In this thesis we prove existence and uniqueness for reflected stochastic differential equation on a specific non-smooth, time-dependent domain. The domain is the intersection of a finite number of smooth domains that are allowed to vary in time. The reflection is oblique to the domain and at the corners more than one direction of reflection is allowed. The time restrictions on the domain is firstly the existence of a semiconcave family of sets that are C¹;+ in time. Secondly that the distance function to the domain is in W¹;p. The first part of the proof is to construct of three kinds of test functions with desired properties. Using these test functions, existence is proved to the Skorokhod problem. Finally uniqueness is proved for the reflected stochastic differential equation. / I den här mastersuppsatsen så bevisar vi existens och entydighet för reflekterade stokastiska differentialekvation på ett icke slätt, tidsberoende område. Området är snittet mellan ett ändligt antal släta områden som tillåts variera i tiden. Reflektionen är ej nödvändigtvis vinkelrät till området och i hörnen finns det mer än en tillåten riktning. Tidsrestriktionen på området är dels existensen av en familj av semikonkava mängder som är C¹;+ i tiden. Dessutom att avståndet till området är W¹;p i tiden. Första delen av beviset är att konstruera tre hjälp funktioner med eftersökta egenskaper. Med hjälp av de här funktionerna så bevisas sedan existens av lösningar till Skorokhod problemet. Slutligen så bevisas entydighet av den reflekterade stokastiska differentialekvationen.

Diabetes mellitus, which is largely driven by nutritional and behavioral factors, is characterized by accelerated atherosclerosis with impaired plaque stability. Atherosclerosis and associated complications are the major cause of mortality in diabetic patients. Efficient therapeutic concepts for diabetes-associated atherosclerosis are lacking. Atherosclerosis among diabetic patients is associated with reduced endothelial thrombomodulin (TM) expression and impaired activated protein C (aPC) generation. Here, we demonstrate that atherosclerotic plaque stability is reduced in hyperglycemic mice expressing dysfunctional TM (TMPro/Pro mice), which have a pro-coagulant phenotype due to impaired thrombin inhibition and markedly reduced aPC generation. The vessel lumen and plaque size of atherosclerotic lesions in the truncus brachiocephalic were decreased in diabetic TMPro/Pro ApoE-/- mice compared to diabetic ApoE-/- mice. While lipid accumulation in lesions of diabetic TMPro/Pro ApoE-/- mice was lower than that in diabetic ApoE-/- mice, morphometric analyses revealed more prominent signs of instable plaques, such as a larger necrotic core area and decreased fibrous cap thickness in diabetic TMPro/Pro ApoE-/- mice. Congruently, more macrophages and fewer smooth muscle cells were observed within lesions of diabetic TMPro/Pro ApoE-/- mice. Thus, impaired TM function reduces plaque stability, a characteristic of hyperglycemia-associated plaques, thus suggesting the crucial role of impaired TM function in mediating diabetes-associated atherosclerosis.

