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This thesis has two major goals; first to develop scalable scripts for steady-state analysis, then to perform a case study on the dynamic properties of a vertical pile. The scripts are based on the numerical library PETSc for parallel linear algebra. This opens up the opportunity to use the scripts to solve large-scale models on supercomputers. The performance of the scripts are verified against problems with analytical solutions and the commercial software ABAQUS. The case study compares the numerical results with those obtained from an approximate solution.   The results from this thesis are verified scripts that can find a steady-state solution for linear-elastic isotropic solids on supercomputers. The case study has shown differences between numerical and semi-analytical solutions for a vertical pile. The dynamic stiffness show differences within reasonable limits but the equivalent viscous damping show larger differences. This is believed to come from the material damping in the soil that has been excluded from the approximate solution.   These two results make it possible for further case studies on typical three-dimensional problems, that result in large-scale models, such as the dynamic properties of a slanted pile or pile-groups. The scripts can easily be expanded and used for other interesting research projects and this is the major outcome of from this thesis.

This dissertation documents the building of computational propellant/ingredient models toward predicting AP/HTPB/Al cookoff events. Two computer codes were used to complete this work; a steady-state code and a transient ignition code Numerous levels of verification resulted in a robust set of codes to which several propellant/ingredient models were applied. To validate the final cookoff predictions, several levels of validation were completed, including the comparison of model predictions to experimental data for: AP steady-state combustion, fine-AP/HTPB steady-state combustion, AP laser ignition, fine-AP/HTPB laser ignition, AP/HTPB/Al ignition, and AP/HTPB/Al cookoff. A previous AP steady-state model was updated, and then a new AP steady-state model was developed, to predict steady-state combustion. Burning rate, temperature sensitivity, surface temperature, melt-layer thickness, surface species at low pressure and high initial temperature, final flame temperature, final species fractions, and laser-augmented burning rate were all predicted accurately by the new model. AP ignition predictions gave accurate times to ignition for the limited experimental data available. A previous fine-AP/HTPB steady-state model was improved to predict a melt layer consistent with observation and avoid numerical divergence in the ignition code. The current fine-AP/HTPB model predicts burning rate, surface temperature, final flame temperature, and final species fractions for several different propellant formulations with decent success. Results indicate that the modeled condensed-phase decomposition should be exothermic, instead of endothermic, as currently formulated. Changing the model in this way would allow for accurate predictions of temperature sensitivity, laser-augmented burning rate, and surface temperature trends. AP/HTPB ignition predictions bounded the data across a wide range of heat fluxes. The AP/HTPB/Al model was based upon the kinetics of the AP/HTPB model, with the inclusion of aluminum being inert in both the solid and gas phases. AP/HTPB/Al ignition predictions bound the data for all but one source. AP/HTPB/Al cookoff predictions were accurate when compared to the limited data, being slightly low (shorter time) in general. Comparisons of AP/HTPB/Al ignition and cookoff data showed that the experimental data might be igniting earlier than expected.

The development of a new deposition technique called evaporative vapor deposition (EVD) is reported, allowing deposition and formation of atomically-thin, large area materials on arbitrary substrates. This work focuses on the highly popular monolayer material – graphene oxide (GO). A droplet of a GO solution is formed on a heated polymer substrate, and maintained at steady-state evaporation (all droplet parameters are held constant over time). The polymer substrate is laser patterned to control the droplet's contact line dynamics and the droplet's contact angle is maintained using a computer controlled syringe pump. A room temperature silicon wafer is translated through the vapor field of the evaporating GO droplet using a computer controlled translation stage. Dropwise condensation formed on the silicon wafer is monitored using both optical and infrared cameras. The condensation rate is measured to be ~50pL/mm2?s – 500 pL/mm2?s and dependent on the substrate translation speed and height difference between the droplet's apex and substrate surface. Nano-sized GO flakes carried through the vapor phase are captured in the condensate, depositing on the translating wafer. Deposition rate is dependent on the stability of the solution and droplet condensate size. Characterization with Raman spectroscopy show expected shifts for graphene/graphite. The presented EVD technique is promising toward formation of large scale 2D materials with applications to developing new technologies.

