ROUGHENING
AND NON-LINEAR DIFFUSION
Non-linear diffusion in the presence of random temporal
and spatial perturbations
Many phenomena
are described by non-linear diffusion:
· The formation of landscape and river
networks in geology
· Fluid transport in porous media (e.g.
important for oil extraction).
· Growth patterns of bacterial
colonies.
· Growth of interfaces between
thermodynamic phases.
· Kinetic roughening phenomena during
deposition of materials.
· Development of the fire-front of
forest fires and in the slow combustion of paper.
· Start and deployment of avalanches in
snow and mud, but also in superconductors (leading to the quenching of
high-field
magnets).