Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.

Studies of the effects of molecular encounters on N.M.R. spin-lattice relaxation times

This thesis is concerned with investigations of the effects of molecular encounters on nuclear magnetic resonance spin-lattice relaxation times, with particular reference to mesitylene in mixtures with cyclohexane and TMS. The purpose of the work was to establish the best theoretical description of T1 and assess whether a recently identified mechanism (buffeting), that influences n.m.r. chemical shifts, governs Tl also. A set of experimental conditions are presented that allow reliable measurements of Tl and the N. O. E. for 1H and 13C using both C. W. and F.T. n.m.r. spectroscopy. Literature data for benzene, cyclohexane and chlorobenzene diluted by CC14 and CS2 are used to show that the Hill theory affords the best estimation of their correlation times but appears to be mass dependent. Evaluation of the T1 of the mesitylene protons indicates that a combined Hill-Bloembergen-Purcell-Pound model gives an accurate estimation of T1; subsequently this was shown to be due to cancellation of errors in the calculated intra and intemolecular components. Three experimental methods for the separation of the intra and intermolecular relaxation times are described. The relaxation times of the 13C proton satellite of neat bezene, 1,4 dioxane and mesitylene were measured. Theoretical analyses of the data allow the calculation of Tl intra. Studies of intermolecular NOE's were found to afford a general method of separating observed T1's into their intra and intermolecular components. The aryl 1H and corresponding 13C T1 values and the NOE for the ring carbon of mesitylene in CC14 and C6H12-TMS have been used in combination to determine T1intra and T1inter. The Hill and B.P.P. models are shown to predict similarly inaccurate values for T1linter. A buffeting contribution to T1inter is proposed which when applied to the BPP model and to the Gutowsky-Woessner expression for T1inter gives an inaccuracy of 12% and 6% respectively with respect to theexperimentally based T1inter.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.

Study of neutral Fe(III) complexes of pyridoxal-N-substituted thiosemicarbazone with desolvation induced spin-state transformation above room temperature

The preparation and characterization of two new neutral ferric complexes with desolvation-induced discontinuous spin-state transformation above room temperature are reported. The compounds, Fe(Hthpy)(thpy).CH3OH.3H2O (1) and Fe(Hmthpy)(mthpy).2H2O (2), are low-spin (LS) at room temperature and below, whereas their nonsolvated forms are high-spin (HS), exhibiting zero-field splitting. In these complexes, Hthpy, Hmthpy, and thpy, mthpy are the deprotonated forms of pyridoxal thiosemicarbazone and pyridoxal methylthiosemicarbazone, respectively; each is an O,N,S-tridentate ligand. The molecular structures have been determined at 100(1) K using single-crystal X-ray diffraction techniques and resulted in a triclinic system (space group P1) and monoclinic unit cell (space group P21/c) for 1 and 2, respectively. Structures were refined to the final error indices, where RF = 0.0560 for 1 and RF = 0.0522 for 2. The chemical inequivalence of the ligands was clearly established, for the "extra" hydrogen atom on the monodeprotonated ligands (Hthpy, Hmthpy) was found to be bound to the nitrogen of the pyridine ring. The ligands are all of the thiol form; the doubly deprotonated chelates (thpy, mthpy) have C-S bond lengths slightly longer than those of the singly deprotonated forms. There is a three-dimensional network of hydrogen bonds in both compounds. The discontinuous spin-state transformation is accompanied with liberation of solvate molecules. This is evidenced also from DSC analysis. Heat capacity data for the LS and HS phases are tabulated at selected temperatures, the values of the enthalpy and entropy changes connected with the change of spin state were reckoned at DeltaH = 12.5 0.3 kJ mol-1 and DeltaS = 33.3 0.8 J mol-1 K-1, respectively, for 1 and DeltaH = 6.5 0.3 kJ mol-1 and DeltaS = 17.6 0.8 J mol-1 K-1, respectively, for 2

In situ imaging and height reconstruction of phase separation processes in polymer blends during spin coating

