Computational Physics, FYTN03 - fall 2010
Projects
Guide to writing reports
Below is a (tentative) description of the four projects in the
course. The projects are done in groups of two, with the reports
written individually.
How hard can I kick that football?
High school text-books tell us that the optimum angle for projectile motion is
45 degrees. However, in many sports disciplines it is rather found that one
can throw a ball, spear etc farther if the angle is closer to 30 degrees. The
aim of this project is to numerically investigate your favorite (or most
hated) sports discipline, and include realistic effects such as air
resistance. The parks of Lund will serve as crucial testing places for the
modeling and numerical results.
More details
You will learn: Numerically solving ordinary
differential equations.
Suggested reading:
G&N chapters 1,2, appendix A.
What is the best way keeping by beer cold?
Drinking beer is doing physics. Imagine you want to keep your beer cold during
a hot summer's day - the transport of heat in your beverage is described by
the heat equation. In this project your objective is to numerically
investigate different ways of keeping a enjoyable temperature of your beer.
More details
You will learn: Numerically solving partial
differential equations.
Suggested reading: G&N chapters 5,6,10 (note
that the heat equation is the same as the Schrödinger equation in
imaginary time).
Reaction-diffusion - vicious walkers
Many processes requires molecules to meet and react. How long does this take?
In this project the aim is to, as a model for chemical reactions, simulate
random walkers in a box which kill each other (vicious walkers) whenever they
meet. How will the density of particles decay with time in such a system? For
realistic chemical reactions, not every encounter results in a reaction - you
may therefore want consider a finite probability for an encounter to result in
death. Or, perhaps there are many different types of particles? Feel free to
explore different scenarios.
More
details
You will learn: Simulating stochastic processes.
Suggested reading: G&N chapter 7, appendix
F and G.
How do proteins fold?
Biology offers many opportunities for doing interesting
physics. Proteins are important players in our cells, and their
functionality depends strongly on their structure. This structure in
turn depends on the sequence of aminoacids. So, how do we get from
sequence to structure? In this project you will attempt to answer this
question, and will be brought up to the forefront of modern research
in the field.
More details
pivot.c C code to be used or inspired by for updating
the chain with a pivot move and making sure self avoidance.
You will learn: Monte Carlo techniques.
Suggested reading: G&N chapter 8 and 12.1.
G&N=N.J. Giordano and H. Nakanishi, Computational Physics, 2nd ed.