Berlin 2012 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 27: Transport and Anomalous Diffusion
DY 27.6: Talk
Thursday, March 29, 2012, 16:00–16:15, MA 004
Efficient simulation of Fractional Brownian Motion for several values of the Hurst exponent — •Alexander K. Hartmann1, Satya N. Majumdar2, and Alberto Rosso2 — 1Institute of Physics, University of Oldenburg, Germany — 2LPTMS, Université Paris-Sud, France
We study Fractional Brownian Motion (FBM), i.e., Gaussian processes with zero mean and a correlator of the form C(t,t′)= t2H+(t′)2H−|t−t′|2H, in the presence of an absorbing boundary. The strength of the correlation is described by the Hurst exponent H, whereas H=0.5 corresponds to the uncorrelated random walk (diffusion), H>0.5 to positive correlations (superdiffusion) and H<0.5 to anticorrelations (subdiffusion) of the movement. FBM is, e.g., believed to describe the translocation of polymers through pores.
Recently, analytical predictions [1,2] were obtained for the distribution P(x) of walk endpoints x. Standard numerical simulations study FBM via generating (discrete-time) random walks directly. They are, in particular for H<0.5, very demanding, since the success probability of generating a non-absorbed trajectory is very small. Hence, such simulations were restricted to a small number L of discrete steps. Here, using a special Monte Carlo Simulation, long walks up to L=107 could be generated for values H=1/4, 4/9, 1/2 and 2/3. The results are compared with the analytical predictions.
[1] A. Zoia, A. Rosso, S. N. Majumdar, Phys. Rev. Lett. 102, 120602 (2009)
[2] K. J. Wiese, S. N. Majumdar, A. Rosso, arXiv:1011.4807