Theoretical gain optimization studies in CO2-N2 lasers. III. Inclusion of line shape effects

The influence of Lorentz and Doppler line-broadening mechanisms on the small-signal optical gain of lasers and, in particular, gasdynamic lasers, is discussed. A relationship between the critical parameter reflecting the line-broadening mechanisms and some of the important parameters arising out of the gain optimization studies in CO2-N2 gasdynamic lasers is established. Using this relationship, methods by which the deleterious effect of the Doppler mechanisms on small-signal gain can be suppressed are suggested. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Non-Abelian monopoles break color. I. Classical mechanics

Monopoles which are sources of non-Abelian magnetic flux are predicted by many models of grand unification. It has been argued elsewhere that a generic transformation of the "unbroken" symmetry group H cannot be globally implemented on such monopoles for reasons of topology. In this paper, we show that similar topological obstructions are encountered in the mechanics of a test particle in the field of these monopoles and that the transformations of H cannot all be globally implemented as canonical transformations. For the SU(5) model, if H is SU(3)C×U(1)em, a consequence is that color multiplets are not globally defined, while if H is SU(3)C×SU(2)WS×U(1)Y, the same is the case for both color and electroweak multiplets. There are, however, several subgroups KT, KT′,… of H which can be globally implemented, with the transformation laws of the observables differing from group to group in a novel way. For H=SU(3)C×U(1)em, a choice for KT is SU(2)C×U(1)em, while for H=SU(3)C×SU(2)WS×U(1)Y, a choice is SU(2)C×U(1)×U(1)×U(1). The paper also develops the differential geometry of monopoles in a form convenient for computations.

Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.

Porphyrins with multiple crown ether voids: novel systems for cation complexation studies

Porphyrins appended with crown ether, benzo-15-crown-5, at the methine positions have been synthesized and characterized. The fully and partially substituted porphyrins and their metallo (Co, Cu, and Zn) derivatives describe one or more ether cavities in the periphery that are capable of recognizing spherical cations. The ability of these macrocycles to complex cations (Na+, K+, Mg2+, Ca2+, Ba2', and NH4+) is investigated by use of visible, 'H NMR, ESR, and emission spectral studies. The tetrasubstituted crown porphyrin (TCP) exhibits very high selectivity for K+. The cations (K', Ba2+, and NH4+) that require two crown ether cavities for complexation promote dimerization of the porphyrins. The ESR study of the cation-induced porphyrin dimers reveals axial symmetry with the porphyrin planes separated by -4.2 A. This distance increases from the fully substituted to partially substituted porphyrins. The cations (K', Ba2+, and NH4') quench efficiently the fluorescence of the free base porphyrins and their metallo derivatives. The quenching process is attributed to the steric geometry of the dimers.

Laser Raman spectroscopic study of ferroelastic LiCsSO4

Lithium caesium sulphate has been reported to undergo a phase transition from the room temperature orthorhombic phase with space groupP cmn to a final phase with space groupP 22/n. Though a sharp anomaly in its physical properties has been found at 202.0;K, it was found that there was a need for careful investigations in the vicinity of 240 and 210.0;K. Since the changes in the crystal structure involve primarily a rotation of the SO4 tetrahedron about thec-axis and as this may be reflected both in the intensity and polarisation of the internal as well as external phonon modes, the laser Raman spectra of oriented single crystals of LiCsSO4 at different temperatures were investigated. For correlation and definite identification of the spectral features, its infrared absorption spectrum was also studied. An analysis of the intensities and polarizations of the internal modes of the sulphate ions reveals the change in symmetry of the crystal. The integrated intensity and peak height of thev 1 line, plotted against temperature show anomalous peaks in the region of the phase transition. Differential scanning calorimetric study gives the enthalpy change ΔH across the phase transition to be 0.213 kJ/mol.

