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ÖgeMachine learning analysis of pulsar timing data(Graduate School, 20211217)In 1967, radio pulsations from a celestial body were discovered by a graduate student Jocelyn Bell and her advisor Antony Hewish. This was the first sample of about three thousand similar sources, called pulsars, to be discovered in our galaxy to date. It has been understood that pulsars are rapidly spinning, strongly magnetized neutron stars. Neutron stars are very dense objects formed by the collapse of the cores of massive stars at the end of their life. Each pulsar has its characteristic pulse shape and rotational frequency. The rotational frequency of pulsars can be measured very precisely. The rotation frequencies of pulsars are observed to decrease in time. Pulsars tap their radiative energy from their rotational kinetic energy. The mechanisms by which pulsars achieve this energy conversion is not wellunderstood. According to a prominent model, the pulsars convert their kinetic energy into radiation by emission of magnetic dipole radiation (MDR). However, studies with young pulsar data show that the MDR model does not fully explain the observations and there should be other mechanisms assisting the spindown. The ejection of highenergy particles, the growth of the dipole magnetic field over time, interaction with a supernova debris disc, increasing inclination angle between the rotation and magnetic axis, and gravitational wave emission are some of the processes proposed to affect spinevolution. Occasionally, some pulsars suffer sudden increases in their spin, also known as "glitches" which decay in the following weeks or months. When they were first discovered, it was thought that glitches result from the breaking of the crust and hence they were called "stellar quakes". Today, it is conceived that this model can only account for the smallest glitches or that it could be a triggering mechanism for the main cause of the glitches. According to the more favoured view, the glitches are caused by the dynamics of the crustal superfluid. Sometimes a new glitch occurs before the previous glitch decayed. The presence of glitches in the pulsar data complicates the understanding of the spin evolution. The aim of the thesis is to contribute to the understanding of the spin evolution of pulsars by machine learning methods. To this end, longterm timedependent spin frequency data of Crab and Vela pulsars are used. These are the two bestknown pulsars that have been studied the most. Since the frequency changes by a small fraction throughout the timespan of the observations, we have eliminated the basic trend by fitting the data with a polynomial function. By subtracting this basic trend from the data, we obtained the residuals that clearly show the complicated features of spin evolution such as glitches. We tested the performance of two machine learning methods in reproducing the evolution of the residuals. The first method is called the sparse identification of nonlinear dynamics (SINDY). Given a timeseries data, SINDY can identify the governing system of ordinary differential equations. We thus used this method to find the governing equations for the evolution of the residuals. The SINDy method gave information about the order of the equations and their coefficients. In addition, we used a recurrent neural network (RNN) architecture called long shortterm memory (LSTM) method on the same data sets. We found that LSTM can predict the dates of glitches in the test data. The results show that SINDy and LSTM applications can contribute to the studies on the spin evolution of pulsars and may take place more in studies related to pulsars in the future.

ÖgeProspects of nonresonant Higgs boson pair production measurement in the WWγγ channel at the HLLHC with the phaseII CMS detector(Graduate School, 20220602)Since the discovery of the Higgs boson in 2012 by the CMS and ATLAS experiments at the CERN's Large Hadron Collider in Geneva, Switzerland, physicists have tried to measure accurately its properties and to understand better the underlying electroweak symmetry breaking mechanism. In this pursuit, the search for Higgs boson pair production is crucial to test our understanding of the Higgs potential and to search for clues for the Beyond the Standard Model searches. This thesis describes the search for the Higgs boson pair production in decays to a W boson pair and a photon pair. The ττγγ channel of the Higgs boson pair decay is analysed alongside since an overlap is expected in the final states. Monte Carlo simulations of protonproton collisions corresponding to an integrated luminosity of 3000 fb^1 at a centreofmass energy of 14 TeV are used. The gluongluon fusion production mode of the Higgs boson pair is considered only. The Delphes fast detector simulation is used with an average pileup of 200 per interaction with a dedicated card for Phase2upgraded CMS detector. A Pythonbased analysis library called Bamboo is used to perform the object selections and event categorisation in the data analysis of the study. Cutflow tables reporting the number of events at each final state of interest are shown. Two binary Deep Neural Networks (DNN) are employed using the Keras API for TensorFlow machine learning library in order to increase the signal and background discrimination in the semileptonic final state of WWγγ and single τ final state of ττγγ channels. DNN score cuts are applied to each final state and the diphoton invariant mass distributions are obtained. The results are then used in the Higgs Combine Tool with the statistical and systematic uncertainties applied. The significance levels are reported for each final state along with their combination.

