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Articles 1 - 4 of 4
Full-Text Articles in Dynamic Systems
Lexicographic Sensitivity Functions For Nonsmooth Models In Mathematical Biology, Matthew D. Ackley
Lexicographic Sensitivity Functions For Nonsmooth Models In Mathematical Biology, Matthew D. Ackley
Electronic Theses and Dissertations
Systems of ordinary differential equations (ODEs) may be used to model a wide variety of real-world phenomena in biology and engineering. Classical sensitivity theory is well-established and concerns itself with quantifying the responsiveness of such models to changes in parameter values. By performing a sensitivity analysis, a variety of insights can be gained into a model (and hence, the real-world system that it represents); in particular, the information gained can uncover a system's most important aspects, for use in design, control or optimization of the system. However, while the results of such analysis are desirable, the approach that classical theory …
Paper Structure Formation Simulation, Tyler R. Seekins
Paper Structure Formation Simulation, Tyler R. Seekins
Electronic Theses and Dissertations
On the surface, paper appears simple, but closer inspection yields a rich collection of chaotic dynamics and random variables. Predictive simulation of paper product properties is desirable for screening candidate experiments and optimizing recipes but existing models are inadequate for practical use. We present a novel structure simulation and generation system designed to narrow the gap between mathematical model and practical prediction. Realistic inputs to the system are preserved as randomly distributed variables. Rapid fiber placement (~1 second/fiber) is achieved with probabilistic approximation of chaotic fluid dynamics and minimization of potential energy to determine flexible fiber conformations. Resulting digital packed …
Nonspreading Solutions In Integro-Difference Models With Allee And Overcompensation Effects., Garrett Luther Otto
Nonspreading Solutions In Integro-Difference Models With Allee And Overcompensation Effects., Garrett Luther Otto
Electronic Theses and Dissertations
Previous work in Integro-Difference models have generally considered Allee effects and over-compensation separately, and have either focused on bounded domain problems or asymptotic spreading results. Some recent results by Sullivan et al. (2017 PNAS 114(19), 5053-5058) combining Allee and over-compensation in an Integro-Difference framework have shown chaotic fluctuating spreading speeds. In this thesis, using a tractable parameterized growth function, we analytically demonstrate that when Allee and over-compensation are present solutions which persist but essentially remain in a compact domain exist. We investigate the stability of these solutions numerically. We also numerically demonstrate the existence of such solutions for more general …
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Electronic Theses and Dissertations
Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …