1. Computational methods in physics

2. 1
Introduction to Lattice Models
Introduction to Easy Java Simulations software 2
Deterministic cellular automata
Conway model 3
Monte-Carlo method
Ising model 4
Random and self-avoiding walk
Brownian motion and diffusion 5
Percolation theory
Site square model 6
Pattern and dendrite growth
Diffusion limited aggregation model
Colouring model 7
Protein folding
HP (hydrophobic-polar) model

3. Deterministic cellular automata
Conway model

5. Introduction to Lattice Models Introduction to Easy Java Simulations software

10. Period 1

11. Life objects:
Still life
Oscilators
Gliders
Exponential growth
Can simulate:
Nuclear chain reaction
Spread of forest fire
Plague or epidemic
Cellular automata characteristics:
Parallelism: every cell is updated simultaneously
Homogeneity: every cell is updated using the same rules
Localism: every cell is updated based upon its neighbors
Book online: S.Wolfram – A new kind of science

12. Moore Neighborhood   Van Neumann Neighborhood
Boundary conditions Right: Cells beyond the grid boundary
Left: toroidal topology are always treated as if they were dead.

15. Homework 1: Use cellLattice to color your squares
from 1 to 8 depending on the number of neighbours.

16. Homework 2: Find all 3x3 “creatures”
(total number 2^18= ) and find the number of creatures (up to vertical, horizontal, diagonal mirror symmetry):
* Stable - Patterns that do not change over time
* Oscillators - Patterns that change over time but repeat themselves every n cycles.
* Flyers - Patterns that essentially stay the same over time but move across the board like a bird or spaceship.
Other patterns - Discover your own type of pattern
Homework 3: Find the lifespans of 3x3 “creatures” classified to Other patterns. Find methuselahs with long lifespan
Lifespan – number of generations until the pattern dies or becomes stable, oscillator or flyer.
 R-pentomimo with 1103 generations

17. Statistics
N.Johnston toroidal 20x20 lattice
Density=initial nr.alive cells/400
random chosen initial states
random chosen initial states
Longest lifespan 2092
Homework 4:
For all 3x3 “creatures” find:
Lifespan vs. density
Lifespan frequency histogram

18. Survive if two or three cells are alive B36/S23 – High Life
Homework 5:
Explore other rules
B3/S23 Conway Game of life
– Born when 3 cells alive,
Survive if two or three cells are alive
B36/S23 – High Life
B2/S –Seeds
B23/S3 –Reversed GOL
B02468/S02468 – Evens
B3678/S34678 – Day and night
B3/S12345 – Maze
B45678/S2345 – Walled cities

19. Forest Fire

22. Other: couple – distance 1  quarantine type A
couple – distance 1  quarantine type B
coworkers- distance 2

24. Real and simulated epidemic results for the SARS outbreak in Singapore 2003

26. Game of Plague: The four key quantities are the infectivity (the rate at which the disease spreads), latency, (how long before it becomes active in the host), duration (how long it remains in the host and mortality (the percentage of people the disease kills)