Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006. / Includes bibliographical references (p. 55). / The symmetry function of a convex set offers us numerous useful information about the set in relation to probabilistic theory and geometric properties. The symmetry function is a measure of how symmetric the convex set is, and for a point, intuitively it measures how symmetric the set is with respect to that point. We call a point of high symmetry value a deep point. A random walk is a procedure that starts from a particular point in Rn and at each iteration, moves to a "neighboring" point according to some probability distribution that depends solely on the current point. The Hit-and-Run random walk on a convex set S picks a random line e through the point, and at next iteration goes to a new point that is chosen uniformly on the chord ℓ [intersection] S. In this thesis, we analyze and investigate the effectiveness of the Hit-and-Run random walk to compute a deep point in a convex body, given a randomly generated convex set. The effectiveness is evaluated in terms of the role of the starting point and the likelihood that the random walk will enter the zone of high symmetry. Additionally, some known probabilistic properties of the symmetry function are tested using the random walk, from which the integrity of the code is also verified. / (cont.) The final portion of this thesis analyzes the behavioral properties of convex sets that have non-Euclidean rounding, which renders the random walk less efficient. Therefore the pre-conditioned Hit-and-Run random walk is performed, and the performance is quantitatively presented in a power law equation that predicts the preconditioning iterations required, given the dimension of the convex set, a starting point near a corner and the width of that corner. / by Jiajie Liang. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / Includes bibliographical references (p. 41-45). / Although perfectly matched layers (PMLs) have been widely used to truncate numerical simulations of electromagnetism and other wave equations, we point out important cases in which a PML fails to be reflectionless even in the limit of infinite resolution. In particular, the underlying coordinate-stretching idea behind PML breaks down in photonic crystals and in other structures where the material is not an analytic function in the direction perpendicular to the boundary, leading to substantial reflections. The alternative is an adiabatic absorber, in which reflections are made negligible by gradually increasing the material absorption at the boundaries, similar to a common strategy to combat discretization reflections in PMLs. We demonstrate the fundamental connection between such reflections and the smoothness of the absorption profile via coupled-mode theory, and show how to obtain higher-order and even exponential vanishing of the reflection with absorber thickness. / by Ardavan F. Oskooi. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2011. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 75-79). / Over 10,000 premature mortalities per year globally are attributed to the exposure to particulate matter caused by aircraft emissions. Unlike previous studies that focus on the regional impacts from the aircraft emissions below 3,000 feet, this thesis studies the impact from emissions at all altitudes and across continents on increasing particulates in a receptor region, thereby increasing exposure. In addition to these intercontinental impacts, the thesis analyzes the temporal variations of sensitivities of the air quality and health, the proportion of the impacts attributable to different emission species, and the background emissions' influence on the impact of aircraft emissions. To quantify the impacts of aircraft emissions at various locations and times, this study uses the adjoint model of GEOS-Chem, a chemical transport model. The adjoint method efficiently computes sensitivities of a few objective functions, such as aggregated PM concentration and human exposure to PM concentration, with respect to many input parameters, i.e. emissions at different locations and times. Whereas emissions below 3,000 feet have mostly local impacts, cruise emissions from North America impair the air quality in Europe and Asia, and European cruise emissions affect Asia. Due to emissions entering Asia, the premature mortalities in Asia were approximately two to three times larger than the global mortalities caused by the Asian emissions. In contrast, North America observed only about one-ninth of the global premature mortalities caused by North American emissions because emissions get carried out of the region. This thesis calculates that most of the premature mortalities occured in Europe and Asia in 2006. Sensitivities to emissions also have seasonal and diurnal cycles. For example, ground level NOx emissions in the evening contribute to 50% more surface PM formation than the same emissions in the morning, and cruise level NOx emissions in early winter cause six times more PM concentration increase than the same emissions in spring. Aircraft NOx emissions cause 78% of PM from aviation emissions, and given the population exposure to PM concentration increase, NOx contributes 90% of the total impact. By showing the second-order sensitivities, this study finds that increases in background emissions of ammonia increase the impact of aircraft emissions on the air quality and increases in background NOx emissions decrease the impact. These results show the effectiveness of the adjoint model for analyzing the longterm sensitivities. Some of the analyses presented are practically only possible with the adjoint method. By regulating emissions at high sensitivities in time and region, calculated by the adjoint model, governments can design effective pollutant reduction policies. / by Jamin Koo. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 73-76). / This thesis consists of a simulation-based study and a data visualization framework development focusing on malaria transmission in West Africa. The simulation-based study introduces the concept of hysteresis in malaria transmission, which is defined as the dependence of malaria transmission on initial conditions of the system, characterizing the dry season. The simulation results confirm that the hysteresis effect does exist in malaria transmission demonstrated in the significant effects of initial prevalence and immunity level of the population. The persistence of the hysteresis effect is stronger in a relatively high transmission environment than in low transmission environments. In addition, the study highlights the importance of sustainable malaria control and resource allocation in the reduction of malaria transmission. It illustrates that exposure-reduction malaria control programs like the distribution of insecticide-treated nets (ITNs) will result in a loss of acquired immunity for the population. If the ITN coverage is discontinued after a period of time, relatively strong malaria resurgence will occur. This thesis also presents a web-based mapping and visualization tool for spatio-temporal data like malaria transmission predictions. The framework is developed using open source software and is not only interactive but also web-based; hence, it can deliver spatio-temporal data to the public more effectively than traditional applications. The tool contains the following two main components: the visualization interface and the interactive maps. When the user interacts with the tool, such as clicking on the map, relevant graphics and numerical data will be requested and displayed in the visualization interface. The interactive map, facilitated by animation controls, allows users to view map animations and explore how different climate and malaria transmission data changes over time and space. The visualization framework itself is customizable and has also been used to publish and visualize temperature projections in Southwest Asia. / by Xin Qiu. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2014. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 89-94). / The ability to achieve accurate predictions of turbulent flow over arbitrarily complex geometries proves critical in the advancement of aerospace design. However, quantitatively accurate results from modern Computational Fluid Dynamics (CFD) tools are often accompanied by intractably high computational expenses and are significantly hindered by the lack of automation. In particular, the generation of a suitable mesh for a given flow problem often requires significant amounts of human input. This process however encounters difficulties for turbulent flows which exhibit a wide range of length scales that must be spatially resolved for an accurate solution. Higher-order adaptive methods are attractive candidates for addressing these deficiencies by promising accurate solutions at a reduced cost in a highly automated fashion. However, these methods in general are still not robust enough for industrial applications and significant advances must be made before the true realization of robust automated three-dimensional turbulent CFD. This thesis presents steps towards this realization of a robust high-order adaptive Reynolds-Averaged Navier-Stokes (RANS) method for the analysis of turbulent flows. Specifically, a discontinuous Galerkin (DG) discretization of the RANS equations and an output-based error estimation with an associated mesh adaptation algorithm is demonstrated. To improve the robustness associated with the RANS discretization, modifications to the negative continuation of the Spalart-Allmaras turbulence model are reviewed and numerically demonstrated on a test case. An existing metric-based adaptation framework is adopted and modified to improve the procedure's global convergence behavior. The resulting discretization and modified adaptation procedure is then applied to two-dimensional and three-dimensional turbulent flows to demonstrate the overall capability of the method. / by Jun Kudo. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. / Includes bibliographical references (p. 53). / In the last three decades, with rapid advancements in the hardware and software industry, a large number of commercial and free open source languages and software have evolved. Many of these are Very High Level Languages (VHLLs) which can be easily used for scientific computing purposes such as algorithm testing and engineering computations. However, this vast pool of resources has not been utilized to its full potential. In this analysis, we will be looking at various simple and complex problems and how they can be approached in various languages. All the results will be uploaded on a website in the form of a wiki intended to be accessible to everyone. By analyzing standard problems encountered frequently in scientific computing, this wiki provides the users a performance based report which they can use to choose the best option for their particular applications. Simultaneously, a lexicon of standard codes will help them in learning those options which they want to use so that fear is not a barrier. The analysis also addresses some incompatibility issues within languages and their impact. This work is a preliminary investigation as part of Professor Alan Edelman's participation in the Numerical Mathematics Consortium. We expect the scientific computing community to benefit from this research as a whole, as this analysis will give them better alternatives for their computational needs. / by Amit Soni. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. / Includes bibliographical references (p. 127-130). / BioMEM microfluidic weirs enable biologists to study biological processes at the cell level. A novel substrate-affixed microfluidic array of weirs allows active sorting of cells via control electrodes. The ability of the weirs to retain cells hydrodynamically is vital to the functionality of the substrate-affixed array of weirs. The objective of this thesis is to give insight using numeric tools to the microfluidic weir designer on how to improve the ability of the microfluidic weir to retain cells. Simulations of the interactions between the cell and the weir were performed using a computer simulation of Stokes flow. The computational approach uses a pre-corrected Fast Fourier Transform Boundary Element Method to evaluate the drag forces acting on the cell and a rigid body physics library to handle rigid body collision dynamics between the cell and the weir. This model was used to address two research questions which are the two main discussions of the thesis. The first discussion studies in detail the mechanisms behind the 'Around The