ÖgeHigh resolution dielectric anisotropy investigation of carbon nanotube  smectic A liquid crystal dispersion(Graduate School, 20221208)It is wellknown that there are three common phases in condensed matter which are crystal, liquid, and gas. Crystalline solids are anisotropic, which means that many physical properties are different in direction. Besides, liquids are isotropic, which means they present the same properties in all directions. Liquid crystals (LCs) have physical features like an ordinary liquid, though their molecules are ordered, leading to anisotropy. Many liquid crytsalline materials which have one or more different mesophases exhibit properties between crystalline solid and isotropic liquid. Mesophases, which liquid crystals have, are mostly characterized by their properties of orientation. One of the mesophases is entitled nematic (N) phase, which has a longrange orientational order. Molecules which have orientational order tend to align along a director, which is the measure of the average direction of the molecules. The other phase is called has smectic phase (Sm), which has partial positional order in addition to the orientational order. Thereby, molecules are arranged in layers in smectic phases which are coded alphabetical according to the order of the discovery. Smectic A (SmA) phases have a wide range usage in a smectic phases. In the smectic A phase, molecules have a layered structure which is normal to the layers. It is worthwhile noting that knowledge of the phase transition is crucial to understanding the properties of the liquid crystals. According to de Gennes, a physical system which has a physical property can be a measure of the order. In nematic phase, molecules have a property of anisotropy which can be measured with a dielectric anisotropy. Therefore, dielectric measurements, which are an example of physical quantities, can be used for testing liquid crystalline behavior. Phase transition is a change of a phase from one to another by external effects like temperature or pressure. The point in phase transition where two phases cannot be distinguished from each other is defined as a critical point. Temperature refers to the critical point is called critical temperature Tc. If there is a latent heat and discontinuous change in entropy near the critical point, it is called a first order phase transition. Otherwise, it is called second order phase transition. Worthwhile recalling that critical behaviour of the liquid crystalline materials can be determined by the order parameter S(T) which is produced from dielectric anisotropy data. In this work, high resolution dielectric data have been obtained for 8CB (octylcyanobiphenyl) liquid crystals in addition to 8CB nanocomposites doped with both pristine multiwalled carbon nanotubes (pMWCNT) and carboxyl group (COOH) functionalized MWCNTs (fMWCNTs). Nematic order parameter for both the nematicisotropic (NI) and nematic smectic A (NSmA) of the neat 8CB and 8CB+MWCNT has been derived from MaierMeier theory, which can be used to examine the effect of dielectric anisotropy in the nematic phase. In 8CB doped with both pMWCNT and fMWCNT, the NI and NSmA transition temperatures shifted to a lower value compared to pure 8CB. NI transitions for all 8CB+MWCNT nanocomposites manifests weakly first order, on the other hand, NSmA transition remains continuous. Sufficiently far away from the SmA phase, the critical exponent β which determines the tricritical behavior of order parameter S(T) are obtained 0.238 ± 0.002 on average, which is in excellent agreement with the obtained from optical birefringence data. The obtained β value is compatible with the hypothesis that the NI phase transition exhibits tricritical behavior. All investigated compounds present the temperature dependence of NI and the nematiccrystalline phase transitions of the order parameter is quasitricritical. Previous studies show that, the critical behaviour at NSmA transition is an important research area. For the first time, the upper limits for a latent heat ∆HNA for the neat 8CB and MWCNT doped 8CB have been derived from the detailed dielectric anisotropy data in the NSmA transition. Besides, the ∆HNA values produced in this way appear to be in agreement when compared with the values obtained from optical birefringence data and ASC measurements. By using the power law analysis of the ∆ε(T) data, which is the temperature gradient of the nematic order parameter through the NSmA transition, the effective specific heat capacity exponents α have been yielded for all samples. For the first time, high resolution dielectric measurements ∆ε enable to invetigate the NSmA transition behaviour.

