
Conference publicationsAbstractsXIX conferenceСomputer simulations of diffusion of clusters on grathite surfaceRussia, 119991, Moscow, Leninskie Gori 1, Bld. 62 1 pp. (accepted)We consider movement of clusters, which consist of many atoms, on graphite surface. Such clusters diffuse with anomalous high velocities \cite{1}. As far as diffusion coefficients on other surfaces are significantly smaller one can assume that properties of graphite are the reason of this effect. We model cluster diffusion using billiards with timedependent boundaries and present numerical simulations of such system. Billiard is a dynamical system which describes movement of material point in some finite area. Particle undergo elastic collisions with boundary of the billiard. In billiards with timedependent boundaries there is an effect, named Fermi acceleration, in which particle energy increase unrestrictedly \cite{2}. Fermi acceleration in billiards cause superdiffusion, notably meansquare displacement increase linearly in time\cite{3}. This result was confirmed numerically. We used Fortran. Numerical value is close to the analytical one. It was shown that dependence of diffusion coefficient on geometric and dynamic parameters conform the analytical formula. We has obtained plot of meansquare displacement of the particle. It confirm that superdiffusion occurs in such system. We use MachtaZwanzig approximation where correlation time is much smaller then time that particle remains in cell. It was shown that mean length of the trajectory of the particle in the cell has exponential distribution. Mean lengths of the trajectories of particles in the lattices with different scatterer radii are found. Numerical values are compared with the theoretical one. Thus, superdiffusion which appear as the result of Fermi acceleration can be the reason of the fast diffusion in experiments. \begin{thebibliography}{100} \bibitem{grafit} \textit{L.J.Lewis, P. Jensen, N. Combe, J.L. Barrat} Diffusion of gold nanoclusters on grathite // Phys. Rev. B., v. 61, 16084, 2000 \bibitem{bil} \textit{Loscutov A.Yu., Ryabov A.B., Krasnova A.K.,Chichigina O.A.} // Nonlinear dynamics, V.7, 2010, P. 132 \end{thebibliography}
