The development of infectious disease models remains important to provide scientists with tools to better understand disease dynamics and develop more effective control strategies. In this work we focus on the estimation of seasonally varying transmission parameters in infectious disease models from real measles case data. We formulate both discrete-time and continuous-time models and discussed the benefits and shortcomings of both types of models. Additionally, this work demonstrates the flexibility inherent in large-scale nonlinear programming techniques and the ability of these techniques to efficiently estimate transmission parameters even in very large-scale problems. This computational efficiency and flexibility opens the door for investigating many alternative model formulations and encourages use of these techniques for estimation of larger, more complex models like those with age-dependent dynamics, more complex compartment models, and spatially distributed data. How- ever, the size of these problems can become excessively large even for these powerful estimation techniques, and parallel estimation strategies must be explored. Two parallel decomposition approaches are presented that exploited scenario based de- composition and decomposition in time. These approaches show promise for certain types of estimation problems.

In recent years, technologies using supercritical water have gained considerable attention, mainly due to versatility and uniqueness of water at elevated temperatures and pressures. The physical conditions required to generate supercritical water also make it prone to large intrinsic thermal and density fluctuations, exacerbated if there are impurities present in the system. These fluctuations induce nucleation, the initial stage of a first-order phase transition, and subsequent mixing of the new phase within the original phase. When this new phase reaches its critical size it grows irreversibly to macroscopic proportions, otherwise, tending to disintegrate. The presence of a polydispersed solid phase within the supercritical phase is responsible for unfavorable phenomena such as particle deposition and corrosion of structural components, both of which result in decreased efficiency and reliability of the supercritical water employing process. Molecular Dynamics (MD) simulation method has been the primary tool of investigation. Molecular motions are tracked on the femto and picosecond time-scales which are particularly important for the study of nucleation. Sodium chloride has been chosen in this research since it is computationally tractable and is unavoidably involved in most industrial water based applications. Cluster size distributions, the size of critical nuclei and cluster life-times are reported. The size distribution of emerging clusters shows a very strong dependence on the system’s density, with larger clusters preferentially formed at lower densities. Also, a materials science application is presented where the rapid quenching of hydrothermally formed sodium chloride clusters leads to a variety of nanostructures, characterizable by prominent vibrational modes. And lastly, during the conditions prior to crystallization, water is not only physically adsorbed to the cluster’s surface but also exists in a “confined” state within subsurface regions for several picoseconds during the nucleation process. A mechanism for the sodium chloride hydrolysis reaction is presented as well as showing that asymmetric electrostatic fields generated by the coalescing ions are on the order of 1010 V/m, sufficient to drive the hydrolysis of confined water molecules. The HCl molecule and hydroxide ions are formed, with the latter segregating preferentially to sub-surface regions in the amorphous NaCl particles. Both HCl and hydroxide are implicated in corrosion. / Thesis (Master, Chemistry) -- Queen's University, 2008-11-03 13:54:56.021

The problem of parameter and state estimation of a class of nonlinear systems is addressed. An adaptive identifier and observer are used to estimate the parameters and the state variables simultaneously. The proposed method is derived using a new formulation. Uncertainty sets are defined for the parameters and a set of auxiliary variables for the state variables. An algorithm is developed to update these sets using the available information. The algorithm proposed guarantees the convergence of parameters and the state variables to their true value. In addition to its application in difficult estimation problems, the algorithm has also been adapted to handle fault detection problems. The technique of estimation is applied to two broad classes of systems. The first involves a class of continuous time nonlinear systems subject to bounded unknown exogenous disturbance with constant parameters. Using the proposed set-based adaptive estimation, the parameters are updated only when an improvement in the precision of the parameter estimates can be guaranteed. The formulation provides robustness to parameter estimation error and bounded disturbance. The parameter uncertainty set and the uncertainty associated with an auxiliary variable is updated such that the set is guaranteed to contain the unknown true values. The second class of system considered is a class of nonlinear systems with timevarying parameters. Using a generalization of the set-based adaptive estimation technique proposed, the estimates of the parameters and state are updated to guarantee convergence to a neighborhood of their true value. The algorithm proposed can also be extended to detect the fault in the system, injected by drastic change in the time-varying parameter values. To study the practical applicability of the developed method, the estimation of state variables and time-varying parameters of salt in a stirred tank process has been performed. The results of the experimental application demonstrate the ability of the proposed techniques to estimate the state variables and time-varying parameters of an uncertain practical system. / Thesis (Master, Chemical Engineering) -- Queen's University, 2011-10-31 22:04:58.762

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