Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Institution
Articles 1 - 2 of 2
Full-Text Articles in Probability
Analyzing The Probabilistic Spread Of A Virus On Various Networks, Teagan Decusatis
Analyzing The Probabilistic Spread Of A Virus On Various Networks, Teagan Decusatis
Senior Projects Spring 2018
In this project we model the spread of a virus on networks as a probabilistic process. We assume the virus breaks out at one vertex on a network and then spreads to neighboring vertices in each time step with a certain probability. Our objective is to find probability distributions that describe the uncertain number of infected vertices at a given time step. The networks we consider are paths, cycles, star graphs, complete graphs, and broom graphs. Through the use of Markov chains and Jordan Normal Form we analyze the probability distribution of these graphs, characterizing the transition matrix for each …
Numerical Solutions To The Gross-Pitaevskii Equation For Bose-Einstein Condensates, Luigi Galati
Numerical Solutions To The Gross-Pitaevskii Equation For Bose-Einstein Condensates, Luigi Galati
Electronic Theses and Dissertations
In this thesis we compare various potential operators for the two-dimensional (2D) Gross-Pitaevskii equation (GPE) for Bose-Einstein condensates. Both the 2D and the 1D models are scaled to get a three parameter model. Smoothness of initial conditions is considered and choice of method (Split-Step Fourier method with Strang Splitting) is justied. Numerical simulations provide graphical evidence of properties of both focusing and nonfocusing cases.