Master Tezleri

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Algebraic methods and exact solutions of quantum parametric oscillators
(Izmir Institute of Technology, 2019-06) Çetindaş, Osman; Atılgan Büyükaşık, Şirin; Pashaev, Oktay
In this thesis, we study different approaches for solving the Schrödinger equation for quantum parametric oscillators. The Wei-Norman algebraic approach, the Lewis- Riesenfeld invariant approach, the Malkin-Manko-Trifonov approach are investigated. For each approach, the wave function solutions of the Schrödinger equation, the propagator and dynamical invariants are found and their relations with each other are shown. In the Wei-Norman Algebraic approach, for constructing wave functions, explicit form of evolution operator is obtained uniquely in terms of two linearly independent classical solutions of the corresponding classical equation of motion. In Lewis-Riesenfeld approach, quadratic invariants are found in terms of the solution of Ermakov-Pinney equation and using the eigenstates of these invariants, wave function solutions are constructed. Setting initial values for Ermakov-Pinney solution, results of Wei-Norman and Lewis- Riesenfeld approaches are compared, then this solution is expressed in terms of same two linearly independent classical solutions. In Malkin-Manko-Trifonov approach, linear invariants which are symmetry operators for the Schrödinger equation, are constructed in terms of complex-valued solutions of the classical equation. Using these invariants, quadratic invariants are constructed and their eigenstates are used to find wave function solutions. Moreover, initial values for complex solutions of classical equation of motion are posed, and comparison of the three approaches is given.
All optical switching via diffraction grating formed by interference of Gaussian beams
(Izmir Institute of Technology, 2005) Akın, Osman; Dinleyici, Mehmet Salih
In this study we investigate an all-optical switching node which can be controlled via transient grating formed by interference of two Gaussian beams. This design considers 3-D architecture of switching fabrics, real profile of Gaussian beams and nonlinearity for fast switching time requirements. Four Wave Mixing (FWM) is applied in the evanescent field region of waveguide to estimate the reflection angle and the efficiency of switching node. The effect of the formed grating on the propagation of mode is analysed by coupled mode theory and co-directional mode coupling coefficient is found by using Distributed Feedback Laser approach. A method for overall diffraction efficiency is proposed and optimization parameters for better efficiency are described.
Almost local-global rings
(Izmir Institute of Technology, 2017-07) Susuzlu, İdem; Ay Saylam, Başak
The main purpose of this thesis is to investigate the Invariant Factor Theorem for Prüfer domains. In accordance with this aim, we give a survey of necessary and su cient conditions on a Prüfer domain to satisfy the Invariant Factor Theorem. In this process, almost local-global rings have important role since they satisfy the USC-property. Regarding to the UCS-property, BCS-rings together with their properties are also investigeted.
Analysis of cantilevers for high-speed atomic force microscopy
(Izmir Institute of Technology, 2018-07) Brar, Harpreet Singh; Balantekin, Müjdat
In life sciences, High-Speed Atomic Force Microscopy (HS-AFM) is now widely accepted as a dynamic event visualizer for numerous biological samples such as live cells, membrane lipids, ATP-proteins, enzymatic reactions, DNA-protein interactions, etc. HSAFM’s unique ability to observe surface topography of the samples with height data and with a resolution of up-to a single atom makes it a prominent tool in Nano measurements. HS-AFM Imaging technique’s speed and response is limited by various factors including cantilever probes, operating environment, scanning techniques etc. Cantilevers are indispensable and integral part of HS-AFM Systems, thereby necessitating their own critical evaluations. Therefore, evaluation of various parameters like resonance frequency, stiffness and Q-factor of cantilevers is an active area of research. The simulated research work mimics the experimental conditions of HS-AFM operation in air and liquid environment. The damping mechanisms such as viscous and acoustic damping of the medium, squeeze film damping, and damping due to viscoelasticity of the material are included in the finite element simulations. High frequency soft cantilevers suitable for HS-AFM with the stiffness of ~1 N/m and with the first flexural eigenmode resonance frequency of ~1.5 MHz (in liquid) and ~5 MHz (in air) are studied. Numerous small rectangular and modified cantilevers of Silicon and Polymer (SU-8) materials with the length of ~5 to 10 μm, width of ~1 to 2.5 μm and thickness of ~0.1 to 0.6 μm are analyzed. Our aim in this research is to identify appropriate cantilever geometries and materials for HS-AFM applications.