Technicolor

In technicolor theories the scalar sector of the Standard Model is replaced by a strongly interacting sector. Although the Standard Model has been exceptionally successful, the scalar sector causes theoretical problems that make these theories seem an attractive alternative. I begin my thesis by considering QCD, which is the known example of strong interactions. The theory exhibits two phenomena: confinement and chiral symmetry breaking. I find the low-energy dynamics to be similar to that of the sigma models. Then I analyze the problems of the Standard Model Higgs sector, mainly the unnaturalness and triviality. Motivated by the example of QCD, I introduce the minimal technicolor model to resolve these problems. I demonstrate the minimal model to be free of anomalies and then deduce the main elements of its low-energy particle spectrum. I find the particle spectrum contains massless or very light technipions, and also technibaryons and techni-vector mesons with a high mass of over 1 TeV. Standard Model fermions remain strictly massless at this stage. Thus I introduce the technicolor companion theory of flavor, called extended technicolor. I show that the Standard Model fermions and technihadrons receive masses, but that they remain too light. I also discuss flavor-changing neutral currents and precision electroweak measurements. I then show that walking technicolor models partly solve these problems. In these models, contrary to QCD, the coupling evolves slowly over a large energy scale. This behavior adds to the masses so that even the light technihadrons are too heavy to be detected at current particle accelerators. Also all observed masses of the Standard Model particles can be generated, except for the bottom and top quarks. Thus it is shown in this thesis that, excluding the masses of third generation quarks, theories based on walking technicolor can in principle produce the observed particle spectrum.

Zeeman effect of nuclear quadrupole resonance in 1-chloro-2,4-dinitrobenzene

The Zeeman effect of NQR was studied in 1-chloro-2,4-dinitrobenzene. A low value of the asymmetry parameter (0.10) was obtained. Four physically inequivalent field gradients were located and their orientations in the crystallographic abc system were determined using symmetry considerations. From these data the orientations of the molecules in the unit cell were determined. The results agree well with the two-dimensional x-ray structural data. The bond characters of the C[Single Bond]Cl bond were calculated, and the values compare well with those generally obtained for C[Single Bond]Cl bonds in chlorine derivatives of benzene. ©1973 The American Institute of Physics.

Structure of pentacyclo[7.4.2.02,6.06,15.011,14]pentadec-4-ene-7,13-dione, a novel pentacyclic C15 quinane system

C 15H 1602 (a synthetic precursor to dodecahedrane), monoclinic, P21/n, a = 12.171 (5), b = 6.976(5), c = 13.868 (3) A, B = 102.56 (3) ° , Z = 4, D m = 1.30, D c = 1.318 g cm -3, F(000) = 488, g(Mo K¢t) = 0.92 cm- 1. Intensity data were collected on a Nonius CAD-4 diffractometer and the structure was solved by direct methods. Full-matrix least-squares refinement gave R = 0.077 (R w = 0.076) for 1337 observed reflections. All the five-membered rings are cis fused and have envelope (C s symmetry) conformations.

Quantum Chemical Studies of Intermolecular Interactions

This thesis studies the intermolecular interactions in (i) boron-nitrogen based systems for hydrogen splitting and storage, (ii) endohedral complexes, A@C60, and (iii) aurophilic dimers. We first present an introduction of intermolecular interactions. The theoretical background is then described. The research results are summarized in the following sections. In the boron-nitrogen systems, the electrostatic interaction is found to be the leading contribution, as 'Coulomb Pays for Heitler and London' (CHL). For the endohedral complex, the intermolecular interaction is formulated by a one-center expansion of the Coulomb operator 1/rab. For the aurophilic attraction between two C2v monomers, a London-type formula was derived by fully accounting for the anisotropy and point-group symmetry of the monomers.

