Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: We investigate the procedure of assigning probabilities to logical statements. The simplest case is that of equilibrium statistical mechanics and its fundamental assumption of equally likely states. Rederiving the formulation led us to question the assumption of logical independence inherent to the construction and speci cally its inability to update probability when data becomes available. Consequently we replace the assumption of logical independence with De Finetti's concept of exchangeability. To use the corresponding representation theorems of De Finetti requires us to assign prior distributions for some general parameter spaces. We propose the use of stability properties to identify suitable prior distributions. The combination of exchangeable likelihoods and corresponding prior distributions results in more general evidence distribution assignments. These new evidence assignments generalise the Shannon entropy to other entropy measures. The goal of these entropy formulations is to provide a general framework for constructing models. / AFRIKAANSE OPSOMMING: Ons ondersoek the prosedure om waarskynlikhede aan logiese stellings toe te ken. Die eenvoudigste geval is die van ewewig-statistiese meganika en die ooreenkomstige fundamentele aanname van ewekansige toestande. Hera eiding van die standaard formulering lei ons tot die bevraagtekening van die aanname van logiese onafhanklikheid en spesi ek die onmoontlikheid van opdatering van waarskynlikheid wanneer data beskikbaar raak. Gevolglik vervang ons die aanname van logiese onafhanklikheid met De Finetti se aanname van omruilbaarheid. Om die ooreenkomstige voorstelling stellings te gebruik moet ons a priori verdelings konstrueer vir 'n paar algemene parameter-ruimtes. Ons stel voor dat stabiliteits-eienskappe gebruik moet word om geskikte a priori distribusies te identi seer. Die kombinase van omruilbare aanneemlikheids funksies en die ooreenkomstige a priori verdelings lei ons tot nuwe toekennings van getuienis-verdelings. Hierdie nuwe getuienesverdelings is n veralgemening van Shannon se entropie na ander entropie-maatstawwe. Die doel van hierdie entropie formalismes is om 'n raamwerk vir modelkonstruksie te verskaf.

Thesis (MSc)--University of Stellenbosch, 2007. / ENGLISH ABSTRACT: Buying and selling in financial markets are driven by demand. The demand can be quantified by the imbalance in the number of shares QB and QS transacted by buyers and sellers respectively over a given time interval t. The demand in an interval t is given by (t) = QB − QS. The local noise intensity is given by = h|aiqi − haiqii|i where i = 1, . . . ,N labels the transactions in t, qi is the number of shares traded in transaction i, ai = ±1 denotes buyer- initiated and seller- initiated trades respectively and h· · · i is the local expectation value computed from all the transactions during the interval t. In a paper [1] based on data from the New York Stock Exchange Trade and Quote database during the period 1995-1996, Plerou, Gopikrishnan and Stanley [1] reported that the analysis of the probability distribution P( | ) of demand conditioned on the local noise intensity revealed the surprising existence of a critical threshold c. For < c, the most probable value of demand is roughly zero; they interpreted this as an equilibrium phase in which neither buying nor selling predominates. For > c two most probable values emerge that are symmetrical around zero demand, corresponding to excess demand and excess supply; they interpreted this as an out-of-equilibrium phase in which the market behaviour is buying for half of the time, and selling for the other half. It was suggested [1] that the two-phase behaviour indicates a link between the dynamics of a financial market with many interacting participants and the phenomenon of phase transitions that occurs in physical systems with many interacting units. This thesis reproduces the two-phase behaviour by means of experiments using sequences of random variables. We reproduce the two-phase behaviour based on correlated and uncorrelatd data. We use a Markov modulated Bernoulli process to model the transactions and investigate a simple interpretation of the two-phase behaviour. We sample data from heavy-tailed distributions and reproduce the two-phase behaviour. Our experiments show that the results presented in [1] do not provide evidence for the presence of complex phenomena in a trading market; the results are a consequence of the sampling method employed. / AFRIKAANSE OPSOMMING: Aankope en verkope in finansi¨ele markte word deur aanvraag gedryf. Aanvraag kan gekwantifiseer word in terme van die ongebalanseerdheid in