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Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

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Updated: Jun 12, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Hamiltonian approach for explosive percolation.

A A Moreira1, E A Oliveira, S D S Reis

  • 1Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, CE, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2010
PubMed
Summary
This summary is machine-generated.

We developed a cluster growth model connecting statistical mechanics and explosive percolation. This model achieves abrupt transitions by maintaining similar cluster sizes and prioritizing merging bonds over redundant ones.

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Last Updated: Jun 12, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Area of Science:

  • Statistical Mechanics
  • Network Science
  • Complex Systems

Background:

  • Percolation theory describes phase transitions in random networks.
  • Explosive percolation models exhibit sudden, dramatic changes in network structure.
  • Understanding abrupt transitions is crucial for modeling real-world growth and fragmentation processes.

Purpose of the Study:

  • To establish a clear link between equilibrium statistical mechanics and explosive percolation models.
  • To identify key mechanisms driving abrupt transitions in cluster growth.
  • To generalize standard percolation theory for broader applications.

Main Methods:

  • Developed a novel cluster growth process.
  • Incorporated two key conditions: approximate equality of cluster sizes and dominance of merging bonds.
  • Utilized treelike graphs for exact solutions in an extreme limit.

Main Results:

  • Demonstrated that specific cluster growth conditions lead to a first-order phase transition.
  • Showcased that maintaining similar cluster sizes and prioritizing merging bonds are sufficient for abrupt transitions.
  • Obtained an exact solution for a simplified model exhibiting a first-order transition.

Conclusions:

  • The presented cluster growth model bridges statistical mechanics and explosive percolation.
  • The findings offer a generalized framework for understanding network growth and fragmentation.
  • This mechanism has potential applications in diverse real-world network systems.