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Ion channel models are related to non-equilibrium statistical physics, fluid mechanics and electromagnetism. Some classes of ordinary differential equations that model ion channels can be seen as a limit of finite state-space continuous-time Markov chains. The purpose of this thesis is to qualitatively investigate the numerical results of systems of equations that incorporate ion channels modeled by such Markov chains and an electrical circuit model of a single neuron with isopotential extracellular space. This may be useful for making more detailed micro-physical simulations of neurons. A subset of the Rallpack benchmarks is conducted in order to evaluate the accuracy of the electrical circuit model of the transmembrane voltage propagation. In order to test the tau-leap method employed to simulate the Markov-chain based ion channel models a cylindrical geometry is implemented. Convergence properties are presented in terms of mean interspike intervals of the transmembrane voltages for different time- and spatial discretisations. Accuracy of the tau-leap method is presented in relation to the deterministic versions of the ion channel models. The results show that the method used to simulate the transmembrane voltages is accurate and that while the tau-leap method is convergent in the mean interspike interval sense, it is not conclusive how accurate it is compared to the corresponding ordinary differential equations or how efficient it is.

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This thesis is concerned with the use of L² or square integrable functions as a representation of the electronic continua in ion-atom collisions. An exact representation of the continuum states is considered for comparison. The functions are optimised in an attempt to remove some of the arbitrary features present in such calculations. The original work of this thesis is mainly concerned with the calculation of single electron processes in collisions between He²⁺ ions and neutral lithium atoms. The cross sections for single electron capture were calculated in a close-coupled approximation, using the semi-classical impact parameter method. A maximum of thirty-two atomic orbitals with plane-wave translational factors attached were centred upon the target and projectile. Satisfactory agreement with experimental data is obtained over the He(^2+)laboratory energy range from 8 to 2000 keV. The results show the importance of the continuum over a restricted range of impact energies. The rest of the research is concerned with direct excitation and ionisation in the same collision system and results are given for He²⁺ laboratory energies between 20 and 6000 keV. The calculations used a similar close-coupled approximation with up to sixty-five basis states. The best ionisation cross sections reproduce the experimental data apart from a normalization factor. The excitation results were more sensitive to basis set choice. The ionisation cross sections were also investigated using an exact representation of the continuum states, using the First Born Approximation and a t-matrix approximation in an attempt to improve upon the L² results. The relationship between the present calculations and some previous methods are discussed and suggestions for future work are made. These are the first close-coupled estimates of ionisation for this sytem and show that contributions from target d- and f- states dominate the ionisation cross section around its maximum.

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This study investigates the efficiency of a calcia stabilised zirconia (CaSZ) solid electrolyte as an oxygen ion conductor. The study also examines the behaviour of the oxygen species conducted by the solid electrolyte compared to species provided in the gas phase for partial oxidation of hydrocarbons. In this work, an electrochemical cell of the form Air, AgHCaSZ//Ag, Carrier gas was used to investigate the electrochemical efficiency and stability of the solid electrolyte CaSZ conducting of oxygen ions under atmospheric pressure conditions at 500 degrees C by applying a range of electrical potentials from I to 16 volts across the electrochemical cell. Due to the applied potential oxygen anions are transferred across the solid electrolyte from the cathode side of the cell to the anode side. It was found that the employed electrolyte is approximately a 100% purely ionic conductor of oxygen ions in the range of electrical voltage applied from I to 10 volts. Above that range the cell started to degrade and loose its ionic efficiency. It was possible to generate gas mixtures containing trace quantities of oxygen. The viscosity of these gas mixtures as a function of oxygen concentration was determined using an established flow perturbation technique (Flux Response Technology). Partial oxidation of propene was used to investigate the difference between the oxygen species produced electrochemically via electrical potential application across the electrochemical cell Air, AgHCaSZ//Ag, Propene, Ar and oxygen provided in the gaseous state co-fed with propene over silver electrode under atmospheric pressure and 450 degrees C and 500 degrees C. It was found that the method of electrochemical provision of oxygen caused the silver catalyst to be more selective to 1,5-hexadeine, whereas the gaseous oxygen provision produced acrolein as the major product. Carbon dioxide formation was not affected by the method of oxygen provision. The Ag electrode was compared to an Au-rich Ag alloy electrode for propene partial oxidation using electrochemical provision. It was found that 1,5-hexadiene was the major product over both electrodes, but the Au-rich alloy was more selective for acrolein than the Ag electrode. This might be due to the gold serving as a separator between Ag particles which hinder the back-spill over of oxygen and allow desorption of molecular oxygen in the gas phase, which then re-adsorb molecularly on silver sites producing acrolein. The effect of the sequence of the method of oxygen provision on the partial oxidation of propene was tested using the electrochemical cell Y-BiMoHAg//CaSZ//Ag at 450 degrees C and atmospheric pressure. A sharp decrease in acrolein selectivity was found when oxygen was provided in the gas phase after treatment with electrochemical oxygen, while no significant effect was noticed when the electrochemical oxygen was used after treatment with gaseous oxygen. This large decrease in acrolein selectivity might be attributed to the severe reduction of the catalyst, which is probably caused by high electrical potential application. A temperature increase from 450 to 500 degrees C seemed to suppress the formation of acrolein for both methods of oxygen provision and enhance the 1,5-hexadiene formation.

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I have developed an analytical method for the determination of molecular hydrogen in seawater. It is based on the change of hydrogen concentration in a 30 cc. volume of air as it is equilibrated with a one-liter sample of seawater. The change in hydrogen concentration in the air is measured using a gas chromatograph with a helium ionization detector. The system has been utilized aboard ship on several occasions and has been proven to be both dependable and readily transportable. The accuracy of a single measurement is limited to about plus or minus fifteen per cent by the analytical precision of the method. The precision is limited by the random errors in the GC analysis. Shipboard and laboratory experiments have shown that contamination of near-surface and near-bottom samples can be a major problem unless special precautions are taken. / Graduation date: 1978