Soluble models in two-dimensional dilaton gravity

A one-parameter class of simple models of two-dimensional dilaton gravity, which can be exactly solved including back-reaction effects, is investigated at both classical and quantum levels. This family contains the RST model as a special case, and it continuously interpolates between models having a flat (Rindler) geometry and a constant curvature metric with a nontrivial dilaton field. The processes of formation of black hole singularities from collapsing matter and Hawking evaporation are considered in detail. Various physical aspects of these geometries are discussed, including the cosmological interpretation.

Effect of competitive situation and price on diffusion of mobile communications

Työn päätavoitteena oli selvittää hinnan ja kilpailutilanteen vaikutusta matkaviestinnän diffuusioon. Työn empiirinen osuus tarkasteli matkapuhelinliittymien hinnan vaikutusta liittymien diffuusioon sekä sitä, miten alan kilpailu on vaikuttanut matkaviestinnän hintatasoon. Työssä analysoitiin myös matkaviestinnän kilpailutilannetta Suomen markkinoilla. Tutkimuksen empiirinen aineisto kerättiin toissijaisista lähteistä, esimerkiksi EMC-tietokannasta. Tutkimus oli luonteeltaan kvantitatiivinen.Empiirisessä osassa käytetyt mallit oli muodostettu aikaisempien tutkimuksien perusteella. Regressioanalyysiä käytettiin arvioitaessa hinnan vaikutusta diffuusionopeuteen ja mahdollisten omaksujien määrään. Regressioanalyysissä sovellettiin ei-lineaarista mallia.Tutkimustulokset osoittivat, että tasaisesti laskevilla matkapuhelinliittymien sekä matkapuhelimien hinnoilla ei ole merkittävää vaikutusta matkaviestinnän diffuusioon. Myöskään kilpailutilanne ei ole vaikuttanut paljon matkaviestinnän yleiseen hintatasoon. Työn tulosten perusteella voitiin antaa myös muutamia toimenpide-ehdotuksia jatkotutkimuksia varten.

Connectivity and tissue microstructural alterations in right and left temporal lobe epilepsy revealed by diffusion spectrum imaging.

Focal epilepsy is increasingly recognized as the result of an altered brain network, both on the structural and functional levels and the characterization of these widespread brain alterations is crucial for our understanding of the clinical manifestation of seizure and cognitive deficits as well as for the management of candidates to epilepsy surgery. Tractography based on Diffusion Tensor Imaging allows non-invasive mapping of white matter tracts in vivo. Recently, diffusion spectrum imaging (DSI), based on an increased number of diffusion directions and intensities, has improved the sensitivity of tractography, notably with respect to the problem of fiber crossing and recent developments allow acquisition times compatible with clinical application. We used DSI and parcellation of the gray matter in regions of interest to build whole-brain connectivity matrices describing the mutual connections between cortical and subcortical regions in patients with focal epilepsy and healthy controls. In addition, the high angular and radial resolution of DSI allowed us to evaluate also some of the biophysical compartment models, to better understand the cause of the changes in diffusion anisotropy. Global connectivity, hub architecture and regional connectivity patterns were altered in TLE patients and showed different characteristics in RTLE vs LTLE with stronger abnormalities in RTLE. The microstructural analysis suggested that disturbed axonal density contributed more than fiber orientation to the connectivity changes affecting the temporal lobes whereas fiber orientation changes were more involved in extratemporal lobe changes. Our study provides further structural evidence that RTLE and LTLE are not symmetrical entities and DSI-based imaging could help investigate the microstructural correlate of these imaging abnormalities.