die getal aandele QB en QB soos onderskeidelik verhandel deur kopers en verkopers in ’n gegewe tyd-interval t. Die aanvraag in ’n interval t word gegee deur (t) = QB −QS. Die lokale geraasintensiteit word gegee deur = h|aiqi − haiqii|i waar i = 1, . . . ,N die transaksies in t benoem, qi die getal aandele verhandel in transaksies verwys, en h· · · i op die lokale verwagte waarde dui, bereken van al die tansaksies tydens die interval t. In ’n referaat [1] wat op data van die New York Effektebeurs se Trade and Quote databasis in die periode tussen 1995 en 1996 geskoei was, het Plerou, Gopikrishnan en Stanley [1] gerapporteer dat ’n analise van die waarskynlikheidsverspreiding P( | ) van aanvraag gekondisioneer op die lokale geraasintensiteit , die verrassende bestaan van ’n kritieke drempelwaarde c na vore bring. Vir < c is die mees waarskynlike aanvraagwaarde nagenoeg nul; hulle het dit ge¨ınterpreteer as ’n ekwilibriumfase waartydens n`og aankope n`og verkope die oormag het. Vir > c is die twee mees waarskynlike aanvraagwaardes wat te voorskyn kom simmetries rondom nul aanvraag, wat oorenstem met ’n oormaat aanvraag en ’n oormaat aanbod; hulle het dit geinterpreteer as ’n buite-ewewigfase waartydens die markgedrag die helfte van die tyd koop en die anderhelfte verkoop. Daar is voorgestel [1] dat die tweefase gedrag op ’n verband tussen die dinamiek van ’n finansiele mark met baie deelnemende partye, en die verskynsel van fase-oorgange wat in fisieke sisteme met baie wisselwerkende eenhede voorkom, dui. Hierdie tesis reproduseer die tweefase gedrag deur middel van eksperimente wat gebruik maak van reekse van lukrake veranderlikes. Ons reproduseer die tweefase gedrag gebaseer op gekorreleerde en ongekorreleerde data. Ons gebruik ’n Markov-gemoduleerde Bernoulli proses om die transaksies te moduleer en ondersoek ’n eenvoudige interpretasie van die tweefase gedrag. Ons seem steekproefdata van “heavy-tailed” verspreidings en reproduseer die tweefase gedrag. Ons ekperimente wys dat die resultate in [1] voorgested is nie bewys lewer vir die teenwoordigheid van komplekse verskynsel in’n handelsmark nie; die resultate is as gevolg van die metode wat gebruik is vir die generering van die steekproefdata.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. May 30, 2016. / In statistics, a model is as good as the data fed to it. Data about hydrological events continues to grow rapidly over the years, with different variables being recorded on a continuous scale. These variables can be interpreted and used in a different manner among disciplines. Thus, choosing the right variables and interactions among variables is an important statistical step in building a good and accurate model. This dissertation involved the development of a statistical model which can be used to predict weekly water level within the Okavango river in northern Namibia. The parameters of the statistical mixed model were estimated based on two methods for longitudinal data, the Generalised Estimating Equations (GEE) which is a well known method of parameter estimation in longitudinal data analysis when the observed variables are correlated, and the Restricted Maximum Likelihood Estimation (REML) which is a likelihood based approach method, unlike the GEE. Using cross-validation and a simulation study, the GEE method of estimation was found to be less accurate and inconsistent in terms of prediction of parameter estimation of water level while the well known REML was found to predict the water level with a good degree of accuracy, consistency and with lower variance. Parameters from a simulation study have also shown less bias in REML method and predicted the cross-validation test-set with less bias. / GR 2016

This thesis focuses on the phase transitions, including ferro-magnetic, anti-ferromagnetic, metal to "Mott" insulator and structural transitions in perovskite and Ruddlesden-Popper ruthenates. The thesis is mainly composed of two parts. The first half presents Density Functional Theory (DFT)+Dynamical Mean Field Theory (DMFT) studies of the electronically driven phase transitions in various ruthenate materials. We study cubic perovskite BaRuO$_3$ via DFT add DMFT method using interaction parameters which were found in previous studies to be appropriate for the related materials, CaRuO$_3$ and SrRuO$_3$. The calculated variation in transition temperature between the Ba and Sr compounds is consistent with experiment, confirming the assignment of the compounds to the Hund's metal family of materials, the appropriateness of the single-site dynamical mean field approximation for these materials as well as confirming the appropriateness of the values for the interaction parameters. The