Phys690: (Fall 2003)
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: 
              T&G: H. Gould and J. Tobochnik
              Gi:  Text, by N.J.Giordano
              K&W: M.H. Kalos and P.A. Whitlock
              NR:  Numerical Recipes
M 9/1
  • General information.

  • Why is a course focusing on computations useful? 
    
  
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  W
  9/3
  

  • What is Monte Carlo? Example of pi. 

        -  T&G, Sec. 11.2, 11.3; K&W, p1-6; Gi, P157-169. 
    

  • Random numbers and their testing.

        -  T&G, Sec. 12.6; K&W, Appendix; Gi, P157-169.  
    

  • Intro. to the central limit theorem.

        -  T&G, Sec. 11.4, Prob 12.9; K&W, p25-28. 
    
  
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  M
  9/8
  

  • MC error analysis, the central limit theorem.

        -  T&G, Sec. 11.4, Prob 12.9; Gi, Sec. 7.3.
 
    

  • General reading assignment on probability:

        -  K&W, p2-15.

    

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

        -  T&G, Sec.'s 7.3, 12.1; Gi, Sec. 7.4. 
    

-- Homework Assignment 1 out.

  
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  W
  9/10
  

  • Monte Carlo sampling, concept; probability.

        -  T&G, Sec. 11.5; K&W, p39-50; Gi, P160-162.  
    

  • The accumulant and inversion technique.

        -  T&G, Sec. 11.5; K&W, p39-50. 
    

  • Gaussian distributions --- the Box-Muller algorithm & testing of results
        -  T&G, Sec. 11.5; K&W, p39-50, p86-87.
    
  
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  M
  9/15
  

  • Particle transport simulations.

        -  T&G, Sec. 11.6; K&W, Chap. 6.

    

  • Intro. to Monte Carlo integration.

        -  T&G Sec. 11.2; K&W, p89-92.  

    
  
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    W
  9/17
  

No class today --- W&M closed due to Hurricane Isabel.

  

    

    
    
     
    
    

    
  M
  9/22
  

Post Isabel --- W&M remains closed.

  

    

    
  W
  9/24
  
  

    

    
    
     
    
    

    
  M
  9/29
  

  • Monte Carlo integration.

        -  T&G Sec.'s 11.2, 11.6; K&W, p89-92.  

    

  • Why and when is MC integration useful?

        -  K&W, Chap. 6.
    

-- Homework Assignment 2 out.
  
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    W
  10/1
  

  •  Importance sampling

        -  T&G Sec.'s 11.2, 11.7; K&W, p89-92.  

    
  
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  M
  10/6
  

  •  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 
    
  
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    W
  10/8
  

  •  The double-well problem by the Metropolis algorithm.

    

  •  The generalized Metropolis algorithm.

        -  T&G Sec. 11.8 
    
  
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  M
  10/13
  

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

        -  T&G, Chap. 16, Chap. 17; K&W, p73-86, p117-126. 
    

        -  lecture notes 
    

-- Homework Assignment 3 out.
  
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    W
  10/15
  

  • The Metropolis algorithm and applications.

    

  •  Intro to Ising model

    

  •  -- Materials on Metropolis and applications:

        -  TXT, Sec's 8.3, 8.4, 8.5;
       T&G, Chap. 16, Chap. 17; K&W, p73-86, p117-126. 

    

    
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  M
  10/20
  

  •  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

    

    

  •  Classical liquids.

    

  •  -- Materials on Metropolis and applications:

        -  TXT, Sec's 8.3, 8.4, 8.5;
       T&G, Chap. 16, Chap. 17; K&W, p73-86, p117-126. 

    
  
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    W
  10/22
  

  •  Hard disks and spheres.

    

  •  Simulated annealing.

    

  •  Travelling salesman problem.

        -  Lecture notes.  
    

        -  General reading meterial:
       Paper by Silverman and Adler --- I'll hand out next lecture
    

    

-- Homework Assignment 4 out.
  
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  M
  10/27
  

  •  Brief review of quantum mechanics.

    

  •  Variational Monte Carlo

        -  T&G, Sec. 18.5; K&W, p123-125.
       Gi, Sec 10.3.

    

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

        -  T&G, Sec. 18.7 (Diffusion QMC); A&T, p282-285.

