# Alumni Dissertations

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### Generalization of the three-term recurrence formula and its applications

Author:Yoon Seok ChounYear of Dissertation:2012Program:PhysicsAdvisor:Sultan CattoAbstract:In an earlier paper we showed development of a bilocal baryon-meson field from two quark-antiquark fields. In the local approximation the hadron field was shown to exhibit supersymmetry which was then extended to hadronic mother trajectories and to inclusion of multiquark states. The Hamiltonian in the case of vanishing quark masses was shown to have a very good agreement with experiments. The theory for vanishing mass was solved using confluent hypergeometric functions. In order to solve the spin-free Hamiltonian with light quark masses we are led to develop a totally new kind of special function theory in mathematics that generalize all existing theories of confluent hypergeometric types. We call it the `Grand Confluent Hypergeometric Function.' Our new solution produces previously unknown extra "hidden" quantum numbers relevant for description of supersymmetry and for generating new mass formulas. Furthermore, we show for the first time how to solve mathematical equations having three term recursion relations and go on producing the exact solutions of some of the well-known special function theories that include Mathieu, Heun, Lame and the Grand Confluent Hypergeometric Function. We hope these new functions and their solutions will produce remarkable new range of applications not only in supersymmetric field theories as is shown here, but in the areas of all different classes of mathematical physics, applied mathematics and in engineering applications.

### The Impact of Context on Learning and Epistemology in Physics

Author:Sebastien CormierYear of Dissertation:2009Program:PhysicsAdvisor:Richard SteinbergAbstract:This dissertation investigates the impact that various contexts have on student learning and epistemology. This is accomplished by analyzing diverse student populations learning various subjects in physics in distinctive classroom environments at City College New York (CCNY). Studies in Physics Education Research (PER) have found that many students lack proper conceptual understanding after instruction in physics and that their epistemology, or approaches to learning and doing science, is different from those of experts. The PER community has used these results to develop models of learning and tools for teaching introductory and modern physics with goals that include improving the conceptual understanding, problem solving abilities, and epistemologies. These curricula are applied in a wide variety of contexts here at CCNY. The student contexts in this dissertation range from high school to graduate school, and the topics range from introductory to modern physics. We apply many tools commonly used in PER, such as multiple-choice surveys, essay questions, and guided interviews to study these classrooms. We find that PER- based curriculum implemented in these different contexts is able to improve both conceptual understanding and epistemology.

### Yang-Mills Theories as Deformations of Massive Integrable Models

Author:Axel Cortes CuberoYear of Dissertation:2014Program:PhysicsAdvisor:Peter OrlandAbstract:Yang Mills theory in 2+1 dimensions can be expressed as an array of coupled (1+1)-dimensional principal chiral sigma models. The SU(N) principal chiral sigma model in 1+1 dimensions is integrable, asymptotically free and has massive excitations. We calculate all the form factors and two- point correlation functions of the Noether current and energy-momentum tensor, in 't Hooft's large-N limit (some form factors can be found even at finite N). We use these new form factors to calculate physical quantities in (2+1)-dimensional Yang-Mills theory, generalizing previous SU(2) by P. Orland to SU(N). The anisotropic gauge theory is related to standard isotropic one by a Wilsonian renormalization group with ellipsoidal cutoffs in momentum. We calculate quantum corrections to the effective action of QED and QCD, as the theory flows from isotropic to anisotropic. The exact principal chiral sigma model S-matrix is used to examine the spectrum of (1+1)-dimensional massive Yang Mills theory.

