title: First-passage-time processes and subordinated Schramm-Loewner evolution.
abstract: We study the first-passage-time processes of the anomalous diffusion on the self-similar curves in two dimensions. The scaling properties of the mean-square displacement and mean first passage time of the fractional Brownian motion and subordinated walk on the different fractal curves (loop-erased random walk, harmonic explorer, and percolation front) are derived. We also define natural parametrized subordinated Schramm-Loewner evolution (NS-SLE) as a mathematical tool that can model diffusion on fractal curves. The scaling properties of the mean-square displacement and mean first passage time for NS-SLE are obtained by numerical means.
authors.affiliation: Department of Physics, Sharif University of Technology, Tehran, PO Box 11365-9161, Iran.
authors.forename: M Ghasemi
authors.initials: MG
authors.lastname: Nezhadhaghighi
authors.forename: M A
authors.initials: MA
authors.lastname: Rajabpour
authors.forename: S
authors.initials: S
authors.lastname: Rouhani
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D003198:Computer Simulation; D004058:Diffusion; D017709:Fractals; D015233:Models, Statistical; D008962:Models, Theoretical; D009038:Motion; D011336:Probability