Related Experiment Video
Updated: May 13, 2026

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
Published on: February 25, 2015
Critical phenomena in heterogeneous k-core percolation
Davide Cellai1, Aonghus Lawlor, Kenneth A Dawson
1MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland.
Abstract:
k-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analyzing the resilience of a network under random damage, an extension of this model is introduced, allowing different vertices to have their own degree of resilience. This extension is named heterogeneous k-core percolation and it is characterized by several interesting critical phenomena. Here we analytically investigate binary mixtures in a wide class of configuration model networks and categorize the different critical phenomena which may occur. We observe the presence of critical and tricritical points and give a general criterion for the occurrence of a tricritical point. The calculated critical exponents show cases in which the model belongs to the same universality class of facilitated spin models studied in the context of the glass transition.
Related Concept Videos
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Cyclic Processes And Isolated Systems
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each path...
Heterogeneous Catalysis
Phase Transitions: Vaporization and Condensation
Ostwald’s Dilution Law
Colloidal precipitates