Side' (ATS) and 'Over The Top' (OTT) modes of escape that were observed experimentally. A model example was studied for each mode. The forces and torques experienced by the cell when it escaped through either mode are explained in detail. Each mode was segmented into time periods and the mechanisms behind these modes of escape were discussed to give insight to the microfluidic weir designer. The second discussion focuses on design space exploration and optimization of the ability of the microfluidic weir to retain the cell. In order to make design optimization computationally tractable a surrogate is derived; that is, a model that provides an accurate approximation to the input/output map of the simulation but that is much cheaper computationally to evaluate. / (cont.) The surrogate was built using the Support Vector Machine (SVM) algorithm and was then used for the design space exploration and optimization. The weir geometry and flow rate were used as design variables to maximize the ability of the microfluidic weir to retain cells in the design optimization problem. Results from the design space exploration and optimization showed that a minimal depth of the mouth of the weir is required for the weir to be able to retain any beads. However, the ability of the weir to retain beads is more sensitive to the width of the mouth than the depth. / by Boon Hooi Ooi. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 53-59). / The pressure-correction projection method for the incompressible Navier-Stokes equation is approached as a preconditioned Richardson iterative method for the pressure- Schur complement equation. Typical pressure correction methods perform only one iteration and suffer from a splitting error that results in a spurious numerical boundary layer, and a limited order of convergence in time. We investigate the benefit of performing more than one iteration. We show that that not only performing more iterations attenuates the effects of the splitting error, but also that it can be more computationally efficient than reducing the time step, for the same level of accuracy. We also devise a stopping criterion that helps achieve a desired order of temporal convergence, and implement our method with multi-stage and multi-step time integration schemes. In order to further reduce the computational cost of our iterative method, we combine it with an Aitken acceleration scheme. Our theoretical results are validated and illustrated by numerical test cases for the Stokes and Navier-Stokes equations, using Implicit-Explicit Backwards Difference Formula and Runge-Kutta time integration solvers. The test cases comprises a now classical manufactured solution in the projection method literature and a modified version of a more recently proposed manufactured solution. / by Jean Philippe Aoussou. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 133-140). / The present work deals with the process of fluidized bed biomass gasification (FBBG), which is the thermochemical conversion of solid biomass into combustible synthetic gas using a fluidized bed. Fluidized bed gasifiers encounter high tar concentrations at the gasifier outlet necessitating expensive downstream cleaning equipment. Apart from the complex chemical pathways involved, tar production is also strongly dependent on the transport processes occurring inside the gasifier. Hence, the development of a detailed model to predict the variation of tar production under different operating conditions needs to include two important considerations: a comprehensive chemical kinetic sub-model and a detailed hydrodynamic sub-model. However, due to the huge computational expense associated with such a detailed simulation coupling the complex chemistry and hydrodynamics, there is a need to develop simplified models on both fronts. The first part of this work presents a detailed discussion on the chemistry models for biomass gasification: after introducing the existing state-of-the-art reaction mechanisms (both detailed and compact), two new global chemistry models, incorporating a global primary tar cracking reaction, for air-blown gasification and steam-blown gasification conditions are developed. The major gas species and total tar concentrations predicted using the global models in reactor network simulations of the gasifiers are compared with the corresponding predictions obtained using the detailed CRECK mechanism for biomass gasification, as well as with the available experimental observations. On the hydrodynamics front, an improved reactor network model based on the two-phase theory has been developed to better capture the mixing inhomogeneities in the bubbling fluidized bed, including mass transfer considerations between the bubble and emulsion phases. Finally, the predictions of various tar class concentrations and major gas species concentrations, obtained using the improved reactor network model in conjunction with the detailed CRECK kinetic reaction mechanism, for both air-blown gasification and steam gasification, are presented. Key words: Biomass gasification, Fluidized beds, Chemical reactor network modeling, chemical kinetics, chemistry mechanism reduction, Global chemistry model / by Rajesh Sridhar. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / Cataloged from student submitted PDF version of thesis. / Includes bibliographical references (p. 95-97). / In a DNA sequencing workflow, a biological sample has to pass through multiple process steps. Two consecutive steps are hydroshearing and library construction. Samples arrive randomly into the inventory and are to complete both processes before their due dates. The research project is to decide the optimal sequence of samples to go through these two processes subject to operational constraints. Two approaches, namely, heuristic and integer programming have been pursued in this thesis. A heuristic algorithm is proposed to solve the scheduling problem. A variant of the problem involving deterministic arrivals of samples is also considered for comparison purposes. Comparison tests between the two approaches are carried out to investigate the performance of the proposed heuristic for the original problem and its variant. Sensitivity analysis of the schedule to parameters of the problem is also conducted when using both approaches. / by Yuwei Hu and Chin Soon Lim. / S.M.