%0 Journal Article %1 Cho2010Finitesize %A Cho, Y. S. %A Kim, S. %A Noh, J. D. %A Kahng, B. %A Kim, D. %D 2010 %J Physical Review E %K explosive-percolation finite-size %N 4 %R 10.1103/PhysRevE.82.042102 %T Finite-size scaling theory for explosive percolation transitions %U http://dx.doi.org/10.1103/PhysRevE.82.042102 %V 82 %X When an explosion takes place, energy is accumulated beforehand and released during the explosion. Here we study an explosive percolation transition and find that such accumulation and release processes proceed in a self-organized manner. The cluster size distribution exhibits a hump, composed of excess large-size clusters to those in the critical state, regarded as energy, before a percolation threshold. The energy is released by cluster merging during the explosion progress. Interestingly, this release proceeds to make remaining finite clusters organize a power-law behavior in their size distribution. We characterize such self-organizing dynamics by applying a finite-size scaling theory for the Erd\Hos and Rényi model based on the Achlioptas process. This study will help in understanding the origin of discontinuous transitions occurring in other non-equilibrium kinetic systems.

@article{Cho2010Finitesize, abstract = {When an explosion takes place, energy is accumulated beforehand and released during the explosion. Here we study an explosive percolation transition and find that such accumulation and release processes proceed in a self-organized manner. The cluster size distribution exhibits a hump, composed of excess large-size clusters to those in the critical state, regarded as energy, before a percolation threshold. The energy is released by cluster merging during the explosion progress. Interestingly, this release proceeds to make remaining finite clusters organize a power-law behavior in their size distribution. We characterize such self-organizing dynamics by applying a finite-size scaling theory for the Erd\H{o}s and R\'enyi model based on the Achlioptas process. This study will help in understanding the origin of discontinuous transitions occurring in other non-equilibrium kinetic systems.}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Cho, Y. S. and Kim, S. and Noh, J. D. and Kahng, B. and Kim, D.}, biburl = {https://www.bibsonomy.org/bibtex/2244fbef3f0c7cb8fd2634481bb2ac0e3/nonancourt}, citeulike-article-id = {7346885}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.82.042102}, citeulike-linkout-1 = {http://arxiv.org/abs/1006.2194}, citeulike-linkout-2 = {http://arxiv.org/pdf/1006.2194}, day = 11, doi = {10.1103/PhysRevE.82.042102}, eprint = {1006.2194}, interhash = {f68318b31feddca5b02f3905caff6283}, intrahash = {244fbef3f0c7cb8fd2634481bb2ac0e3}, issn = {1550-2376}, journal = {Physical Review E}, keywords = {explosive-percolation finite-size}, month = oct, number = 4, posted-at = {2010-06-21 15:56:19}, priority = {2}, timestamp = {2019-08-23T11:00:01.000+0200}, title = {{Finite-size scaling theory for explosive percolation transitions}}, url = {http://dx.doi.org/10.1103/PhysRevE.82.042102}, volume = 82, year = 2010 }