The land (or ‘terrestrial’) biosphere strongly influences the exchange of carbon, energy and water between the land surface and the atmosphere. The size of the land carbon store and the magnitude of the interannual variability of the carbon exchange make models of the land surface a vital component in climate models. This thesis addresses two aspects of land surface modelling: soil respiration and phenology modelling, using different techniques with the goal of improving model representation of land-atmosphere interaction. The release of heat associated with soil respiration is neglected in the vast majority of large-scale models but may be critically important under certain circumstances. In this thesis, the effect of this heat release is considered in two ways. Firstly, a deliberately simple model for soil temperature and soil carbon, including biological heating, is constructed to investigate the effect of thermal energy generated by microbial respiration on soil temperature and soil carbon stocks, specifically in organic soils. Secondly, the mechanism for biological self-heating is implemented in the Joint UK Land Environment Simulator (JULES), in order to investigate the impacts of the extra feedback in a complex model. With the intention of improving estimates of the parameters governing modelled land surface processes, a data assimilation system based on the JULES land surface model is presented. The ADJULES data assimilation system uses information from the derivative of JULES (or adjoint) to search for a locally optimum parameter set by calibrating against observations. In this thesis, ADJULES is used with satellite-derived vegetation indices to improve the modelling of phenology in JULES.

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Since mammalian target of rapamycin (mTOR) and N-myristoltransferase (NMT) have been shown to be potentially related to breast cancer, mTOR-NMT signalling pathway is taken into specific consideration. In this thesis, mathematical models are developed to not only describe the mTORNMT signalling pathways, but also to analyze and predict the response to a treatment. Based on different biological hypotheses, candidate models are obtained by using an ordinary differential equation formalism. An optimization method called the Differential Evolution algorithm is applied to find the best parameter sets for our candidates. Doing so, will give the smallest distance between experimental data and simulated results. The experimental data are provided by Dr Shrivastav’s laboratory, Department of Biology, University of Winnipeg. Furthermore, the mathematical analysis for our candidate models has been found to show their asymptotic behaviours.To determine which candidate model is most likely to be the ”best” among the subgroup of models, model selection is used. Ultimately, the collaboration with Dr Shrivastav’s laboratory let us understand the simplified mTOR-NMT signalling pathway. / October 2016

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The pyrolysis of dimethyl ether in the presence of a methane bath, over the temperature range 790-850K, follows the simplified reaction scheme numbered 1-5: CH3OCH3 CH3O + CH3 (l) CH3O + CH4 CH3OH + CH3 (2), CH3O + M CH2O + H + M (3),H + CH4H2 + CH3 (4),CH3 + CH3 C2H6 (5) Thus monitoring the level of ethane, or ethylene derived from ethane, yields a measure of the rate of dimethyl ether decomposition, (l) Results obtained from the current work, together with those of other workers obtained over a wider temperature range, yields the rate constant for reaction (l): k1 = 10l6.3 1 .3 exp-81.4 0.3 k cal mol-1. Hence a value for the heat of formation of the methoxy radical is calculated to be 4.1 kcal mol-1. However, both computer modelling of the full reaction scheme and further experimental work has highlighted the importance of sensitised decomposition reactions within this system, reactions (6), (7): CH3 + CH3OCH3 CH4 + CH2OCH3 (6), CH2OCH3 + M CH2O + CH3 (7) For the case where neat dimethyl ether is pyrolysed the reaction is dominated by sensitised decomposition. Computer modeling successfully resolved the mechanism of reaction under the experimental conditions. Attempts to obtain an experimental rate constant for the decomposition of the methoxy radical have proved unsuccessful due to the complex nature of this reaction system. This also proved to be the case where dimethyl ether-d6 acted as the precursor of methoxy-d3. The decomposition of the trifluoromethoxy radical was examined using an RRKM computer model, reconciling the calculated parameters for this radical with the pressure dependent data of Descamps and Forst. This study of the trifluoromethoxy radical yielded data which enabled application of Unimolecular Gas Kinetic Theory to the similar methoxy radical. With so few experimental data on the decomposition of the methoxy radical it was essential to reduce the number of variables prior to applying the RRKM model to this reaction (3). Formaldehyde pyrolysis in a methane bath, over the temperature range 740-910K, was examined to resolve controversy over the mode of formaldehyde decomposition: whether the reaction proceeds by a molecular elimination path, A, or via a radical chain mechanism, B. Although ethane was not observed as a principle product, computer modelling of this reaction indicated that the combination of methyl radicals was the principle termination step. To test for the participation of the molecular elimination pathway (15), the ratio CD2O + M CO + D2 + M (15) RD2/RHD was followed as a fuction of both the formaldehyde-d2 concentration and temperature. As (D) is a function of the concentration of formaldehyde-d2, an intercept will be obtained upon plotting RD2/RHD versus (CD2O)/(CH4) where the molecular elimination path participates. No evidence of the molecular elimination route was obtained. Reaction data for steps (10) and (11) were obtained together with evidence of heterogeneous reaction contributing to the rate of formaldehyde decay.

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