Factorized domain wall partition functions in trigonometric vertex models

We obtain factorized domain wall partition functions for two sets of trigonometric vertex models: 1. The N-state Deguchi-Akutsu models, for N = {2, 3, 4} (and conjecture the result for all N >= 5), and 2. The sl(r+1|s+1) Perk-Schultz models, for {r, s = \N}, where (given the symmetries of these models) the result is independent of {r, s}.Comment: 12 page

Coordination polymers and isomerism; a study using silver(I) and a ∏-stacked ligand

The ligand 2,5-bis(2-pyridylmethylsulfanylmethyl)pyrazine (L) was prepared by the base coupling of 2-(sulfanylmethyl)pyridine and 2,5-bis(chloromethyl)pyrazine. This new ligand was treated with AgClO₄ in a 1 1 metal-to-ligand ratio and with AgNO₃in a 2 1 metal-to-ligand ratio to give coordination polymers. The crystal structures of {[Ag(L)]ClO₄}∞ ( 1) and {[Ag₂(L)](NO₃)₂}∞ ( 2) were determined. The Ag(I) ions in the one-dimensional polymeric chains of 1 adopted square-pyramidal geometries with the pyridine and pyrazine N donors coordinated in an extremely bent fashion. The structure of 2 revealed two isomeric polymer chains in the one crystal forming a single supramolecular array. The isomeric polymers differed in the donor atoms about the Ag(I) ions and in the arrangement of adjacent ligands along the chain. A feature of both structures was that L adopted a three-layer ∏-stacked arrangement

An exploration of alkali metal ferrate chemistry : synthesis and exploitation for N-heterocyclic carbene and fluoroarene functionalisation

Building on previous developments on cooperative heterobimetallic reagents, this thesis aims to advance the understanding of the preparation and synthetic exploitation of alkali metal ferrates of Fe(II). Using bis(amide) Fe{N(SiMe3)2}2 as a precursor, here we report the syntheses and structures of a variety of sodium ferrates that have been prepared via direct co-complexation, where the single metal components NaN(SiMe3)2 and Fe{N(SiMe3)2}2 self-assemble in the presence of a range of Lewis donors with different electronic properties and denticities. Furthermore, in some cases the presence of these donors is not required and the isolation and structural elucidation of two novel unsolvated sodium ferrates has been accomplished which display unique polymeric arrangements in the solid state.;The ability of sodium ferrates to functionalise NHC ligands has also been assessed, finding that when unsaturated NHC IPr (IPr = 1,3-bis(diisopropylphenyl)-imidazol-2-ylidene) is treated sequentially with NaCH2SiMe3 and Fe{N(SiMe3)2}2, sodium ferrate (THF)3·Na[:C{[N(2,6-iPr2C6H3)]2CHCFe(HMDS)2}] (15) is formed, containing an anionic NHC which binds to Fe via its C4 position and to Na through its C2 site. Interestingly, this complex was found to be an excellent precursor for Fe-abnormal NHC complexes and when treated with MeOTf afforded [CH3C{[N(2,6-iPr2C6H3)]2CHCFe(HMDS)2}] (16). 1,4-dioxane solvate [dioxane·NaFe(HMDS)3] (17a) has been found to be an efficient chemoselective base to promote the direct ferration at room temperature of a wide range of fluoroaromatic molecules.;Structural elucidation of key organometallic intermediates has revealed the synergic bonding of the metals with Fe occupying the position previously filled by an H atom forming a strong Fe-C sigma bond, whereas the Na atom forms a dative bond with the F atom. These studies have revealed an important alkali metal effect, thus when the Na atom in 17a is replaced by Li or K, the ferration processes are inhibited. Remarkably, by using two molar equivalents of 17a, it is possible to di-ferrate tri-and tetrafluoro-substituted aromatics. These reactions take place at ambient temperature with excellent yields. Reaction of 1,3,5-trifluorobenzene with three molar equivalents of 17a, led to the isolation of [1,3-bis(FeHMDS)-2,4,6-tris(HMDS)-C6H] (38) resulting from the unprecedented two-fold C-H metallation/three-fold C-F activation of the substrate. Mechanistic studies suggest the reaction is partly driven by the formation of NaF. Magnetic studies using have revealed that this new compound displays single-molecule magnet behaviour.Building on previous developments on cooperative heterobimetallic reagents, this thesis aims to advance the understanding of the preparation and synthetic exploitation of alkali metal ferrates of Fe(II). Using bis(amide) Fe{N(SiMe3)2}2 as a precursor, here we report the syntheses and structures of a variety of sodium ferrates that have been prepared via direct co-complexation, where the single metal components NaN(SiMe3)2 and Fe{N(SiMe3)2}2 self-assemble in the presence of a range of Lewis donors with different electronic properties and denticities. Furthermore, in some cases the presence of these donors is not required and the isolation and structural elucidation of two novel unsolvated sodium ferrates has been accomplished which display unique polymeric arrangements in the solid state.;The ability of sodium ferrates to functionalise NHC ligands has also been assessed, finding that when unsaturated NHC IPr (IPr = 1,3-bis(diisopropylphenyl)-imidazol-2-ylidene) is treated sequentially with NaCH2SiMe3 and Fe{N(SiMe3)2}2, sodium ferrate (THF)3·Na[:C{[N(2,6-iPr2C6H3)]2CHCFe(HMDS)2}] (15) is formed, containing an anionic NHC which binds to Fe via its C4 position and to Na through its C2 site. Interestingly, this complex was found to be an excellent precursor for Fe-abnormal NHC complexes and when treated with MeOTf afforded [CH3C{[N(2,6-iPr2C6H3)]2CHCFe(HMDS)2}] (16). 1,4-dioxane solvate [dioxane·NaFe(HMDS)3] (17a) has been found to be an efficient chemoselective base to promote the direct ferration at room temperature of a wide range of fluoroaromatic molecules.;Structural elucidation of key organometallic intermediates has revealed the synergic bonding of the metals with Fe occupying the position previously filled by an H atom forming a strong Fe-C sigma bond, whereas the Na atom forms a dative bond with the F atom. These studies have revealed an important alkali metal effect, thus when the Na atom in 17a is replaced by Li or K, the ferration processes are inhibited. Remarkably, by using two molar equivalents of 17a, it is possible to di-ferrate tri-and tetrafluoro-substituted aromatics. These reactions take place at ambient temperature with excellent yields. Reaction of 1,3,5-trifluorobenzene with three molar equivalents of 17a, led to the isolation of [1,3-bis(FeHMDS)-2,4,6-tris(HMDS)-C6H] (38) resulting from the unprecedented two-fold C-H metallation/three-fold C-F activation of the substrate. Mechanistic studies suggest the reaction is partly driven by the formation of NaF. Magnetic studies using have revealed that this new compound displays single-molecule magnet behaviour

