An analysis of decoupling procedures in generating thermal Green's functions of O([lambda]â ´) by the Zubarev equation of motion method

The Zubarev equation of motion method has been applied to an anharmonic crystal of O( ,,4). All possible decoupling schemes have been interpreted in order to determine finite temperature expressions for the one phonon Green's function (and self energy) to 0()\4) for a crystal in which every atom is on a site of inversion symmetry. In order to provide a check of these results, the Helmholtz free energy expressions derived from the self energy expressions, have been shown to agree in the high temperature limit with the results obtained from the diagrammatic method. Expressions for the correlation functions that are related to the mean square displacement have been derived to 0(1\4) in the high temperature limit.

Tetrathiafulvalene and 2,2'-Bipyridine: Bridging both Worlds in the Pursuit of Novel Molecular Materials

The preparation and characterization of two families of building blocks for molecule-based magnetic and conducting materials are described in three projects. In the first project the synthesis and characterization of three bis-imine ligands LI - L3 is reported. Coordination of LI to a series of metal salts afforded the five novel coordination complexes Sn(L4)C4 (I), [Mn(L4)(u-CI)(CI)(EtOH)h (II), [CU(L4)(u-sal) h(CI04)2 (sal = salicylaldehyde anion) (III), [Fe(Ls)2]CI (IV) and [Fe(LI)h(u-O) (V). All complexes have been structurally and magnetically characterized. X-ray diffraction studies revealed that, upon coordination to Lewis acidic metal salts, the imine bonds of LI are susceptible to nucleophilic attack. As a consequence, the coordination complexes (I) - (IV) contain either the cyclised ligand L4 or hydrolysed ligand Ls. In contrast, the dimeric Fe3+ complex (V) comprises two intact ligand LI molecules. In. this complex, the ligand chelates two Fe(III) centres in a bis-bidentate manner through the lone pairs of a phenoxy oxygen and an imine nitrogen atom. Magnetic studies of complexes (II-V) indicate that the dominant interactions between neighbouring metal centres in all of the complexes are antiferromagnetic. In the second project the synthesis and characterization two families of TTF donors, namely the cyano aryl compounds (VI) - (XI) and the his-aryl TTF derivatives (XII) - (XIV) are reported. The crystal structures of compounds (VI), (VII), (IX) and (XII) exhibit regular stacks comprising of neutral donors. The UV -Vis spectra of compounds (VI) - (XIV) present an leT band, indicative of the transfer of electron density from the TTF donors to the aryl acceptor molecules. Chemical oxidation of donors (VI), (VII), (IX) and (XII) with iodine afforded a series of CT salts that where possible have been characterized by single crystal X -ray diffraction. Structural studies showed that the radical cations in these salts are organized in stacks comprising of dimers of oxidized TTF donors. All four salts behave as semiconductors, displaying room temperature conductivities ranging from 1.852 x 10-7 to 9.620 X 10-3 Scm-I. A second series of CT salts were successfully prepared via the technique of electrocrystallization. Following this methodology, single crystals of two CT salts were obtained. The single crystal X-ray structures of both salts are isostructural, displaying stacks formed by trimers of oxidized donors. Variable temperature conductivity measurements carried out on this series of CT salts reveal they also are semiconductors with conductivities ranging from 2.94 x 10-7 to 1.960 X 10-3 S em-I at room temperature. In the third project the synthesis and characterization of a series of MII(hfac)2 coordination complexes of donor ligand (XII) where M2+ = Co2+, Cu2+, Ni2+ and Zn2+ are reported. These complexes crystallize in a head-to-tail arrangement of TTF donor and bipyridine moieties, placing the metal centres and hfac ligands are located outside the stacks. Magnetic studies of the complexes (XV) - (XVIII) indicate that the bulky hfac ligands prevent neighbouring metal centres from assembling in close proximity, and thus they are magnetically isolated.

Object-Oriented Genetic Programming for the Automatic Inference of Graph Models for Complex Networks

Complex networks are systems of entities that are interconnected through meaningful relationships. The result of the relations between entities forms a structure that has a statistical complexity that is not formed by random chance. In the study of complex networks, many graph models have been proposed to model the behaviours observed. However, constructing graph models manually is tedious and problematic. Many of the models proposed in the literature have been cited as having inaccuracies with respect to the complex networks they represent. However, recently, an approach that automates the inference of graph models was proposed by Bailey [10] The proposed methodology employs genetic programming (GP) to produce graph models that approximate various properties of an exemplary graph of a targeted complex network. However, there is a great deal already known about complex networks, in general, and often specific knowledge is held about the network being modelled. The knowledge, albeit incomplete, is important in constructing a graph model. However it is difficult to incorporate such knowledge using existing GP techniques. Thus, this thesis proposes a novel GP system which can incorporate incomplete expert knowledge that assists in the evolution of a graph model. Inspired by existing graph models, an abstract graph model was developed to serve as an embryo for inferring graph models of some complex networks. The GP system and abstract model were used to reproduce well-known graph models. The results indicated that the system was able to evolve models that produced networks that had structural similarities to the networks generated by the respective target models.