Related Experiment Video
Updated: May 31, 2026

Research and Development of High-performance Explosives
Published on: February 20, 2016
Explosive percolation is continuous
1Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, UK. riordan@maths.ox.ac.uk
Abstract:
"Explosive percolation" is said to occur in an evolving network when a macroscopic connected component emerges in a number of steps that is much smaller than the system size. Recent predictions based on simulations suggested that certain Achlioptas processes (much-studied local modifications of the classical mean-field growth model of Erdős and Rényi) exhibit this phenomenon, undergoing a phase transition that is discontinuous in the scaling limit. We show that, in fact, all Achlioptas processes have continuous phase transitions, although related models in which the number of nodes sampled may grow with the network size can indeed exhibit explosive percolation.
Related Concept Videos
Properties of Continuous Functions
Continuity Equation
The mass flow rate is expressed as:
Continuity Equation
Continuity of a Function
Spontaneity
Continuous Charge Distributions
The electric charge can also be subjected to an analogical...

