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Related Concept Videos

Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write numerous physical laws...
Cyclic Processes And Isolated Systems01:19

Cyclic Processes And Isolated Systems

A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
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Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

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Multicompartment Models: Overview

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Related Experiment Video

Updated: May 13, 2026

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Avoiding a spanning cluster in percolation models.

Y S Cho1, S Hwang, H J Herrmann

  • 1Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.

Science (New York, N.Y.)
|March 9, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a new explosive percolation (EP) model to understand abrupt phase transitions in systems with suppressive bias. The research clarifies the transition order, finding it depends on spatial dimension and control parameters.

Related Experiment Videos

Last Updated: May 13, 2026

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Systems under suppressive bias can exhibit abrupt phase transitions, similar to epidemic spread.
  • The explosive percolation (EP) model was recently developed to study these phenomena.
  • A unified framework for the EP transition order across different dimensions is lacking.

Purpose of the Study:

  • To introduce a novel stochastic model for explosive percolation.
  • To clarify the order of the explosive percolation transition in a unified framework.
  • To investigate the role of spatial dimension and control parameters in transition dynamics.

Main Methods:

  • Development of a stochastic model with dynamics designed to prevent spanning cluster formation via competitive selection.
  • Application of heuristic arguments to analyze system behavior in the thermodynamic limit.
  • Examination of transition order based on spatial dimension (d) and upper critical dimension (d(c)).

Main Results:

  • The proposed model exhibits a transition order dependent on the spatial dimension and control parameters.
  • For dimensions d < d(c), the EP transition can be either continuous or discontinuous.
  • For dimensions d ≥ d(c), the EP transition is always continuous.

Conclusions:

  • The study provides a unified framework for understanding the order of explosive percolation transitions.
  • The findings highlight the critical role of spatial dimensionality in determining transition behavior.
  • The model offers new insights into abrupt phase transitions in complex systems.