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Diffusion01:21

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Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
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Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
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The plasma membrane, a critical structure in cellular biology, houses an array of transporters, or carrier proteins, interspersed within its lipid bilayer. These proteins play a crucial role in solute transport through facilitated diffusion, a form of passive diffusion that uses transporters to move the molecules across the membrane.
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Updated: Apr 15, 2026

Monitoring Spatial Segregation in Surface Colonizing Microbial Populations
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Social diffusion and global drift on networks.

Hiroki Sayama1,2, Roberta Sinatra2,3

  • 1Collective Dynamics of Complex Systems Research Group, Binghamton University, Binghamton, New York 13902, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 15, 2015
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Summary

This study models social diffusion, revealing that while global states aren't conserved, the inner product of strength and state vectors is. Positive correlations drive upward global drift, with strength assortativity slowing homogenization.

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Area of Science:

  • Mathematical modeling
  • Network science
  • Social dynamics

Background:

  • Social diffusion models often assume state conservation, unlike physical diffusion.
  • Understanding state drift in social networks is crucial for predicting collective behavior.

Purpose of the Study:

  • To analyze a mathematical model of social diffusion on weighted networks.
  • To identify conserved quantities and factors influencing global state drift.
  • To propose a method for controlling global drift in social networks.

Main Methods:

  • Developed a mathematical model for social diffusion on symmetric weighted networks.
  • Analyzed the conservation properties of the system.
  • Investigated the relationship between node states, strengths, and global drift.
  • Proposed and simulated an adaptive link weight adjustment method.

Main Results:

  • The inner product of strength and state vectors is conserved, not the global state.
  • Perfect positive correlation between node states and local strength ratios leads to upward global drift.
  • Strength assortativity negatively impacts the speed of network homogenization.

Conclusions:

  • Social diffusion processes can exhibit non-conservational global states but conserved vector inner products.
  • Adaptive link weight adjustments can steer global drift by enhancing strength-state correlations.
  • Findings have implications for designing interventions in real-world social systems.