In Natural Systems

1
Multiscale Modelling

• In Natural Systems

Chris Green and Lincoln Paterson 12 August 2005
2
Sydney sandstone outcrop
3
Multiscale modelling Upscaling
4
Upscaling
5
2D equivalent resistor network
6
Renormalisation in 2D
7
3D
8
No simple closed form expression in 3D
Peter King (per. comm.) I am sure there is some
deep group theroetic reason why 3D is intractable
whereas 2D is tractable-ish (like why you can't
solve the Ising model in 3D but can in 2D)
9
With most blocks equal
7 blocks equal, 1 different
6 blocks equal, 2 different
10
Approximate renormalisation in 3D
Chris Greens approximate solution
11
Stratified granular mixes
12
Stratification
13
Sandpile top view