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.

Exchange energy calculation of He-He with supermolecular one-matrix

Exch~nge energy of the He-He system is calculated using the one-density matrix which has been modified according to the supermolecular density formula quoted by Kolos. The exchange energy integrals are computed analytically and by the Monte Carlo method. The results obtained from both ways compared favourably,with the results obtained from the SCF program HONDO

Transfection of newt blastema mesenchyme using the techniques of lipofection and direct gene transfer

The regenerating amphibian limb provides a useful system for studying genes involved in the establishment of positional information. While a number of candidate genes that may playa role in pattern formation have been identified, their function in vivo is unknown in this system. To better ascertain the role of these genes, it would be useful to be able to alter their normal patterns of expression in vivo and to assess the effects of this misexpression on limb pattern. In order to achieve this, a method of introducing a plasmid containing the eDNA of a gene of interest into a newt blastema (a growth zone of mesenchymal progenitor cells) is needed. Unfortunately, most commonly used transfection techniques cannot be used with newt blastema cells. In this study, I have used the techniques of lipofection and direct gene transfer to introduce plasmid DNA containing reporter genes into the cells of a regenerating newt limb. The technique of lipofection was most effective when the blastema cells were transfected in vitro. The optimal ratio for transfection was shown to be 1:3 DNA:Lipofectin (W/w) , and an increase in the amount of DNA present in the mixture (1:3 ratio maintained) resulted in a corresponding increase in gene expression. The technique of direct gene transfer was used to transfect newt blastema cells with and without prior complex formation with Lipofectin. Injection of plasmid DNA alone provided the most 3 promising results. It was possible to introduce plasmid DNA containing the reporter gene ~-galactosidase and achieve significant gene expression in cells associated with the injection site. In the future, it would be interesting to use this technique to inject plasmid DNA containing a gene which may have a role in pattern formation into specific areas of the newt blastema and to analyze the resulting limb pattern that emerges.

Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes

Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map.