Theses & Dissertations
http://hdl.handle.net/10214/2189
Department of Mathematics and StatisticsFri, 23 Aug 2019 13:39:27 GMT2019-08-23T13:39:27ZTopological Climate Change and Anthropogenic Forcing
http://hdl.handle.net/10214/16248
Topological Climate Change and Anthropogenic Forcing
Kypke, Kolja
The mathematical theory of bifurcation is applied to an energy balance model of the Earthâ€™s climate. Bifurcation theory explains how nonlinear systems can exhibit drastically different solutions when certain parameters, though varied gradually, cause catastrophic changes. Such a model is better able to forecast major changes in the climate than traditional methods that capture gradual variations. This thesis presents the first mathematical proof of the existence of a cusp bifurcation in a paleoclimate energy balance model. This result leads to rational explanations for three outstanding problems of paleoclimate science: the Pliocene paradox, the abruptness of the Eocene-Oligocene transition, and the warm, equable Cretaceous-Eocene climate problem. The refinement of this paleoclimate energy balance model using modern climate data adapts it to modern day and near-future parameters up to the year 2300, focusing on climate forcing caused by human activity. Results suggest an even greater future warming effect in the Arctic and Antarctic than currently projected, as a result of a bifurcation that causes a jump to a much warmer climate state in these regions.
Tue, 18 Jun 2019 00:00:00 GMThttp://hdl.handle.net/10214/162482019-06-18T00:00:00ZControlling Games, Replicator Dynamics and Predator-Prey Models with Transmission Dynamics
http://hdl.handle.net/10214/16127
Controlling Games, Replicator Dynamics and Predator-Prey Models with Transmission Dynamics
Jaber, Ahmed Shawki
The concept of optimal control is one of the significant techniques to observe the evolution of various dynamical systems that can be modeled in a mathematical framework. In optimal control problem, the aim is to minimize a performance measure function by defining a control and state trajectories for a dynamical system over a specified period. The context of optimal control is widely used in various disciplines such as engineering, economics, biomathematics, and ecology.
In this thesis, we use control theory methods to undertake the study of specific models of dynamical systems. For instance, we apply the structure of optimal control on the replicator dynamic systems associated with certain classes of games, to further study the game equilibria (or Nash equilibrium points). In essence, we aim to control the game model of population groups who use some pure and mixed strategies and to move their Nash choices to a newer Nash strategy choice with a different outcome. In our first game, we control the Nash strategies to minimize defectors from a social norm, in the second game, we minimize the nonvaccinators in a population contemplating vaccination against infectious disease. In a related way, we utilize classical control theory to analyze an epidemiological model with two different biological populations (species). The aim is to examine endemic equilibrium points of a susceptible-infections-susceptible (SIS) or a susceptible-infections-recovered (SIR) models and control them with a vaccine uptake rate in order to decrease the overall level of infection in both species. All the optimal control problems we introduce are treated with a numerical approach to get the required solutions and to comments on the effect of model parameters on the optimal system states.
Thu, 16 May 2019 00:00:00 GMThttp://hdl.handle.net/10214/161272019-05-16T00:00:00ZBiocontrol of Competing Species with Allee effect
http://hdl.handle.net/10214/16072
Biocontrol of Competing Species with Allee effect
Hodgins, Valerie
Biocontrol of a system relies on the addition of a predator, competitor or parasite to control another species. We develop a model of four autonomous ordinary differential equa- tions with biocontrol of two species of fungus in competition. Both populations have motile and sessile spores with the sessile spores subject to an Allee effect. The one-dimensional sin- gle species model, the two-dimensional competition model, and the two-dimensional single species model, are studied using phase portrait analysis and linear stability analysis to gain insight into how the four dimensional model behaves. The effect of stocking duration, the start time of stocking, and varying initial data on the amount of control agent required to ensure the controlled population survives is explored. We find that by incorporating motile and sessile spores we eliminate any possible trivial equilibriums. Furthermore, applying the control agent sooner results in less being required to ensure the survival of the stocked population.
Mon, 13 May 2019 00:00:00 GMThttp://hdl.handle.net/10214/160722019-05-13T00:00:00ZIdeal--Gas Thermochemical Property Calculations for Alkanolamine and Other Species Important in Carbon Capture
http://hdl.handle.net/10214/16008
Ideal--Gas Thermochemical Property Calculations for Alkanolamine and Other Species Important in Carbon Capture
Hatefi, Nayyereh
It is believed that anthropogenic CO2 emission from point sources is a primary reason for the global temperature increase. Among available CO2 capture technologies, amine-based reactive absorption is regarded as the most mature and commercially available. However, to reduce the disadvantages of the currently used solvent, it is necessary to replace it with a solvent that has both high capture capacity (CO2 solubility) and low energy demand. Our project goal is to screen a large set of potential aqueous alkanolamine solvents for improved solubility properties using molecular level modeling of the process.
Modeling of CO2 reactive absorption in candidate aqueous alkanolamine solvents requires ideal--gas free energies for the species involved. This thesis describes methodology for the calculation of the ideal--gas free energies of candidate alkanolamines. We generate the data using quantum mechanical software and present it in a convenient format. Our calculations are accompanied by an approximate Uncertainty Analysis.
Thu, 09 May 2019 00:00:00 GMThttp://hdl.handle.net/10214/160082019-05-09T00:00:00Z