IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2024-03-29T14:49:17ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2012-02-27T09:29:04Z2012-02-27T09:29:04Zhttp://eprints.imtlucca.it/id/eprint/1187This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11872012-02-27T09:29:04ZFixed scale transformation for fracture growth processes governed by vectorial fieldsWe use the Fixed Scale Transformation (FST) approach to study the problem of fractal growth in fracture patterns generated by using the Born Model. The application of the method to this model is very complex because of the vectorial nature of the system considered. In particular, the implementation of this scheme requires a careful choice of the fracture path and the identification of the appropriate way to take into account screening effects. The good agreements of our results with computer simulations shows the validity and flexibility of the FST method which represents a general theoretical approach for the study of fractal patterns evolution.Guido Caldarelliguido.caldarelli@imtlucca.itAlessandro VespignaniLuciano Pietronero2012-02-27T09:19:37Z2012-02-27T09:19:37Zhttp://eprints.imtlucca.it/id/eprint/1186This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11862012-02-27T09:19:37ZFixed scale transformation approach for born model of fracturesWe use the Fixed Scale Transformation theoretical approach to study the problem of fractal growth in fractures generated by using the Born Model. In this case the application of the method is more complex because of the vectorial nature of the model considered. In particular, one needs a careful choice of the lattice path integral for the fracture evolution and the identification of the appropriate way to take effectively into account screening effects. The good agreement of our results with computer simulations shows the validity and flexibility of the FST method in the study of fractal patterns evolution.Guido Caldarelliguido.caldarelli@imtlucca.itAlessandro Vespignani2012-02-27T09:08:26Z2012-02-27T09:08:26Zhttp://eprints.imtlucca.it/id/eprint/1185This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11852012-02-27T09:08:26ZSelf-organized critical scaling at surfacesAt dissipative boundaries, models of self-organized criticality show peculiar scalings, different from the bulk ones, in the distributions characterizing avalanches. For Abelian models with Dirichlet boundary conditions, evidence of this is obtained by a mean field approach to semi-infinite sandpiles, and by numerical simulations in two and three dimensions. On the other hand, within the mean field description, closed Neumann conditions restore bulk scaling exponents also at the border. Numerical results are consistent with this property also at finite d.Attilio StellaClaudio TebaldiGuido Caldarelliguido.caldarelli@imtlucca.it