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Investigations And Analysis Of Dynamical And Steady State Properties Of Chemical Reaction Systems, Diego Ortega Hernandez
Investigations And Analysis Of Dynamical And Steady State Properties Of Chemical Reaction Systems, Diego Ortega Hernandez
Master's Theses
In this paper, we investigate results from chemical reaction network theory and a list of techniques to test for the reaction-coordinates dynamical system to have a partial order induced by a positive orthant cone. A successful result from one of these tests guarantees mono-stationarity (and indeed convergence). We also investigate a recently published algorithmic and computational approach to determine whether a reaction network establishes mono- or multi-stationarity. We test new reactions that have not been previously introduced in the literature for mono- or multi-stationarity using this approach. This includes the two-site phosphorylation reaction network and a modified double phosphorylation reaction …
A Numerical Study Of The Van Roosbroeck System For Semiconductors, Alan Ghazarians
A Numerical Study Of The Van Roosbroeck System For Semiconductors, Alan Ghazarians
Master's Theses
Since the 1950s, semiconductors have played a significant and daily role in our lives, as they are the foundation of our computers, phones, and other electronic devices. Aside from their obvious uses, the equations that govern semiconductors have peaked the interest of mathematicians and numerical analysts. In 1950, van Roosbroeck described the fundamental semiconductor device equations as a system of three nonlinear coupled partial di↵erential equations. The van Roosbroeck system poses a challenge numerically because of its strong nonlinearity and coupled equations. Its diculties lie in simultaneously solving drift-di↵usion equations for electrons and holes and using their solutions to solve …