosmological Friedmann Equation which relates the expansion rate H of the universe to the various fractions of energy density is analyzed rigorously. And it is shown that Brans-Dicke scalar tensor theory of gravitation brings a negligible correction to the power of the scale size term in the matter density component of Friedmann equation. In addition to 歔 and M in standard Einstein cosmology, another density parameter, ¢, is expected by the theory. This implies that if ¢ is found to be nonzero, data will favor this model instead of the standard Einstein cosmological model with cosmological constant and will enable more accurate predictions for the rate of change of Newtonian gravitational constant in the future.
Black holes, cosmology and Brans-Dicke theories in 4+1 dimensional universe
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2007., 2007.) Çiftci, Dilek.; Arık, Metin.
We consider the embedding of 3+1 dimensional cosmology in 4+1 dimensional Jordan-Brans-Dicke theory. We show that exponentially growing and power law scale factors are implied. We solve the Brans-Dicke equations and we realize that only a linear warp factor satisfies these equations. In both exponentially expanding and power law expanding cases we find out that the scalar field is a function of the warp factor and the scale factor. Whereas the 4 + 1 dimensional scalar field is approximately constant for each case, the effective 3 + 1 dimensional scalar field is constant for exponentially growing scale factor and time dependent for power law scale factor. We calculate the effective gravitational constant and realize that same results are valid. We construct a static solution for 4 + 1 dimensional bulk such that the 3 + 1 dimensional world has a linear warp factor and describes the Schwarzschild-dS4 black hole. The 4 + 1 dimensional space-time is taken to be flat. For zero mass this four dimensional universe and Friedmann-Robertson-Walker universe are related with an explicit coordinate transformation. Also we realize that if there is a contribution from the mass term, both energy momentum and cosmological constant vanish in the bulk. We explain the four dimensional cosmological constant originates from the hidden brane and its effects cause the localized mass densities in our visible brane. Using hierarchy between the Planck mass and electroweak energy scale, we obtain the size of the extra dimension as close to Hubble length but smaller than it. We emphasize that for linear warp factors the effect of bulk on the brane world shows up as the dS4 background which is favored by the Big Bang cosmology.
Effects of gases on optical properties of polyethylene glycol
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2007., 2007.) Bilen, Bükem.; Skarlatos, Yani.
Humidity induced changes in the refractive index and thickness of polyethylene glycol (PEG) thin films are in situ determined by optical waveguide spectroscopy. PEG brushes are covalently attached to the surface of a thin gold film on a BK7 glass using a grafting-from chemical synthesis technique. The measurements are carried out in an attenuated total reflection setup. At low humidity levels, both the refractive index and the thickness change gradually due to water intake and swelling of the PEG thin films. At around 80% relative humidity, a steep decrease in the refractive index and a steep increase in the thickness are observed as a result of a phase change from a semicrystalline state to a physical gel state. The hydrogenation of PEG films caused a less pronounced phase change from a semicrystalline state to a gel state. Moreover, the phase change is observed at around 85% relative humidity. Due to fewer ether oxygen atoms available for the water molecules to make hydrogen bonding, the polymer has a more stable structure than before and the phase change is observed at a higher humidity level. The response of PEG thin films exposed to various gases is also observed by optical waveguide spectroscopy. A decrease in the refractive index and an increase in the thickness are observed due to methanol, acetone and hexane exposure. However, no response to toluene and benzene vapors is observed. When exposed to xylene, an increase in the refractive index of PEG films and a decrease in the thickness are observed. The changes in the refractive index and thickness due to methanol absorption are observed to be greater than those of others, since the amounts of alcohols sorbed into the PEG films are greater than those of ketones, alkanes and aromatics.
Bound state solutions of the Schrödinger equation for potentials with dirac delta functions
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2007., 2007.) Uncu, Haydar.; Demiralp, Ersan.
A general method for the bound state solutions of the SchrÄodinger equation for analytically solvable potentials with any ¯nite number of Dirac delta functions is intro- duced for n-dimensional systems. Then, the potentials with Dirac delta functions are used to model some physical systems. The eigenvalue equations for harmonic and linear potentials with a ¯nite number of Dirac delta functions located randomly are derived for one dimensional systems. For the latter potential, the behavior of the eigenvalues of the ground and the ¯rst excited states for various strengths and locations of Dirac delta functions is investigated. The eigenvalues and the number of bound states for a PT -symmetric system with two Dirac delta functions are studied. In case of a contact interaction, to get the changes from a liner potential, the changes in the masses of s states for charmonium is presented. It is also shown that the Fermi energy of a trian- gular well changes if there is an impurity in the well. By describing a dimple potential with a Dirac delta function, it is shown that tight and deep dimple potentials can in- crease the condensate fraction and critical temperature of a Bose-Einstein condensate. We conclude that addition of the point interactions which can be modelled by Dirac delta functions changes the properties of the physical systems considerably.
