Percolation theory examines the emergence of connected clusters in systems composed of randomly occupied sites or bonds, making it an invaluable framework for understanding phase transitions in ...

Bootstrap percolation, a model of irreversible activation on graphs, has emerged as a pivotal area within graph theory and statistical mechanics. In this process, nodes (or vertices) on a network are ...

Bootstrap percolation models have been extensively studied during the two past decades. In this article, we study the following "anisotropic" bootstrap percolation model: the neighborhood of a point ...

(a, d, g) The percolation transition processes during the morning peak, off-peak, and evening peak periods for the URT system. (b, c) The network phase transitions occurring during the morning peak ...

Different carbon nanoparticle allotropes, be it graphite nanoplatelets or carbon nanotubes, are promising candidates as filler materials for polymer composites. However, traditional composites ...

The jigsaw percolation process on graphs was introduced by Brummitt et al. (2015) as a model of collaborative solutions of puzzles in social networks. Percolation in this process may be viewed as the ...