<p> This thesis contributes to the development of a novel electromagnetic (EM) time-domain computational approach, the self-adjoint variable method, for the scattering parameter (S-parameter) sensitivity analysis of high frequency problems. </p> <p> The design sensitivity analysis provides sensitivity information in the form of the response gradient (response Jacobian). For that, various techniques are used, ranging from finite-difference approximations to quadratic and spline interpolations. However, when the number of design parameters becomes large, the simulation time would become unaffordable, which is especially the case with EM simulations. The proposed self-adjoint sensitivity analysis (SASA) approach aims at providing sensitivity information efficiently without sacrificing the accuracy. Its efficiency lies in the fact that regardless of the number of design parameters, only one simulation of the original structure is required- the one used to compute the S-parameters. Thus, the sensitivity computation has negligible overhead. At the same time, it has second-order accuracy. </p> <p> Currently, commercial EM simulators provide only specific engineering responses, such as Z- or S-parameters. No sensitivity information is actually made available. With the SASA approach, the only requirement for the EM solver is the ability to access the field solution at the perturbation grid points. This feature is generally available with all time-domain EM simulators. The manipulation of the field solutions in this approach is simple and it adds practically negligible overhead to the -simulation time. </p> <p> We confirm the validity of this approach for both the shape and constitutive parameters of the design structures. 2-D examples including metallic and dielectric details are presented, using the field solutions from an in-house time-domain solver. We also explore the feasibility of implementing this approach with one of the commercial solvers, XFDTD v. 6.3. </p> <p> Suggestions for future research are provided. </P> / Thesis / Master of Applied Science (MASc)

In this thesis we develop new mathematical models, using dynamical systems, to represent localized gene delivery of bone morphogenetic protein 2 into bone marrow-derived mesenchymal stem cells and rat calvarial defects. We examine two approaches, using pDNA or cmRNA treatments, respectively, towards the production of calcium deposition and bone regeneration in in vitro and in vivo experiments. We first review the relevant scientific literature and survey existing mathematical representations for similar treatment approaches. We then motivate and develop our new models and determine model parameters from literature, heuristic approaches, and estimation using sparse data. We next conduct a qualitative analysis using dynamical systems theory. Due to the nature of the parameter estimation, it was important that we obtain local and global sensitivity analyses of model outputs to changes in model inputs. Finally we compared results from different treatment protocols. Our model suggests that cmRNA treatments may perform better than pDNA treatments towards bone fracture healing. This work is intended to be a foundation for predictive models of non-viral local gene delivery systems.

Anticipating how stream water quality will respond to change, such as increased pollution or water diversions, requires knowledge of the main mechanisms controlling water and chemical constituent movement and a reasonable representation of those mechanisms. By deriving mathematical models to represent a stream system and collecting supporting field-based measurements, water quality response can be predicted. However, because each stream is unique and the movement of water and constituents is spatially and temporally complex, assessing whether the stream is appropriately represented and whether predictions are trustworthy is still a challenge within the scientific and management communities. Building on decades of stream research, this dissertation provides a step towards better representing some of the complexities found within streams and rivers to better predict water quality responses over long stream distances. First, a method is presented to assess which mechanisms are considered most important in chemical constituent predictions. Next, the number of measurements necessary to represent the general complexities of water, mass, and heat movement in streams was determined. The advancements developed in this dissertation provide a foundation to more efficiently and accurately inform water resource management.

The lymphatic system is responsible for several vital roles in human body, one of which is maintaining fluid and protein balance. There is no central pump in the lymphatic system and the transport of fluid against gravity and adverse pressure gradient is maintained by the extrinsic and intrinsic pumping mechanisms. Any disruption of the lymphatic system due to trauma or injury can lead to edema. There is no cure for lymphedema partly because the knowledge of the function of the lymphatic system is lacking. Thus, a well-developed model of the lymphatic system is crucial to improve our understanding of its function. Here we used a lumped parameter approach to model a chain of lymphangions in series. Equations of conservation of mass, conservation of momentum, and vessel wall force balance were solved for each lymphangion computationally. Due to the lack of knowledge of the parameters describing the system in the literature, more accurate measurements of these parameters should be pursued to advance the model. Because of the difficulty of the isolated vessel and in-situ experiments, we performed a parameter sensitivity analysis to determine the parameters that affect the system most strongly. Our results showed that more accurate estimations of active contractile force and physiologic features of lymphangions, such as length/diameter ratios, should be pursued in future experiments. Also further experiments are required to refine the valve behavior and valve parameters.