Exactly solvable potentials with Dirac delta point interactions
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2009., 2009.) Erkol, Hakan.; Demiralp, Ersan.
A general method to obtain s-wave bound states of the Schrödinger equation for analytically solvable potentials together with a finite number of the Dirac delta functions is presented for three-dimensional systems. The eigenvalue equations for the finite number of the Dirac delta decorated Woods-Saxon potential and Morse potential are obtained and the eigenvalue equations are calculated numerically for one Dirac delta function. The eigenvalue equation is solved numerically for two delta function case for the Woods-Saxon potential. The change of the ground state energies as a function of strength and locations of the Dirac delta functions are investigated for these potentials. For a hydrogen molecule, which is described by the Morse potential, transition probabilities between the initial state of the Hamiltonian and the final state of the perturbed Hamiltonian for a sudden, very local perturbation are calculated. The conditions for the number of bound states for given parameters of the Woods-Saxon and the Morse potentials are analyzed. Our results for the Woods-Saxon potential can be used to model very short range interactions for atomic and nuclear systems. Our method is applied to hydrogen molecule, which is described by the Morse potential, in C60 fullerene cage and the stabilization energy is calculated by representing the interaction potential between H2 and C60 by the Dirac delta interaction. Interatomic interactions that are described by the Morse potential together with local deformations can be investigated by using our model.
General unitary quantum groups and generalized Fermion algebras
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2009., 2009.) Altıntaş, Azmi Ali.; Arık, Metin.
Since the middle of the twentieth century, physicists have concentrated on finding quantum counterparts of classical systems. When a classical system is quantized its invariance group may still be a classical group. In the nineteen-eighties it was shown that when some classical systems are quantized, their classical group becomes a quantum group so that the system is invariant under a quantum group. So quantum groups play an important role in carrying physical properties to the quantum world. In this thesis, after presenting structure of Hopf algebra as a quantum group, structure of matrix quantum groups are investigated using inhomogeneous quantum groups, fermionic inhomogeneous orthogonal quantum invariance groups FIO, and bosonic inhomogeneous symplectic quantum invariance groups BISp. Then using invariance quantum groups of orthofermion algebra a general structure for unitary quantum groups are constructed in chapter three. Commuting fermion algebra is defined using the Heisenberg spin algebra and its inhomogeneous quantum group is defined in chapter four. Chapter three and chapter four of the thesis is based on original research.
Chaoticity analysis of the current through pure, hydrogenated and hydrophobically modified PEG-SI thin films under varying relative humidity
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2009., 2009.) Atak, Kaan.; Skarlatos, Yani.; Hacinliyan, Avadis.
Polyethylene Glycol is known to have an irregular current characteristic under constant voltage and slowly varying relative humidity. In this study the current through a thin film of Gamma-isocyanatopropyltriethoxysilane added polyethylene glycol (PEG-Si), its hydrogenated, and hydrophobically modified forms is measured as a function of increasing relative humidity at equal time steps and analyzed for chaoticity. In previous studies it has been suggested that, after reaching a certain relative humidity level, a phase transition occurs from a semi crystalline state to a gel state. We propose that the irregular behavior of current through PEG-Si thin films as a function of increasing relative humidity could best be analyzed for chaoticity using both time series analysis and detrended fluctuation analysis; the relative humidity is kept as a slowly varying parameter. The presence of more then one regime is suggested by the calculation of the maximal Lyapunov exponents. Furthermore, the maximal Lyapunov exponent in each of the regimes was positive, thus confirming the presence of low dimensional chaos. The regime change signaled by the changing values of the maximal Lyapunov exponent occurs around a relative humidity of 70% consistent with the phase transition from semi crystalline state to gel state. Detrended fluctuation analysis has also been performed; this also confirms the presence of at least two different regimes, in agreement with the behavior of the maximal Lyapunov exponent in the time series analysis. Our study also confirms that the improvement in stability of the current through PEG-Si can be performed by hydrogenating and hydrophobically modifying PEG-Si.

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