Large Deviations for a Class of Semilinear Stochastic Partial Differential Equations

We prove the large deviations principle (LDP) for the law of the solutions to a class of semilinear stochastic partial differential equations driven by multiplicative noise. Our proof is based on the weak convergence approach and significantly improves earlier methods

Principles of Mechanical Design in Overhead Transmission Lines

Technical infrastructures are of significant importance for a modern society to develop continuously, and dependence of society to electric power is ever-increasing. Power supply is also a must for economic growth and life convenience, and both industry and households have confidence in proper functionality of power network. Interruption in the power system due to technical faults, adverse weather and operational problems may result in irreparable consequences. Electricity, through Transformers and Transmission Lines, flows from Power Plants to Substations and Distribution System, and then to consumers .The Power and Distribution System is highly interconnected, which means that the Transmission Grid functions as one entity. This master thesis reviews the principles of mechanical design in Transmission Lines. Overhead Transmission Lines are expected to withstand climatic conditions and other outside disturbances. The applied forces must be tolerated mechanically by structural components of Transmission Line. Transmission Line must not fail in the hardest climatic situations. This fact obliges engineers to anticipate worst loading conditions, and select the best design in order to be confident of consistency and stability of operation in the Line

Numerical bifurcation diagram for the two-dimensional boundary-fed chlorine-dioxide–iodine–malonic-acid system

We present a numerical solution of the chlorine-dioxide–iodine–malonic-acid reaction-diffusion system in two dimensions in a boundary-fed system using a realistic model. The bifurcation diagram for the transition from nonsymmetry-breaking structures along boundary feed gradients to transverse symmetry-breaking patterns in a single layer is numerically determined. We find this transition to be discontinuous. We make a connection with earlier results and discuss prospects for future work

DIETARY INTAKE IN RELATION TO METABOLIC SYNDROME AND ASSOCIATED RISKS IN CANADIAN ADULTS AND ADOLESCENTS

Type 2 diabetes and cardiovascular disease (CVD), major public health concerns in Canada and worldwide, are the main outcomes of Metabolic Syndrome (MetS). MetS is a clustering of five chronic disease risk factors, including abdominal obesity, dyslipidemia (elevated triglycerides and reduced high-density lipoprotein cholesterol level), hypertension, and elevated fasting plasma glucose. Abdominal obesity and insulin resistance are the main factors contributing to development of MetS and thus CVD and diabetes. Further, dyslipidemia (specifically the total cholesterol/HDL-C ratio) is necessary to be monitored in people with these diseases or risk factors. The Canadian Health Measures Survey (CHMS) has direct health measurements that provide the opportunity to identify risk factors associated with chronic disease. Further, dietary intake has been assessed in CHMS, which can be utilized to evaluate the association with diseases and risk factors controlling for potential covariates. To examine the association between dietary intake with MetS and associated risks and diseases in Canadian adults and adolescents, data from CHMS cycle1, 2007-2009 (n=5604, aged 6-79 y) were used in which dietary intake was assessed using a semi-quantitative food frequency questionnaire. Frequency of food intake (times/day) and the distribution of individuals with and without disease or risk factors by socio-demographic characteristic was determined. Further, the association between dietary intake and each disease or risk factor was evaluated using logistic models. Data manipulation, cleaning, and creation of new variables were done using IBM SPSS statistics for windows, version 20. All statistical analyses were conducted by STATA/SE 11, StataCorp. As per Statistics Canada’s recommendation, data were weighted and bootstrapped using specific commands in STATA in order to be representative of the Canadian population. Physically active Canadians had significantly more milk and dairy product, fresh fruit and vegetable, and fruit and vegetable juice intake compared to inactive Canadians. Low-income households had significantly greater intakes of sugar-sweetened beverages (SSBs) and lower amounts of fresh fruit and vegetables than high-income households. Individuals with the lowest level of education had greatest potato and lowest fruit and vegetable juice intake. The prevalence of abdominal obesity (12-79 y), elevated TC/HDL-C ratio (20-79 y), MetS (12-79 y), and diabetes (20-79 y) was 35.7%, 20.5%, 18.3%, and 7.5%, respectively. The overall estimated percent risk of CVD over 10 years in adults aged 30-74 y was 8.66%. Abdominal obesity had the greatest contribution (~90%) to development of MetS in each age group compared to other components of MetS. Also, abdominal obesity was a strong significant predictor for development of other risk factors and chronic diseases including elevated TC/HDL-C ratio, diabetes, and CVD (OR: 6.12, CI: 2.68-13.96; OR: 2.25, CI: 1.24-4.06, OR: 1.4, CI: 1.06-1.87, respectively). High consumption of diet soft drink was associated with increased risk of abdominal obesity, Mets, diabetes, and elevated TC/HDL-C ratio. High consumption of fruit and vegetables and cereal was associated with decreased risk of CVD over 10 years whereas potato intake increased the risk. Intake of nuts appeared to be associated with reduction in the risk of MetS among Canadians. Dietary fat intake of one to less than 5 times/week was associated with increased risk of abdominal obesity in individuals over 40 years of age compared to 12-19 y individuals. Further, “ever drinking” alcohol compared to “never drinking” alcohol was associated with decreased risk of diabetes and elevated TC/HDL-C ratio. Low level of education contributed to development of abdominal obesity. Thus, abdominally obese individuals with specifically elevated TC/HDL-C ratio are at risk of developing MetS, CVD, and diabetes. They need to be educated with specific focus on physical activity, and greater intake of fruit and vegetables, nuts, and lower intake of dietary fat, diet soft drinks, and potato. Additionally, considering the social determinants which might contribute to increase the risk of chronic diseases or risk factors such as income, housing, accessibility to facilities in neighborhoods, school programs, or community programs is essential

Scroll Waves in the Presence of Slowly Varying Anisotropy with Application to the Heart

We consider the dynamics of scroll waves in the presence of rotating anisotropy, a model of the left ventricle of the heart in which the orientation of fibers in successive layers of tissue rotates. By choosing a coordinate system aligned with the fiber rotation and studying the phase dynamics of a straight but twisted scroll wave, we derive a Burgers’ equation with forcing associated with the fiber rotation rate. We present asymptotic solutions for scroll twist, verified by numerics, using a realistic fiber distribution profile. We make connection with earlier numerical and analytical work on scroll dynamics