helmut g. katzgraber
  Computational Physics
  401 & 619 (Spring 2014)

general information

The class will be held in room MPHY 107 (new Mitchell Physics Building) Wednesday and Friday at the following times
401 (undergraduate) 11:30 - 12:20 lab in MPHY 303A 15:00 - 17:00
619 (graduate) 12:40 - 13:30 lab in MPHY 303A 15:00 - 17:00

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:  Ross McDonald

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. 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.

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]
01/13 Class logistics
Computer hardware & introduction to software engineering
01/20 Root finding, ODEs (Euler, Runge Kutta, symplectic), Kepler problem LAB & HOMEWORK 02 [SOLN]
01/27 PDEs, finite elements, heat equation
Introduction to Mathematica [notebook]
Mathematica applications [notebook]
Poisson equation relaxation method demo
Heat equation forward Euler demo
02/03 Chaos (Lyapunov exponents, logistic map, Duffing equation) & Fractals
Chaos and fractals with Mathematica [notebook]
02/10 Numerical integration methods, random number generators
Random number generators (code)
02/17 Random walks, phase transitions in percolation, Monte Carlo integration (simple & importance sampling, Markov chains) LAB & HOMEWORK 06 [SOLN]
02/24 Simple Monte Carlo methods in statistical physics (Ising model, phase transitions, finite-size scaling) LAB & HOMEWORK 07 [SOLN]
03/03 Advanced Monte Carlo methods (cluster algorithms, parallel tempering, Wang Landau sampling) LAB & HOMEWORK 08 [SOLN]
03/10 SPRING BREAK - no classes  
03/17 Optimization & complexity (annealing, genetic, extremal, quantum annealing algorithms) LAB & HOMEWORK 09 [SOLN]
03/24 Quantum one-body problem (Numerov, shooting, matrix methods)
Quantum one-body problems with Mathematica [notebook]
03/31 HPC clusters, basic parallelization with OpenMP and MPI
Parallel processing with GPUs [example code]
04/07 Many-body problems and molecular dynamics (Ross McDonald)
Statistical data analysis
04/14 Stochastic ODEs - FRIDAY READING DAY (no lab, no class)  
04/21 Pointers on how to give a scientific presentation
Example 10-minute talk (low-resolution images)
FRIDAY FINAL COURSE PRESENTATIONS (undergrads during class, grads during class)
04/28 READING DAY - no classes this week  

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 Friday and due the Friday after. 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... Projects marked with a 'G' are intended for graduate students, with a 'U' for undergrads. Projects in red have been taken.

type topic
U Michael Allen: Percolation transition in two space dimensions (HGK)
U Nick Amin: Self-avoiding random walks and polymers (HGK)
U Two-dimensional Ising Model on GPUs (RMD)
U Dimitri Michaelides: Closed orbits in the 3-body problems with 4th order methods (RMD)
U Casey Perkins & Wang Jizhou: Optimization with genetic algorithms (RMD)
U Caitlin Campbell: Traveling salesman problem (ZZ)
U Chris Akers: Bak-Tang-Wisenfeld sandpile model (ZZ)
U Alex Gary: Avalanches in the random-field Ising model (ZZ)
U Weiguang Huo: Solitons (RMD)
U Robert Bordovsky: Predator-prey models (AJO)
U Heat transfer on nontrivial topologies (RMD)
U William Baker: Testing random number generators with the Wolff algorithm (AJO)
U Richard Vega: Fractals on GPUs and visualization (RMD)
G Jianing Zhang: 2D Ising model with simple MC and cluster algorithms (critical slowing down, autocorrelation times, finite-size scaling)
G Yunsong Wu & Zhikun Xing: Variational Quantum Monte Carlo (ground state of the anharmonic oscillator)
G Sriteja Upadhyayula & Petr Zhokhov: Molecular dynamics (breathing mode of fullerenes)
G Jamming of hard spheres (Krauth algorithms)
G Wenchao Ge & Han Cai: Exact diagonalization (one-dimensional Hubbard model)
G Hysteretic vs extremal optimization of the Sherrington-Kirkpatrick model
G Laziz Saribaev: Wang-Landau algorithm for the 2D Potts Model
G Andrew Ochoa: Simulations of the 2D random-bond Ising model
  More on request...
The LaTeX macro for the report can be found HERE. The different undergrad projects will be guided by Helmut Katzgraber (HGK), Andrew Ochoa (AJO), Zheng Zhu (ZZ), and Ross McDonald (RMD). Graduate students are expected to work independently with some guidance from Ross McDonald and Helmut Katzgraber.
Final reports click here


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