results provide insights into the origin of magnetism and the role of the van Hove singularity in the physics of Hund's metals. We also study the metal-insulator transition (MIT) and magnetic transitions in Ca$_2$RuO$_4$. The Ru-O bonds lengths are found to be the most important control parameters for the metal-insulator transitions and rotations are found to be less important. The calculation successfully captures the important features of the para-magnetic (PM) "Mott" insulating state, including the orbital occupancy disproportionation and the orbitally resolved electron spectral function. It shows the advantage of single set DFT+DMFT in dealing with strongly correlated multi-orbital systems without the assumption of spin symmetry breaking. In the second half, we present a Landau free energy model that incorporates the electronic energetics, the coupling of the electronic state to local distortions and the coupling of local distortions to long-wavelength strains. The model is used to elucidate important experimental features in thermal and current-induced MIT in Ca$_2$RuO$_4$ and Ca$_3$Ru$_{2-x}$Ti$_x$O$_7$ materials. The investigation of lattice and electronic energetics and determination of parameters using DFT+DMFT methods is explained. The change in lattice energy across the metal-insulator transition is shown to be comparable to the change in electronic energy. Important consequences are a strongly first order transition, a sensitive dependence of the phase boundary on pressure and that the geometrical constraints on in-plane lattice parameter associated with epitaxial growth on a substrate typically change the lattice energetics enough to eliminate the metal-insulator transition entirely. The change in elasto-resistance across the MIT is determined. The DFT+U relaxation study shows the octahedron relaxation with respect to uniaxial strain on a and b axes are very different. This sensitive a and b axes dependence is observed in calculations on both Ca$_2$RuO$_4$ and Ca$_3$Ru$_2$O$_7$. The theory model is also generalized to investigate spatially non-homogeneous solutions. Important features of the stripe patterns at the domain boundaries of metallic and insulating phases are discussed and compared with experiments.

Stable and metastable phases of Fe and Al and structural anomalies of Zn and Cd have been studied by epitaxial Bain path (EBP) and minimum path (MNP) first-principles procedures, based on finding equilibrium structures from minimizing the Gibbs free energy G with respect to structure at a given hydrostatic pressure p and temperature T . The main accomplishments are as follows. (1) This dissertation illustrates the effectiveness of the MNP procedure for finding stable and metastable phases of an element by studying four Bravais phases of Fe including body-centered tetragonal (bct), body-centered cubic (bcc), face-centered cubic (fcc) and rhombohedral (rh) phases. The determination of absolute stability using MNP is new; MNP finds all the elastic constants cjj of a given state and the eigenvalues of the elastic constants matrix, which determine the absolute stability of the state. / (2) We have extended our search for stable and metastable phases from zero temperature to finite temperature, which requires the calculations of the Debye temperature Od from cjj in the case of no symmetry. The Debye theory is modified by introducing a parameter B2 that gives the fraction of the full Debye zero-point energy possessed by the actual dispersive mode frequencies. The value of the lattice parameter of fcc Al at low temperatures,a(T) , is shown to be accurately determined by the modified Debye theory of lattice vibrations and first-principles total energy band calculations with the MNP procedure. (3) The existence of structural anomalies in hcp Zn and Cd has been shown from first-principles total-energy calculations using WIEN2k with the EBP procedure. / Evaluation of the pressure dependence of various elastic quantities which are much more sensitive to the anomaly shows that the anomalies in hcp Zn and hcp Cd exist over a considerable range of pressure; several abrupt changes in the electron distribution are thereby indicated in that pressure range. (4) Calculations on the zone-center transverse optical phonon frequencies Vto(p) of hcp Zn, which found oscillatory behavior of Vto(p) in the pressure range of the anomalies, support the conclusions made in (3) on the structural anomalies. Based on this dissertation research four papers have been published in refereed journals. / by Florin Apostol. / Thesis (Ph.D.)--Florida Atlantic University, 2008. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2008. Mode of access: World Wide Web.

