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.

  1. Introduction.nb Laboratory that introduces one to the Mathematica computing environment.

  2. GraphicApps.nb Laboratory that demonstates some more graphics applications in the process of investigating AC circuits and blackbody radiation.

  3. samplePlots.nb Some examples showing how to put multiple curves on a single plot and using grayscales, dashing, line thickness, etc to distinguish among different curves. Useful for people without easy access to a color printer.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. Chaos2.nb The investigation of the realistic, non-linear, damped, driven physical pendulum continues. The extraction of the Poincare section is developed.

  10. 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.

  11. threeBody1.nb The limited, three-body problem is studied with a projectile launched at high speed from the Earth in a two-body (Earth and Sun) solar system. A map of the dependence of the final position of the projectile on the initial velocity is generated. To test the new plotting function use the data set here.

  12. highPerformanceComputing1.nb First of two laboratories to introduce students to the Richmond Physics Cluster (RPC). This laboratory includes a quick introduction to the software needed to work the the RPC from the Windows-based, Physics lab computers, a primer on the Linux operating system, and documentation on the use of the cluster. An example of running parallel jobs is demonstrated.

  13. highPerformanceComputing2.nb Second lab in the sequence introducing the Richmond Physics Cluster (RPC). Here, the steps needed to prepare a Mathematica notebook for batch running on the cluster are shown along with an example of going through the procedure to submit, monitor, and analyze parallel calculation on the cluster.

  14. 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.

  15. 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.

  16. 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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