
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 29^{th} 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.
 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
 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 (QuicksheetsAnimationsRotating 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.
 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.
 Radioactive Decay
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.
http://www.eserc.stonybrook.edu/ProjectJava/Radiation/index.html
 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.
 Rossler Attractor
Three coupled first order differential equations that exhibit nonlinear
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 RungeKutta routine and use threedimensional 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]
 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.
 Wave Propagation
Use MathCad to describe the growth of a wave perturbation in temperature
as it propagates vertically upwards into the atmosphere.