ÖgeVorticity dependent quantum kinetic equation in three dimensions(Graduate School, 20220629)In this thesis, we formulate a 3dimensional transport theory for massive Dirac particles in vortical systems by means of QKE that includes the vorticity tensor and the Wigner function. Furthermore, we investigate the results of such formalism. The Wigner function is the quantum mechanical analog of the classical distribution function that governs the collective behavior of nonequilibrium systems. 3dimensional distribution functions and the equations that govern them can be extracted from the Wigner function after decomposing it in terms of the Clifford algebra basis elements. We employ a method called equaltime formalism which can be roughly summarized as the method that obtains the 3dimensional Wigner function by integrating the 4dimensional Wigner function over the zeroth component of the momentum variable. Another method called the covariant formalism prefers to stick with the 4dimensional fields. Both of the formalism includes the semiclassical expansion which allows us to proceed order by order in terms of Planck constant as the zeroth order corresponding to the classical limit. The zeroth order kinetic equation for the Wigner function is the quadratic massshell equation. Thus, the solutions involves the delta function that enforces the massshell condition with negative and positiveenergy. The classical relations between the distribution functions follows directly from the zeroth order constraint equations that is obtained after performing the momentum's zeroth component integration. The first order equations can be found by expanding the onshell delta function mentioned in the previous paragraph around the shell. It follows from this expansion that the energy shift terms needs to be determined in order to proceed. A natural and the way we will follow is to obtain this energy shifts from the connection between the covariant and equaltime formulations. In order to progress, we semiclassicaly expand our equations. After plugging the energy shift terms we are able to express the full set of the first order components of distribution functions in terms of the vector and axial vector distribution functions. Finally, we find the zeroth and first order kinetic equations for vector and axial vector distribution functions. By fixing the spatial component of the axial vector distribution function, we find the kinetic equation for the temporal component of this function. A special choice of the spatial axial vector distribution function allows us to establish kinetic equations for the left and righthanded distribution functions. We can find the rate of changes of phase space variables. Hence insofar, we obtain the current density for the equilibrium chiral distribution function and therefore calculate it both in its zero temperature and massless limits. The results in these limits are compatible with the ones obtained in other studies.

ÖgeHo(1x)ErxNi2B2C yapısında gözlemlenen burgaç oluşumu(Lisansüstü Eğitim Enstitüsü, 20220111)Nadir toprak elementlerinin farklı oranlardaki katkılanmaları ile Ho(1x)ErxNi2B2C (x = 0, 0.25, 0.50, 0.75, 1) tek kristal numunelerdeki manyetik düzen gerek manyetizasyon deneyleriyle gerekse nötron difraksiyon deneyleriyle incelenmiştir. Kristal yapıda olan numunelerimizden nötron deneyleri sırasında güçlü sinyaller elde edebilmek adına elimizdeki birden çok tek kristalin birlikte yönlendirilmesi, Laue Xışını ölçümleriyle, Kanada'da (Hamilton, Ontario) McMaster Üniversitesi bünyesinde bulunan Brockhouse Institute for Materials Research (BIMR)'de yapılmıştır. Manyetizasyon ve manyetik duygunluk ölçümleri de yine aynı enstitünün PPMS (Physical Properties Measurement Systems), yani Fiziksel Parametreler Ölçüm Düzeneği, manyetik ve Küçük Açı Nötron Saçılması KANS (Small Angle Neutron Scattering, SANS) deneyleri ise Washington DC, ABD'de kurulu bulunan National Institute of Standards and Technology (NIST) enstitüsünün nötron kısmı olan NIST Center for Neutron Research (NCNR) laboratuvarında sırasıyla BT9, NG7, NG5 ve BT7 deney mahalleri (beamline) kullanılarak gerçekleştirilmiştir. Geçiş sıcaklığı, R2CuO4 süperiletken bileşiğinde, R'nin Er ve Ho olduğu durumlar için yaklaşık 10 K'dir. Ne var ki, bu malzemeleri asıl ilginç kılan husus, bunların, içlerinde tam da bu sıcaklıklar civarında bir manyetik düzen oluşturmalarıdır. Nadir toprak kısmın yapısına bağlı olmakla birlikte süperiletkenlik ile manyetizma arasındaki bağlaşma, yeniden girilen süperiletkenliğin oranlı ve oransız antiferromanyetizma ile eşzamanlı olarak varolmasından tutun da zayıf bir ferromanyetik düzen ile tamamıyla oransız antiferromanyetik bir spin modülasyonunun birlikte varolmasına kadar çeşitli fazların oluşmasına sebebiyet verir. Tüm bu fazlar süperiletkenlik ile eşzamanlı olarak varolurlar. "Saf" bileşiklerdeki manyetik düzen RKKY manyetik etkileşmesi ile açıklanmış olup katkılı numunelerdeki manyetik yapıyla saf numunelerin manyetik yapıları üzerinde yapılan nötron saçılması deneylerinin sonuçları da karşılaştırılmıştır. Saf Ho yapısında Er katkısının artmasıyla 1. Derece düzenli fazdan 3D XY düzen değerlerine doğru bir değişim gözlemlenmiştir. Özellikle Er katkısının oranı 0.75 olduğunda manyetik pik diğer numunelerden daha farklı bir yansıma oluşturmuş ve bu pik, daha önce başka bir araştırmada R2CuO4 (R = Nd ve Pr) kuantum mıknatısında gözlemlenmiş olan manyetik tepe profiline benzetilmiştir.