Modeling reaction kinetics and mass transfer in ozonation in water solutions

This dissertation is based on four articles dealing with modeling of ozonation. The literature part of this considers some models for hydrodynamics in bubble column simulation. A literature review of methods for obtaining mass transfer coefficients is presented. The methods presented to obtain mass transfer are general models and can be applied to any gas-liquid system. Ozonation reaction models and methods for obtaining stoichiometric coefficients and reaction rate coefficients for ozonation reactions are discussed in the final section of the literature part. In the first article, ozone gas-liquid mass transfer into water in a bubble column was investigated for different pH values. A more general method for estimation of mass transfer and Henry’s coefficient was developed from the Beltrán method. The ozone volumetric mass transfer coefficient and the Henry’s coefficient were determined simultaneously by parameter estimation using a nonlinear optimization method. A minor dependence of the Henry’s law constant on pH was detected at the pH range 4 - 9. In the second article, a new method using the axial dispersion model for estimation of ozone self-decomposition kinetics in a semi-batch bubble column reactor was developed. The reaction rate coefficients for literature equations of ozone decomposition and the gas phase dispersion coefficient were estimated and compared with the literature data. The reaction order in the pH range 7-10 with respect to ozone 1.12 and 0.51 the hydroxyl ion were obtained, which is in good agreement with literature. The model parameters were determined by parameter estimation using a nonlinear optimization method. Sensitivity analysis was conducted using object function method to obtain information about the reliability and identifiability of the estimated parameters. In the third article, the reaction rate coefficients and the stoichiometric coefficients in the reaction of ozone with the model component p-nitrophenol were estimated at low pH of water using nonlinear optimization. A novel method for estimation of multireaction model parameters in ozonation was developed. In this method the concentration of unknown intermediate compounds is presented as a residual COD (chemical oxygen demand) calculated from the measured COD and the theoretical COD for the known species. The decomposition rate of p-nitrophenol on the pathway producing hydroquinone was found to be about two times faster than the p-nitrophenol decomposition rate on the pathway producing 4- nitrocatechol. In the fourth article, the reaction kinetics of p-nitrophenol ozonation was studied in a bubble column at pH 2. Using the new reaction kinetic model presented in the previous article, the reaction kinetic parameters, rate coefficients, and stoichiometric coefficients as well as the mass transfer coefficient were estimated with nonlinear estimation. The decomposition rate of pnitrophenol was found to be equal both on the pathway producing hydroquinone and on the path way producing 4-nitrocathecol. Comparison of the rate coefficients with the case at initial pH 5 indicates that the p-nitrophenol degradation producing 4- nitrocathecol is more selective towards molecular ozone than the reaction producing hydroquinone. The identifiability and reliability of the estimated parameters were analyzed with the Marcov chain Monte Carlo (MCMC) method. @All rights reserved. No part of the publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the author.

Reaction Kinetics and Viscosity Modelling in the Fusion Syntheses of Ca- and Ca/Mg-resinates

Rosin is a natural product from pine forests and it is used as a raw material in resinate syntheses. Resinates are polyvalent metal salts of rosin acids and especially Ca- and Ca/Mg- resinates find wide application in the printing ink industry. In this thesis, analytical methods were applied to increase general knowledge of resinate chemistry and the reaction kinetics was studied in order to model the non linear solution viscosity increase during resinate syntheses by the fusion method. Solution viscosity in toluene is an important quality factor for resinates to be used in printing inks. The concept of critical resinate concentration, c crit, was introduced to define an abrupt change in viscosity dependence on resinate concentration in the solution. The concept was then used to explain the non-inear solution viscosity increase during resinate syntheses. A semi empirical model with two estimated parameters was derived for the viscosity increase on the basis of apparent reaction kinetics. The model was used to control the viscosity and to predict the total reaction time of the resinate process. The kinetic data from the complex reaction media was obtained by acid value titration and by FTIR spectroscopic analyses using a conventional calibration method to measure the resinate concentration and the concentration of free rosin acids. A multivariate calibration method was successfully applied to make partial least square (PLS) models for monitoring acid value and solution viscosity in both mid-infrared (MIR) and near infrared (NIR) regions during the syntheses. The calibration models can be used for on line resinate process monitoring. In kinetic studies, two main reaction steps were observed during the syntheses. First a fast irreversible resination reaction occurs at 235 °C and then a slow thermal decarboxylation of rosin acids starts to take place at 265 °C. Rosin oil is formed during the decarboxylation reaction step causing significant mass loss as the rosin oil evaporates from the system while the viscosity increases to the target level. The mass balance of the syntheses was determined based on the resinate concentration increase during the decarboxylation reaction step. A mechanistic study of the decarboxylation reaction was based on the observation that resinate molecules are partly solvated by rosin acids during the syntheses. Different decarboxylation mechanisms were proposed for the free and solvating rosin acids. The deduced kinetic model supported the analytical data of the syntheses in a wide resinate concentration region, over a wide range of viscosity values and at different reaction temperatures. In addition, the application of the kinetic model to the modified resinate syntheses gave a good fit. A novel synthesis method with the addition of decarboxylated rosin (i.e. rosin oil) to the reaction mixture was introduced. The conversion of rosin acid to resinate was increased to the level necessary to obtain the target viscosity for the product at 235 °C. Due to a lower reaction temperature than in traditional fusion synthesis at 265 °C, thermal decarboxylation is avoided. As a consequence, the mass yield of the resinate syntheses can be increased from ca. 70% to almost 100% by recycling the added rosin oil.

