Mathematics – Logic
Scientific paper
May 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008dda....39.1508h&link_type=abstract
American Astronomical Society, DDA meeting #39, #15.08
Mathematics
Logic
Scientific paper
Numerical simulations of collisionless systems form the backbone of our theoretical understand of galaxy, cluster, and cosmological evolution. Simulation provides the crucial link between our microscopic understanding of gravity (Newtonian and Relativistic), and the macroscopic dynamical evolution of gravitational systems. Such simulations have been used to test and even invalidate theories. Thus, establishing their trustworthiness is critical. Since gravitational systems are chaotic, they display sensitive dependence on initial conditions (SDIC), so that numerical errors become exponentially magnified with time. In short order, these errors become magnified to the size of the system, leading some (eg., Heggie) to question if such simulations are the result of nothing but magnified noise. Although the existence of SDIC has been known for decades, its effect on macroscopic properties of solutions is still not yet well understood. To answer the question of their validity, we turn to the study of shadowing. A shadow is an exact solution that remains close to a numerical solution for a long time, despite the magnification of small errors. If a shadow solution exists, then the numerical solution can be viewed as an observation of an exact solution, and thus its dynamical properties can be trusted, to within "observational” error. In this poster, I will discuss recent results on shadowing a million-particle simulation of a collision between two galaxies. (This abstract is identical to my last year's abstract because I discovered a major flaw in my code since last year. This poster corrects the results of last year's talk.)
Hayes Wayne B.
Zhu Yaming
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