Synthetic routes to Bis-Calix [n]areness : a thesis presented in partial fulfilment of the requirements for the degree of Masterate of Science in Chemistry at Massey University

The literature procedures for the targeted syntheses of p-tert-butylcalix[4]arene, p-tert-butylcalix[5]arene, p-tert-butylcalix[6]arene, p-tert-butylcalix[7]arene, and p-tert-butylcalix[8]arene have been repeated successfully. In the case of p-tert-butylcalix[4]arene, alterations led to a less capricious procedure, synthesis of the pure product directly and in higher yield. The residual xylene and toluene solutions from the targeted p-tert-butylcalix[8]arene preparation were utilised to obtain workable quantities of the rare calix[5]- and calix[7]arenes, a protocol that is far simpler and less time-consuming than the low-yielding targeted synthesis of these compounds. Dealkylation of p-tert-butylcalix[n]arenes is best accomplished at 30°C in 0.16-0.05 molL−¹ toluene solution. The insolubility of calix[8]arene in all common organic solvents is expected to limit its synthetic use. Two new protocols have been devised for the highly selective mono-O-alkylation of calixarenes 4 through 8. This work represents the realisation of the first selective functionalisation methods that are applicable to the calixarene family, and also the first selective functionalisation of a calix[7]arene. These findings will lead to more efficient synthesis of multiple calixarenes (cf. Chapter 3) and may allow for a better understanding of the reasons for selectivity in calixarene-O-alkylations. We have been able to synthesise a variety of bis-calixarenes by two different routes. Glaser-Hay coupling allowed the synthesis of symmetrical diyne bridged bis-calix[4, 6 and 8]arenes in high yield. Extension of the first general mono-O-alkylation procedure for calixarenes has made it possible to synthesise hom o-bis-calixarenes in good yield in one step from the parent calixarenes. The unexpected formation of monobromoxylyl calixarenes allows the prospect of the synthesis of hetero-bis-calixarenes under more forcing conditions. Most importantly this allows us to further explore the chemistry of bis-calixarenes by making them readily available (in large quantities) for more elaborate syntheses

Path storage in the particle filter

This article considers the problem of storing the paths generated by a particle filter and more generally by a sequential Monte Carlo algorithm. It provides a theoretical result bounding the expected memory cost by $T + C N \log N$ where $T$ is the time horizon, $N$ is the number of particles and $C$ is a constant, as well as an efficient algorithm to realise this. The theoretical result and the algorithm are illustrated with numerical experiments.Comment: 9 pages, 5 figures. To appear in Statistics and Computin

Parallel resampling in the particle filter

Modern parallel computing devices, such as the graphics processing unit (GPU), have gained significant traction in scientific and statistical computing. They are particularly well-suited to data-parallel algorithms such as the particle filter, or more generally Sequential Monte Carlo (SMC), which are increasingly used in statistical inference. SMC methods carry a set of weighted particles through repeated propagation, weighting and resampling steps. The propagation and weighting steps are straightforward to parallelise, as they require only independent operations on each particle. The resampling step is more difficult, as standard schemes require a collective operation, such as a sum, across particle weights. Focusing on this resampling step, we analyse two alternative schemes that do not involve a collective operation (Metropolis and rejection resamplers), and compare them to standard schemes (multinomial, stratified and systematic resamplers). We find that, in certain circumstances, the alternative resamplers can perform significantly faster on a GPU, and to a lesser extent on a CPU, than the standard approaches. Moreover, in single precision, the standard approaches are numerically biased for upwards of hundreds of thousands of particles, while the alternatives are not. This is particularly important given greater single- than double-precision throughput on modern devices, and the consequent temptation to use single precision with a greater number of particles. Finally, we provide auxiliary functions useful for implementation, such as for the permutation of ancestry vectors to enable in-place propagation.Comment: 21 pages, 6 figure

Cloud Observations from the Mars Science Laboratory Mission: Seasonal Variability, Scattering Phase Function, and Validation of Optical Depths using Lidar Measurements of Terrestrial Cirrus Clouds

Using images from the Navigation Cameras onboard the Mars Science Laboratory (MSL) rover Curiosity, atmospheric movies were created to monitor the cloud activity above its landing site, Gale Crater. Over the course of two Martian years of operations (LS = 160 of MY 31 to LS = 160 of MY 33), over 500 cloud imaging sequences have been returned to Earth, revealing tenuous clouds that form predominantly in the autumn and winter seasons. This thesis examines the results of these cloud observations, including a detailed overview of the seasonality, opacity, spacing, and scattering properties of the clouds that appear in the observations. The cloud opacities were validated by testing the high cloud method by imaging high altitude cirrus clouds using a radiometrically calibrated camera and captur- ing simultaneous measurements wth the York University Lidar. In total, four coordinated experiments were conducted between September of 2015 and June of 2016

A Possible Regenerative, Molten-Salt, Thermoelectric Fuel Cell

Molten or fused salts have been evaluated as possible thermoelectric materials because of the relatively good values of their figures of merit, their chemical stability, their long liquid range, and their ability to operate in conjunction with a nuclear reactor to produce heat. In general, molten salts are electrolytic conductors; therefore, there will be a transport of materials and subsequent decomposition with the passage of an electric current. It is possible nonetheless to overcome this disadvantage by using the decomposition products of the molten-salt electrolyte in a fuel cell. The combination of a thermoelectric converter and a fuel cell would lead to a regenerative system that may be useful

On the geometry of Hamiltonian chaos

We show that Gutzwiller's characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian can be extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model when a transition is made to the dual manifold, and the geodesics in the dual space coincide with the orbits of the Hamiltonian potential model. We therefore find a direct geometrical description of the time development of a Hamiltonian potential model. The second covariant derivative of the geodesic deviation in this dual manifold generates a dynamical curvature, resulting in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions giving, in particular, detailed results for a potential obtained from a fifth order expansion of a Toda lattice Hamiltonian.Comment: 7 pages TeX, Figure captions, 4 figures (eps). Some clarifications, added reference

Entropy measures as geometrical tools in the study of cosmology

Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by $S = \ln \chi (x)$ with $\chi(x)$ being the distance between two nearby geodesics. We derive an equation for the entropy which by transformation to a Ricatti-type equation becomes similar to the Jacobi equation. We further show that the geodesic equation for a null geodesic in a double warped space time leads to the same entropy equation. By applying a Robertson-Walker metric for a flat three-dimensional Euclidian space expanding as a function of time, we again reach the entropy equation stressing the connection between the chosen entropy measure and time. We finally turn to the Raychaudhuri equation for expansion, which also is a Ricatti equation similar to the transformed entropy equation. Those Ricatti-type equations have solutions of the same form as the Jacobi equation. The Raychaudhuri equation can be transformed to a harmonic oscillator equation, and it has been shown that the geodesic deviation equation of Jacobi is essentially equivalent to that of a harmonic oscillator. The Raychaudhuri equations are strong geometrical tools in the study of General Relativity and Cosmology. We suggest a refined entropy measure applicable in Cosmology and defined by the average deviation of the geodesics in a congruence.Comment: Final Versio