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Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
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Updated: Jun 14, 2026

Determination of Aggregate Surface Morphology at the Interfacial Transition Zone (ITZ)
08:59

Determination of Aggregate Surface Morphology at the Interfacial Transition Zone (ITZ)

Published on: December 16, 2019

Cluster aggregation model for discontinuous percolation transitions.

Y S Cho1, B Kahng, D Kim

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

This study explores how discouraging the growth of large clusters in Erdos-Rényi (ER) networks using specific connection rules can lead to a discontinuous percolation transition (PT). This finding offers insights into discontinuous transitions in nonequilibrium systems.

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Area of Science:

  • Statistical physics
  • Network science
  • Complex systems

Background:

  • Erdos-Rényi (ER) networks are fundamental models for irreversible kinetic aggregation.
  • ER processes are often described by rate equations with connection kernels, typically proportional to the product of merging cluster sizes (Kij ~ ij).

Purpose of the Study:

  • To investigate the impact of sublinear connection kernels (Kij ~ (ij)^omega, 0 <= omega < 1/2) on the percolation transition (PT) in ER networks.
  • To determine if discouraging the growth of the giant cluster can induce a discontinuous PT.

Main Methods:

  • Modeling the evolution of cluster-size distribution using rate equations.
  • Analyzing the effect of sublinear connection kernels on network aggregation dynamics.
  • Investigating the conditions under which a discontinuous PT emerges.

Main Results:

  • A sublinear connection kernel (Kij ~ (ij)^omega with 0 <= omega < 1/2) discourages the development of the giant cluster.
  • This specific kernel modification leads to a discontinuous percolation transition (PT).
  • Discontinuous PT can occur even with appropriate initial conditions.

Conclusions:

  • The study demonstrates that modifying the connection kernel in ER network evolution can alter the nature of the percolation transition.
  • The findings suggest a mechanism for discontinuous PT in nonequilibrium kinetic systems by controlling the growth of large clusters.