Analysis of climate sensitivity in outdoor space: Evaluating urban patterns in different climates
(Izmir Institute of Technology, 2009) Mengi, Onur; Kaya Erol, Nursen
Many urban design projects we produce today underestimate the design strategies as utilizing the same design criteria for every urban environment regardless their different localities. This problem leads to increasing demands for active heating, cooling and lighting systems, rising energy consumption, declining quality of urban living, environmental deterioration, and expensive and hardly maintained built-up areas.The intention of this study, on one hand, is to present a method of how to examine the climatic factors in an urban area, and on the other hand, is to reconsider urban patterns of Konak Square in Izmir and Kızılay Square in Ankara, from climate sensitive design view point. The overall aim here is to find to what extend designs of the built environment are sensitive to the climate. Specifically, the present study investigates if those urban patterns take the advantage of their particular climate while eliminating the inconveniences.In this framework, the case study was conducted in the summer period, comprising two steps; site surveying and climatic measurements. The findings were processed through the comparison of field measurements with the meteorological data, and the evaluation of the spatial structure in relation to the given comparisons. The study found that Konak Square is more sensitive to the climate comparing to Kızılay Square. The results show that urban pattern of Konak Square takes the advantage of the existing wind conditions, accelerating it throughout the site and decreases air temperature in many locations through its design.
Analysis of finite difference methods for convection-diffusion problem
(Izmir Institute of Technology, 2004) Demirayak, Murat; Neslitürk, Ali İhsan
We consider finite difference methods for one dimensional convection diffusion problem. An error analysis shows that the solution of the upwind scheme is not uniformly convergent in the discrete maximum norm due to its behavior in the layer. Then, we introduce and analyze a numerical method, Il.inAllen-Southwell scheme, that is first-order uniformly convergent in the discrete maximum norm throughout the domain. Finally, we present numerical results that confirm theoretical findings.
Analytic functions on time scales
(Izmir Institute of Technology, 2007) Kapçak, Sinan; Ufuktepe, Ünal
The concept of analyticity for complex functions on time scale complex plane was introduced by Bohner and Guseinov in 2005. They developed completely delta differentiability, delta analytic functions on products of two time scales, and Cauchy Riemann equations for delta case. In this thesis, beside the paper of Bohner and Guseinov, we worked on continuous, discrete and semi-discrete analytic functions and developed completely nabla differentiability, nabla analytic functions on products of two time scales, and Cauchy-Riemann equations for nabla case.
An application of the finite differences method to a dynamical interface problem
(Izmir Institute of Technology, 2004) Ağıroğlu, İzzet Onur; Tanoğlu, Gamze
A multiple-order-parameter model for Cu-Au system on a face cubic centered lattice was recently developed in the presence of anisotropy. In that model, three order parameters (non-conserved) and one concentration order parameter (conserved), which has been taken as a constant, were considered. Later on, the model has been extended, so that, concentration has been taken as a variable. It has been seen that two models were in a good agreement near critical temperature since the non-conserved order parameter behaves like a constant near critical temperature in both models. Thus, we extended the rst model to a dynamical diffuse interface model near critical temperature. After writing the free energy of the system in terms of the order parameters, minimizing the energy with respect to the order parameters and Langevin equation yield the non-linear system of parabolic equations. The finite differences method was implemented to solve this non-linear system of parabolic equations. The forward difference discretization was applied for the rst derivative of the solution with respect to time and centered difference discretization was applied for the second order derivative of the solution with respect to spatial variable. We obtained stability criteria and nd the error bound. The orientation dependence proles, variation of interfacial energy and the effect of the degree of the anisotropy on the width of the diffuse interface are simulated when the time evolves.
Approximation theorems for Krull domains
(Izmir Institute of Technology, 2014) Yeşil, Mehmet; Ay Saylam, Başak
Let R be an integrally closed domain, and denote by I(R) the multiplicative group of all invertible fractional ideals of R. Let {Vi}i∈I be the family of valuation overrings of R, and denote by Gi the corresponding value group of the valuation domain Vi. We show that R = Ti∈I Vi, and there is a map from I(R) into Qi∈I Gi, the cardinal product of the Gi’s. Furthermore, it is well known when R is a Dedekind domain, this map becomes an isomorphism onto `i∈I Gi, the cardinal sum of the Gi’s. In this case, Gi ∼= Z for each i. It is shown, by J. Brewer and L. Klingler, that this map is also an isomorphism onto`i∈I Gi when R is an h-local Prüfer domain. In this thesis, we investigate the existence of such a map, and whether it is injective when R is a Krull domain.
