PHY 411-506 Computational Physics 2 Spring 2013
Syllabus  |  Tools  |  Topic 1  |  Topic 2  |  Topic 3  |  Topic 4  |  Topic 5  |  Topic 6  |  Topic 7
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Final Exam

Date: Thursday May 2, 7:15 pm - 10:15 pm in NSC 215

Format: 16 questions on Topics 4,5,6,7 similar to quizzes

Exam is closed computer/book

One binder of personal written notes and/or printouts allowed, see Syllabus - exams

Lecture Preparation

Review references for Topic 7 Fluid Dynamics

White Dwarf - Pulsar binary system in today's news: A Massive Pulsar in a Compact Relativistic Binary

Wikipedia: White dwarfs   Chandrasekhar limit   Neutron stars

M.M. May and R.H. White, "Hydrodynamic Calculations of General-Relativistic Collapse", Phys. Rev. 141, 1232-1241 (1966)

K.A. van Riper, "General relativistic hydrodynamics and the adiabatic collapse of stellar cores", Astrophys. J. 232, 558-571 (1979)

S. Woosley and T. Janka, "The physics of core-collapse supernovae", Nature Phys. 1, 147-154 (2005)

Computational Supernova Groups: ORNL Computational Astrophysics Max-Planck Garching How a supernova obtains its shape

M. Trenti and P. Hut, "N-body simulations (gravitational)", Scholarpedia, 3(5):3930 (2008)

Topic 7: Fluid Dynamics

Lecture 1 Slides  |  burgers.cpp

Lecture 2 Slides  |  shocktube.cpp  |  riemann-solver.hpp  |  roe-solver.hpp

Lecture 3 Slides

Lecture 4 Slides  |  eos.hpp

Lecture 5 Slides

Lecture 6 Slides

Topic 6: Quantum Field Theory

Lecture 1 Slides  |  gsl-monte.c

Lecture 2 Slides  |  compton.cpp

Lecture 3 Slides  |  mstw.cpp  |  mstwpdf.cc  |  mstwpdf.h  |  mstw2008lo.00.dat

Lecture 4 Slides

Lecture 5 Slides  |  abelian.cpp

Lecture 6 Slides

Homework Assignment 8 due Sunday April 21

  1. Use the compton.cpp code and GSL VEGAS to reproduce all the curves in Figure 14.18 from Jackson versus .
  2. Use the mstw.cpp code to generate LO (lowest order) versions of the plots on the MSTW PDFs webpage (more accurate NLO plots with uncertainty bands). Modify the code to use VEGAS to check the momentum sum rule
    which just says that the sum of fractional momenta of all of the partons inside of the hadron must add up to the momentum of the hadron! Also check that the proton has 2 valence up quarks and 1 valence down quark
  3. Use the abelian.cpp code to reproduce the thermal cycle results in Figure 1 of M. Creutz, L. Jacobs, C. Rebbi, Phys. Rev. D20, 1915-1922 (1979). Modify the code to reproduce Figure 8 on square Wilson loops of size 1 and 2 for the model.

Topic 5: Quantum Monte Carlo

Lecture 1 Slides  |  vmc.cpp  |  random.hpp

Lecture 2 Slides  |  vmc-he.cpp  |  gsl.hpp

Lecture 3 Slides  |  vmc-he2.cpp

Lecture 4 Slides  |  dmc.cpp

Lecture 5 Slides  |  pimc.cpp

Homework Assignment 7 due Sunday April 7

  1. Variational Quantum Monte Carlo: Modify the code vmc.cpp for the Hydrogen atom using a trial function . Here are some results using 300 walkers with 2,000 thermalization steps and 10,000 production steps per walker to check your code is working correctly:
    <E> <E2> - <E>2
    0.8 -0.4813(6) 0.0092(5)
    0.9 -0.4954(3) 0.0048(2)
    1.0 -0.5000 0.0000
    1.1 -0.4947(6) 0.0060(2)
    1.2 -0.4793(8) 0.0133(4)
  2. Diffusion Quantum Monte Carlo: Compare output of the code dmc.cpp with the exact ground state wavefunction of the 3-D harmonic oscillator by plotting the DMC and exact results on the same plot. Modify the code to simulate the isotropic harmonic oscillator in dimensions D = 2 and D = 4, and check that the numerical output agrees with the exact solution.
  3. Path Integral Quantum Monte Carlo: Use the code pimc.cpp to find the energy of the quantum harmonic oscillator at several temperatures and compare with the expected values computed from the energy spectrum

