Master's theses

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    Supernova distribution about the Galaxy Center
    (Nazarbayev University School of Science and Technology, 2017-04) Nussupbekov, Ayan
    The discovery of the gravitational waves opened various possibilities in astrophysics. One of them is to use the supermassive black holes at the Galaxy center as focusing lenses for gravitational waves. Because of it, it is essential to know the radial distribution of supernova about the Galaxy center. In this thesis work, we presented supernovas radial distribution through the distribution of supernova remnants. We analyzed existing catalogs of supernova remnants by plotting their histograms. We used Bayesian approach to find the best-fitting probability density function. We used the exponential model to determine the radial surface distribution of supernova remnants. Our the best fitting exponential model is in great correspondence with the distribution obtained by G.L.Case&D.Bhattacharya [5] and Kodaira [12]. Also, we discussed applied observational selection effects. Moreover, we examined uncertainties related to the distance estimates of supernova remnants.
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    The correlation expansion method used in quantum computation
    (Nazarbayev University School of Science and Technology, 2017-04) Baitenov, Adil
    In this master thesis, 3 methods of solving of Quantum Ising model have been outlined and compared, they include ABC. We investigate the entanglement dynamics and find energy and spin values for 1-dimensional Quantum Ising chain and 2 and 3-dimensional Quantum Ising models. System starts in a paramagnetic regime and switches to ferromagnetic spin-spin coupling constant J. In this work, we consider instantaneous (step function) switch, which demonstrates the instantaneous switch from paramagnetic to ferromagnetic state. Solution of the system is made by quantum simulation using Microsofts’ Corporations computational simulator called The Language-Integrated Quantum Operations (LIQUi|>) Simulator, 1/Z expansion method and Exact Diagonalization method. Accuracy and precision of results of first two methods are compared with Exact Diagonalization that provides the exact solution of the system. With that it can be seen to what extent 1/Z expansion method is applicable for solving of Quantum Ising model.
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    Interaction of Turbulence with Shock Waves in the Context of Core-Collapse Supernovae
    (Nazarbayev University School of Science and Technology, 2017-04) Berdibek, Shapagat
    The supernova explosion of massive stars is a complex physical event. Nuclear shell burning in the nal stages of the lives of massive stars is accompanied by strong turbulent convection. The resulting uctuations aid supernova explosion by amplifying the non-radial ow in the post-shock region. We investigate the physical mechanism behind this ampli cation using a linear perturbation theory. We model the shock wave as a one-dimensional planar discontinuity and consider its interaction with vorticity and entropy perturbations in the upstream ow. We nd that, as the perturbations cross the shock, their total turbulent kinetic energy is ampli ed by a factor of 2, while the average linear size of turbulent eddies decreases by about the same factor. We also study the e ects of the interaction of acoustic perturbations with the shock wave. We determine that the post-shock turbulent kinetic energy is dominated by vorticity waves. In addition, we nd that the kinetic energy ampli cation of perturbations increases as / M21 . Finally, we discuss the implication of our results for the supernova explosion mechanism. We show that the upstream perturbations can decrease the critical neutrino luminosity for producing explosion by several percent.
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    Brillouin visco-elastometry and Raman spectroscopy of potassium permanganate aqueous solutions
    (Nazarbayev University School of Science and Technology, 2017-04) Omarkulova, Aziza
    This thesis tries to find connection between mechanical and chemical properties of KMnO4 aqueous solutions with variable opacity. To the best of our knowledge, there was no research done on this or similar topic. The aqueous solutions of KMnO4 with various concentrations of KMnO4 were studied using Brillouin and Raman spectroscopies. Elastic and viscous properties and their change due to sample concentration is investigated by Brillouin experiment. Graphs and tables showing these changes are also included in this work. Raman spectra of the sample solutions gives information about molecular interaction on a microscopic level. The thesis includes derivation of the frequency shift and linewidth for Brillouin and Raman scatterings, as well as the assignment of vibrational modes for Raman scattering. For Brillouin scattering it was found that the solutions become stiffer and less viscous with increase of concentration of KMnO4 in water and Raman scattering showed that the solutions possess stretching vibration modes of permanganate ions and intramolecular O-H bending modes of water molecules. At the end possible relation between elastic property and active stretching vibrational modes is discussed. Also application of viscous property of aqueous KMnO4 for more effective water treatment is proposed.
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    Deploying Nonlinear Circuits on Wireless Power Transmitters and Receivers
    (Nazarbayev University School of Science and Technology, 2017-04) Shaikhov, Aidyn
    In this thesis, several methods that increase the tolerance of a wireless power transfer system are illustrated. For that reason, a Duffing oscillator (the second order differential equation with a third order of nonlinearity) equation is introduced. Also, an electrical analysis of a Duffing oscillator is presented. The detailed characteristics discussion is provided. Even though the Duffing oscillator circuit does not improve the efficiency of wireless power transfer drastically, it provides a significant wider bandwidth as compared to linear oscillators. The Duffing oscillator’s bandwidth is enhanced by a factor of 2.7 as compared to the linear oscillator with the same quality factor. Therefore, the Duffing oscillator improves the tolerance to coupling factor fluctuations arising from varying transmission distance and adjustment of coupled coils. The results are demonstrated using a MATLAB script.
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    Discrete Vortices in Photonic Graphene
    (Nazarbayev University School of Science and Technology, 2017-04) Dybyspayeva, Kumiszhan
    Graphene is a relatively new 2D material consisting of carbon atoms in honeycomb structure. Because of this structure, it has various interesting properties such as linear dispersion relation in the low energy spectrum that governs relativistic nature of electrons in graphene. Since there is an analogy between an electron wavepacket dynamics in time and paraxial wave propagation in z-direction, a honeycomb lattice of evanescently coupled optical waveguides, so called "photonic graphene", can be used to study dynamics of optical wavepackets and to mimic quantum relativistic behaviour in table-top experiments. Another interesting property of graphene is the pseudospin that is associated with generation of vortices. The goal of the present thesis is to investigate the unusual behaviour of the wavepacket in photonic graphene by observing the role of pseudospin for discrete optical vortices in the photonic lattice.
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    KNOTTED OPTICAL VORTEX LINES IN NONLINEAR SATURABLE MEDIUM
    (Nazarbayev University School of Science and Technology, 2018-06) Issakhanov, Alfarabi
    In last 50 years, a significant progress was noticed in medicine, communications and entertainment. Such advanced development of these fields was directly related to ability of controlling light. Photonics is exactly about this ability. At the present time, photonics is walking together with a fundamental physical concept, optical soliton. Optical solitons are shape-preserving laser beams. They are found potentially useful in data transmission, which is very significant nowadays. Hence, research in the field of optical solitons is still a vital issue. When optical soliton is perturbed in a specific manner, there appear zeros of optical field around the soliton, which are called optical vortices. In general optical vortices are lines in space. Hence, we might expect them to become knotted. Knotting optical vortices around perturbed seems spontaneous and cannot be directly predicted. To explain this phenomenon, a similar system is constructed based on perturbation theory. In this system, however, we have a mathematical problem which yet lacks a full understanding. We address this problem by introducing concepts from three disciplines: laser physics, knot theory and singular optics. We believe that understanding the mechanism underlying spontaneous knotting of optical vortices will be a step forward in other systems too, such as quantum turbulence in superfluids and formation of optical vortices around other types of optical solitons.