The archaeological sublime: history and architecture in Piranesi's drawings
(Izmir Institute of Technology, 2006) Ek, Fatma İpek; Şengel, Deniz
In the architectural, historical, and archaeological context of the eighteenth century, Italian architect Giovanni Battista Piranesi (1720-1778) played an important role. He posited crucial theses in the debates on the 'origins of architecture' and 'aesthetics'. He is numbered foremost among the founders of modern archaeology. But Piranesi was misinterpreted both in his day and posthumously. The vectors of approach yielding misinterpretation of Piranesi derived from two phenomena: one is the early nineteenth-century Romanticist reception of Piranesi.s character and work. The second is the mode of codification of architectural history. The former interpretation derived from Piranesi.s position on aesthetics, the latter from his argument concerning origins. Both of these served the identification of Piranesi as .unclassifiable.. He has thus been excluded from the 'story' of the progress of western architectural history.Piranesi, however, conceived of these two debates as one interrelated topic.Concerning origins, he developed a history of architecture not based on the East/West division, and supported this by the argument that Roman architecture depended on Etruscans which was rooted in Egypt. Secondly, he distinguished Roman from Grecian architecture identified with 'ingenious beauty'.Thus Piranesi placed Romans in another aesthetical category which the eighteenth century called 'the sublime'.Piranesi's perception caused him to be described as madman or idiosyncratic. However, most of these evaluations lack a stable historical base. Therefore, restoring Piranesi, his arguments, executed works and drawings to architectural history appear as a necessity.
Classical and Quantum Euler equation
(Izmir Institute of Technology, 2007) Eti, Neslihan; Pashaev, Oktay
In the present thesis we give generalization of analytical mechanics to describe dynamical systems with dissipation. The Lagrangian function in this case is determined by nonstationary pseudo-Riemannian metric for the kinetic energy, and by general quadratic form, nondiagonal in the generalized coordinates and velocities. Skew symmetric nondiagonal terms in our approach play the role of dissipation coefficients. As an application we study in details the classical damped harmonic oscillator. We show that two known formulations of this oscillator, the Bateman dual and the Caldirola Kanai formulations are particular realizations of our general approach. The Hamiltonian formulation and quantization of the model in both representations are given. Moreover Ostrogradsky generalization of Lagrangian and Hamiltonian formalism for description of systems with higher order derivatives and its application to the constant coefficient equations of an arbitrary order are considered. We construct related with the last one the Euler differential equation of an arbitrary order and its Lagrangian and Hamiltonian structure. Quantum Euler systems are introduced and solved for the stationary Schrodinger picture. Nonstationary nonlinear quantum models corresponding to arbitrary Euler Hamiltonian are solved exactly in the Heisenberg picture.
Classical time splitting approaches and their error anlyses for nonlinear differential equations
(Izmir Institute of Technology, 2018-06) Hacısalihoğlu, Elif; Tanoğlu, Gamze
In this thesis, Lie - Trotter splitting, Strang - Marchuk splitting and symmetrically weighted sequential (SWS) splitting methods which are known as classical operator splitting methods are considered to find the numerical solution of the various ordinary differential equations (ODEs) and partial differential equations (PDEs). We also presented their error analyses in order to show advantages and disadvantages of these methods. Firstly, we considered simple linear and nonlinear ODE examples to motivate for the classical operator splitting methods. Then, two numerical examples which consist of a kinetic model of phage infection and the Newell - Whitehead - Segel (NWS) equation are studied. All these examples show that the operator splitting methods are a powerful technique with respect to the accuracy and robustness.
A compact finite difference method of lines for solving non-linear partial differential equations
(Izmir Institute of Technology, 2022-07) Ismoilov, Shodijon; Tanoğlu, Gamze; Gürarslan, Gürhan
In this thesis, an efficient numerical method is proposed for the numerical solution of the chemical reaction-diffusion model governed by a non-linear system of partial differential equations known as a Brusselator model. The method proposed is based on a combination of higher-order Compact Finite Difference schemes and stable time integrator known as an adaptive step-size Runge-Kutta method. The performance of adaptive step-size Runge-Kutta formula of fifth-order accurate in time and Compact Finite Difference scheme of sixth-order in space are investigated. The method is implemented to solve three test problems and reveals that the method is capable of achieving high efficiency, accuracy and reliability. The results obtained are sufficiently accurate compared to some available results in the literature.