Nonequilibrium charge transport in an interacting open system: Two-particle resonance and current asymmetry

We use the Lippman-Schwinger scattering theory to study nonequilibrium electron transport through an interacting open quantum dot. The two-particle current is evaluated exactly while we use perturbation theory to calculate the current when the leads are Fermi liquids at different chemical potentials. We find an interesting two-particle resonance induced by the interaction and obtain criteria to observe it when a small bias is applied across the dot. Finally, for a system without spatial inversion symmetry, we find that the two-particle current is quite different depending on whether the electrons are incident from the left or the right lead.

Convex-transitive Banach spaces and their hyperplanes

The topic of this dissertation is the geometric and isometric theory of Banach spaces. This work is motivated by the known Banach-Mazur rotation problem, which asks whether each transitive separable Banach space is isometrically a Hilbert space. A Banach space X is said to be transitive if the isometry group of X acts transitively on the unit sphere of X. In fact, some weaker symmetry conditions than transitivity are studied in the dissertation. One such condition is an almost isometric version of transitivity. Another investigated condition is convex-transitivity, which requires that the closed convex hull of the orbit of any point of the unit sphere under the rotation group is the whole unit ball. Following the tradition developed around the rotation problem, some contemporary problems are studied. Namely, we attempt to characterize Hilbert spaces by using convex-transitivity together with the existence of a 1-dimensional bicontractive projection on the space, and some mild geometric assumptions. The convex-transitivity of some vector-valued function spaces is studied as well. The thesis also touches convex-transitivity of Banach lattices and resembling geometric cases.

Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

Numerical computation of the module of a quadrilateral

The module of a quadrilateral is a positive real number which divides quadrilaterals into conformal equivalence classes. This is an introductory text to the module of a quadrilateral with some historical background and some numerical aspects. This work discusses the following topics: 1. Preliminaries 2. The module of a quadrilateral 3. The Schwarz-Christoffel Mapping 4. Symmetry properties of the module 5. Computational results 6. Other numerical methods Appendices include: Numerical evaluation of the elliptic integrals of the first kind. Matlab programs and scripts and possible topics for future research. Numerical results section covers additive quadrilaterals and the module of a quadrilateral under the movement of one of its vertex.

Isotope shifts and hyperfine structure in the 555.8-nm S-1(0) -> P-3(1) line of Yb

We apply our technique of using a Rb-stabilized ring-cavity resonator to measure the frequencies of various spectral components in the 555.8-nm 1S0-->3P1 line of Yb. We determine the isotope shifts with 60 kHz precision, which is an order-of-magnitude improvement over the best previous measurement on this line. There are two overlapping transitions, 171Yb(1/2-->3/2) and 173Yb(5/2-->3/2), which we resolve by applying a magnetic field. We thus obtain the hyperfine constants in the 3P1 state of the odd isotopes with a significantly improved precision. Knowledge of isotope shifts and hyperfine structure should prove useful for high-precision calculations in Yb necessary to interpret ongoing experiments testing parity and time-reversal symmetry violation in the laws of physics.

Stem anatomy and adventitious root formation in cuttings of Angophora, Corymbia and Eucalyptus

Many plantation eucalypts are difficult to propagate from cuttings, and their rooted cuttings often possess very few adventitious roots. We microscopically examined the stem anatomy of cuttings from 12 species of eucalypts and we determined whether adventitious root formation in auxin-treated cuttings of four species was limited to particular positions around the vascular tissue. Most species contained a central pith that was arranged in a four-pointed stellate pattern. The surrounding vascular tissue was also arranged in a stellate pattern near the shoot apex but it developed a more rectangular shape at the outer phloem as the stems enlarged radially. Adventitious roots formed at, or slightly peripheral to, the vascular cambium, and they formed at both the corners and the sides of the rectangular-shaped vascular tissue. The study highlighted that auxin-treated eucalypt cuttings can produce roots at multiple positions around the vascular tissue and so propagation methods can aim to produce more than four adventitious roots per rooted cutting. Higher numbers of adventitious roots could improve the root system symmetry, stability, survival and growth rate of clonal eucalypt trees. © 2015 by the authors; licensee MDPI, Basel, Switzerland.