This project is about numerical studies using advanced Monte Carlo Analysis and the supercomputers at the NASA advanced supercomputing division at the Ames research center and JPL. This research may then be applied to astrophysical studies and simulations such as that of cosmic rays at the California High School Cosmic Ray Observatory (CHICOS) sponsored by Caltech. In the cosmic ray and other potential applications the numerical problem to be computed is a high dimension numerical integration over potentially hundreds of variables. If classical integration rules were applied to solve such a problem it would take beyond the current estimated lifetime of the universe to solve even with a supercomputer!

Fortunately, current research in Monte Carlo Analysis has proceeded along three general lines to speed up such numerical investigations to within a reasonable fraction of a human lifetime. In addition, the ability to divide the problem by using the parallelism of a modern supercomputer will allow that time to be reduced even further. The three lines of investigation listed in increasing order of convergence rate are: pseudo-random, quasi random and lattice methods.

**CURE student tasks**: Student will learn how to use the parallelism of the supercomputer on test problems with each of these three methods and compare the results. In addition to the future physical applications in cosmic rays and other fields one of the ultimate goals of the research is to numerically explore the open mathematical questions of optimal lattices in dimension three and higher.

*CURE interns*: Eva Zaykova, Summer 2009 -

E. Zaykova, Presentation at the 2010 JPL Seminar Days.

- Last Updated: 6/21/12