Comparison od side effects of anti-cancer drugs in 2D and 3D and, classical and cell-on-a-chip cultures
(Izmir Institute of Technology, 2016-07) Kankale, Deniz; Pesen Okvur, Devrim; Çağır, Ali
The studies that aim to assess the effects of drugs developed against cancer at the cellular level use multiwell plates. However, these classical systems fail to reproduce the in-vivo like microenvironment necessary for realistic assessment. In addition, classical cell culture systems use high amount of materials increasing cost. On the other hand, lab-on-a-chip systems use minimal volumes of reagents and more importantly can mimic the in-vivo microenvironment via spatial and temporal control. Furthermore, it is known that cell response to drugs can be very different in 2D and 3D cell culture setups. Doxorubicin is a widely used anticancer drug. Here, doxorubicin uptake by highly metastatic human breast cancer cell line MDA-MB-231 and normal mammary epithelial cell line MCF10A were investigated using 2D and 3D, classical and cell-on-a-chip cultures. Drug uptake at 24, 48 and 72 hours various concentrations of the drug determined by measuring signal intensities from fluorescence microscopy images of cells. For cell viability assay, cells were stained with dapi and two cell lines were compared in systems. According to results, it was observed that 3D cell culture environment in chip provides more in-vivo like environment with less reagent consumption and cell viability is not correlated only with drug uptake.
Computation of the convection diffusion equation by the fourth order compact finite difference method
(Izmir Institute of Technology, 2015) Bajellan, Asan Ali Akbar Fatah; Tayfur, Gökmen
This dissertation aims to develop various numerical techniques for solving the one dimensional convection–diffusion equation with constant coefficient. These techniques are based on the explicit finite difference approximations using second, third and fourth-order compact difference schemes in space and a first-order explicit scheme in time. The suggested scheme has been seen to be very accurate and a relatively flexible solution approach in solving the contaminant transport equation for Pe ≤ 5. For the solution, the combined technique has been used instead of conventional solution techniques. The accuracy and validity of the numerical model are verified. The computed results showed that the use of the current method in the simulation is very applicable for the solution of the convection-diffusion equation. The technique is seen to be alternative to existing techniques. This dissertation is divided into six chapters: The derivation of the convective diffusion equation is given in Chapter 2. The main idea behind the higher order finite difference technique is given in Chapter 3. The numerical approximations to CDE described with ten different explicit schemes are introduced in Chapter 4. The results of numerical experiments using second, third and fourth-order compact difference schemes are presented in Chapter 5. Chapter 6 is devoted to a brief conclusion. Finally the references are introduced at the end.
Convergence analysis and numerical solutions of the Fisher's and Benjamin-Bono-Mahony equations by operator splitting method
(Izmir Institute of Technology, 2014) Zürnacı, Fatma; Tanoğlu, Gamze
This thesis is concerned with the operator splitting method for the Fisher’s and Benjamin-Bono-Mahony type equations. We showthat the correct convergence rates inHs(R) space for Lie- Trotter and Strang splitting method which are obtained for these equations. In the proofs, the new framework originally introduced in (Holden, Lubich, and Risebro, 2013) is used. Numerical quadratures and Peano Kernel theorem, which is followed by the differentiation in Banach space are discussed In addition, we discuss the Sobolev space Hs(R) and give several properties of this space. With the help of these subjects, we derive error bounds for the first and second order splitting methods. Finally, we numerically check the convergence rates for the time step ∆t.
The deformation rate sensitivities of additively and conventionally fabricated 316L alloys
(01. Izmir Institute of Technology, 2021-12) Enser, Samed; Güden, Mustafa; 01. Izmir Institute of Technology
The compression stress-strain behavior of a Scanning Laser Melt 316L (SLM-316L) and an annealed and extruded commercial 316L (C-316L) were determined between 1x10-3 s-1 and 2500-3150 s-1. SLM-316L deformed by twinning and slip, while C-316L by martensitic transformation and slip with no fracture until about 0.51 strain. The higher yield strength of SLM-316L than C-316L was attributed to the higher dislocation density of SLM-316L. The higher work hardening rate of C-316L alloy was proved due to the higher resistance of martensite plate than twin boundary to the dislocation motion. As the strain rate increased, both alloys showed increased flow stresses. However, the rate sensitivities declined as the strain increased due to the adiabatic heating at high strain rates. The Johnson and Cook flow stress material models of both alloys were further determined for the adiabatic and isothermal conditions. The martensite formation in C-316L specimens and twinning formation in SLM-316L alloys decreased at high strain rates compared to quasi-static strain rates. The XRD spectra of C-316L also confirmed the reduced martensite formation at high strain rates. The reduced twin and martensite formation at high strain rates were attributed to the increased stacking fault energy due to the adiabatic heating of the test specimens. The increase of stacking fault energy at high strain rates promoted a higher fraction of the deformation by slip. Lastly, the reloading tests revealed a strain-rate history effect in SLM-316L and no strain-rate history effect in C-316L.
