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Articles 1 - 4 of 4
Full-Text Articles in Numerical Analysis and Computation
Impacts Of Climate Change On The Evolution Of The Electrical Grid, Melissa Ree Allen
Impacts Of Climate Change On The Evolution Of The Electrical Grid, Melissa Ree Allen
Doctoral Dissertations
Maintaining interdependent infrastructures exposed to a changing climate requires understanding 1) the local impact on power assets; 2) how the infrastructure will evolve as the demand for infrastructure changes location and volume and; 3) what vulnerabilities are introduced by these changing infrastructure topologies. This dissertation attempts to develop a methodology that will a) downscale the climate direct effect on the infrastructure; b) allow population to redistribute in response to increasing extreme events that will increase under climate impacts; and c) project new distributions of electricity demand in the mid-21st century.
The research was structured in three parts. The first …
Numerical Methods And Algorithms For High Frequency Wave Scattering Problems In Homogeneous And Random Media, Cody Samuel Lorton
Numerical Methods And Algorithms For High Frequency Wave Scattering Problems In Homogeneous And Random Media, Cody Samuel Lorton
Doctoral Dissertations
This dissertation consists of four integral parts with a unified objective of developing efficient numerical methods for high frequency time-harmonic wave equations defined on both homogeneous and random media. The first part investigates the generalized weak coercivity of the acoustic Helmholtz, elastic Helmholtz, and time-harmonic Maxwell wave operators. We prove that such a weak coercivity holds for these wave operators on a class of more general domains called generalized star-shape domains. As a by-product, solution estimates for the corresponding Helmholtz-type problems are obtained.
The second part of the dissertation develops an absolutely stable (i.e. stable in all mesh regimes) interior …
Statistical Mechanics And Schramm-Loewner Evolution With Applications To Crack Propagation Processes, Christopher Borut Mesic
Statistical Mechanics And Schramm-Loewner Evolution With Applications To Crack Propagation Processes, Christopher Borut Mesic
Masters Theses
Schramm-Loewner Evolution (SLE) has both mathematical and physical roots that extend as far back as the early 20th century. We present the progression of these humble roots from the Ideal Gas Law, all the way to the renormalization group and conformal field theory, to better understand the impact SLE has had on modern statistical mechanics. We then explore the potential application of the percolation exploration process to crack propagation processes, illustrating the interplay between mathematics and physics.
Mathematically Modeling Fetal Electrocardiograms, Samuel Estes, Kiersten Utsey, Erick Kalobwe
Mathematically Modeling Fetal Electrocardiograms, Samuel Estes, Kiersten Utsey, Erick Kalobwe
Pursuit - The Journal of Undergraduate Research at The University of Tennessee
Abstract
Some of the most common and fatal birth defects are those related to the heart. In adults, possible heart conditions are often identified through the use of an electrocardiogram (ECG). However, due to the presence of other signals and noise in the recording, fetal eletrocardiography has not yet proven effective in diagnosing these defects. This paper develops a mathematical model of three-dimensional heart vector trajectories, which was used to generate synthetic maternal and fetal ECG signals. The dipole model is a useful simplification in which the electrical activity of the heart is viewed as a single time-varying vector originating …