Physical Sciences and Mathematics Commons^™

Mathematical Models Of Combustion At High Pressure, Daniel Fong

Dissertations

In this dissertation, we develop new mathematical theories of flame propagation that are valid at elevated, or extreme, pressures. Of particular interest is the regime of burning in which the pressure exceeds the critical pressure of the species undergoing chemical reaction. Fluids and flames are known to behave differently under these extreme conditions as opposed to atmospheric pressure. The focus of this dissertation is to investigate these differences by deriving reduced models that contain the unique features.

In the first part of this dissertation, we analyze the structure of laminar diffusion flames at high pressure in the limit of large …

Computational Modeling And Numerical Methods For Spaciotemporal Calcium Cycling In Ventricular Myocytes, Robert Rovetti

Mathematics Faculty Works

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain …

Mathematical Modeling Of Fluid Spills In Hydraulically Fractured Well Sites, Oluwafemi Michael Taiwo

Graduate Theses and Dissertations

Improved drilling technology and favorable energy prices have contributed to the rapid pace at which the exploitation of unconventional natural gas is taking place across the United States. As a natural gas well is being drilled, reserve pits are constructed to hold the drilling fluids and other materials returned from the drilling process. These reserve pits can fail, and when they do, plant and animal life of the surrounding area may be adversely affected. This project develops a screening tool for a suitable location for a reserve pit. This work will be a critical piece of the Infrastructure Placement Analysis …

Computational Modeling And Numerical Methods For Spatiotemporal Calcium Cycling In Ventricular Myocytes, Michael Nivala, Enno De Lange, Robert J. Rovetti, Zhilin Qu

Mathematics Faculty Works

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain …

Modeling Of Growth Kinetics And Characterization Of Membrane Mechanics, Antonio Nava

Electronic Theses and Dissertations

One growing field in alternative energy is biofuel production through microorganisms. These fields of research include hydrogen and biofuel production through the cultivation of algae. We've selected 2 different algae, Anabaena sp. cpcc 387 and Tetraselmis to study. Through mathematical modeling of Anabaena we investigate the complex multicellular relationships and colony stability when noise is introduced. In conjunction with researchers at NREL, we've set out to characterize Tetraselmis cells' membrane elasticity.

Mathematical Modeling In The High School Classroom, Selena Oswalt

LSU Master's Theses

Mathematical modeling is the procedure whereby students apply mathematical concepts learned in class to new and unfamiliar situations. A modeling task is a mathematically-rich problem that engages students in mathematical thinking, drawing upon their previously learned knowledge and supporting their understanding of the mathematical concepts currently being covered. Modeling requires students to assign meaning to the mathematical concepts and to extend the concepts beyond rote learning. In order for students to be successful in a classroom that is centered around the idea of mathematical modeling, the students must be taught how to collaborate with other students, persevere through challenging problems, …

Mathematical Model Development Of Super-Resolution Image Wiener Restoration, Amr H. Yousef, Jiang Li, Mohammad A. Karim

Electrical & Computer Engineering Faculty Publications

In super-resolution (SR), a set of degraded low-resolution (LR) images are used to reconstruct a higher-resolution image that suffers from acquisition degradations. One way to boost SR images visual quality is to use restoration filters to remove reconstructed images artifacts. We propose an efficient method to optimally allocate the LR pixels on the high-resolution grid and introduce a mathematical derivation of a stochastic Wiener filter. It relies on the continuous-discrete-continuous model and is constrained by the periodic and nonperiodic interrelationships between the different frequency components of the proposed SR system. We analyze an end-to-end model and formulate the Wiener filter …