helmut g. katzgraber
  Computational Physics
  401 & 619 (Spring 2015)

general information

The class will be held in room MPHY 107 (new Mitchell Physics Building) Wednesday and Friday at the following times
401 (undergraduate) 09:10 - 10:00 lab in MPHY 330A Friday 13:50 - 15:50 (501) and 16:00 - 18:00 (502)
619 (graduate) 12:40 - 13:30 lab in MPHY 330A Friday 13:50 - 15:50 (601) and 16:00 - 18:00 (602)
The instructor will be present the first hour of each lab.

Instructor:  Helmut Katzgraber
Office:  MPHY 409
Phone: (979) 209 0207
E-mail: click here
Hours:  By appointment via email.
401 reqs:  MATH311, MATH412, PHYS302, PHYS309, knowledge of a programming/scripting language
619 reqs:  PHYS408, PHYS412, knowledge of a programming/scripting language
Books:  see literature list provided in class
Grading:  Lab (20%)
  Homework (20%)
  Semester project (40%)
  Semester project report in LaTeX (10%)
  Semester project presentation (10%)
TA:  Andrew Ochoa (MPHYS 403)
  Zheng Zhu (MPHYS 403)

Note: You must score 70% or higher in the Lab work to pass the course. Although homework and lab combined only count 40%, I highly encourage you to do the homework sets regularly. You are allowed to miss one lab that will not be counted towards the final grade. However, you will have to show me a university-approved excuse. A 10-point grade scale will be used and no curve will be made. I encourage you to use email as a means of communicating with me about any problems concerning the course: questions about the material from lecture, about the homework problems, or about the course administration. In an effort to save some trees, there will be no printed handouts. The lecture notes will (usually...) be placed online the day before the class. All necessary information can be obtained online.

If you do not know Unix, please check out this cheat sheet.

syllabus & slides


The lecture slides for each class can be accessed by clicking on the title. Note that these are being prepared 'on the fly' meaning that the page will be updated periodically.

week topic lab & homework [solution]
01/19 Class logistics
Computer hardware & introduction to software engineering
01/26 Root finding, ODEs (Euler, Runge Kutta, symplectic), Kepler problem LAB & HOMEWORK 02 [SOLN]
02/02 PDEs, finite elements, heat equation
Introduction to Mathematica [notebook]
Mathematica applications [notebook]
Poisson equation relaxation method demo
Heat equation forward Euler demo
02/09 Chaos (Lyapunov exponents, logistic map, Duffing equation) & Fractals
Chaos and fractals with Mathematica [notebook]
02/16 Numerical integration methods, random number generators
Random number generators (code)
02/23 Random walks, phase transitions in percolation, Monte Carlo integration (simple & importance sampling, Markov chains) LAB & HOMEWORK 06 [SOLN]
03/02 Simple Monte Carlo methods in statistical physics (Ising model, phase transitions, finite-size scaling) LAB & HOMEWORK 07 [SOLN]
03/09 Advanced Monte Carlo methods (cluster algorithms, parallel tempering, Wang Landau sampling) LAB & HOMEWORK 08 [SOLN]
03/16 SPRING BREAK - no classes  
03/23 Optimization & complexity (annealing, genetic, extremal, quantum annealing algorithms) LAB & HOMEWORK 09 [SOLN]
03/30 Stochastic ODEs - FRIDAY READING DAY (no lab, no class)  
04/06 Quantum one-body problem (Numerov, shooting, matrix methods)
Quantum one-body problems with Mathematica [notebook]
04/13 HPC clusters, basic parallelization (OpenMP, MPI), cellular automata LAB & HOMEWORK 12 [SOLN]
04/20 Statistical data analysis, (fast) Fourier transforms LAB & HOMEWORK 13 [SOLN]
04/27 Pointers on how to give a scientific presentation
Example 10-minute talk (low-resolution images)
FRIDAY FINAL COURSE PRESENTATION (undergrads during class, grads during lab)

Please make sure to submit your code (source) as well as homework write-up electronically each week. The homework files are published each week on the day of the lab and due one week later. There will be NO extensions.

If you would like to access the lectures slides (PDF) please send an email to the instructor and you might receive the username and password. Students can find the username and password on the slides in the first class. All material on this website is copyrighted by H. G. Katzgraber. No material shall be used for commercial purposes (e.g., A+ Tutoring and similar) without prior written consent from the owner of the material. Failure to do so will result in legal prosecution.

semester projects

It might be necessary to make teams for the semester projects. However, you are responsible to clearly state what each student's contribution was. Keep in mind that a simple Q&A during the presentation will show if you did the work or not... The projects will be supervised by Helmut Katzgraber (HGK), Andrew Ochoa (AJO), Zheng Zhu (ZZ) and Richard Lawrence (RL). Please contact your assistants as early as possible to get reading material. The LaTeX macro for the report can be found HERE.

Easier projects (undergrads preferred)
Percolation transition on different lattices (Lazar Kish, AJO)
Self-avoiding random walks in d = 1...4 (Cristian Cernov, HGK)
The three-dimensional Ising model (Brendan Hill, AJO)
Closed orbits for the 3-body problem with 4th-order symplectic algs (Nick Mondrik, AJO)
Optimize a class or train schedule using genetic algorithms (Frank Chu, ZZ)
Study the traveling salemesman problem with genetic algorithms (Max Shannon, ZZ)
Avalanches in the BTW sand-pile model (Sarah Henry, ZZ)
Avalanches in the random-field Ising model using Glauber dynamics (ZZ)
Predator-prey models (Joseph Garvie, AJO)
Solitons (Roberto Ortiz, RL)
Heat transfer simulations by solving PDEs on nontrivial topologies (Colin Whisler, ZZ)
Testing RNGs using the Wolff cluster algorithm (Kirk Byers, HGK)
Fractals and parallel computing (Richard Haines, HGK)
Wang-Landau simulation of the Ising model (James Bounds, AJO)
Simulated annealing for spin glasses (Layla Bakhtiari, HGK)
Stochastic ODEs in finance and the Black-Scholes (Brian Kelly & Elliott Levin, ZZ)
Population annealing of the Ising model, compare to exact (RL)
Time-dependent quantum problem (Daniel Krause, ZZ)
Crank-Nicols method for the diffusion equation in 1D (Jeena Khatri, AJO)
Relaxation method for electric potentials on 2D C-shaped cavity (ZZ)
Minimum vertex covers (Leonardo Bello, HGK)
Analyze music with Fourier transforms (Michelle Thomas, AJO)
Variational ansatz for ground state of simple atoms/molecules (AJO)
Autocorrelation times of the Ising ferromagnet in 2D (Jared Nelson, ZZ)
Harder projects (grads preferred)
2D Ising model with different cluster algorithms; critical parameters (Ben Schroeder, AJO)
2D q-state Potts model via Wang Landau (Saeed Asiri and Abdullah Alturki, HGK)
Variational QMC to find ground state of anharmonic oscillator potential (Dangallage Jayatissa and Joshua Hooker, ZZ)
Close packings of hard spheres and jamming/crystallization (ZZ)
Exact diagonalization of the 1D Hubbard model (Amin Barzegar, HGK)
Hysteretic optimization for Sherrington-Kirkpatrick model (Longfei Fan, ZZ)
Tensor network algorithm for 2D Ising model (Austin Schneider & Nicholas Closuit, ZZ)
Monte Carlo simulation of the 3D Heisenberg model (Timur Akhmedzhanov, HGK)
Final reports click here


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