Physical Sciences and Mathematics Commons^™

Stochastic Modeling Of Flows In Membrane Pore Networks, Binan Gu

Dissertations

Membrane filters provide immediate solutions to many urgent problems such as water purification, and effective remedies to pressing environmental concerns such as waste and air treatment. The ubiquity of applications gives rise to a significant amount of research in membrane material selection and structural design to optimize filter efficiency. As physical experiments tend to be costly, numerical simulation and analysis of fluid flow, foulant transport and geometric evolution due to foulant deposition in complex geometries become particularly relevant. In this dissertation, several mathematical modeling and analytical aspects of the industrial membrane filtration process are investigated. A first-principles mathematical model for …

Modeling Dewetting, Demixing, And Thermal Effects In Nanoscale Metal Films, Ryan Howard Allaire

Dissertations

Thin film dynamics, particularly on the nanoscale, is a topic of extensive interest. The process by which thin liquids evolve is far from trivial and can lead to dewetting and drop formation. Understanding this process involves not only resolving the fluid mechanical aspects of the problem, but also requires the coupling of other physical processes, including liquid-solid interactions, thermal transport, and dependence of material parameters on temperature and material composition. The focus of this dissertation is on the mathematical modeling and simulation of nanoscale liquid metal films, which are deposited on thermally conductive substrates, liquefied by laser heating, and subsequently …

Modeling And Design Optimization For Membrane Filters, Yixuan Sun

Dissertations

Membrane filtration is widely used in many applications, ranging from industrial processes to everyday living activities. With growing interest from both industrial and academic sectors in understanding the various types of filtration processes in use, and in improving filter performance, the past few decades have seen significant research activity in this area. Experimental studies can be very valuable, but are expensive and time-consuming, therefore theoretical studies offer potential as a cost-effective and predictive way to improve on current filter designs. In this work, mathematical models, derived from first principles and simplified using asymptotic analysis, are proposed for: (1) pleated membrane …

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 …

Prediction Of Mrna Polyadenylation Sites In The Human Genome And Mathematical Modeling Of Alternative Polyadenylation, Yiming Cheng

Dissertations

Messenger RNA (mRNA) polyadenylation plays many important roles in the cell, such as transcription termination, mRNA stability and transportation, and mRNA translation in eukaryotic cells. A large number of human and mouse genes have multiple polyadenylation sites (referred to as poly(A) sites) that lead to variable transcripts, some of which are translated into various protein products with different functions. However, the details about when and where the polyadenylation occurs, and how pre-mRNA switches from one poly(A) site to another are still unknown. This kind of 3 '-end processing can be regulated by the cell environment, cell cycle stage, and tissue …

Modeling Projection Neuron And Neuromodulatory Effects On A Rhythmic Neuronal Network, Nicholas Kintos

Dissertations

Projection neurons shape the activity of many neural networks. In particular, neuromodulatory substances, which are often released by projection neurons, alter the cellular and/or synaptic properties within a target network. However, neural networks in turn influence projection neuron input via synaptic feedback. This dissertation uses mathematical and biophysically-realistic modeling to investigate these issues in the gastric mill (chewing) motor network of the crab, Cancer borealis. The projection neuron MCN1 elicits a gastric mill rhythm in which the LG neuron and INTl burst in anti-phase due to their reciprocal inhibition. However, bath application of the neuromodulator PK elicits a similar gastric …