Three-dimensional vortex dynamics in Bose-Einstein condensates

We simulate in the mean-field limit the effects of rotationally stirring a three-dimensional trapped Bose-Einstein condensate with a Gaussian laser beam. A single vortex cycling regime is found for a range of trap geometries, and is well described as coherent cycling between the ground and the first excited vortex states. The critical angular speed of stirring for vortex formation is quantitatively predicted by a simple model. We report preliminary results for the collisions of vortex lines, in which sections may be exchanged.Comment: 4 pages, 4 figures, REVTeX 3.1; Submitted to Physical Review A (6 March 2000

Gene therapy for pyoderma gangrenosum: optimal transfection conditions and effect of drugs on gene delivery in the HaCaT cell line using cationic liposomes

Background/Aims: Pyoderma gangrenosum (PG) is a rare ulcerative skin disease, currently treated empirically with immunosuppression. PG is a good target for gene therapy since the skin is easily accessible. This study used the FDA-approved vector Lipofectamine® 2000 to investigate in vitro transfection of skin keratinocytes. The aim was to determine an optimum transfection protocol, including the effect of drugs currently used to treat PG on the efficiency of gene transfer, since gene therapy is unlikely to be used as monotherapy. Methods: Cells of the HaCaT line were transfected with the lacZ reporter gene, and transgene expression was measured after a given time period. Conditions tested were: relative concentrations of DNA and Lipofectamine®, time from transfection to measurement of expression, pH, and exposure to clinically relevant drugs (hydrocortisone, methotrexate, infliximab). Results: The greatest levels of β-galactosidase expression were observed using a DNA:Lipofectamine® ratio of 1:5 (μg/μl) on day 3 after transfection, using culture medium at pH 7, and in the presence of hydrocortisone. Transfection efficiency was reduced by the presence of methotrexate and not significantly affected by infliximab. Conclusion: Gene therapy is a potential future strategy for the management of PG; this study is a step towards the development of a topical gene-based agent