Eletrocatálise das reações de oxidação de hidrogênio e de redução de oxigênio

This work discusses the electrocatalytic processes taking place in the polymer electrolyte fuel cell electrodes, specifically the hydrogen oxidation reaction (HOR) and the oxygen reduction reaction (ORR), because these are clear examples of electrochemical reactions favored by the use of electrocatalysts. Since the gaseous reactants are very little soluble in the electrolyte, the use of special electrodes, named gas diffusion electrodes, is required to promote easy and continuous access of reactant gases to the electrocatalytic sites. Besides this, other important aspects such as the use of spectroscopic techniques and of theoretical models to improve the knowledge of the electrocatalytic systems are shortly discussed.

MCMC Analysis for Optimization of Stochastic Models

In any decision making under uncertainties, the goal is mostly to minimize the expected cost. The minimization of cost under uncertainties is usually done by optimization. For simple models, the optimization can easily be done using deterministic methods.However, many models practically contain some complex and varying parameters that can not easily be taken into account using usual deterministic methods of optimization. Thus, it is very important to look for other methods that can be used to get insight into such models. MCMC method is one of the practical methods that can be used for optimization of stochastic models under uncertainty. This method is based on simulation that provides a general methodology which can be applied in nonlinear and non-Gaussian state models. MCMC method is very important for practical applications because it is a uni ed estimation procedure which simultaneously estimates both parameters and state variables. MCMC computes the distribution of the state variables and parameters of the given data measurements. MCMC method is faster in terms of computing time when compared to other optimization methods. This thesis discusses the use of Markov chain Monte Carlo (MCMC) methods for optimization of Stochastic models under uncertainties .The thesis begins with a short discussion about Bayesian Inference, MCMC and Stochastic optimization methods. Then an example is given of how MCMC can be applied for maximizing production at a minimum cost in a chemical reaction process. It is observed that this method performs better in optimizing the given cost function with a very high certainty.

