Theses supervised by Prof. Dr. Tekin Dereli
10 theses · Koç University
Tek katlı karbon nanotüplerinin burulma deformasyonunun moleküler dinamik simulasyon çalışması
Thesis Title : A MOLECULAR DYNAMICS SIMULATION STUDYOF TORSIONAL DEFORMATIONS OF SINGLE-WALLED CARBONNANOTUBESAbstractIn this study we present the tight binding molecular dynamics (TBMD) simulationresults for torsional response of 10x10 single-walled carbon nanotubes for varyingnumbers of layers, twist angles and temperature conditions. TBMD method we use hasO(N) complexity and it has been executed both in sequential and parallel modes. Thecode is executed in a distributed memory system utilizing the concept of parallel virtualmachines (PVM). The mechanical properties of the simulated structure such as bondlength distribution, bond angle distribution, torsional deformations, total energy, shearmodulus and torsion stiffness were studied under various simulation conditions. We alsopresented the efficiency and speedup graphs of the parallel computation.Advisor: Prof. Dr . Tekin Dereli Date:3/08/2005Director: Date:
Kuantum hesaplama için bloch vektör formalismi
The Bloch vector formalism provides a useful approach to both fundamental andapplied problems of the finite dimensional, composite quantum systems, andtherefore it is a very important tool for the research on quantum computation andinformation. This thesis deals with the systematic treatment of Bloch vectorformalism for quantum mechanics of one node, two node and three node systems.Each chapter is divided into three sections dealing with state vectors, measurementsand time evolutions. Also, the geometric picture of the space of states will be givenin the section on one node systems. Classically correlated states i.e. separablestates, for two and three node systems will be investigated in the relevant chapters. Iwill also briefly mentioned the well-known EPR paradox, Bell's inequality, Mermin'sproofs on the problems with the elements of reality by using GHZ state and the twodifferent classes of the genuine tripartite entanglement to comprehend the unusualnature of entanglement.Advisor: Prof. Tekin Dereli Date:Director: Prof. Süleyman Özekici Date:
Silikon nanotüplerin moleküler dinamik simulasyon çalışması
Since carbon and silicon lie in the same group of elements in the periodic table and have similar electronic configurations, the possibility of having silicon nanotubes similar to the conventional carbon nanotubes have attracted much recent attention. Single walled silicon hexagonal nanotubes (hNTs) should be formed by rolling-up graphene-like silicon sheets. In recent literature, many correlative theoretical predictions have been performed on such silicon nanotubes.In this thesis work, a semi-empirical tight-binding molecular dynamics (TBMD) technique is employed in the simulation studies of single walled silicon hNTs. Appropriate tight-binding pair potential parameters are obtained by fitting the results of ab initio calculations. We optimized the silicon hNTs having the same predicted total energy values reported in the literature. The effects of chirality and diameter on the energetics, strain energies, and electronic density of states of single walled silicon hNTs have been studied on several types of armchair and zigzag nanotubes. We present the results of our TBMD simulations and discuss about the possible stability of silicon hNTs.
6 boyutlu kommutatif olmayan \phi^3 etkilesmeli skaler alan teorisinin asimptotik bagimsizligi
Quantization of a real, massive scalar field with ?3 interactions in D=6 dimensionalnoncommutative flat space-time will be reviewed. 1- loop perturbative renormalization ofthe scattering amplitudes and the derivation of the renormalization group equations willbe shown explicitly. Analysis of these equations will show the asymptotic freedom of thisparticular quantum field theory. Quantitative results from perturbative calculations will be compared to those from exact calculations.
Karanlık kütleçekiminin f(R) teorileri
A review of f(R) theories of Dark Gravity is given. The variational field equations are derivedfor space-time geometries both with and without torsion. The method of Lagrangemultipliers is used. Possible modifications to cosmological solutions are discussed in general.A specific solution to modified Friedmann equations with an exponential expansion isobtained. Finally further generalizations of theories of dark gravity are pointed out.
2+1 boyutlu yer çekimi teorileri
(2+1) dimensional Topologically Massive Gravity (TMG) and New Massive Gravity (NMG) theories are studied. These theories have higher order derivatives of metrictensor in their field equations which make them both renormalizable and unitary. Field equations of TMG are derived using variational methods. A null frame is introducedin general and TMG field equations are written in the null frame. pp-wave solutions of TMG are given. NMG field equations in the null frame are also derived. The pp-wave and recently found bending AdS wave solutions of NMG are given.
Kuantum anahtar dağıtımı protokolleri
A review of quantum key distribution protocols has been made.A simulation of BB84 protocol with reconciliation and privacy amplification has been presented.Intervension of an eavesdropper has been implemented.
Anyonik kuantum hesaplama
Quantum computation can be done by using non-abelian anyons which are neither bosonsnor fermions. Quasi-particles of v=5/2 fractional quantum Hall state will provide nonabeliananyons. We discuss a NOT gate operation using these anyons. In the thesis fundamentalconcepts of quantum computation are reviewed. Non-abelian anyons and topologicalphases are introduced. Some basic facts about fractional quantum Hall state are given.
Süper iletken devrelerle kübit tasarlama
We start by reviewing methods to derive hamiltonians for superconducting circuits. By canonical quantization we obtain quantum mechanical description of electrical circuits in the low temperature limit. We then look at some basic superconducting qubit circuits. Some schemes for tunable coupling of qubits to transmission lines are analyzed. We also propose a way to protect qubits during measurement using frequency modulation (FM).
Abelyen olmayan manyetik monopol ve dyonlar
We first review Dirac's Abelian magnetic monopole solutions in Maxwell's electrodynamics.Then after a short discussion of the unified electroweak gauge fiield theories and the Higgsmechanism for mass generation we derived the non-Abelian magnetic monopole solutions of't Hooft and Polyakov. We discussed the topological nature of such solutions. We calculatedthe total mass and the magnetic charge of these solutions and verified that they saturatethe BPS bound. Dyon solutions are also given. Finally, we briefly comment on Montonenand Olive's non-Abelian duality conjecture.