The fast-growing electric vehicles (EVs) market demands huge efforts from car manufacturers to develop and improve their current products’ systems. A fast charge of the battery pack is one of the challenges encountered due to the battery limitations regarding behaviour and additional degradation when exposed to such a rough situation. In addition, the outcome of a study performed on a battery does not apply to others, especially if their chemistries are different. Hence, extensive testing is required to understand the influence of design decisions on the particular energy storage device to be implemented. Due to batteries’ nonlinear behaviour that is highly dependent on external variables such as temperature, the dynamic load and aging, another defying task is the widely studied state of charge (SOC) estimation, commonly considered one of the most significant functions in a battery management system (BMS). This thesis presents an extensive battery fast charging aging test study equipped with promising current charging profiles from published literature to minimize aging. Four charging protocols are carefully designed to charge the cell from 10 to 80% SOC within fifteen minutes and have their performances discussed. A dual state estimation algorithm is modelled to estimate the SOC with the assistance of a capacity state of health (SOHcap) estimation. Finally, the dual state estimation model is validated with the fast charging aging test data. / Thesis / Master of Science in Mechanical Engineering (MSME)

Lithium-ion (Li-ion) batteries are amongst the most commonly used types in Electric (EVs) and Hybrid Electric (HEVs) Vehicles due to their high energy and power densities, as well as long lifetime. A battery is one of the most important components of an EV and hence it needs to be monitored and controlled accurately. The safety, and reliability of battery packs must then, be ensured by accurate management, control, and monitoring functions by using a Battery Management System (BMS). A BMS is also responsible for accurate real-time estimation of the State of Charge (SoC), State of Health (SoH) and State of Power (SoP) of the battery. The battery SoC provides information on the amount of energy left in the battery. The SoH determines the remaining capacity and health of a pack, and the SoP represents the maximum available power. These critical battery states cannot be directly measured. Therefore, they have to be inferred from measurable parameters such as the current delivered by the battery as well as its terminal voltage. Consequently, in order to offer accurate monitoring of SoC, SoH and SoP, advanced numerical estimation methods need to be deployed. In the estimation process, the states and parameters of a system are extracted from measurements. The objective is to reduce the estimation errors in the presence of uncertainties and noise under different operating conditions. This thesis uses and provides different enhancements to a robust estimation strategy referred to as the Smooth Variable Structure Filter (SVSF) for condition monitoring of batteries. The SVSF is a predictor-corrector method based on sliding mode control that enhances the robustness in the presence of noise and uncertainties. The methods are proposed to provide accurate estimates of the battery states of operation and can be implemented in real-time in BMS. To improve the performance of battery condition monitoring, a measurement-based SoC estimation method called coulomb counting is paired with model-based state estimation strategy. Important considerations in parameter and state estimation are model formulation and observability. In this research, a new model formulation that treats coulomb counting as an added measurement is proposed. It is shown that this formulation enhanced information extraction, leading to a more accurate state estimation, as well as an increase in the number of parameters and variables that can be estimated while maintaining observability. This model formulation is used for characterizing the battery in a range of operating conditions. In turn, the models are integral to a proposed adaptive filter that is a combination of the Interacting Multiple Model (IMM) concept and the SVSF. It is shown that this combined strategy is an efficient estimation approach that can effectively deal with battery aging. The proposed method provides accurate estimation for various SoH of a battery. Further to battery aging adaptation, measurement errors such as sensor noise, drift, and bias that affect estimation performance, are considered. To improve the accuracy of battery state estimation, a noise covariance adaptation scheme is developed for the SVSF method. This strategy further improves the robustness of the SVSF in the presence of unknown physical disturbances, noise, and initial conditions. The proposed estimation strategies are also considered for their implementation on battery packs. An important consideration in pack level battery management is cell-to-cell variations that impact battery safety. This study considers online battery parametrization to update the pack’s model over time and to detect cell-to-cell variability in parallel-connected battery cells configurations. Experimental data are used to validate and test the efficacy of the proposed methods in this thesis. / Thesis / Doctor of Philosophy (PhD) / To address the critical issue of climate change, it is necessary to replace fossil-fuel vehicles with battery-powered electric vehicles. Despite the benefits of electric vehicles, their popularity is still limited by the range anxiety and the cost determined by the battery pack. The range of an electric vehicle is determined by the amount of charge in its battery pack. This is comparable to the amount of gasoline in a gasoline vehicle’s tank. In consideration of the need for methods to address range anxiety, it is necessary to develop advanced algorithms for continuous monitoring and control of a battery pack to maximize its performance. However, the amount of charge and health of a battery pack cannot be measured directly and must be inferred from measurable variables including current, voltage and temperature. This research presents several algorithms for detecting the range and health of a battery pack under a variety of operating conditions. With a more accurate algorithm, a battery pack can be monitored closely, resulting in lower long-term costs. Adaptive methods for determining a battery’s state of charge and health in uncertain and noisy conditions have been developed to provide an accurate measure of available charge and capacity. Methods are then extended to improve the determination of state of charge and health for a battery module.