Synthesis of percarboxylic acids in microreactor

Percarboxylic acids are commonly used as disinfection and bleaching agents in textile, paper, and fine chemical industries. All of these applications are based on the oxidative potential of these compounds. In spite of high interest in these chemicals, they are unstable and explosive chemicals, which increase the risk of synthesis processes and transportation. Therefore, the safety criteria in the production process should be considered. Microreactors represent a technology that efficiently utilizes safety advantages resulting from small scale. Therefore, microreactor technology was used in the synthesis of peracetic acid and performic acid. These percarboxylic acids were produced at different temperatures, residence times and catalyst i.e. sulfuric acid concentrations. Both synthesis reactions seemed to be rather fast because with performic acid equilibrium was reached in 4 min at 313 K and with peracetic acid in 10 min at 343 K. In addition, the experimental results were used to study the kinetics of the formation of performic acid and peracetic acid. The advantages of the microreactors in this study were the efficient temperature control even in very exothermic reaction and good mixing due to the short diffusion distances. Therefore, reaction rates were determined with high accuracy. Three different models were considered in order to estimate the kinetic parameters such as reaction rate constants and activation energies. From these three models, the laminar flow model with radial velocity distribution gave most precise parameters. However, sulfuric acid creates many drawbacks in this synthesis process. Therefore, a ´´greener´´ way to use heterogeneous catalyst in the synthesis of performic acid in microreactor was studied. The cation exchange resin, Dowex 50 Wx8, presented very high activity and a long life time in this reaction. In the presence of this catalyst, the equilibrium was reached in 120 second at 313 K which indicates a rather fast reaction. In addition, the safety advantages of microreactors were investigated in this study. Four different conventional methods were used. Production of peracetic acid was used as a test case, and the safety of one conventional batch process was compared with an on-site continuous microprocess. It was found that the conventional methods for the analysis of process safety might not be reliable and adequate for radically novel technology, such as microreactors. This is understandable because the conventional methods are partly based on experience, which is very limited in connection with totally novel technology. Therefore, one checklist-based method was developed to study the safety of intensified and novel processes at the early stage of process development. The checklist was formulated using the concept of layers of protection for a chemical process. The traditional and three intensified processes of hydrogen peroxide synthesis were selected as test cases. With these real cases, it was shown that several positive and negative effects on safety can be detected in process intensification. The general claim that safety is always improved by process intensification was questioned.

Oxidation rates of carbon and nitrogen in char residues from solid fuels

Computational fluid dynamics (CFD) modeling is an important tool in designing new combustion systems. By using CFD modeling, entire combustion systems can be modeled and the emissions and the performance can be predicted. CFD modeling can also be used to develop new and better combustion systems from an economical and environmental point of view. In CFD modeling of solid fuel combustion, the combustible fuel is generally treated as single fuel particles. One of the limitations with the CFD modeling concerns the sub-models describing the combustion of single fuel particles. Available models in the scientific literature are in many cases not suitable as submodels for CFD modeling since they depend on a large number of input parameters and are computationally heavy. In this thesis CFD-applicable models are developed for the combustion of single fuel particles. The single particle models can be used to improve the combustion performance in various combustion devices or develop completely new technologies. The investigated fields are oxidation of carbon (C) and nitrogen (N) in char residues from solid fuels. Modeled char-C oxidation rates are compared to experimental oxidation rates for a large number of pulverized solid fuel chars under relevant combustion conditions. The experiments have been performed in an isothermal plug flow reactor operating at 1123-1673 K and 3-15 vol.% O2. In the single particle model, the char oxidation is based on apparent kinetics and depends on three fuel specific parameters: apparent pre-exponential factor, apparent activation energy, and apparent reaction order. The single particle model can be incorporated as a sub-model into a CFD code. The results show that the modeled char oxidation rates are in good agreement with experimental char oxidation rates up to around 70% of burnout. Moreover, the results show that the activation energy and the reaction order can be assumed to be constant for a large number of bituminous coal chars under conditions limited by the combined effects of chemical kinetics and pore diffusion. Based on this, a new model based on only one fuel specific parameter is developed (Paper III). The results also show that reaction orders of bituminous coal chars and anthracite chars differ under similar conditions (Paper I and Paper II); reaction orders of bituminous coal chars were found to be one, while reaction orders of anthracite chars were determined to be zero. This difference in reaction orders has not previously been observed in the literature and should be considered in future char oxidation models. One of the most frequently used comprehensive char oxidation models could not explain the difference in the reaction orders. In the thesis (Paper II), a modification to the model is suggested in order to explain the difference in reaction orders between anthracite chars and bituminous coal chars. Two single particle models are also developed for the NO formation and reduction during the oxidation of single biomass char particles. In the models the char-N is assumed to be oxidized to NO and the NO is partly reduced inside the particle. The first model (Paper IV) is based on the concentration gradients of NO inside and outside the particle and the second model is simplified to such an extent that it is based on apparent kinetics and can be incorporated as a sub-model into a CFD code (Paper V). Modeled NO release rates from both models were in good agreement with experimental measurements from a single particle reactor of quartz glass operating at 1173-1323 K and 3-19 vol.% O2. In the future, the models can be used to reduce NO emissions in new combustion systems.

