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Ordinary Differential Equations and Applied Dynamics Commons™
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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
The Mathematics Of Cancer: Fitting The Gompertz Equation To Tumor Growth, Dyjuan Tatro
The Mathematics Of Cancer: Fitting The Gompertz Equation To Tumor Growth, Dyjuan Tatro
Senior Projects Spring 2018
Mathematical models are finding increased use in biology, and partuculary in the field of cancer research. In relation to cancer, systems of differential equations have been proven to model tumor growth for many types of cancer while taking into account one or many features of tumor growth. One feature of tumor growth that models must take into account is that tumors do not grow exponentially. One model that embodies this feature is the Gomperts Model of Cell Growth. By fitting this model to long-term breast cancer study data, this project ascertains gompertzian parameters that can be used to predicts tumor …
Modeling Purple Sea Urchin And California Sheephead Populations In Southern California Kelp Forests, Olivia Rachel Williams
Modeling Purple Sea Urchin And California Sheephead Populations In Southern California Kelp Forests, Olivia Rachel Williams
Senior Projects Spring 2017
In this project I am modelling the predator-prey relationship between California sheephead and purple sea urchin populations, respectively, in kelp forests off the coast of southern California. The Lotka-Volterra equations explain predator-prey relationships in their most basic form. These equations incorporate a set of biological assumptions that can be unrepresentative of many ecological systems. I will consider alternate models that incorporate variations of the Lotka-Volterra model which may better represent the biology of the purple sea urchins and California sheephead. Using biological characteristics of both species in kelp forests, I will set possible and likely parameters and solve for unknown …
Complex Semiclassics: Classical Models For Tunneling Using Complex Trajectories, Max Edward Meynig
Complex Semiclassics: Classical Models For Tunneling Using Complex Trajectories, Max Edward Meynig
Senior Projects Spring 2017
This project is inspired by the idea that black holes could explode due to a quantum process somewhat analogous to quantum mechanical tunneling. This idea was presented in recent research that also proposed that semiclassical physics could be used to investigate the so called black hole fireworks. Semiclassical physics connects quantum and classical physics and because of this it is a powerful tool for investigating gravity where the classical theory is known but there is no complete quantum theory. Unfortunately, the traditional tools in semiclassics that are needed fail to treat tunneling. However, if classical mechanics is extended to complex …