Anomalous diffusion of a tethered membrane: A Monte Carlo investigation
  Using a continuum bead-spring Monte Carlo model, we study the anomalous diffusion dynamics of a self-avoiding tethered membrane by means of extensive computer simulations. We focus on the subdiffusive stochastic motion of the membrane's central node in the regime of flat membranes at temperatures above the membrane folding transition. While at times, larger than the characteristic membrane relaxation time $\tau_R$, the mean-square displacement of the center of mass of the sheet, $<R_c^2>$, as well as that of its central node, $<R_n^2>$, show the normal Rouse diffusive behavior with a diffusion coefficient $D_N$ scaling as $D_N \propto N^{-1}$ with respect to the number of segments $N$ in the membrane, for short times $t\le \tau_R$ we observe a {\em multiscale dynamics} of the central node, $<R_n^2> \propto t^\alpha$, where the anomalous diffusion exponent $\alpha$ changes from $\alpha \approx 0.86$ to $\alpha \approx 0.27$, and then to $\alpha \approx 0.5$, before diffusion turns eventually to normal. By means of simple scaling arguments we show that our main result, $\alpha \approx 0.27$, can be related to particular mechanisms of membrane dynamics which involve different groups of segments in the membrane sheet. A comparative study involving also linear polymers demonstrates that the diffusion coefficient of self-avoiding tethered membranes, containing $N$ segments, is three times smaller than that of linear polymer chains with the same number of segments. 
Hristina Popova and Andrey Milchev