The generalized likelihood ratio (GLR) control charts are studied for monitoring a process proportion of defective or nonconforming items. The type of process change considered is an abrupt sustained increase in the process proportion, which implies deterioration of the process quality. The objective is to effectively detect a wide range of shift sizes. For the first part of this research, we assume samples are collected using rational subgrouping with sample size n>1, and the binomial GLR statistic is constructed based on a moving window of past sample statistics that follow a binomial distribution. Steady state performance is evaluated for the binomial GLR chart and the other widely used binomial charts. We find that in terms of the overall performance, the binomial GLR chart is at least as good as the other charts. In addition, since it has only two charting parameters that both can be easily obtained based on the approach we propose, less effort is required to design the binomial GLR chart for practical applications. The second part of this research develops a Bernoulli GLR chart to monitor processes based on the continuous inspection, in which case samples of size n=1 are observed. A constant upper bound is imposed on the estimate of the process shift, preventing the corresponding Bernoulli GLR statistic from being undefined. Performance comparisons between the Bernoulli GLR chart and the other charts show that the Bernoulli GLR chart has better overall performance than its competitors, especially for detecting small shifts. / Ph. D.

<p> A new computer executive system for the steady state simulation of chemical processes has been developed which combines modular (GEMCS) approach with the simultaneous linear equation (SYMBØL) approach to simulation. In the combined system, a GEMCS simulation, using non-linear models, is used to generate the coefficients for the set of linear equations describing the process. This linear system of equations may also include the constraints on the process which dictate the operating conditions for the actual process. The solution of the linear equations then provide new operating conditions (feed flowrates together with the component flowrates in the recycle streams) for the modular simulation, which in turn provides new coefficients; etc. This iterative procedure is automatically continued until the system is converged to the desired point. </p> <p> A modular simulation for an actual Naphtha Reforming Plant has also been achieved and it was used as a test case to demonstrate the use and effectiveness of this new executive system. In the course of developing this simulation, the application of a method for correcting plant data was demonstrated. This is the first real application of this method to be reported in the current literature. </p> / Thesis / Master of Engineering (ME)

Immunotherapy, by enhancing the endogenous anti-tumor immune responses, is showing promising results for the treatment of numerous cancers refractory to conventional therapies. However, its effectiveness for advanced castration-resistant prostate cancer remains unsatisfactory and new therapeutic strategies need to be developed. To this end, mathematical modeling provides a quantitative framework for testing in silico the efficacy of new treatments and combination therapies, as well as understanding unknown biological mechanisms. In this dissertation we present two mathematical models of prostate cancer immunotherapy defined as systems of ordinary differential equations. The first work, introduced in Chapter 2, provides a mathematical model of prostate cancer immunotherapy which has been calibrated using data from pre-clinical experiments in mice. This model describes the evolution of prostate cancer, key components of the immune system, and seven treatments. Numerous combination therapies were evaluated considering both the degree of tumor inhibition and the predicted synergistic effects, integrated into a decision tree. Our simulations predicted cancer vaccine combined with immune checkpoint blockade as the most effective dual-drug combination immunotherapy for subjects treated with androgen-deprivation therapy that developed resistance. Overall, this model serves as a computational framework to support drug development, by generating hypotheses that can be tested experimentally in pre-clinical models. The Chapter 3 is devoted to the description of a human prostate cancer mathematical model. The potential effect of immunotherapies on castration-resistant form has been analyzed. In particular, the model includes the dendritic vaccine sipuleucel-T, the only currently available immunotherapy option for advanced prostate cancer, and the ipilimumab, a drug targeting the cytotoxic T-lymphocyte antigen 4 , exposed on the CTLs membrane, currently under Phase II clinical trial. From a mathematical analysis of a simplified model, it seems likely that, under continuous administration of ipilimumab, the system lies in a bistable situation where both the no-tumor equilibrium and the high-tumor equilibrium are attractive. The schedule of periodic treatments could then determine the outcome, and mathematical models could help in deciding an optimal schedule.

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