Spin coating polymer blend thin films provides a method to produce multiphase functional layers of high uniformity covering large surface areas. Applications for such layers include photovoltaics and light-emitting diodes where performance relies upon the nanoscale phase separation morphology of the spun film. Furthermore, at micrometer scales, phase separation provides a route to produce self-organized structures for templating applications. Understanding the factors that determine the final phase-separated morphology in these systems is consequently an important goal. However, it has to date proved problematic to fully test theoretical models for phase separation during spin coating, due to the high spin speeds, which has limited the spatial resolution of experimental data obtained during the coating process. Without this fundamental understanding, production of optimized micro- and nanoscale structures is hampered. Here, we have employed synchronized stroboscopic illumination together with the high light gathering sensitivity of an electron-multiplying charge-coupled device camera to optically observe structure evolution in such blends during spin coating. Furthermore the use of monochromatic illumination has allowed interference reconstruction of three-dimensional topographies of the spin-coated film as it dries and phase separates with nanometer precision. We have used this new method to directly observe the phase separation process during spinning for a polymer blend (PS-PI) for the first time, providing new insights into the spin-coating process and opening up a route to understand and control phase separation structures. © 2011 American Chemical Society.

The antimicrobial efficacy of copper alloy furnishing in the clinical environment:a crossover study

Objective. To determine whether copper incorporated into hospital ward furnishings and equipment can reduce their surface microbial load. Design. A crossover study. Setting. Acute care medical ward with 19 beds at a large university hospital. Methods. Fourteen types of frequent-touch items made of copper alloy were installed in various locations on an acute care medical ward. These included door handles and push plates, toilet seats and flush handles, grab rails, light switches and pull cord toggles, sockets, overbed tables, dressing trolleys, commodes, taps, and sink fittings. Their surfaces and those of equivalent standard items on the same ward were sampled once weekly for 24 weeks. The copper and standard items were switched over after 12 weeks of sampling to reduce bias in usage patterns. The total aerobic microbial counts and the presence of indicator microorganisms were determined. Results. Eight of the 14 copper item types had microbial counts on their surfaces that were significantly lower than counts on standard materials. The other 6 copper item types had reduced microbial numbers on their surfaces, compared with microbial counts on standard items, but the reduction did not reach statistical significance. Indicator microorganisms were recovered from both types of surfaces; however, significantly fewer copper surfaces were contaminated with vancomycin-resistant enterococci, methicillin-susceptible Staphylococcus aureus, and coliforms, compared with standard surfaces. Conclusions. Copper alloys (greater than or equal to 58% copper), when incorporated into various hospital furnishings and fittings, reduce the surface microorganisms. The use of copper in combination with optimal infection-prevention strategies may therefore further reduce the risk that patients will acquire infection in healthcare environments.

In situ studies of phase separation and crystallization directed by Marangoni instabilities during spin-coating

Results of a pioneering study are presented in which for the first time, crystallization, phase separation and Marangoni instabilities occurring during the spin-coating of polymer blends are directly visualized, in real-space and real-time. The results provide exciting new insights into the process of self-assembly, taking place during spin-coating, paving the way for the rational design of processing conditions, to allow desired morphologies to be obtained. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Emergence of equilibriumlike domains within nonequilibrium Ising spin systems

Many natural, technological and social systems are inherently not in equilibrium. We show, by detailed analysis of exemplar models, the emergence of equilibriumlike behavior in localized or nonlocalized domains within nonequilibrium Ising spin systems. Equilibrium domains are shown to emerge either abruptly or gradually depending on the system parameters and disappear, becoming indistinguishable from the remainder of the system for other parameter values. © 2013 American Physical Society.

Self-sustained clusters and ergodicity breaking in spin models

Self-sustained spin clusters are analytically linked to ergodicity breaking in fully connected Ising and Sherrington-Kirkpatick (SK) models, relating the less understood spin space to the well understood state space. This correspondence is established through the absence of clusters in the paramagnetic phase, the presence of one dominant cluster in the Ising ferromagnet, and the formation of nontrivial clusters in SK spin glass. Yet unobserved phenomena are also revealed such as a first order phase transition in cluster sizes in the SK ferromagnet. The method could be adapted to investigate other spin models. © 2013 American Physical Society.

