Planar Topological Defects in Unconventional Superconductors

In this work, we consider the properties of planar topological defects in unconventional superconductors. Specifically, we calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix. The thesis is structured as follows. We begin with a historical review of the theories of superconductivity (Sec. 1.1), which led the way to the celebrated Bardeen-Cooper- Schrieffer (BCS) theory (Sec. 1.3). Then we proceed to the treatment of superconductors with so-called "unconventional pairing" in Sec. 1.4, and in Sec. 1.5 we introduce the specific case of chiral p-wave superconductivity. After introducing in Sec. 2 the domain wall (DW) model that will be considered throughout the work, we derive the Bogoliubov-de Gennes (BdG) equations in Sec. 3.1, which determine the quasiparticle excitation spectrum for a nonuniform superconductor. In this work, we use the semiclassical (Andreev) approximation, and solve the Andreev equations (which are a particular case of the BdG equations) in Sec. 4 to determine the quasiparticle spectrum for both the single- and two-DW textures. The Andreev equations are derived in Sec. 3.2, and the formal properties of the Andreev scattering coefficients are discussed in the following subsection. In Sec. 5, we use the transfer matrix method to relate the interaction energy of the DWs to the scattering matrix of the Bogoliubov quasiparticles. This facilitates the derivation of an analytical expression for the interaction energy between the two DWs in Sec. 5.3. Finally, to illustrate the general applicability our method, we apply it in Sec. 6 to the interaction between phase solitons in a two-band s-wave superconductor.

Edge-choosability of Planar Graphs

According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s Theorem ∆(G) ≤χ' (G)≤∆(G) + 1. We prove that if G is a planar graph without 7-cycles with ∆(G)≠5,6 , or without adjacent 4-cycles with ∆(G)≠5, or with no 3-cycles adjacent to 5-cycles, then G is edge-(∆ + 1)-choosable.

Diastereoselective Synthesis of Planar Chiral N-Substituted Ferrocenes Derived from Epimeric Imidazolones and their Application to Asymmetric Hydrogenation of Quinolines

This thesis describes the synthesis and use of an N-substituted ferrocene bearing a proline-derived chiral directing group and diastereoselective lithiation-electrophile quench of the pro-Sp hydrogen of the ferrocene to give planar chiral products in >95:5 dr. The auxiliary group is found to be stable to lithium bases of types RLi and R2NLi giving the same diastereoselectivity. The anti- epimer of the previously mentioned syn auxiliary induces lithiation of pro Rp rather than pro Sp hydrogen in >95:5 dr. Upon electrophile quench and elimination, the enantiomer of the syn-derived planar chiral imidazolone is obtained. Hence, this method provides a practical way to prepare planar chiral enantiomers in this series without the use of a more expensive D-proline derived starting material. The syn and anti epimers have β, γ-stereogenic centers and the origin of stereoselectivity in lithiation appears to be driven by the conformational bias exerted by the β-silyloxy moiety in each chiral auxiliary. In the thesis, this conclusion is supported using insensitivity of lithiation selectivity to the bulkiness of the base, comparison of enantiomers, deuteration experiments, nOe difference studies and computational modeling of the ground states and lithiation transition states for both substrates. The products are then converted to ligand precursors to make iridium and rhodium complexes. Among them, one of the cationic iridium complex is found to be effective in the asymmetric hydrogenation of 2-substituted quinolines with enantioselectivities up to 80% at pressures as low as 5 atm.

Certificate for Sixty Shares of Capital Stock in High Pressure Oil and Gas Syndicate, Limited

Certificate for 60 shares of capital stock in High Pressure Oil and Gas Syndicate, Limited to Hamilton K. Woodruff, Nov. 1, 1922.

Letter from S.D. Woodruff to the president and directors of the Port Robinson and Thorold Macadamized Road Committee regarding extra work done

Letter from S.D. Woodruff to the president and directors of the Port Robinson and Thorold Macadamized Road Committee regarding extra work done (3 pages, handwritten), Aug. 6, 1857.

Receipt from G. Lloyd, dealer in hot air furnaces, stoves, ranges, gas fixtures and pumps

Receipt from G. Lloyd, dealer in hot air furnaces, stoves, ranges, gas fixtures and pumps, located on King Street, St. Catharines regarding payment received for burners, dampers and other gas fixtures, Jan. 1, 1875.

Receipt from Mitchell, Vance and Co. of New York for gas fixtures

Receipt from Mitchell, Vance and Co. of New York for gas fixtures, Sept. 13, 1876.

Letter to Mr. W.D. Woodruff of Lincoln Paper Mills, Merritton from P.J. Price of the United Gas Companies

Letter to Mr. W.D. Woodruff of Lincoln Paper Mills, Merritton from P.J. Price of the United Gas Companies, St. Catharines regarding a cheque received from E.J. McIntyre for $200. Included with this letter is an envelope addressed to W.D. Woodruff, Dec. 27, 1910.

Receipt from John Burrow, Steam and Gas Fitter and Plumber

Receipt from John Burrow, Steam and Gas Fitter and Plumber, St. Catharines for work done, March 31, 1887.

Receipt from the St. Catharines and Welland Canal Gas Light Company

Receipt from the St. Catharines and Welland Canal Gas Light Company for gas rent, April 4, 1887.

Receipt from St. Catharines and Welland Canal Gas Light Company

Receipt from St. Catharines and Welland Canal Gas Light Company for gas rent, May 1, 1887.

Receipt from St. Catharines and Welland Canal Gas Light Company

Receipt from St. Catharines and Welland Canal Gas Light Company for gas rent, June 6, 1887.

Receipt from St. Catharines and Welland Canal Gas Light Company for gas rent

Receipt from St. Catharines and Welland Canal Gas Light Company for gas rent, July 4, 1887.

Receipt from St. Catharines and Welland Canal Gas Light Company for gas rent

Receipt from St. Catharines and Welland Canal Gas Light Company for gas rent, Sept. 3, 1887.

Receipt from St. Catharines and Welland Canal Gas Light Company for gas rent

Receipt from St. Catharines and Welland Canal Gas Light Company for gas rent, Dec. 31, 1887.