Barkerma-Final Project

# Barkerma-Final Project - The Need for Alternative N-body...

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The Need for Alternative  N -body Simulation Methods for Large  N Michael Barker CSA 464 Final Project Department of Computer Science and Systems Analysis Miami University [email protected]

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1 Abstract This document discusses the importance of N -body simulations and the need to run these simulations for large values of N . We will examine a basic method for computing particle-particle interactions as well as more advanced methods which allow for much larger simulations. Accuracy is also a topic of concern when using these more advanced methods where approximations are made. 2 Introduction and Motivation N -body simulations are a means by which to determine the motion of particles given their mass, initial position, and initial velocities. The resulting motion of the particles is a factor of their interactions through classical mechanics (Newton's laws of motion and Newton's law of gravity). Astrophysics, which is the study of the universe, is perhaps the area of science in which N -body simulations are of most interest. Other areas of physics have a significant advantage over astrophysics as most have an easy means of experimentation with real-world objects. In astrophysics there is currently no way to run experiments on a galaxy or the universe as a whole. These experiments must in turn be run through simulations. The formation of galaxies, galaxy clusters, and dark matter halos are just a few things of interest in astrophysics. Simulations are the only way to experiment and observe such phenomena. All of these simulations involve the interaction of vast amounts of particles, hence the need for N -body simulations. 3 Problem In order to determine the forces on a single particle, all other particles in the system must be examined to determine the amount of force they exert on the particle in question. This process must be repeated for every particle in the system. This leads to a number of calculations that is on the magnitude of N ² where N   is the number of particles in the system. This same process must then be
repeated for each subsequent timestep in the simulation where the particle-particle interactions are considered and all the particles velocities are modified based on the force exerted by all other particles to produce the corresponding accelerations of the particles for the timestep. The Sloan Digital Sky Survey[SDSS] or SDSS is a massive undertaking in which the positions of around 100 million celestial bodies have been mapped in comparison to 10 20   solar masses contained in the SDSS volume[WRN1]. One of the largest N -body simulations, known as the Millennium Simulation, was carried out in 2005 and modeled an astonishing 10 10   particles[SPRING]. Such a simulation still pales in comparison to the SDSS volume. The Millennium Simulation was merely a statistical analysis. Galaxies roughly the size of the Milky Way in this simulation were represented by about 1000 particles and some larger galaxy clusters by several million particles. In order to draw a comparison

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## This note was uploaded on 05/01/2008 for the course CSA 273 taught by Professor Patton during the Winter '08 term at Miami University.

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Barkerma-Final Project - The Need for Alternative N-body...

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