### LONG-RANGE DIPOLAR FIELDS AS A TOOL FOR NUCLEAR MAGNETIC RESONANCE MICROSCOPY

Author:Wei DongYear of Dissertation:2009Program:PhysicsAdvisor:Carlos MerilesAbstract:ABSTRACT Long-Range Dipolar Fields as a Tool for Nuclear Magnetic Resonance Microscopy By Wei Dong Mentor: Prof. Carlos Meriles Nuclear Magnetic Resonance (NMR) is widely used today for structural and dynamical studies of the properties of diverse materials. However, due to the relatively low sensitivity of the standard induction detection method, NMR is strongly constrained when probing samples whose effective dimensions are less than a few microns. To overcome these limitations, our novel strategy based on the manipulation of the long-range dipolar interactions between the sample and a hyperpolarized semiconductor tip located close to its surface. These interactions are used to modulate the tip nuclear magnetization in a way proportional to the local sample magnetization. The advantage of this strategy lies in that the highly sensitive detection methods - e.g., optical detection - can be used to monitor the semiconductor tip, thus providing the opportunity to indirectly probe the sample neighboring the tip with a favorable signal-to-noise ratio. Because the detected portion of the sample is comparable to the size of the tip, resolution exceeding the currently attainable could be possible. As an initial demonstration of our methodology we designed an experiment in which a 3 mm diameter distilled water droplet - playing the role of a sensor - was used to detect the NMR signal of the sample surrounding the droplet, in this case, silicon oil (Sigma-Aldrich) contained in a 5 mm diameter glass tube. Notice the sample (oil) and the detection center (water) are distinct and discernible objects only connected through long range intermolecular dipolar couplings. A special pulse sequence was designed and applied in the experiment to encode the sample magnetization for detection. By utilizing the Runge-Kutta algorithm, I modeled a 2000 spins ensemble based on the given geometry and numerically calculated the Bloch differential equations of this coupled spins system. Experimental results have a very good agreement with the numerical calculations. This preliminary experiment proves that not only the sample NMR signal can be indirectly detected, also many other sample information - e.g., relaxation time, sample spectrum, etc. - are attainable. Minimizing the short range dipolar couplings is a very crucial part to achieve the final goal of this strategy when the solid state semiconductor was used as the sensor. At the second stage, a modified MREV16 decoupling pulse sequence was designed and applied to greatly reduce the short range dipolar couplings inside the solid state sensor. A 3 mm thick disk GaAs crystal has been chosen as the sensor due to its excellent optical hyperpolarization properties. By acquiring 71Ga NMR signal, I successfully indirectly detected a tiny nuclear dipolar field induced by proton spins from an adjacent organic sample (as small as 7 nT). Optical enhancing the bulk averaged nuclear spin polarization in semiconductors is another critical technique that will be integrated into our strategy. Comparing to the thermal nuclear magnetization, we achieved 2-3 orders of magnitude optical enhancement for 71Ga in GaAs crystal and 3 orders for 125Te in CdTe crystal. Finally optical Faraday rotation will be used as an ultrasensitive detection to incorporate into the strategy. Optical reading of the electronic Larmor frequency shift in the semiconductor by using Time-Resolved Faraday Rotation (TRFR) to probe the sample magnetization change is the basic idea of our optical detection scheme. Through collaboration with Attocube AG, a leading company specialized on low temperature optical microscopy, our cutting-edge cryogenic optical NMR probe has been finished. Certainly, integrating optical hyperpolarization and optical detection with modern NMR technique is very challenging and requires tremendous work. However given the steady progress in the area of nanotechnology, our strategy's future still appears quite promising.

### Averaged dynamics of the advection-diffusion equation and applications to ocean flows.

Author:Yauheni DzedzitsYear of Dissertation:2012Program:PhysicsAdvisor:Tobias SchaferAbstract:This dissertation presents some aspects of an advection-diffusion equation and its applications to physical oceanography. We propose a perturbative scheme of averaging the advection-diffusion equation in the limit of vanishing diffusivity. Under the restriction that the time-dependence of the advective field is completely separable we construct an exact solution of the purely advective part via action-angle coordinates and treat diffusion as a perturbation using Lie transform techniques. The developed method is applied to a regularized vortical flow field which is periodically modulated in time. Numerical simulations of the vortical flow advection in presence of small diffusion are discussed. We present numerical evidence that the spectrum of of the averaged time-independent advection-diffusion operator converges to the spectrum of the operator with fully enabled time dynamics. A formal generalization of the method for three-dimensional time-periodic flows is discussed. We also discuss the importance of advection and diffusion in problems of transport and mixing in complicated dynamical systems, such as hydrodynamical systems, in particular describing ocean currents. We propose a method to visualize and analyze the structure of complex flows using data from HYbrid Coordinate Ocean Model (HYCOM) as an example. We present results of simulations obtained with highly parallel Co-array Fortran code that can be run on modern computing systems that support partitioned global address space (PGAS) programming model.