Topic 4: Electronic Structure

Review references for Topic 4 Electronic Structure

Wikipedia: Electronic band structure

J.C. Slater, "Wave Functions in a Periodic Potential", Phys. Rev. 51, 846-851 (1937)

G.A. Burdick, "Energy Band Structure of Copper", Phys. Rev. 129, 138-150 (1963)

Lecture 1 Slides  |  hydrogen.cpp  |  helium-var.cpp

Lecture 2 Slides  |  helium-scf.cpp

Lecture 3 Slides  | 

Lecture 4 Slides  | 

Lecture 5 Slides  | 

Topic 3: Polymers and Neurons

Lecture 1 Slides  |  sawalk.cpp  |  saw-exact.cpp  |  reptation.cpp

Self-avoiding Walk Applet  |  Reptation Applet

Lecture 2 Slides  |  folding.cpp

Protein Folding Applet

Lecture 3 Slides  |  genetic.cpp

Lecture 4 Slides  |  hodgkin-huxley.cpp

Lecture 5 Slides  |  hopfield.cpp  |  letters.hpp

Hopfield Model Applet

Lecture 6 Slides

Homework Assignment 6 due Sunday March 24

  1. Reproduce the computational results given by Hodgkin and Huxley J. Physiol. 117(4), 500-544 (1952) for the membrane action potentials, Eqn. (26) and Fig. (12), and the propagated action potential, Eqn. (31) and Fig. (15), and comment on what you have learned.
  2. Reproduce the results in Fig. 2 of Hopfield's article Proc. Natl. Acad. Sci. USA 79, 2554-2558 (1982).
  3. Write C++ codes to implement artificial neural networks for the Boolean functions AND, OR, and XOR given in Table 3.1 and Table 3.2 of C. Peterson and T. Rognvaldsson, "An introduction to artificial neural networks", Proc. 1991 CERN Summer School of Computing, CERN Yellow Report 92-02, 113-170 (1992) and verify that they work.

Topic 2: Monte Carlo Methods

Lecture 1 Slides  |  pi.cpp  |  gauss.cpp

Metropolis Walker Applet

Lecture 2 Slides  |  metropolis.cpp  |  disks.cpp

HD Applet

Lecture 3 Slides  |  ising.cpp

Ising Model Applet

Lecture 4 Slides  |  auto.cpp

Autocorrelation Times Applet

Lecture 5 Slides  |  percolation.cpp  |  wolff.cpp  |  cluster.cpp

Lecture 6 Slides  |  xy.cpp

Topic 1: Molecular Dynamics

Lecture 1 Slides  |  vpp-rk4.c

Lecture 2 Slides  |  md.cpp  |  md2.cpp

Lecture 3 Slides  |  md3.cpp  |  md4.cpp

Lecture 4 Slides  |  fpu.cpp

Lecture 5 Slides  |  kdv.cpp

Lecture 6 Slides  |  hd.cpp

F. Ercolessi, A Molecular Dynamics Primer, and Examples in Fortran 90.

Preparing and Submitting Homework Assignments

It is important to learn how to present your work in a professional way.

The LaTeX document preparation system is very widely used in physics, mathematics and computer science, and is recommended for preparing assignments.

If you prefer to use Microsoft Office you should format formulas and equations properly with the built-in Equation Editor and Save as PDF for submission on UBlearns.

In an emergency scan handwritten solutions to PDF.

Please make sure you hit the "Submit" button on UBlearns, see Blackboard Help: Submitting Assignments.

Information

Syllabus and Course Information

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PHY 410-505 Fall 2012 Website




Copyright © 2013

Richard J. Gonsalves  |  Department of Physics  |  University at Buffalo