Computational Methods in Physics
Mathematica Notebooks
The Mathematica electronic notebooks developed
for Computational Methods in Physics (Physics 215) are
available below along with a description of how
to load them onto your computer.
All of the notebooks have been
tested on a Linux
machine using Mathematica version 6.0.
If you have any problems send me email
at ggilfoyl@richmond.edu
The Mathematica Notebook files
contain ASCII text, and can be
transferred by email, scp, or other text-file transfer utility.
If you click on the file with a web browser you will
see all the formatting instructions in addition to the
actual contents of the notebook.
You should save the file as it appears with
a
name ending with ".nb" to allow Mathematica to recognize it as a Notebook.
The file can then
be read or edited using a copy of Mathematica or MathReader.
If you
received a file through
another route (e.g., email) copy/paste to save
everything in the file
from the line containing (*^ down to the line containing ^*)
into a plain text file.
- Introduction.nb
Laboratory
that introduces one to the Mathematica computing environment.
- GraphicApps.nb
Laboratory
that demonstates some more graphics applications in the process of
investigating AC circuits and blackbody radiation.
- Differentiation.nb
Different methods of approximating derivatives are used to study
the effect of step size on the accuracy of the calculation and
to compare the algorithms with the 'true' derivative.
- FirstOrderDE.nb
A model of the friction force is used to write a first-order
differential equation derived from Newton's Second Law.
The fall of Lieutenant Chisov, a Soviet pilot shot down by German gunfire
in 1942,
from a height of 22,000 feet
is investigated numerically.
- CoupledDE.nb
The investigation of Lieutenant Chisov's fall (see previous lab)
is completed using a set of coupled, first-order, differential
equations to determine x(t) and v(t).
The methods are demonstrated first with a simple, harmonic oscillator
problem.
- SecondOrderDE.nb
A direct method for solving second order differential equations is
developed and applied to the simple harmonic oscillator first.
The method is then used to find the trajectory of the non-linear,
physical pendulum.
- Chaos1.nb
The attributes of a realistic model of the physical pendulum are
investigated.
The model includes a damping term due to friction and a driving term
due to the influence of a periodic outside force.
- Chaos2.nb
The investigation of the realistic, non-linear, damped, driven
physical pendulum continues.
The extraction of the Poincare section is developed.
- Nukes.nb
Investigation of the self-attenuation of a 232-U tag placed
in a uranium
'pit', the central core of a nuclear weapon.
This subject is relevant to a scheme for making uranium less
vulnerable to nuclear smuggling.
- MonteCarlo.nb
Part 1 of the study of the passage of an electron through a gas.
An external,
magnetic field is applied to bend the path of the particle.
An acceptance-rejection method is introduced and the 'unscattered'
trajectory is calculated first.
- MonteCarlo2.nb
Part 2 of the study of the passage of an electron through a gas.
The smearing effect of multiple scattering is incorporated into the
stepwise integration of the equations of motion.
The effect on the momentum resolution of a spectrometer is investigated.
- NeutronDiffusion.nb
Investigation of the solution of a partial differential equation describing
diffusion of neutrons.
Uses an explicit method to solve the diffusion equation with a source term and to
probe the conditions when the system will reach critical mass.
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