%0 Journal Article %1 Porto1999Distribution %A Porto, Markus %A Bunde, Armin %A Havlin, Shlomo %D 1999 %J Physica A: Statistical Mechanics and its Applications %K clusters, percolation %N 1-4 %P 96--99 %R 10.1016/s0378-4371(98)00581-0 %T Distribution of dangling ends on the incipient percolation cluster %U http://dx.doi.org/10.1016/s0378-4371(98)00581-0 %V 266 %X We study numerically and by scaling arguments the probability P(M) dM that a given dangling end of the incipient percolation cluster has a mass between M and M+dM. We find by scaling arguments that P(M) decays with a power law, P(M)M−(1+κ), with an exponent κ=dfB/df, where df and dfB are the fractal dimensions of the cluster and its backbone, respectively. Our numerical results yield κ=0.83 in d=2 and κ=0.74 in d=3 in very good agreement with theory.

@article{Porto1999Distribution, abstract = {{We study numerically and by scaling arguments the probability P(M) dM that a given dangling end of the incipient percolation cluster has a mass between M and M+dM. We find by scaling arguments that P(M) decays with a power law, P(M)M−(1+κ), with an exponent κ=dfB/df, where df and dfB are the fractal dimensions of the cluster and its backbone, respectively. Our numerical results yield κ=0.83 in d=2 and κ=0.74 in d=3 in very good agreement with theory.}}, added-at = {2019-06-10T14:53:09.000+0200}, author = {Porto, Markus and Bunde, Armin and Havlin, Shlomo}, biburl = {https://www.bibsonomy.org/bibtex/2181d053de2b6f1d97ea75322ac2ba7d8/nonancourt}, citeulike-article-id = {9174477}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/s0378-4371(98)00581-0}, day = 15, doi = {10.1016/s0378-4371(98)00581-0}, interhash = {3f62d144e73e8b015ce7572d14d2b223}, intrahash = {181d053de2b6f1d97ea75322ac2ba7d8}, issn = {03784371}, journal = {Physica A: Statistical Mechanics and its Applications}, keywords = {clusters, percolation}, month = apr, number = {1-4}, pages = {96--99}, posted-at = {2011-04-20 11:40:32}, priority = {2}, timestamp = {2019-06-10T14:53:09.000+0200}, title = {{Distribution of dangling ends on the incipient percolation cluster}}, url = {http://dx.doi.org/10.1016/s0378-4371(98)00581-0}, volume = 266, year = 1999 }