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<p>The main contributions of this thesis include two points: firstly, we originally establish Complex STM to semi-analytically calculate the mode profiles of multi-layer planar waveguide terminated with both PML and PRB ; secondly, although CMMM has been generally applied to the simulation of waveguide facets, Bragg gratings, etc[52-53], we for the first time demonstrate that CMMM can also be utilized for the modeling of couplings of radiation field outgoing perpendicularly to the waveguide axis with an incident wave launched in the examples of high-index-contrast waveguide crossings and corners. CMMM is proved to be able to estimate the field profiles and power flows accurately through the validation with FDTD.</p> / <p>Optical waveguides are basic building blocks of high-density photonic integrated circuits and play crucial roles in optical access networks, biomedical system, sensors and so on. Various kinds of dielectric waveguides apply the total internal reflection condition to transmit optical field [9] and even more complicated structures based on waveguide interconnects, Bragg grating, photonic crystals are actively developed by corporations and academic institutes. Especially, the fast developing pace of Metal-Organic Chemical Vapor Deposition (MOCVD), Molecular Beam Epitaxy (MBE) and other fabrication techniques has predicted the increasing complication and thus more advanced function of modern optics integrated circuits. Under such circumstances, convenient and accurate modeling and simulation schemes are necessary for the exploration, designing and optimization of photonic devices, systems and networks before the time-consuming and expensive fabrication process.</p> <p>The thesis summarizes several frequency-domain modeling schemes for the calculation of mode profile or beam propagation in 2D dielectric waveguide. The thesis mainly covers conventional Smooth Transition Method (STM), High Order Finite Difference (HOFD) scheme, Complex STM, and Complex Mode Matching Method (CMMM) based on the 2D waveguide model terminated with Perfect Matching Layer (PML) and Perfect Reflection Boundary (PRB). The mode spectrums and modal patterns obtained from Complex STM are compared with those of HOFD, and the simulation of waveguide crossings and corners with CMMM is validated with Finite-Difference-Time-Domain (FDTD) Method.</p> <p><strong> </strong></p> / Master of Applied Science (MASc)

Purpose: Evidence has accumulated to show that blood pressure variability (BPV) has a striking relationship with cardiovascular (CV) risk. Despite the mounting evidence implicating BPV as a CV risk factor, scant attention has been paid to: (1) the mechanisms by which high BPV confers greater CV risk; and (2) the efficacy of non-pharmacologic treatment modalities in the attenuation of BPV. In order to address these two unresolved questions, the purpose of this dissertation was twofold. The purpose of study #1 was to investigate the association between measures of short-term BPV (24-hour BPV) and long-term BPV (visit-to-visit BPV) with markers of endothelial health in a cohort of African Americans in order to determine if increased BPV may confer greater CV risk by eliciting injury to the endothelium. The purpose of study #2 was to investigate the effects of a 6-month aerobic exercise training (AEXT) intervention on visit-to-visit BPV and 24-hour BPV in the same cohort of African Americans in order to provide the first available data on the efficacy of a non-pharmacologic treatment modality in the lowering of BPV. Methods: We recruited 72 African Americans who were sedentary, non-diabetic, non-smoking, and free of CV and renal disease. Before and after a 6-month AEXT intervention, office blood pressure (BP) was measured at 3 separate visits and 24-hour ambulatory BP monitoring (ABPM) was conducted to measure visit-to-visit BPV and 24-hour BPV, respectively. Right brachial artery diameter was assessed at rest, during flow-mediated dilation (FMD), and after nitroglycerin-mediated dilation (NMD). Peak and area under the curve (AUC) were calculated as measures of FMD and NMD, and