On the domain wall partition functions of level-1 affine so(n) vertex models

We derive determinant expressions for domain wall partition functions of level-1 affine so(n) vertex models, n >= 4, at discrete values of the crossing parameter lambda = m pi / 2(n-3), m in Z, in the critical regime.Comment: 14 pages, 13 figures included in latex fil

Spin accumulation and transport studied in double magnetic tunnel junctions

Magnetic CoFe nanoparticles have been produced by gas-aggregation and incorporated into sputtered MgO tunnel junction structures. Scanning tunnelling microscopy (STM) has been developed as a technique for examining spin accumulation and transport in these nanoscale junctions. The particles were initially characterised for their magnetic properties; x-ray magnetic circular dichroism on 11-14~nm diameter clusters was performed. The orbital-to-spin moment ratio was found to be enhanced over the bulk value and to decrease with increasing average diameter, which complements previous studies on smaller particles. The size dependence of the combined data is found not to follow predicted trends based on reduced orbital moment quenching in the outer shell. In particular for these large particles, the quenching is far more rapid than expected. Magnetometry studies on random arrays of nanoparticles at percolation show interesting effects attributed to complex magnetic dipolar interactions. This includes very broad range anisotropy and large blocking temperatures. For transport measurements, cryogenic STM is used to address individual islands and forms the top electrode of a double magnetic tunnel junction. Single electron charging effects are observed in these confined structures and the charging energy correlates to the size of the particle. New theory was developed to simulate these structures, giving an analytical solution to the current numerical orthodox theory. These solutions showed that TMR measurements, a current major barrier to studying nanospintronics using STM, were unnecessary. We are able characterise the tunnel junction parameters, including spin polarisation and accumulation, in a single I-V sweep of high information density. The spin polarisations of the opposing electrodes are found to be aligned anti-parallel despite a parallel magnetisation axis. Finally the spin lifetime on the island was calculated and found to exceed 1 us, longer than measured in previous studies

An Izergin-Korepin procedure for calculating scalar products in six-vertex models

Using the framework of the algebraic Bethe Ansatz, we study the scalar product of the inhomogeneous XXZ spin-1/2 chain. Inspired by the Izergin-Korepin procedure for evaluating the domain wall partition function, we obtain a set of conditions which uniquely determine the scalar product. Assuming the Bethe equations for one set of variables within the scalar product, these conditions may be solved to produce a determinant expression originally found by Slavnov. We also consider the inhomogeneous XX spin-1/2 chain in an external magnetic field. Repeating our earlier procedure, we find a set of conditions on the scalar product of this model and solve them in the presence of the Bethe equations. The expression obtained is in factorized form.Comment: 32 pages, 24 figure

Evaluating the sensitivity, reproducibility and flexibility of a method to test hard shell capsules intended for use in dry powder inhalers

Pharmaceutical tests for hard shell capsules are designed for orally administered capsules. The use of capsules in dry powder inhalers is widespread and increasing and therefore more appropriate tests are required to ensure quality and determine if these capsules are fit for purpose. This study aims to determine the flexibility, reproducibility and sensitivity of a quantitative method that is designed to evaluate the puncture characteristics of different capsule shell formulations under different climatic conditions. A puncture testing method was used to generate force displacement curves for five capsule formulations that were stored and tested at two different temperatures (5 °C and 19 °C). Force-displacement puncture profiles were reproducible for individual capsule shell formulations. The methodology was able to discriminate between capsules produced using different primary materials i.e. gelatin versus hypromellose, as well as more minor changes to capsule formulation i.e. different material grades and excipients. Reduced temperature increased the forces required for capsule puncture however further work is required to confirm its significance. Results indicate the method provides a reproducible and sensitive means of evaluating capsule puncture. Future studies should validate the methodology at different test sites, using different operators and with different capsule shell formulations

Fourier transforming a trapped Bose-Einstein condensate by waiting a quarter of the trap period: simulation and applications

We investigate the property of isotropic harmonic traps to Fourier transform a weakly interacting Bose–Einstein condensate (BEC) every quarter of a trap period. We solve the Gross–Pitaevskii equation numerically to investigate the time evolution of interacting BECs in the context of the Fourier transform, and we suggest potential applications