1. Discrete diffusion modeling
Anders Malthe-Sørenssen

2. Discrete diffusion modeling
Random walks
Theory and simulations
Central limit theorem
Self-avoiding walks and polymers
Characterization of diffusional patterns
Ant in labyrinth
Diffusion-limited processes
Erosion as a diffusional process

3. Practical exercise Create algorithm for
Using random walkers to model erosional patterns
Characterize the erosional patterns using simple fractal measures

6. Diffusion – random walks
Brownian motion
Random jumps at constants rate
Algorithmic: lattice based

7. Singlewalk.avi

8. Statistics of a random walk
<r>(t) ?
r(t) ?
P(r>R;t) ?

9. <r>(t) ?
r(t) ?
P(r>R;t) ?

10. <r>(t) ?
r(t) ?
P(r>R;t) ?

11. Theory

12. Geometry of a random walk

13. Theory

14. Diffusion fronts
Image(latt)

15. Diffusion fronts
Image(latt > 100)

16. Physical processes with random walks
Diffusion limited processes:
Diffusion of material is limiting growth or reaction processes: example DLA
Diffusion as basis for physical processes
Diffusion Limited erosion
Drainage networks

17. Diffusion limited aggregation