### STRUCTURAL AND DYNAMICAL FEATURES OF PROTEIN P7 FROM BACTERIOPHAGE 12: INSIGHTS INTO A FUNCTIONAL ROLE IN THE CYSTOVIRAL POLYMERASE COMPLEX

Author:Ertan EryilmazYear of Dissertation:2010Program:PhysicsAdvisor:Ranajeet GhoseAbstract:Cystoviruses are a class of enveloped double-stranded RNA viruses that use a multi- protein polymerase complex (PX) to replicate and transcribe the viral genome. The cystoviral PX, that is amenable to in vitro and in vivo manipulation, comprises a unique model system for similar polymerase machinery. Containing three segmented double stranded RNA genome, the cystoviral PX is a simplified model for the polymerase machinery in more complex RNA viruses like reoviruses sharing structural and functional similarities at the level of the constituent proteins. Though the structures of the RNA dependent RNA polymerase (RdRp) and ATPase components of the cystoviral PX are known and their functional behaviors understood to a large extent, no atomic- resolution structural information is available for the major capsid protein P1 that defines the overall structure and symmetry of the viral capsid, and the essential protein P7. Towards obtaining a complete structural and functional understanding of the cystoviral PX, we have obtained the structure of P7 from the cystovirus 12 at a resolution of 1.8 Å. The N-terminal core region (1-129) of P7 forms a novel homodimeric αβ-fold with structural similarities with BRCT domains implicated in multiple protein-protein interactions in DNA repair proteins. Our results combined with the known role of P7 in stabilizing the nucleation complex during capsid assembly hints towards its participation in key protein-protein interactions within the cystoviral PX. Additionally, we have found through solution NMR studies that the C-terminal tail of P7 (130-169) that is essential for virus viability, though highly disordered, contains a nascent helix. We demonstrate through NMR-based titrations, that P7 is capable of interacting with RNA. We find that both the N-terminal core and the dynamic C-terminus tail of P7 play a role in RNA recognition leading to a significant reduction of the degree of disorder in the C-terminal tail. Given the additional role of P7 in maintaining transcriptional fidelity, our data suggest a central biological role for P7/RNA interactions.

### Variable Pressure and Temperature NMR Studies of Fuel Cell Polymer Electrolyte Membranes

Author:Jaime FarringtonYear of Dissertation:2010Program:PhysicsAdvisor:Steve GreenbaumAbstract:It was not until the latter half of the 20th century, with the technological developments associated with the space race, that the technical feasibility of the fuel cell was demonstrated. Various fuel cell technologies have emerged in this time period of which Proton Exchange Membrane Fuel Cells (PEMFCs) are of particular interest due to their lower operating temperatures, as compared with other types of fuel cells. Thus, they are ideal for applications such as small portable electronics and transportation. However, there are several challenges facing PEMFC`s such as the development of efficient and durable proton exchange membranes (PEMs). There are several techniques for the characterization of PEMs, One of these techniques is nuclear magnetic resonance (NMR), which has been an important tool in the characterization of ionic motion in liquids and solids. The ionic self-diffusion coefficient is of great importance in understanding the ionic conduction mechanism of electrolytic materials for fuel cells. In hydrated fuel cell membranes, the diffusion coefficient of water molecules also plays a vital role in ionic (protonic) transport. The measurements of the diffusion coefficients are performed by standard NMR methods. These measurements are usually performed as a function of temperature to obtain vital parameters such as activation energies. If an independent thermodynamic parameter such as pressure is employed, additional information about the ion transport process, such as activation volume, may be obtained. Studies of several types of fuel cell membranes based on sulfonated flouoropolymers are presented.

### The Evolution of and Starburst-AGN Connection in Luminous and Ultraluminous Infrared Galaxies and their Link to Globular Cluster Formation

Author:Stephanie FiorenzaYear of Dissertation:2014Program:PhysicsAdvisor:Charles LiuAbstract:The evolutionary connection between nuclear starbursts and active galactic nuclei (AGN) in luminous infrared galaxies (LIRGs; 1011o

