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Classification of rough surfaces using Schramm-Loewner evolution

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Topological Dynamics in the Physical and Biological Sciences

The theory of Schramm-Loewner Evolution (SLEk) was developed originally as the theory of random curves with conformally invariant probability distribution, describing domain interfaces at criticality. I argue that iso-height lines on rough surfaces can also be regarded as SLEk. This may be regarded as evidence of conformal invariance in systems far from equilibrium. Perhaps this connection provides a new avenue for classification of self-affine surfaces in 2+1 dimensions. In this talk I present numerical evidence that SLE curves exist on rough surfaces. In particular I analyze the KPZ surface, having the same exponent as the self avoiding walk (SAW). I also present evidence that a physically grown Deposited WO3 surface has k=3, i.e. it is in the Ising class. Finally I discuss the Abelian Sandpile model and the Explosive Percolation (Watersheds).

This talk is part of the Isaac Newton Institute Seminar Series series.

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