Explosive Continuum Percolation

Complex networks are pervasive in all corners of the world,and the rapid development of high performance computers and the massive collection of data have led to rapid theoretical and empirical developments in complex networks.The intersection of multiple disciplines has led to the theoretical study of complex networks,The structural properties and dynamical characteristics of complex networks continue to be studied in depth.In this paper,we focus on the dynamical evolution of complex networks,especially the study of phase transition and critical phenomena.In this paper,the kinetic processes of complex networks,phase transitions and critical phenomena are discussed through the study of percolation models.In this paper,the generalized Achlioptas process(GAP)of continuum percolation in the two-dimensional plane is proposed,i.e.explosive continuum percolation.This process is a generalization of the continuum percolation process.In GAP,we propose eight models of continuum percolation in the two-dimensional plane based on sum rule,product rule,selection tendency,and duality.In GAP,we investigate the kinetic properties and phase transition processes by studying the sizes of the largest and second largest clusters.By finite scale scalar analysis,we found that the phase transitions of the eight studied percolation models are continuous,their critical indices are different,and their behavior is different from that on a two-dimensional lattice.That is,the universal class of continuous percolation of GAP in the two-dimensional plane depends on the specific model.