%0 Book Section %1 statphys23_0848 %A Cwilich, G.A. %A Buldyrev, S. %A Fox, P. %A Zypman, F.R. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K criticality dynamics extremal flights levy self-organized statphys23 topic-4 %T Numerical simulations of the 2-dimensional Robin-Hood model %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=848 %X The Robin Hood, or Zaitsev model1 has been successfully used to describe depinning of interfaces, friction, dislocation motion and flux creep. It is one of the simplest models which present extremal dynamics and leads to self-organized criticality2. Until now, the properties of this model have been well understood theoretically only in one dimension, and its scaling laws have been numerically verified in that case as well. It is important to extend the range of validity of these laws into higher dimensions, to find precise values for the scaling exponents, and to investigate how they depend on the details of the model (like anisotropy). The case of two dimensions is of particular importance when studying problems of surface friction3. In this work we numerically evaluate several of the important scaling exponents for the model: the avalanche size distribution, the avalanche fractal dimension, and the Levy flight-like distribution of the jumps between extremal active sites, to verify the scaling relationships in dimensions greater than one. 1) S.I. Zaitsev , Physica A 189, 411 (1992).\\ 2) M. Pacuzki, S. Maslov and P.Bak, Phys Rev. E53, 414 (1996)\\ 3) S. Buldyrev, J. Ferrante and F. Zypman Phys. Rev E (accepted)

@incollection{statphys23_0848, abstract = {The Robin Hood, or Zaitsev model[1] has been successfully used to describe depinning of interfaces, friction, dislocation motion and flux creep. It is one of the simplest models which present extremal dynamics and leads to self-organized criticality[2]. Until now, the properties of this model have been well understood theoretically only in one dimension, and its scaling laws have been numerically verified in that case as well. It is important to extend the range of validity of these laws into higher dimensions, to find precise values for the scaling exponents, and to investigate how they depend on the details of the model (like anisotropy). The case of two dimensions is of particular importance when studying problems of surface friction[3]. In this work we numerically evaluate several of the important scaling exponents for the model: the avalanche size distribution, the avalanche fractal dimension, and the Levy flight-like distribution of the jumps between extremal active sites, to verify the scaling relationships in dimensions greater than one. 1) S.I. Zaitsev , Physica A 189, 411 (1992).\\ 2) M. Pacuzki, S. Maslov and P.Bak, Phys Rev. E53, 414 (1996)\\ 3) S. Buldyrev, J. Ferrante and F. Zypman Phys. Rev E (accepted)}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Cwilich, G.A. and Buldyrev, S. and Fox, P. and Zypman, F.R.}, biburl = {https://www.bibsonomy.org/bibtex/27fd5815ad833f246f15094cdca29f7b9/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {3285445a22f638cd94934aac309449cb}, intrahash = {7fd5815ad833f246f15094cdca29f7b9}, keywords = {criticality dynamics extremal flights levy self-organized statphys23 topic-4}, month = {9-13 July}, timestamp = {2007-06-20T10:16:30.000+0200}, title = {Numerical simulations of the 2-dimensional Robin-Hood model}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=848}, year = 2007 }