125 Myr) agree with previous results, while those with younger starbursts show a large dispersion in Mstar. I conclude that this is supporting evidence that the star formation histories and timescales at which the IR power sources in U/LIRGs evolve are responsible for the scatter found for the SFR-Mstar relationship. U/LIRGs that form from merging gas-rich disk galaxies could also represent a stage of galaxy evolution involving heavy formation of globular clusters (GCs). It has been suggested that a large number of stellar clusters form during the merging of two gas-rich disk galaxies, leading to open and young massive clusters with the latter likely evolving into GCs. Furthering our understanding of GC formation can uncover the connection between GCs and their host galaxies, which could, at some point during their formation or evolution, be U/LIRGs. To understand GC formation in the context of hierarchical galaxy formation, it is necessary to understand the origin of their abundance patterns. To this effort, I use SDSS spectra from Data Release 8 and 9 to estimate carbon (C) abundances for five GCs by matching synthetic spectra, created with TURBOSPECTRUM using atmospheric parameters derived from the Segue Stellar Parameter Pipeline, with observed spectra at the CH G-band feature. I find large spreads in the C abundances throughout the color magnitude diagrams of the GCs, which serves as evidence for multiple stellar populations, in contrast to standard models of GC formation. ### Discrimination and Identification of Quantum States

Author:Ulrike FutschikYear of Dissertation:2010Program:PhysicsAdvisor:Janos BergouAbstract:Determining the state of a quantum system is an essential step in quantum information processing. While the case of N=2 arbitrary states is well known the extension to N>2 is highly non-trivial. Unambiguous discrimination among N>2 pure states is one of the longest standing unsolved problems in quantum information. We develop a complete geometric picture that encompasses all aspects of the problem: linear independence of the states, positivity of the detection operators, and a graphic method for finding and classifying the optimal solutions. We illustrate it on the example of three states and also show that the problem depends on an invariant combination of the phases of the complex inner products, the Berry phase. For arbitrary inner products and prior probabilities only numerical solutions are possible but the features of the solution are universal, they hold for any value of the Berry phase up to φ=π at which point it greatly simplifies. We, therefore, present the complete analytical solution for the case of vanishing Berry phase. The corresponding optimal failure probability exhibits full permutational symmetry for a large range of the parameters. However, when the parameters have very different values, a second-order symmetry-breaking phase transition takes place: at a particular value of the parameters the optimal failure probability becomes bi-valued: a second, less symmetric solution branches away in a continuous way from the symmetric one which is optimal in the new regime for some set of parameters. We also study some special cases where the inner products of two or all three states coincide but the phase is arbitrary as well as the case of weighted equal probability measurement. The optimum measurement is derived and it is a general measurement (POVM). The generalization of our results to the discrimination of more than three states will discussed in the conclusion. Finally, we address the problem of identifying one probe qudit with one out of N reference qudits. Two strategies, the unambiguous and the minimum error identification, are studied. The reference states are assumed to be pure states and no classical knowledge about them is available. The probe state is guaranteed to match one of the reference states with equal probability. The problem is shown to be equivalent to distinguishing between mixed quantum states. Through the example of three ququartz states the form of the optimal measurement operators is derived for the unambiguous strategy. Using the positivity constraint for the operator of the inconclusive result the optimum success probability is calculated. In the minimum error identification an upper and a lower bound are derived, the latter by using a square-root measurement. Numerical values of the success probability are calculated to which the lower bound compares favorable.

### Mathematical and Physical Analysis of Pricing Models for Structured Financial Securities

Author:Xin GaoYear of Dissertation:2012Program:PhysicsAdvisor:Brian SchwartzAbstract:In this thesis, we present an extension of the one-factor Gaussian copula model for pricing collateralized debt obligations (CDOs): Instead of using flat default correlation and rate parameters across the whole portfolio, we use individual correlation coefficients between each reference entity and the market (S&P 500 index) based on 5-year daily stock prices, and we use specific rate parameter for each entity by curve-fitting the default probability term structure. Spreads from this improved model are compared to those obtained from the one-factor Gaussian copula model with flat correlation. Results show that uniform correlation and rate parameters fail to capture that a few or even one single asset can substantially impact the credit quality of the whole portfolio. Heterogeneity of correlations and rate parameters of different reference entities is indispensable for constructing reliable and realistic models for pricing synthetic CDOs. We also introduce analytical solutions to the pricing of both homogeneous and heterogeneous CDOs. We compare these analytical solutions with results obtained from simulation models. Results show very good consistency. At the end, we introduce the analysis of another financial derivative - Securitized Life Settlements (SLSs) and present an analytical solution to the pricing of homogeneous SLSs.