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In the usual Achlioptas processes the smallest clusters of a few randomly chosen ones are selected to merge together at each step. The resulting aggregation process leads to the delayed birth of a giant cluster and the so-called explosive percolation transition showing a set of anomalous features. We explore a process with the opposite selection rule, in which the biggest clusters of the randomly chosen ones merge together. We develop a theory of this kind of percolation based on the Smoluchowsky equation, find the percolation threshold, and describe the scaling properties of this continuous transition, namely, the critical exponents and amplitudes, and scaling functions. We show that, qualitatively, this transition is similar to the ordinary percolation one, though occurring in less connected systems.
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http://dx.doi.org/10.1103/PhysRevE.91.042130 | DOI Listing |
Phys Rev Lett
January 2025
The University of Tokyo, Research Center for Advanced Science and Technology, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan.
Gels and attractive glasses-both dynamically arrested states formed through short-range attraction-are commonly found in a range of soft matter systems, including colloids, emulsions, proteins, and wet granular materials. Previous studies have revealed intriguing similarities and distinctions in their structural, dynamic, vibrational, and mechanical properties. However, the microstructural mechanisms underlying the gel-to-glass transition remain elusive.
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January 2025
School of Mechanics and Engineering, Liaoning Technical University, Fuxin, 123000, China.
Uniaxial compression experiments were conducted on coal rock utilizing a computed tomography (CT) scanning system for real-time monitoring to explain the issue of gas volume significantly exceeding reservoir capacity during coal and gas outbursts. A percolation factor a which can make a significant contribution to the research on premonitory information of gas outbursts is introduced to determine whether percolation occurs in coal rock, and supports the outburst percolation theory. It was found that percolation probability and correlation length increase with greater porosity, and that the number of pore clusters decreases as porosity increases.
View Article and Find Full Text PDFPhys Rev E
July 2024
School of Physics, Hefei University of Technology, Hefei, Anhui 230009, China.
By introducing a simple competition mechanism for bond insertion in random graphs, explosive percolation exhibits a sharp phase transition with rich critical phenomena. We investigate high-order connectivity in explosive percolation using an event-based ensemble, focusing on biconnected clusters, where any two sites are connected by at least two independent paths. Our numerical analysis confirms that explosive percolation with different intracluster bond competition rules shares the same percolation threshold and universality, with biconnected clusters percolating simultaneously with simply connected clusters.
View Article and Find Full Text PDFSci Adv
May 2024
School of Earth Sciences, University of Bristol, Bristol, UK.
Large-scale, explosive volcanic eruptions are one of the Earth's most hazardous natural phenomena. We demonstrate that their size, frequency, and composition can be explained by processes in long-lived, high-crystallinity source reservoirs that control the episodic creation of large volumes of eruptible silicic magma and its delivery to the subvolcanic chamber where it is stored before eruption. Melt percolates upward through the reservoir and accumulates a large volume of low-crystallinity silicic magma which remains trapped until buoyancy causes magma-driven fractures to propagate into the overlying crust, allowing rapid magma transfer from the reservoir into the chamber.
View Article and Find Full Text PDFPhys Rev E
September 2023
Deep Dynamics, Centre for Human and Machine Intelligence, Frankfurt School of Finance and Management, Frankfurt am Main 60322, Germany.
We study explosive percolation processes on random graphs for the so-called product rule (PR) and sum rule (SR), in which M candidate edges are randomly selected from all possible ones at each time step, and the edge with the smallest product or sum of the sizes of the two components that would be joined by the edge is added to the graph, while all other M-1 candidate edges are being discarded. These two rules are prototypical "explosive" percolation rules, which exhibit an extremely abrupt yet continuous phase transition in the thermodynamic limit. Recently, it has been demonstrated that PR and SR belong to the same universality class for two competing edges, i.
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