Phys690: (Spring 2007)
Computer Simulations in Physics

Course calendar:

There is a brief description of the content for each lecture, together with links to handouts (HW, etc). The references (in red) point to parts in the text and reference books that may be helpful in complementing your lecture notes. The names of the main references are: 
              GTC: Text, H. Gould, J. Tobochnik, and W. Christian
              Gi:  N.J.Giordano
              KW:  M.H. Kalos and P.A. Whitlock
              NR:  Numerical Recipes
M 1/29
  • General information.

  • Why is a course focusing on computations useful? 
    

  • What is Monte Carlo? Example of pi. 

        -  GTC, Sec. 11.2, 11.3; KW, p1-6; Gi, P157-169. 
    
  
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  W
  1/31
  

  • What is Monte Carlo? Example of pi. 

        -  GTC, Sec. 11.2, 11.3; KW, p1-6; Gi, P157-169. 
    

  • Random numbers and their testing.

        -  GTC, Sec. 7.9; KW, Appendix; Gi, P157-169.  
    

  • Intro. to the central limit theorem.

        -  GTC, Sec. 11.4, Prob 12.9; KW, p25-28. 
    
  
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  M
  2/5
  

  • MC error analysis, the central limit theorem.

        -  GTC, Sec. 11.4, Prob 12.9; Gi, Sec. 7.3.
 
    

  • General reading assignment on probability:

        -  KW, p2-15.

    

  • Random walks (diffusion), Monte Carlo sampling of discrete probabilities.

        -  GTC, Sec.'s 7.2-8; Gi, Sec. 7.4. 
    

-- Homework Assignment 1 out.

  
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  W
  2/7
  

  • Monte Carlo sampling, concept; probability.

        -  GTC, Sec. 11.5; KW, p39-50; Gi, P160-162.  
    

  • The accumulant and inversion technique.

        -  GTC, Sec. 11.5; KW, p39-50. 
    

  • Gaussian distributions --- the Box-Muller algorithm & testing of results
        -  GTC, Sec. 11.5; KW, p39-50, p86-87.
    
  
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  M
  2/12
  

  • Particle transport simulations.

        -  GTC, Sec. 11.6; KW, Chap. 6.

    

  • Intro. to Monte Carlo integration.

        -  GTC Sec. 11.2; KW, p89-92.  

    

  • Why and when is MC integration useful?

        -  KW, Chap. 6.
    
  
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  W
  2/14
  

  • Monte Carlo integration.

        -  GTC Sec.'s 11.2, 11.6; KW, p89-92.  

    

  •  Importance sampling

        -  GTC Sec.'s 11.2, 11.6; KW, p89-92.  

    
  
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  M
  2/19
  

  •  Introduction to the Metropolis algorithm --- the pi game
again, grown-up's version.

    

  •  The scrambling game --- detailed balance and the concept of
rejecting a move.

        -  lecture notes 
    

-- Homework Assignment 2 out.

    		• 

    
  
    W
  2/21
  

  •  The double-well problem by the Metropolis algorithm.

    

  •  The generalized Metropolis algorithm.

        -  GTC Sec. 11.7 
    
  
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  M
  2/26
  

  • The generalized Metropolis algorithm, understanding T(x -> x').

        -  GTC, Chap. 15; K&W, p73-86, p117-126. 
    

        -  lecture notes 
    


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    W
  2/28
  

  • The Metropolis algorithm and applications.

    

  •  -- Materials on Metropolis and applications:

        -  Gi, Sec's 8.3, 8.4, 8.5;
       GTC, Chap. 15; K&W, p73-86, p117-126. 

    

  •  Ising model and phase transitions.

        -  Here's a nice Java program on Ising model: 
    

            http://bartok.ucsc.edu/peter/ising/ising.html

    


-- Homework Assignment 3 out.
  
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  M
  3/5
  

No class this week --- APS March meeting

  

    

    
  W
  3/7
  
  

    

    
    
     
    
    

    
  M
  3/12
  

Have a great Spring break!

  

    

    
  W
  3/14
  
  

    

    
    
     
    
    

    
  M
  3/19
  

  •  Ising model and phase transitions.

        -  The Java program on Ising model that we looked at today in class is at: 
    

            http://bartok.ucsc.edu/peter/ising/ising.html

    

-- Homework Assignment 4 out.

    • 

    
  W
  3/21
  

  •  Critical slowing down

    

  •  Classical liquids.

    

  •  -- Materials on Metropolis and applications:

        -  GTC, Chap. 15; 
       Gi, Sec's 8.3, 8.4, 8.5; K&W, p73-86, p117-126. 

    

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  M
  3/26
  

  •  Simulated annealing.

    

  •  Travelling salesman problem.

        -  Lecture notes.  
    

        -  More reading meterials available from me.