Particle model for simulating limestone reactions in novel fluidised bed energy applications

The development of carbon capture and storage (CCS) has raised interest towards novel fluidised bed (FB) energy applications. In these applications, limestone can be utilized for S02 and/or CO2 capture. The conditions in the new applications differ from the traditional atmospheric and pressurised circulating fluidised bed (CFB) combustion conditions in which the limestone is successfully used for SO2 capture. In this work, a detailed physical single particle model with a description of the mass and energy transfer inside the particle for limestone was developed. The novelty of this model was to take into account the simultaneous reactions, changing conditions, and the effect of advection. Especially, the capability to study the cyclic behaviour of limestone on both sides of the calcination-carbonation equilibrium curve is important in the novel conditions. The significances of including advection or assuming diffusion control were studied in calcination. Especially, the effect of advection in calcination reaction in the novel combustion atmosphere was shown. The model was tested against experimental data; sulphur capture was studied in a laboratory reactor in different fluidised bed conditions. Different Conversion levels and sulphation patterns were examined in different atmospheres for one limestone type. The Conversion curves were well predicted with the model, and the mechanisms leading to the Conversion patterns were explained with the model simulations. In this work, it was also evaluated whether the transient environment has an effect on the limestone behaviour compared to the averaged conditions and in which conditions the effect is the largest. The difference between the averaged and transient conditions was notable only in the conditions which were close to the calcination-carbonation equilibrium curve. The results of this study suggest that the development of a simplified particle model requires a proper understanding of physical and chemical processes taking place in the particle during the reactions. The results of the study will be required when analysing complex limestone reaction phenomena or when developing the description of limestone behaviour in comprehensive 3D process models. In order to transfer the experimental observations to furnace conditions, the relevant mechanisms that take place need to be understood before the important ones can be selected for 3D process model. This study revealed the sulphur capture behaviour under transient oxy-fuel conditions, which is important when the oxy-fuel CFB process and process model are developed.