the FMD/NMD ratio was calculated as a measure of endothelial function normalized by smooth muscle function. Fasted blood samples were obtained and were analyzed for circulating EMPs expressed as CD31+CD42- and CD62E+ EMPs. Results: In study #1, participants with higher 24-hour diastolic BPV (DBPV) had significantly lower CD31+CD42- EMPs compared to participants with lower 24-hour DBPV. When categorized according to visit-to-visit DBPV, participants with higher visit-to-visit DBPV had a significantly lower FMD/NMD ratio, and significantly higher %NMDpeak and NMDAUCs compared to participants with lower visit-to-visit DBPV. When analyzed as continuous variables, 24-hour mean arterial pressure variability (MAPV) was inversely associated with CD31+CD42- EMPs visit-to-visit DBPV was inversely associated with the FMD/NMD ratio and positively associated with %NMDpeak and NMDAUC; and 24-hour DBPV was positively associated with NMDAUC. All associations were independent of age, gender, BMI, mean BP, and pulse pressure. In study #2 investigating the effects of AEXT in 33 participants who completed the study, 24-hour DBPV and 24-hour MAPV were significantly increased after AEXT. The increase in 24-hour DBPV was independent of changes in BMI, mean BP, and self-reported sleep time. Heart rate variability (HRV) derived from ABPM was associated with the changes in 24-hour DBPV and 24-hour MAPV. There were no significant changes in visit-to-visit BPV after AEXT. Conclusions: The results from study #1 provide evidence that BPV is associated with vascular health as endothelial function was decreased in participants with high visit-to-visit DBPV, while smooth muscle function was increased in participants with higher visit-to-visit and 24-hour DBPV. The findings from study #2 show that 6-months of AEXT do not elicit beneficial changes in BPV. The finding of an association between changes in 24-hour BPV with HRV could indicate, however, that changes in activity levels during ABPM, in part, contributed to the observed changes in 24-hour BPV. / Kinesiology

This work identifies the Fragile X-related protein (FXR1) as a reciprocal regulator of HuR target transcripts in vascular smooth muscle cells (VSMC). FXR1 was identified as an HuR interacting protein by liquid chromatography-tandem mass spectrometry (LC-MS/MS). The-HuR-FXR1 interaction is abrogated in RNase-treated extracts, indicating that their association is tethered by mRNAs. FXR1 expression is induced in diseased, but not normal arteries. SiRNA knock down of FXR1 increases abundance and stability of inflammatory mRNAs, while overexpression of FXR1 reduces their abundance and stability. RNA-EMSA and RIP demonstrate that FXR1 directly interacts with an ARE and a previously uncharacterized element in the 3’UTR of TNFa. FXR1 expression is increased in VSMC challenged with the anti-inflammatory cytokine IL-19, and FXR1 is required for IL-19 reduction of HuR. This suggests FXR1 is an anti-inflammation responsive, HuR counter-regulatory protein that reduces abundance of pro-inflammatory transcripts. Additionally, we observed significantly increased poly-A-Binding protein (PABP) expression localizing to discrete punctate structures in both vascular smooth muscle (VSMC) and endothelial cells (EC) of the aortic arch of Ldlr-/- mice, as compared to WT controls. EIF2α phosphorylation, requisite for SG formation, was also induced by clotrimazole and oxLDL in these cells. Interestingly, VSMCs pre-treated with anti-inflammatory cytokine IL-19 followed by clotrimazole significantly reduced the formation of SGs and eIF2a phosphorylation, suggesting a relationship between inflammation and SG formation in vascular cells. Reduction of SG component G3BP1 by siRNA knockdown significantly reduced stress granule formation and inflammatory gene abundance in hVSMC. Microtubule inhibitors reduced SG formation in hVSMC. These results support the hypothesis that SG formation in atherosclerosis is driven by inflammation, SG may mediate the cellular response to inflammation, and that anti-inflammatory treatment may lessen atherosclerosis progression and plaque formation by reduction of SGs. / Biomedical Sciences