Mathematics – Logic
Scientific paper
Jul 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007dda....38.0802h&link_type=abstract
American Astronomical Society, DDA meeting #38, #8.02
Mathematics
Logic
Scientific paper
Numerical simulations of collisionless systems form the backbone of our theoretical understanding of galaxy, cluster, and cosmological evolution. Simulation provides the crucial link between our microscopic understanding of gravity (Newtonion + Relavitistic), and the macroscopic dynamical evolution of gravitational systems. Such simulations have been used to test and even invalidate theories. As such, establishing their trustworthiness is absolutely critical.
Gravitational systems are chaotic, and display sensitive dependence on initial conditions (SDIC), so that numerical errors become exponentially magnified with time. Although the existence of SDIC has been known for decades, its effect on macroscopic properties of solutions is still not well understood.
A shadow is an exact solution that remains close to a numerical solution for a long time. 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 talk, I will discuss recent results on shadowing a million-particle simulation of a collision between two galaxies.
Hayes Wayne B.
Zhu Yong-Kang
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