Design and development of paper-based microfluidics for point-of-care applications
(01. Izmir Institute of Technology, 2020-12) Özefe, Fatih; Arslan Yıldız, Ahu; Yıldız, Ümit Hakan; 01. Izmir Institute of Technology
Paper-based microfluidics is a subarea of microfluidics which is recently used in various applications from diagnostics to environmental monitoring, and to food safety. In such microfluidic systems, a test platform is formed from a paper substrate instead of silicon and polymers, such as poly-dimethylsiloxane, poly-methyl methacrylate, and etc. The main goal of this thesis is the development and fabrication of a paper-based microfluidic device (μPAD), which could be used in point-of-care (POC) applications. The characterizations of μPADs, which were fabricated via laser ablation methodology, were performed in terms of their surface and barrier characteristics, and liquid sample flows within μPADs. Depending on the characterization, nine different fabrication parameters, 10P40S (10%Power & 40%Speed), 10P60S, 20P90S, 30P50S, 30P100S, 40P80S, 40P100S, 70P80S, and 70P100S, were identified as optimized fabrication parameters. Also, two designed models of μPADs, 1S4T-Type2 and 1S4T-Type3, were selected to be used in the detection of BSA and recombinant Hepatitis C Virus (HCV) protein. The BSA and HCV (1 mg/ml) in PBS solution were successfully detected via naked eye depending on the colorimetric sensing through micro-paper enzyme linked immunosorbent assay (μP-ELISA) protocol. Moreover, the limit of detection (LoD) values for HCV were determined in 1S4T-Type2 μPAD as 1.000, 0.883, and 0.796 ng/ml when the detection was performed via naked eye, smart-phone, and bright-field microscope, respectively. Also, the easily-disposable 1S4T-Type2 μPAD provided 14 times faster and 45 times cheaper detection of HCV compared to conventional ELISA techniques. Consequently, the developed 1S4T-Type2 μPAD presented low-cost, easy-to-use, and rapid detection of HCV as POC devices.
Development of a design evaluation tool for primary school projects
(Izmir Institute of Technology, 2003) Çelik, Çelen Ayşe; Eyüce, Ahmet
Education should play an important role in transforming children into productive adults and members of society. School should be the environment of these transformations as an educational milieu in which children collect data through perception. School should also offer a motivating environment while concepts of three-dimensionality, size, proportion and symbolization develop in the child.s mind. Therefore, the spaces in which children are educated have very special importance in their lives.Contemporary schools should have environmental adaptation, be functionally sufficient, aesthetically attractive and structurally appropriate.Since August 18'th 1997, new educational measures have been taking such as renovation of Turkish National Education Program and primary school education which have been extended from five years to eight years. This required capacity increase, restoration of existing school buildings and design of new projects.Development of an evaluation tool for primary school projects has the aim of creating a basis for future primary school projects for both private and national ones.
Development of fast and simple analytical methods for the determination of honey adulteration and forgery based on chemometric multivariate data analysis by using molecular spectroscopy
(Izmir Institute of Technology, 2016-12) Başar, Başak; Özdemir, Durmuş
Honey is one of the most valuable and expensive nutrition due to its health effects on human body. In recent years, honey adulteration has become an important problem and is a subject of many publications. There exists various analytical methods for determination of honey adulteration with 13C/12C isotope ratio mass spectrometry (IR-MS) being the most common. However, one of the recent studies indicates that different honey types depending on geographical and botanical origin may have significantly different 13C/12C isotope ratios rendering this method questionable. Thus, development of an analytical method for qualitative and quantitative determination of forgery and adulteration of honey without tedious and complicated sample preparation while being relatively simple and fast new analytical methods became a must. In this study, Fourier Transform Infrared spectroscopy coupled with Attenuated Total Reflectance and Fourier Transform Near Infrared spectroscopy based chemometrics multivariate calibration models were developed for the quantitative determination of honey adulteration. To simulate adulteration scenarios, artificially adulterated honey samples were prepared by adding beet sugar, corn syrup, glucose and sucrose with various concentrations to pure honey samples. Two different multivariate calibration methods namely Genetic Inverse Least Squares and Partial Least Squares were used and the applicability of these methods have been evaluated with an independent validations and test set composed of FTIR spectra of more than 100 pure honey samples along with the adulterated samples. Standard error of cross validation and standard error of prediction values for honey content of the samples were found 2.52% and 2.19% (w/w %), respectively.

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