Methyl and ethyl chloride synthesis in microreactors

Methyl chloride is an important chemical intermediate with a variety of applications. It is produced today in large units and shipped to the endusers. Most of the derived products are harmless, as silicones, butyl rubber and methyl cellulose. However, methyl chloride is highly toxic and flammable. On-site production in the required quantities is desirable to reduce the risks involved in transportation and storage. Ethyl chloride is a smaller-scale chemical intermediate that is mainly used in the production of cellulose derivatives. Thus, the combination of onsite production of methyl and ethyl chloride is attractive for the cellulose processing industry, e.g. current and future biorefineries. Both alkyl chlorides can be produced by hydrochlorination of the corresponding alcohol, ethanol or methanol. Microreactors are attractive for the on-site production as the reactions are very fast and involve toxic chemicals. In microreactors, the diffusion limitations can be suppressed and the process safety can be improved. The modular setup of microreactors is flexible to adjust the production capacity as needed. Although methyl and ethyl chloride are important chemical intermediates, the literature available on potential catalysts and reaction kinetics is limited. Thus the thesis includes an extensive catalyst screening and characterization, along with kinetic studies and engineering the hydrochlorination process in microreactors. A range of zeolite and alumina based catalysts, neat and impregnated with ZnCl2, were screened for the methanol hydrochlorination. The influence of zinc loading, support, zinc precursor and pH was investigated. The catalysts were characterized with FTIR, TEM, XPS, nitrogen physisorption, XRD and EDX to identify the relationship between the catalyst characteristics and the activity and selectivity in the methyl chloride synthesis. The acidic properties of the catalyst were strongly influenced upon the ZnCl2 modification. In both cases, alumina and zeolite supports, zinc reacted to a certain amount with specific surface sites, which resulted in a decrease of strong and medium Brønsted and Lewis acid sites and the formation of zinc-based weak Lewis acid sites. The latter are highly active and selective in methanol hydrochlorination. Along with the molecular zinc sites, bulk zinc species are present on the support material. Zinc modified zeolite catalysts exhibited the highest activity also at low temperatures (ca 200 °C), however, showing deactivation with time-onstream. Zn/H-ZSM-5 zeolite catalysts had a higher stability than ZnCl2 modified H-Beta and they could be regenerated by burning the coke in air at 400 °C. Neat alumina and zinc modified alumina catalysts were active and selective at 300 °C and higher temperatures. However, zeolite catalysts can be suitable for methyl chloride synthesis at lower temperatures, i.e. 200 °C. Neat γ-alumina was found to be the most stable catalyst when coated in a microreactor channel and it was thus used as the catalyst for systematic kinetic studies in the microreactor. A binder-free and reproducible catalyst coating technique was developed. The uniformity, thickness and stability of the coatings were extensively characterized by SEM, confocal microscopy and EDX analysis. A stable coating could be obtained by thermally pretreating the microreactor platelets and ball milling the alumina to obtain a small particle size. Slurry aging and slow drying improved the coating uniformity. Methyl chloride synthesis from methanol and hydrochloric acid was performed in an alumina-coated microreactor. Conversions from 4% to 83% were achieved in the investigated temperature range of 280-340 °C. This demonstrated that the reaction is fast enough to be successfully performed in a microreactor system. The performance of the microreactor was compared with a tubular fixed bed reactor. The results obtained with both reactors were comparable, but the microreactor allows a rapid catalytic screening with low consumption of chemicals. As a complete conversion of methanol could not be reached in a single microreactor, a second microreactor was coupled in series. A maximum conversion of 97.6 % and a selectivity of 98.8 % were reached at 340°C, which is close to the calculated values at a thermodynamic equilibrium. A kinetic model based on kinetic experiments and thermodynamic calculations was developed. The model was based on a Langmuir Hinshelwood-type mechanism and a plug flow model for the microreactor. The influence of the reactant adsorption on the catalyst surface was investigated by performing transient experiments and comparing different kinetic models. The obtained activation energy for methyl chloride was ca. two fold higher than the previously published, indicating diffusion limitations in the previous studies. A detailed modeling of the diffusion in the porous catalyst layer revealed that severe diffusion limitations occur starting from catalyst coating thicknesses of 50 μm. At a catalyst coating thickness of ca 15 μm as in the microreactor, the conditions of intrinsic kinetics prevail. Ethanol hydrochlorination was performed successfully in the microreactor system. The reaction temperature was 240-340°C. An almost complete conversion of ethanol was achieved at 340°C. The product distribution was broader than for methanol hydrochlorination. Ethylene, diethyl ether and acetaldehyde were detected as by-products, ethylene being the most dominant by-product. A kinetic model including a thorough thermodynamic analysis was developed and the influence of adsorbed HCl on the reaction rate of ethanol dehydration reactions was demonstrated. The separation of methyl chloride using condensers was investigated. The proposed microreactor-condenser concept enables the production of methyl chloride with a high purity of 99%.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.