    

  •  Brief review of quantum mechanics.

    • 

    
  W
  3/28
  

  •  Variational Monte Carlo

        -  GTC, Sec. 16.7; K&W, p123-125.
           Gi, Sec 10.3.
         - McMillan's first paper

    

  •  Intro to diffusion MC --- random walk to study ground states

        -  GTC, Sec. 16.8, 16.9 (Diffusion QMC); A&T, p282-285.
    

-- In place of the take-home mid-term, we will substitute a
course project ``proposal'', due on Mon. 4/2.
This will constitute 10% of the course grade, with
the final project 20%.
The proposal must be complete and concise, no longer than one page
except for references, and must address:


              What is it that you plan to do?
            -- describe the problem

          Why do it?
            -- background (including what has been done) and significance

          How are you going to do it?
            -- method you plan to use, etc

    
  
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  M
  4/2
  

  •  Intro to quantum MC --- diffusion MC, random walks to study ground states

        -  GTC, Sec. 16.8, 16.9 (Diffusion QMC); A&T, p282-285.
    

        -  Here's a HW problem from quantum mechanics which works out some of the "theory"

    

  •  Introduction to percolation theory.

        -  GTC, Chap. 12. 

    

-- Homework Assignment 5 out.
    • 

    
  W
  4/4
  

  •  Introduction to the renormalization group method.

        -  GTC, Sec. 12.5.
    


  •  Forest fire simulation and relation to percolation.

        -  Reference materials are available from me.

    

  •  Fractals

        -  GTC, Sec's 13.1 and 13.2; Gi, Sec. 7.9.

    

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  M
  4/9
  

  •  Earthquakes, sandpiles, and self-orgnized criticality.

        -  GTC, Sec. 14.1-3.
    -  Additional reference materials available.

    

  •  A game of life (an example of cellular automata simulation) web site:

        -  http://www.bitstorm.org/gameoflife/

    

    • 

    
  W
  4/11
  

  •  Intro to finite difference -- heat conduction in a rod.

        -  Reading: GTC, Chap's 2 and 3.

    

  •  Finite difference -- bicycle racing and air resistance.

        -  Reading: GTC, Chap's 2 and 3;
       Gi, Sec.'s 2.2 and 2.3.

    

    

-- Homework Assignment 6 out.

    • 


    
    
     
    
    

    
  M
  4/16
  

  •  Stability in finite difference methods -- advection equation.

        -  Reference materials are available from me.

    

    

  •  Finite difference --- FTCS and Lax methods

    

  •  Traffic flow.

        -  Reference materials are available from me.

    

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  W
  4/18
  

  •  Finite difference --- Lax-Wendroff methods.

    

  •  Electric potentials -- Laplace's equation.

        -  GTC, Sec. 10.1-5; Gi, Sec. 5.1.

    

  •  Connection to random walks

        -  GTC, Sec. 10.6.

    

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  M
  4/23
  

  •  Brief intro to the finite element method.

    

  •  Introduction to molecular dynamics.

        -  GTC, Sec.'s 8.1 - 8.6; Gi, Sec. 9.1;

    

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  W
  4/25
  

  •  Molecular dynamics, the Verlet algorithm.

        -  GTC, Sec.'s 8.1 - 8.6; Gi, Sec. 9.1;
    

  •  The melting transition.

        -  Gi, Sec. 9.2; GTC, Chap. 8. 
    

  •  Molecular dynamics, leap-frog and velocity Verlet algorithms

        -  GTC, Sec.'s 8.1 - 8.6; Gi, Sec. 9.1;
    

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  M
  4/30
  

  •  Short-range potential and near-neighbor lists

        -  lecture notes 
    

  •  Hard disks.

        -  GTC, Sec. 8.9.
    

  •  Connection and differences bt. MC and MD.

    • 

    
  W
  5/2
  

  •  Putting it all together.

        -  Lecture notes available from me.

    

  •  Outlook.

  •  HW Q/A.

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    Wed
  5/9
  

    
-- Final project presentation at 2pm

    
-- Please hand in a copy of your slides before the presentation.

    

    

        Info on presentation:
    

        -  10 min. presentation + 2 min. for questions.

    

        -  The time limit is STRICT.

    

        -  Talk should discuss:

          I.  Introduction
                what have people done related to your work
                what is it that you did
                why is it important

          II. Your work
                method
                results

          III. Summary

          ==>  A short talk like this is very challenging. The single
               most important element in its success is preparation.
               (I recommend that you study and follow the "Wilkins rules": 
                http://www.physics.ohio-state.edu/~wilkins/onepage/
                under "Oral Presentations")
               Design your talk with one question in mind:
               what is the message that you want the audience to
               take away from the talk? Stick to that message
               and eliminate anything that does not directly
               relate to it. Do not include small details.

    



    

    

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