Interface motion in random media. (English) Zbl 1321.82018
The authors propose a multi-scale renormalization procedure to study the dynamics of surfaces in a random environment. According to the main result, assuming that a certain finite size criterion is satisfied, the interface evolves with positive velocity. It is checked that this feasibility criterion holds in a large number of cases. Qualitatively speaking, this result means that, as the surface is evolving, deeper traps are encountered in various scales which locally block the interface dynamics.
Reviewer: Guy Jumarie (Montréal)
MSC:
| 82B26 | Phase transitions (general) in equilibrium statistical mechanics |
| 82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
| 82B24 | Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
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