584 Computational Methods
Mark Alford (Jan 25, Feb 1, Feb 8)
Goal: Mathematica is an incredibly powerful tool for physics: it does symbolic math, numerical calculations, data plotting, etc.
This part of the course will give students a good working knowledge of Mathematica.
Requirements: Before starting the class, students should
- Make sure you have easy access to Mathematica. Preferably it should be installed on your own laptop.
- Physics graduate students: for a free Mathematica license, write to Sai Iyer giving your WUSTL email address and approximate month and year of graduation.
- Undergraduates (and non-physics grads): buy it for $26.00 from Software Licensing. Send email to WU_SoftwareLicensing@wumail.wustl.edu giving your first and last name, Washington University email address, and how payment will be made (check or credit/debit card). Once payment has been satisfied you will receive a unique activation code.
- Reproduce all the examples in my Introduction to Mathematica
- Study (and preferably reproduce) the examples in my Mathematica Techniques
Project: Students should bring their laptop, with Mathematica installed, to class.
- Class 1: Using Mathematica to calculate the stat mech of free fermions at T=0
- First project file containing the exercises that students will start solving in the first class.
- Slides describing the stat mech of degenerate fermions
- Class 2: Using Mathematica to make a model of nuclear matter in terms of free protons, neutrons, and electrons
- Second project file containing the exercises that students will start solving in the second class.
- Slides describing a simple model of nuclear matter
- Class 3: Completion of the nuclear matter project
Ryan Ogliore (Feb 15, Feb 22, Mar 1)
MATLAB stands for matrix laboratory. It is a proprietary, commercial programming language developed by MathWorks. MATLAB is primarily for numerical calculations but can also perform symbolic manipulations. The capabilities of MATLAB can be greatly expanded via toolboxes and packages so that one can build, e.g. graphical-user interfaces in MATLAB. MATLAB is a high-level interpreted language (not compiled), but it can call functions written in C or Fortran. MATLAB is used broadly in science and engineering. MATLAB’s power comes from its ease of use, pre-built set of toolboxes, interactive development environment, and visualization. A feature particular to MATLAB is that arithmetic operations are assumed to be matrix operations unless specified otherwise.
Please install MATLAB on your laptop if you have one, or have easy access to it if you don’t. It works on Linux/Mac/Windows. Please contact Sai Iyer (firstname.lastname@example.org) about obtaining and installing MATLAB.
MATLAB offers a nice introduction to the language in the MATLAB Academy: https://matlabacademy.mathworks.com/
You’ll have to create a login for MathWorks (apologies). But you do not need MATLAB installed on your computer to use the MATLAB Academy. Please familiarize yourself with MATLAB, before class on April 18, by completing the MATLAB Onramp in the MATLAB Academy. This should take less than two hours to complete.
Bhupal Dev (Mar 8, 22, April 5)
- Make sure that you bring to class your computer with a working Python environment (including Numpy, Scipy and Matplotlib). Consider for example the Anaconda distribution, which is available for free and provides a one-click Python installation for Windows, Linux and Mac.
- Our first goal will be to write a script that produces the bifurcation diagram for the tent-map. To develop the script, and to get used to the language itself, it will be very useful to run Python interactively. It is highly recommended that you use Ipython for this purpose. You can think of Ipython as an equivalent to the Mathematica FrontEnd containing an integrated graphics environment, easily accessible help, and many other useful features. You can launch the shell from the command line ('ipython --pylab' loads the graphics environment automatically), which is faster, or use its web-based notebook environment ('jupyter-notebook').
- Some good resources to get acquainted with the basics of the language are listed in the official Python site: Tutorials. An accessible, yet fairly complete, one can be found here; if you have a little bit of programming experience, you might want to browse Google's Python class.
- Matplotlib will allow you to plot functions and it provides the source code for an extensive list of examples.
- Example notebook
- Winking elephant notebook
Mike Ogilvie (Apr 12, 19, 26)
Monte Carlo, Metropolis and the Ising Model
Our goal is to learn to use Monte Carlo simulation to understand the behavior of complex systems with many degrees of freedom. We will study the two-dimensional Ising model, perhaps the most celebrated model in all theoretical physics.
Introductory material on the Ising model can be found in most graduate-level statistical mechanics texts, as well as here: Ising model.
We will continue with Python. You may use the the iPython environment if you like. Notes and a basic Ising simulation in Python will be sent to you. As written, the Ising simulation requires the use of numpy and matplotlib. If you do not want to use matplotlib for plotting, you can comment out the relevant code. The notes contain a number of problems. You will be expected to do at least three of these, and everyone must do the first problem.
- Lecture Notes on Ising Model