We develop a stochastic parametrization, based on a 'simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.

No description available.

The inputs to a microscopic traffic simulation model generally include quantitative, but immeasurable data describing driver behavior and vehicle performance characteristics. Engineers often use default values for parameters such as car-following sensitivity and gap acceptance because it can be difficult to obtain accurate estimates for these parameters. While recent research has indicated that the accuracy of a simulation model can significantly improve if driver behavior parameters are calibrated to local data, this is not a typical practice. Manual calibration of these parameters is often too time-consuming to be cost-effective. Researchers have applied automated calibration procedures using genetic algorithms to these problems with some success, but many engineers lack the tools or the skill set necessary to easily program and implement such a procedure. A graphical user interface (GUI) for a genetic algorithm would make automated calibration much more accessible to students and professional engineers. Another barrier that limits the practicality of calibrating driver behavior parameters is the number of available calibration parameters. The CORSIM (short for CORridor SIMulation) model developed by the Federal Highway Administration contains dozens of optional calibration parameters controlling various aspects of driver behavior. Determining the sensitivity of the model to these parameters is an important step toward finding the appropriate parameter values. The purpose of this thesis is to develop a GUI for a genetic algorithm and perform needed sensitivity analyses to aid in model development and calibration. This thesis tests a simple, automated procedure utilizing a genetic algorithm for the calibration of driver behavior and vehicle performance parameters that can easily be applied by engineers in the field. An existing genetic algorithm script that has been applied to other research has been adapted to fit the purposes of this thesis. As part of this procedure, a sensitivity analysis was performed to recommend which parameters should be included in model calibration. The results of the research suggest that fewer than half of the available driver behavior parameters are necessary to calibrate a model of a linear freeway network. The calibration tests also demonstrate the importance of calibrating to at least two measures of effectiveness in order to better match existing conditions and provide an acceptable level of error for the simulation model.

No description available.

<p> This thesis proposes a sensitivity solver for frequency-domain electromagnetic (EM) simulators based on volume methods such as the finite-element method (FEM). The proposed sensitivity solver computes S-parameter Jacobians directly from the field solutions available from the EM simulation. It exploits the computational efficiency of the self-adjoint sensitivity analysis (SASA) approach where only one EM simulation suffices to obtain both the responses and their gradients in the designable parameter space. The proposed sensitivity solver adopts the system equations of the finite-difference frequency-domain (FDFD) method.</p> <p> There are three major advantages to this development: (1) the Jacobian computation is completely independent of the simulation engine, its grid and its system equations; (2) the implementation is straightforward and in the form of a post-processing algorithm operating on the exported field solutions; and (3) it is computationally very efficient-time requirements are negligible in comparison with conventional field-based optimization procedures utilizing Jacobians computed via response-level finite differences or parameter sweeps.</p> <p> The accuracy and the efficiency of the proposed sensitivity solver are verified in the sensitivity analysis and the gradient-based optimization of filters and antennas. Compared to the finite-difference approximation, drastic reduction of the time required by the overall optimization process is achieved. All examples use a commercial finite-element simulator.</p> <p> Suggestions for future research are provided.</p> / Thesis / Master of Applied Science (MASc)

The objective of this thesis is to develop and implement an algorithm for inverting the sound speed profile via estimation of the parameters embedded in a geoacoustic model. The environmental model inscribes a continuously-varying marine sediment layer with density and sound speed distributions represented by the generalized-exponential and inverse-square functions, respectively. Based upon a forward problem of plane-wave reflection from a non-uniform sediment layer overlying a uniform elastic basement, an inversion procedure for estimating the sound speed profile from the reflected sound field under the influence of noise is established and numerically implemented. The inversion invokes a probabilistic approach quantified by the posterior probability density for measuring the uncertainties of the estimated parameters from synthetic noisy data. Preliminary analysis on the solution of the forward problem and the sensitivity of the model parameters is first conducted, leading to a determination of the parameters chosen for inversion in the ensuing study. The parameter uncertainties referenced 1-D and 2-D marginal posterior probability densities are then examined, followed by the statistical estimation for the sound speed profile in terms of 99 % credibility interval. The effects of, the signal-to-noise ratio (SNR), the dimension of data vector, the region in which the data sampled, on the statistical estimation of sound speed profile are demonstrated and discussed.