Computational Science
COSC1229/1479
Assignment 1
Title: N-body Problem
Due Date : 20/8/2004, 5pm
Due Date : 3/9/2004, 5pm
Assessment : 30%

Overview

The n-body problem is a key problem in computational science. It takes many forms - including two applications at opposite ends of the scale spectrum: molecular systems and cosmological systems. This assignment focuses on molecular systems - gases in particular.

The assignment has three parts, each worth 10 marks and each of which requires a report:

  1. Perform computational investigations (experiments) of the velocity and speed distributions of a 2D hard-sphere particle system with only contact forces. You should attempt to see if steady state distributions are achieved and if they are, what distributions they are. Perform the experiments under various conditions including number of particles, initial velocities (temperature) and box size. Make sure you conduct tests to make sure energy is not being lost in your system.
    1. The brute force approach to finding collisions is O(n^2). Investigate whether this scaling relationship is observed. Predict how long it would take to simulate a 1e3, 1e4, 1e5 and 1e6 particle system for 1e3, 1e4, 1e5 and 1e6 timesteps.
    2. Investigate the performance improvement gained by using a 'cell subdivision' approach for finding collisions.
    1. Introduce a so-called 'van Der Waals' interaction between particles which operates at a distance. The van Der Waals interaction between two particles can be described by the 'Lennard-Jones' potential:
      lennard jones potential
      where sigma is a length scale and epsilon determines the interaction strength.
    2. Again explore the speed and velocity distribution for a range of initial conditions and parameter settings. In particular, explore a low velocity (energy) situation

You may use supplied program code as a basis for your assignment.

Your reports should use MathML for mathematics. This will be confirmed - it depends on MathML being configured for the laboratory.

Assessment

Assessment will be based on reports and program code. As a guide, the reports will be weighted at 2/3 (20 marks) and the code at 1/3 (10 marks).

Submission

Your assignment submission must include: a tar file containing your report(s), source code and any necessary data which must be submitted using turnin. Instructions on how to do this here.

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Last modifed: $Date: 2004/07/02 00:43:31$