# PH36010 – Project Assignments

## This page contains suggestions for assignments you may use for the assessed project part of the course.

All project work should be printed out and handed in to the general office before 23:59 on Saturday 29th May at the latest. At the same time, the mathCAD worksheet and any supporting files should be emailed to dpl@aber.ac.uk

Other project assignments are possible, please discuss your proposal with Dave Langstaff (dpl@aber.ac.uk) before proceeding.

The marks for the project will be allocated on the basis of difficulty and achievement. A simple project which is implemented well may well attract more marks than a more complex project handled badly.

1. Solar System Simulation
The following URL contains details of how to calculate the positions of the planets in space. Use the data contained to create an animation showing the solar system as the planets move over a number of days.
A simple model could show the positions of, say, the inner planets projected in 2D, looking down on the plane of the ecliptic.
A more complex animation would include a representation of the tracks of the planets.
More complex still could include the moon's position as it orbits the earth.
Advanced students may want to perform a 3D animation, with the planets represented by appropriately sized and coloured spheres (these will need to be at an exaggerated scale)   Example of Solar system animation

The orbital data and a tutorial on how to use it can be found at:
http://www.stjarnhimlen.se/comp/ppcomp.html

2.  Orbiting Satellite
Create a simulation of a satellite orbiting the earth.
A simple solution could take the orbital height and inclination and produce a 2D plot showing the orbital track over the surface of the earth.
A more complex solution would produce a 3D animation of the satellite orbiting the earth. Example
In the Resource Centre (Quicksheets|Animations|Rotating Earth) is a sheet showing how to project a map of the earth onto a sphere. This includes a dataset giving the outlines of the continents, which can be used for this project.

3. Bouncing Balls
Simulate a system of balls bouncing.
This could range from a simple 1D system with a single ball falling under gravity and bouncing from the ground up to animating collisions between balls in a snooker table type environment. Example

### 2.   Simulate Ion Implantation. The simulation will use a Monte Carlo technique very similar to the photon scattering example. A simple solution would assume that the ions come to rest after a fixed number of collisions. A more complex solution would model the process more accurately.

The following URL features an animated diagram showing the relative abundances of isotopes in various radioactive decay series. Using the Differential equation solver in mathCAD, produce similar animations.

2. Finite Difference
Use Mathcad script to implement a finite difference scheme to show how thermal waves generated as a result of periodic heating of one end propagate along a rod for a) a thermally isolated rod and b) a rod which looses heat to the surrounding atmosphere at a rate proportional to the temperature of the rod above ambient.

3. Rossler Attractor
Three coupled first order differential equations that exhibit non-linear chaotic evolution. One equation set gives rise to the Rossler attractor (see Chaos by James Gleik and Non linear dynamics and Chaos by Strogartz).  Solve such a system of equations using a Runge-Kutta routine and use three-dimensional plots to illustrate how the evolution of the system varies as the control parameter is varied.  Supplement your investigation by computing/illustrating the variations in the frequency spectrum as the control parameter changes. [Note as the solution changes rapidly it is usually necessary to use the adaptive version of the Runge Kutta integration routine]

4. Resonance in an LCR circuit
Consider the complex impedance of a series resonance circuit and use this illustrate how the magnitude of the current changes as a function of frequency for V = 1, L = 0.01H, R = 20 Ω and C = 5 μF.
Develop a Mathcad animation to illustrate the phenomena of resonance in such a circuit.

5. Wave Propagation
Use MathCad to describe the growth of a wave perturbation in temperature as it propagates vertically upwards into the atmosphere.

This document maintained by dpl@aber.ac.uk.