Los Alamos High School (62)/Interim Report

Interim Report
http://mode.lanl.k12.nm.us/get_interim1112.php?team_id=62

This year in supercomputing our team has decided to approach a class of interesting problems governed by dynamical systems. We are modeling threshold of collapse problems with systems of ordinary differential equations. As of early November we have completed the general code of the threshold of collapse problem in the coding language “C”. This code can create solutions to a general threshold of collapse problem and is producing results that we would expect to be accurate.

In addition to creating the actual code, our team has defined and researched the problem. The threshold of collapse problem can best be explained as an equilibrium problem in which there are two events that can occur. Either the system will reach an equilibrium point, and thus the system will stabilize or, the system will be too far from an equilibrium point and the entire problem will collapse to zero. If the initial data is too far from the carrying capacity or stability point, the solution curve for the differential equation will not make contact with the points of stability. Thus the system will collapse to zero, representing either the destruction of the system, or in biological models, the death of the patient or the population. The goal of the project, in what ever application of the code, is to discover the point at which a system makes the transition from being a system that will revert to a stable position versus a total collapse. During the next half of this year, our team will run different examples of threshold of collapse problems, with the goal of applying it successfully to one or more practical problems. The threshold of collapse problem has a wide range of applications. These applications can range from mathematical models of economic systems or population dynamics to individual biological models and host disease simulations. Before actually applying the code to a problem, the code has to be proven to be accurate. Our team will prove this by applying the code to a simple problem that can be checked against an analytical solution. Once this is checked our team will choose one or more of these problems and model real life systems in the hopes of predicting outcomes within the systems.

Interim Comments
David Rogers Lead of the Scalable Data Analysis and Visualization Group at Sandia National Labs

Nice work. From your report, it seems you're on the right track across the board.

In the final report, it will be important to clearly explain both how you're determining the accuracy (which you call out as a specific area you're addressing), as well as highlighting the results of your optimization. I would just caution you: pose a simple and satisfying test for accuracy, because this is a part of the project that can eat up all your time, if you pose too complex a test.

One thing to work on is including some citations from the source material you're using as a basis for your project. The judges will need to see this in the final report.

Looks great! I look forward to seeing the final.