Fe III in a low-spin state in caesium bis[3-ethoxysalicylaldehyde 4-methylthiosemicarbazonato(2–)-κ3O2,N1,S]ferrate(III) methanol monosolvate

The synthesis and crystal structure (at 100K) of the title compound, Cs[Fe(C11H13N3O2S2) 2] CH3OH, is reported. The asymmetric unit consists of an octahedral [FeIII(L)2]- fragment, where L 2- is 3-ethoxysalicylaldehyde 4-methylthiosemicarbazonate(2-) {systematic name: [2-(3-ethoxy-2-oxidobenzylidene)hydrazin-1-ylidene] (methylamino)methanethiolate}, a caesium cation and a methanol solvent molecule. Each L2- ligand binds through the thiolate S, the imine N and the phenolate O atoms as donors, resulting in an FeIIIS2N 2O2 chromophore. The O,N,S-coordinating ligands are orientated in two perpendicular planes, with the O and S atoms in cis positions and the N atoms in trans positions. The FeIII cation is in the low-spin state at 100K. © 2014 International Union of Crystallography.

[Fe(μ-btzmp)2(btzmp)2](ClO4)2:a doubly-bridged 1D spin-transition bistetrazole-based polymer showing thermal hysteresis behaviour

The reaction of btzmp (1,2-bis(tetrazol-1-yl)-2-methylpropane) with Fe(ClO4)2 generates a 1D polymeric species, [Fe(μ-btzmp)2(btzmp)2](ClO4)2, showing a steep spin transition (T½↑ = 136 K and T ½↓ = 133 K) with a 3 K thermal hysteresis. The crystal structure at 100 and 200 K reveals that, in contrast to other bistetrazole based spin-transition systems such as [Fe(endi)3](BF4)2 and [Fe(btzp)3](ClO4)2, the present compound has only two ligands bridging the metallic centres, while the other two coordination positions are occupied by two mono-coordinated (non-bridging) btzmp ligands. This peculiarity confers an unprecedented crystal packing in the series of 1D bistetrazole based polymers. The change in spin state is accompanied by an order/disorder transition of the ClO4- counterion. A careful examination of the structural changes occurring upon the spin transition indicates that this order/disorder is most likely affected by the modification of the [tetrazole-centroid]-ND-Fe angle (which is typical of bistetrazole spin-transition materials). Apart from X-ray analysis, also magnetic susceptibility, Mössbauer and UV-vis spectroscopies have been used to characterise the HS and the LS states of [Fe(µ-btzmp)2(btzmp)2](ClO4)2. © The Royal Society of Chemistry.

Spin dependent photoconductivity in silicon-on-sapphire

Resonant and non resonant spin dependent photoconductivity is observed in(100) silicon films grown on sapphire by CVD and MBE techniques. The CVD films are either in their as-grown state or have undergone single or double solid phase epitaxial regrowth. For all samples, a resonant decrease in photoconductivity is observed at a field of about 0.34 T for a microwave frequency of about 9.7 GHz and at about 3.3 mT when the frequency is about 92 MHz. For all samples the maximum fractional change in photoconductivity is approximately 10-4 independent of magnetic field strength.

Coverage versus supply cost in facility location:physics of frustrated spin systems

A comprehensive coverage is crucial for communication, supply, and transportation networks, yet it is limited by the requirement of extensive infrastructure and heavy energy consumption. Here, we draw an analogy between spins in antiferromagnet and outlets in supply networks, and apply techniques from the studies of disordered systems to elucidate the effects of balancing the coverage and supply costs on the network behavior. A readily applicable, coverage optimization algorithm is derived. Simulation results show that magnetized and antiferromagnetic domains emerge and coexist to balance the need for coverage and energy saving. The scaling of parameters with system size agrees with the continuum approximation in two dimensions and the tree approximation in random graphs. Due to frustration caused by the competition between coverage and supply cost, a transition between easy and hard computation regimes is observed. We further suggest a local expansion approach to greatly simplify the message updates which shed light on simplifications in other problems. © 2014 American Physical Society.