584 Computational Methods

Tentative Syllabus

Wim Dickhoff (Feb 1, 8)

• Project: diagonalization of quantum mechanical potentials.

The Schroedinger equation of Quantum Mechanics can in some cases be solved analytically for discrete eigenvalues and corresponding wave functions. This is true for potentials with spherical symmetry like the Coulomb or 3-D Harmonic Oscillator. We will extend the solution for discrete eigenvalues for bound states of potentials that do not allow an analytical solution.

Francesc Ferrer (Feb 15, 22)

Python/Matplotlib

• Requirements:
  • Make sure that you bring to class your computer with a working Python environment (including Numpy, Scipy and Matplotlib). Consider for example the Enthought 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.

• Background:
  • 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

File:Elephant.ipynb

Mike Ogilvie (Feb 29, Mar 7)

Monte Carlo, Metropolis and the Ising Model

• Project

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.

• Background

Introductory material on the Ising model can be found in most graduate-level statistical mechanics texts, as well as here: Ising model.

• Requirements

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 project.

Mark Alford (Mar 21, 28)

Mathematica for Statistical Mechanics of Fermions

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 $25.00 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
• Refresh your undergraduate statistical mechanics knowledge. Make sure you understand the following:
  • Pauli exclusion principle
  • Fermi Surface
  • Fermi-Dirac distribution

Project: Students should bring their laptop, with Mathematica installed, to class. The following files should be loaded on the laptop:

• First project file containing the exercises that will be explained and that students will start solving in the first class.
• Second project file containing the exercises that will be explained and that students will start solving in the second class.

Erik Henriksen (Apr 4, 11)

Note: This section will meet in Crow-302.

LabVIEW (Laboratory Virtual Instrument Engineering Workbench) is a graphical programming language that uses graphical drawings instead of lines of text to create applications. In contrast to text-based programming languages that use instructions to determine the order of program execution, LabVIEW uses dataflow programming. In data flow programming, the flow of data through nodes in the block diagram determines the execution order of the VIs and functions. VIs, or virtual instruments, are LabVIEW programs that imitate physical instruments.

In LabVIEW, you build a user interface by using a set of tools and objects. The user interface is known as the "front panel." After you build the front panel, you add code using graphical representations of functions in order to control the front panel objects. You add this graphical code, also known as G code or block diagram code, to the block diagram. The block diagram somewhat resembles a flowchart. The block diagram, front panel, and graphical representations of code compose a VI.

Ultimately the VI is used to acquire, display, analyze and save data. VIs interface with real instruments in a lab through USB, serial, or GPIB connections and can remotely control a wide range of standard laboratory equipment.

We will undertake the measurement of a simple RC circuit using your own VI, a function generator, and an oscilloscope. The basic approaches to communicating with lab equipment will be discussed in class. To prepare, it is best to become familiar with the Labview environment by diving right in!

We will meet in Crow 302 rather than Crow 205. The Mac computers in Crow 302 have Labview 2014 installed on them. You will be given card swipe access to 302.

Assignment:

1. Find time prior to the first class to familiarize yourself with Labview: after launching the program, open "Help/Find Examples," then open "Fundamentals/Waveforms/Waveforms - XY pairs.vi." Run the program to observe its behavior. Then click "Window/Show Block Diagram" to explore the underlying block diagram which displays the code, in graphical form, of this program.

Furthermore, be sure to explore "Fundamentals/Loops," "Structures/Feedback Node - Building An Array.vi," and "/Loop Tunnel Modes.vi." You may wish to open many more examples: there is a wide range of simple VIs illustrating many basic concepts of Labview programming. You will need to have familiarized yourself with these examples in order to complete the assignments below!

Note that right-clicking in a block diagram allows you to add prewritten functions, structures, basic math, &c.

2. Before the first class session on April 4, use your new knowledge of Labview to construct a VI that, when run, graphically displays the sum of a series of arbitrary sines and cosines whose frequencies and amplitudes can be entered in controls on the VI front panel. Keep it simple: at the very least, your VI should be able to display either a composite square wave or triangle wave built of a given number of terms added together (so that we could see a rough square wave approximation with only, say, 5 terms; or a very good approx using 100 terms).

In class on April 4, you will demonstrate your VI to the instructor and the class.

3. A second assignment will be described in class on April 4, to control a particular set of instruments in a mock "data acquisition" excercise. You will demonstrate this capability in class April 11.

Ryan Ogliore (Apr 18, 25)

• Matlab
• Project: Chaotic dynamics.