Implementation of Quantitative Reaction-based Model Refinement

Building a computational model for complex biological systems is an iterative process. It starts from an abstraction of the process and then incorporates more details regarding the specific biochemical reactions which results in the change of the model fit. Meanwhile, the model’s numerical properties such as its numerical fit and validation should be preserved. However, refitting the model after each refinement iteration is computationally expensive resource-wise. There is an alternative approach which ensures the model fit preservation without the need to refit the model after each refinement iteration. And this approach is known as quantitative model refinement. The aim of this thesis is to develop and implement a tool called ModelRef which does the quantitative model refinement automatically. It is both implemented as a stand-alone Java application and as one of Anduril framework components. ModelRef performs data refinement of a model and generates the results in two different well known formats (SBML and CPS formats). The development of this tool successfully reduces the time and resource needed and the errors generated as well by traditional reiteration of the whole model to perform the fitting procedure.

Bayesian analysis of SEIR epidemic models

This thesis concerns the analysis of epidemic models. We adopt the Bayesian paradigm and develop suitable Markov Chain Monte Carlo (MCMC) algorithms. This is done by considering an Ebola outbreak in the Democratic Republic of Congo, former Zaïre, 1995 as a case of SEIR epidemic models. We model the Ebola epidemic deterministically using ODEs and stochastically through SDEs to take into account a possible bias in each compartment. Since the model has unknown parameters, we use different methods to estimate them such as least squares, maximum likelihood and MCMC. The motivation behind choosing MCMC over other existing methods in this thesis is that it has the ability to tackle complicated nonlinear problems with large number of parameters. First, in a deterministic Ebola model, we compute the likelihood function by sum of square of residuals method and estimate parameters using the LSQ and MCMC methods. We sample parameters and then use them to calculate the basic reproduction number and to study the disease-free equilibrium. From the sampled chain from the posterior, we test the convergence diagnostic and confirm the viability of the model. The results show that the Ebola model fits the observed onset data with high precision, and all the unknown model parameters are well identified. Second, we convert the ODE model into a SDE Ebola model. We compute the likelihood function using extended Kalman filter (EKF) and estimate parameters again. The motivation of using the SDE formulation here is to consider the impact of modelling errors. Moreover, the EKF approach allows us to formulate a filtered likelihood for the parameters of such a stochastic model. We use the MCMC procedure to attain the posterior distributions of the parameters of the SDE Ebola model drift and diffusion parts. In this thesis, we analyse two cases: (1) the model error covariance matrix of the dynamic noise is close to zero , i.e. only small stochasticity added into the model. The results are then similar to the ones got from deterministic Ebola model, even if methods of computing the likelihood function are different (2) the model error covariance matrix is different from zero, i.e. a considerable stochasticity is introduced into the Ebola model. This accounts for the situation where we would know that the model is not exact. As a results, we obtain parameter posteriors with larger variances. Consequently, the model predictions then show larger uncertainties, in accordance with the assumption of an incomplete model.

Effect of iron on reactivity of vanillin in wine models /

Phenolic compounds are important components of grapes and wines. They have been found to have important roles in grape and wine systems and properties that are beneficial for human health. Vanillin (3-methoxy-4-hydroxybenzaldehyde) is a phenolic compound coming from the oxidative degradation of lignin in oak-barrels during the aging of wine. Vanillin is an important flavour component of wine and its concentration in wine influences significantly the aroma and flavour of wine. The concentration of vanillin in wine is affected by various factors including the presence of metal ions. In this work, by using HPLC, HPLC-MS, and MS technologies, iron (III) cations were found to affect the oxidation of vanillin in a model system of wine, and the product of the oxidation was identified as divanillin. The mechanism of the redox reaction between vanillin and Fe^"^ is thought to follow that of other phenol oxidations. Increasing the concentration of Fe ^ in the model system accelerates divanillin production. The best pH condition for the divanillin production in the system is the range of 3.0 ~ 3.5. Increasing temperature from 20°C to 40°C accelerates the divanillin production. Divanillin was found to exist in three commercial red wines in this work. Keeping the storage temperature cool and decreasing the contact of grapes and wines with iron are two major measures suggested by this work in order to decrease the oxidation of vanillin during the making and aging of wine.