| Time | Speaker | Title |
|---|---|---|
| Registration and Refreshments | ||
| 10:20-10:30 | Bruce Peckham | Opening Remarks |
| 10:30-11:00 | Robert Pfister | Network Analysis of a Steam Generator |
| 11:00-11:30 | Chandra Balasubramanium | The Double Pendulum |
| 11:30-12:15 | Mike Dvorak and Adam Hornibrook | Freeway Flow: Traffic Model and Analysis |
| 12:15-1:00 | Lunch | |
| 1:00-1:30 | Andrew Renner | An Epidemic Model |
| 1:30-2:15 | Jason Christenson and Steve Law | Development of a Tent Worm Model |
| 2:15-2:30 | Refreshment Break | |
| 2:30-3:00 | Chad Pierson | A Gypsy Moth Model |
| 3:00-3:30 | David Finton | The Behavior of a Coupled Logistic Map |
| 3:30-3:40 | Bruce Peckham | Closing Remarks |
| Time | Speaker/Title/Abstract |
|---|---|
| 10:30-11:00 | Robert Pfister Network Analysis of a Steam Generator This problem involves the study of the flow behavior of a steam generator from a nuclear power plant. Steam generator flow behavior is a significant engineering concern because steam generator tube leakage, which can be caused by chemical action/corrosion, is very often the result of improper steam flow rates. This is an especially significant concern with nuclear power plant steam generators because the tubes contain radioactive reactor coolant from the primary (reactor) side of the power plants. The complexity of steam flow analysis can be mitigated to an extent by reducing the problem from a continuous application to a discrete application by the use of network theory. If the flow of one specific region of interest is subdivided into an imaginary grid of flow cells, we need consinder only the average "lumped" flow into and out of each region. Further, we can formulate laws which these "lumped" flows must obey. |
| 11:00-11:30 | Chandra Balasubramanium The Double Pendulum The double pendulum demonstrates the chaotic unpredictable behavior that can occur in the motions of a pair of coupled nonlinear oscillators. The Model that governs a system of Double Pendulum is a system of two second order equations in the angles, which the bobs cut with the vertical. In this project I will be finding the equations that govern the double pendulum. Henceforth, due to the complex nature of the equations, I will find some numerical solutions using 4th order Runge-kutta method and generate some graphs for various initial conditions to study the chaotic behavior of the system. I will also simulate the system on the computer using some of the graphical capabilities of Java. |
| 11:30-12:15 | Mike Dvorak and Adam Hornibrook Freeway Flow: Traffic Model and Analysis Automobile traffic has long plagued our society with both environmental and economic problems. Mathematical modeling is a powerful tool for analysis of a traffic system. Applying some fundamental ideas of Dynamical Systems, we are able to find both qualitative and quantitative features of an interstate traffic system. Using data from the Atlanta metro area, we are able to find optimal flow rates for specific portions of freeway. |
| 1:00-1:30 | Andrew Renner An Epidemic Model Present various aspects of mathematical epidemiology. Briefly reacquaint the audience with the previously covered models and their predictions. Present a Stochastic approach to the modeling process with comparison of the stochastic predictions to a deterministic model with the same assumptions. Discuss the Reed-Frost Model and its implications and consider a less restricted model. |
| 1:30-2:15 | Jason Christenson and Steve Law Development of a Tent Worm Model In our presentation we want to show the effects of the tent worm population on the biomass growth. We are planning on doing this with three differential equations. We are using one equation to represent tent worms, one to represent black flies, and one to represent biomass. The reason for each is that tent worms live off of biomass, and black flies are the preditors of tent worms. It will be showing a small part of the life cycle. With these equations we plan to show you some graphical solutions to these equations, and try to explain their life cycle. |
| 2:30-3:00 | Chad Pierson A Gypsy Moth Model Gypsy moth populations follow an observable oscillation following a 7 to 10 year growth and crash cycle. A possible model for their dynamics is given by a combination differential equation with a wintering map. This model, under some conditions appears to exhibit a cyclical pattern that maybe benificial in modelling seasonal insect epidemics. Using an SI model developed by Dianna Colt I hope to consider some interesting dynamics including locating one or two bifurcation points by varying some parameters. |
| 3:00-3:30 | David Finton The Behavior of a Coupled Logistic Map Dave will talk about his talk. |