Shik, Hoi Yin = 自旋模型中量子相變與量子糾纏的研究 / 石海燕. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 90-96). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Shik, Hoi Yin = Zi xuan mo xing zhong liang zi xiang bian yu liang zi jiu chan de yan jiu / Shi Haiyan.

by Shui-Qin Zhou. / Publication date from spine. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 152-157). / Acknowledgments --- p.i / Abstract --- p.ii / Contents --- p.vi / Abbreviation --- p.viii / List of Figures --- p.xi / List of Tables --- p.xvi / Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- Project's Significance --- p.1 / Chapter 1.2. --- Research background.....................................: --- p.1 / Chapter 1.2.1. --- Linear PNIPAM chains in aqueous solution --- p.2 / Chapter 1.2.1.1. --- Origins of the LCST --- p.2 / Chapter 1.2.1.2. --- Experimental studies --- p.4 / Chapter 1.2.2. --- PNIPAM gels --- p.9 / Chapter 1.2.2.1. --- Origins of the volume phase transition --- p.10 / Chapter 1.2.2.2. --- Experimental studies --- p.11 / Chapter 1.2.3. --- Surfactant effects --- p.13 / Chapter 1.3. --- The objective of the project --- p.15 / Chapter 1.4. --- Experimental difficulties --- p.17 / Chapter 2. --- Basic Theory --- p.20 / Chapter 2.1. --- Laser light scattering (LLS) --- p.20 / Chapter 2.2. --- Polymer chains in solution --- p.23 / Chapter 2.3. --- Swollen polymer gels --- p.27 / Chapter 3. --- Results and Discussion --- p.32 / Chapter 3.1. --- Linear PNIPAM chains --- p.32 / Chapter 3.1.1. --- D = kDM-αD for PNIPAM in THF and water --- p.32 / Chapter 3.1.2. --- Coil-to-globule transition of single PNIPAM chains in water --- p.46 / Chapter 3.1.3. --- Additional chain-conformation broadening of the line-width distribution in dynamic LLS --- p.64 / Chapter 3.1.4. --- Internal motions of long linear PNIPAM chains --- p.72 / Chapter 3.1.5. --- Structural model of spherical water/AOT/n-hexane microemulsion --- p.80 / Chapter 3.2. --- Spherical PNIPAM microgels --- p.94 / Chapter 3.2.1. --- Volume phase transition of PNIPAM microgels --- p.94 / Chapter 3.2.2. --- Internal motions of short PNIPAM subchains inside the gel networks --- p.107 / Chapter 3.2.3. --- Surfactant effects on the volume phase transition --- p.113 / Chapter 3.2.4. --- Swelling and drying kinetics of a very thin PNIPAM gel film --- p.129 / Chapter 4. --- Conclusions --- p.141 / Chapter 5. --- Experimental --- p.145 / Chapter 5.1 --- Sample preparation --- p.145 / Chapter 5.2 --- Physical measurement --- p.149 / Chapter 6. --- References --- p.152

本論文包含兩個主題。第一部分研究無旋轉波近似下幾種原子與光的相互作用。第二部分研究駐波場耦合的電磁自感透明系統的反射和透射。它們的簡介如下。 / 第一部分。旋轉波近似即忽略掉原子與光相互作用哈密頓量中的反旋轉波項。它的有效性來自於能量守恆定律。但是在時間尺度非常小的情況下，根據海森堡不確定性原理，能量的不確定性可以很大，所以旋轉波近似不能應用于短時間行為的研究，比如量子芝諾和反芝諾效應，蘭姆位移，非共振極化以及超輻射和亞輻射中的能移。為超越旋轉波近似，我們對哈密頓量採用了么正變換。在變換之後的基矢之間，只有由帶修正係數的旋轉波項造成的躍遷。 / 我們從原子和真空的相互作用開始。對於氫原子來說，自由真空中沒有量子反芝諾效應，但是如果對真空態密度用腔或特異性材料做一些調製，量子反芝諾效應就會出現，蘭姆位移也會改變。我們接著研究原子和非真空光場的相互作用。我們計算了滿足光學定理的兩能級原子極化率。然後我們把么正變換用到了兩個全同原子和真空的相互作用，並計算了超輻射和亞輻射的輻射譜以及量子芝諾和反芝諾效應。 / 第二部分。在電磁自感透明系統裏，如果耦合光場為駐波，介質的極化率就會受到週期性調製而形成一維光子晶體。和傳統的傳輸矩陣不同的是，我們採用了麥克斯韋-劉維爾耦合波方程來處理這個系統並得到了光子晶體能帶的一個新的評判標準。起關鍵作用的物理量為非線性耦合係數除以波矢錯差和線性極化率的和，也就是非線性因素除以線性因素。 / 首先，我們研究了光子能帶的位置和寬度與實驗參數的量化關係。然後我們研究了溫度升高时光子晶體的融化以及向多普勒無關的多波混頻的轉化。如果在兩束對向傳播的耦合場之間引入失諧，駐波場的包絡會形成一個“飛行“的光子晶體。因為多普勒效應，順著飛行方向或者逆著飛行方向的探測光在一維光子晶體的坐標系裏具有不同的頻率。在靜止坐標系看，透射譜會在頻率上錯開並形成光學二極體。 / This thesis includes two topics. Part 1 is on the various atom-photon interactions without rotating-wave approximation (RWA). Part 2 is on the reflection and transmission in a standing wave coupled electromagnetically induced transparency (EIT) system. / Part 1. In the RWA, the counter-rotating terms in the atom-photon interaction Hamiltonian are neglected. Its validity is the result of energy conservation. However, if the time scale is sufficiently small, the uncertainly in the energy can become large, according to the Heisenberg uncertainty principle. Thus the RWA can not be applied in the study of the short time behavior, such as the quantum Zeno effect (QZE) and anti-Zeno effect (QAZE), the Lamb shift, the non-resonant polarizability and shifts in the superradiance and subradiance. To go beyond RWA, we apply a unitary transformation on the Hamiltonian. In the transformed basis, there are only secular transitions due to rotating terms with modified coupling constants. / We start from the interactions between atom and vacuum. For the hydrogen atom, there is no QAZE in free vacuum. However, with the modification in the density of states of the vacuum by a cavity or a meta-material, the QAZE appears and the Lamb shift changes. We then turn to the atom in light field, where the polarizability of a two-level atom is calculated and the results satisfy the optical theorem. The unitary transformation is then applied to two identical atoms interacting with vacuum. Their various emission spectra of the superradiance and subradiance and the QZE and QAZE are studied. / Part 2. In an EIT system, if the coupling field is a standing wave, the susceptibility of the medium is periodically modified to form a one-dimensional photonic crystal (1DPC). In contrast to the conventional treatment with transfer matrix, we use Maxwell-Liouville coupled-wave equations and propose new criteria for the bandgap of the photonic crystal (PC). The relevant quantity is the ratio between the nonlinear coupling coefficient and the wave vector mismatch plus the linear susceptibility, which is the nonlinear effect over the linear effect. / First, we study the quantitative relation between the position and width of the photonic bandgap and the experimental parameters. We then show that, as the temperature rises, the 1DPC melts down and enters the Doppler-free wave-mixing regime. By introducing detuning between the two counter-propagating fields in the standing wave, we make the envelope of the standing wave move and form a ‘flying’ 1DPC. Owing to the Doppler Effect, the probe fields propagating along with or counter to the moving direction have different frequencies in the 1DPC frame. In the rest frame, the transmission spectra in two directions are thus shifted with respect to each other and we obtain an optical diode. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Dawei = 無旋轉波近似下原子-光子相互作用和駐波耦合的電磁自感透明系統 / 王大偉. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 128-135). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Wang, Dawei = Wu xuan zhuan bo jin si xia yuan zi-guang zi xiang hu zuo yong he zhu bo ou he de dian ci zi gan tou ming xi tong / Wang Dawei. / Abstract --- p.iv / Acknowledgements --- p.vii / Table of Contents --- p.xi / List of Figures --- p.xiii / Chapter Part 1 --- Atom-photon interactions without rotating-wave approximation --- p.1 / Chapter Chapter 1 --- Introduction on atom-photon interactions --- p.2 / Chapter 1.1 --- Spontaneous emission --- p.2 / Chapter 1.2 --- Quantum Zeno and anti-Zeno effect --- p.8 / Chapter 1.3 --- Rotating-wave approximation --- p.10 / Chapter 1.4 --- Go beyond the rotating-wave approximation --- p.12 / Chapter 1.5 --- Non-dynamic Lamb shift --- p.15 / Chapter 1.6 --- Summary --- p.17 / Chapter Chapter 2 --- QZE, QAZE and Lamb shift in vacuum --- p.18 / Chapter 2.1 --- Introduction --- p.18 / Chapter 2.2 --- QZE in the free vacuum --- p.19 / Chapter 2.3 --- QAZE in modified vacuum --- p.21 / Chapter 2.4 --- Time Evolution of the Lamb Shift --- p.25 / Chapter 2.5 --- The Lamb shift in modified vacuum --- p.30 / Chapter 2.6 --- Summary --- p.35 / Chapter Chapter 3 --- Atom in light: polarizability and scattering --- p.37 / Chapter 3.1 --- Introduction --- p.37 / Chapter 3.2 --- The polarizability of a two-level atom without RWA --- p.39 / Chapter 3.3 --- The optical theorem --- p.43 / Chapter 3.4 --- The effects of the counter rotating terms --- p.46 / Chapter 3.5 --- The frequency shift --- p.48 / Chapter 3.6 --- Summary --- p.50 / Chapter Chapter 4 --- Spontaneous emission of two identicalatoms --- p.51 / Chapter 4.1 --- Introduction --- p.51 / Chapter 4.2 --- Unitary transform of the Hamiltonian --- p.52 / Chapter 4.3 --- Dynamicevolution --- p.57 / Chapter 4.4 --- Decay rates, Lamb shift and emission spectrum in the longtime limit --- p.59 / Chapter a) --- The decayrates --- p.59 / Chapter b) --- The Lamb shift --- p.60 / Chapter c) --- The emission spectra --- p.62 / Chapter 4.5 --- Short time evolution --- p.68 / Chapter 4.6 --- Summary --- p.70 / Chapter Appendix --- the shifts and decay rates of the symmetric and anti-symmetric states --- p.71 / Chapter Part 2 --- Standing wave coupled electromagnetically induced transparency system --- p.74 / Chapter Chapter 5 --- Introduction on electromagnetically induced transparency --- p.75 / Chapter 5.1 --- The electromagnetically induced transparency --- p.75 / Chapter 5.2 --- The susceptibilities of SWEIT --- p.81 / Chapter 5.3 --- Summary --- p.86 / Chapter Appendix --- the recursion relation and the proof of Eq.(212) --- p.86 / Chapter Chapter 6 --- From photonic crystal to Doppler-free wave-mixing --- p.90 / Chapter 6.1 --- Introduction --- p.90 / Chapter 6.2 --- The Maxwell-Liouville equations --- p.91 / Chapter 6.3 --- The photonic bandgaps --- p.93 / Chapter 6.4 --- The meltdown of the photonic crystal and the pulse matching --- p.99 / Chapter 6.5 --- Summary --- p.106 / Chapter Appendix A --- the Maxwell-Liouville equation --- p.106 / Chapter Appendix B --- a new criterion of photonic band-gaps --- p.109 / Chapter Chapter 7 --- The optical-diode by a flying photonic crystal --- p.112 / Chapter 7.1 --- Introduction --- p.112 / Chapter 7.2 --- Coupled-wave equations of the ‘flying’ photonic crystal --- p.113 / Chapter 7.3 --- The spectra of the optical diode --- p.118 / Chapter 7.4 --- The influence of the experimental parameters --- p.120 / Chapter 7.5 --- Summary --- p.126 / CURRICULUM VITAE --- p.136

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Physics. / M̲i̲c̲ṟo̲f̲i̲c̲ẖe̲ c̲o̲p̲y̲ a̲v̲a̲i̲ḻa̲ḇḻe̲ i̲ṉ A̲ṟc̲ẖi̲v̲e̲s̲ a̲ṉḏ S̲c̲i̲e̲ṉc̲e̲. / Vita. / Bibliography : leaf 134. / Ph.D.

No description available.