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    W
  10/29
  

  •  Random walk to study ground states: drunkard + decay.

        -  T&G, Sec. 18.7 (Diffusion QMC); A&T, p282-285.
    

        -  Lecture notes and some additional materials on
       DMC are available from me.
      

  •  Introduction to percolation theory.

        -  T&G, Sec's 13.1 & 13.2. 

    

-- In place of the take-home mid-term, we will substitute a
course project ``proposal'', due on Wed. 11/5.
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
  11/3
  

  •  Introduction to the renormalization group method.

        -  T&G, Sec. 13.5.
    


  •  Forest fire simulation and relation to percolation.

        -  Reference materials are available from me.

    

  •  Fractals 

        -  TXT, Sec. 7.9; T&G, Sec's 14.1 and 14.2.

    

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    W
  11/5
  

  •  Fractal dimensions

        -  TXT, Sec. 7.9; T&G, Sec's 14.1 and 14.2.

    

  •  Diffusion in porous media.

    

  •  Earthquakes, sandpiles, and self-orgnized criticality.

        -  T&G, Sec. 15.3.
    -  Additional reference materials available.

    

    

-- Homework Assignment 5 out.
  
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  M
  11/10
  

  •  Earthquakes, sandpiles, and self-orgnized criticality, cont'd.

        -  T&G, Sec. 15.3.
    -  Additional reference materials available.

    

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

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

    

    

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

        -  Reading: T&G, Chap's 2 and 3.

    

    

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  W
  11/12
  

    

  •  Finite difference -- bicycle racing and air resistance.

        -  Reading: T&G, Chap's 2 and 3;
       Gi, Sec.'s 2.2 and 2.3.

    

    

  •  Stability in finite difference methods -- advection equation.

        -  Reference materials are available from me.

    

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  M
  11/17
  

    

  •  Finite difference --- FTCS, Lax, and Lax-Wendroff methods.

    

  •  Traffic flow.

        -  Reference materials are available from me.

    

    

  •  Electric potentials -- Laplace's equation.

        -  T&G, Sec. 10.2; Gi, Sec. 5.1.

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  W
  11/19
  

    

  •  Electric potentials, with charge; convergence issues.

        -  Gi, Sec. 5.2.

    

    

  •  Brief intro to the finite element method.

    

  •  Introduction to molecular dynamics.

        -  T&G, Sec.'s 8.1 - 8.6; Gi, Sec. 9.1;

    

    

-- Homework Assignment 6 out.

    • 

    
    
     
    
    

    
  M
  11/24
  

  •  Molecular dynamics, the Verlet algorithm.

        -  T&G, Sec.'s 8.1 - 8.6; Gi, Sec. 9.1;
    

  •  The melting transition.

        -  Gi, Sec. 9.2; T&G, Chap. 8. 

    • 

    
  W
  11/26
  
 Thanksgiving Break 

    

    
    
     
    
    

    
  M
  12/1
  

  •  Molecular dynamics, leap-frog and velocity Verlet algorithms

        -  T&G, Sec.'s 8.1 - 8.6; Gi, Sec. 9.1;
    

  •  Short-range potential and near-neighbor lists

        -  lecture notes 
    

  •  Hard disks.

        -  T&G, Sec. 8.9.
    

    • 

    
  W
  12/3
  

  •  Molecular dynamics --- hard disks, cont'd.

        -  T&G, Chap. 8; Gi, Sec. 9.2.
    

  •  Putting it all together.

        -  Lecture notes available from me.

    

  •  Outlook.

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    Th
  12/18
  

    
-- Final project report due in my mailbox. Guidelines on the write-up:
  
      

    •  The report should give a description of your work, 

at a level accessible to a general physics audience, 
without compromising rigor or failing to convey the technical 
advance that you have made and its significance. 

    •  The report should be in the format and style of a 
Physical Review Letter, observing the length limit (4 double-columned pages, everything included) and other formatting requirements. 
It should contain an abstract, main body, and references.

    •  Here are some "rules" on how to write a PRL (by Prof. John Wilkins at Ohio State University) that may be helpful.

    •  If you wish to include code listings, please do so separately as an appendix.

    •  I encourage you to use the RevTex 4 package, which you will most likely use again later when you write papers. You can choose other text processing packages, as long as you observe all the format and length requirements of PRL.


    


    

    

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