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Related Concept Videos

Diffusion01:21

Diffusion

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...
Diffusion01:12

Diffusion

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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Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
Conservation of Mass in Moving, Nondeforming Control Volume01:14

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Stormwater detention basins are essential in managing runoff during heavy rainfall, particularly in urban areas where impervious surfaces increase the risk of flooding. Understanding the conservation of mass in these systems allows engineers to optimize basin performance, balancing inflow, outflow, and water storage.
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Passive Diffusion: Overview and Kinetics01:17

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Passive diffusion is a critical process that allows small lipophilic drugs to cross the cell membrane along a concentration gradient. This mechanism's efficiency depends on four primary factors: the membrane's surface area, the drug's lipid-water partition coefficient, the concentration gradient, and the membrane's thickness.
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Modeling with Differential Equations01:25

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Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

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Updated: Jun 21, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Conserved-mass aggregation model with mass-dependent diffusion rate on complex networks.

Sungchul Kwon1, Dong-Jin Lee, Yup Kim

  • 1Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 8, 2009
PubMed
Summary
This summary is machine-generated.

Condensation phenomena in conserved-mass aggregation (CA) models occur on scale-free networks (SFNs) due to mass-dependent diffusion. Network structure significantly influences these condensation behaviors, unlike on regular lattices.

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Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • Conserved-mass aggregation (CA) models are crucial for understanding particle systems.
  • Previous studies showed no condensation on regular lattices.
  • Scale-free networks (SFNs) exhibit unique properties due to their heterogeneous degree distributions.

Purpose of the Study:

  • Investigate condensation phenomena in CA models with mass-dependent diffusion on SFNs.
  • Analyze the influence of diffusion rate (alpha) and network structure (gamma) on condensation.
  • Compare condensation behavior on SFNs with that on regular lattices.

Main Methods:

  • Mean-field approximation to analyze condensation phase transitions.
  • Mathematical derivation of critical exponents and phase boundaries.
  • Numerical simulations to validate theoretical predictions.

Main Results:

  • Condensation phenomena on SFNs depend critically on diffusion rate (alpha) and network degree distribution exponent (gamma).
  • A crossover exponent, alpha_c = (gamma-2)/(gamma-1), determines transitions.
  • For alpha < alpha_c, network structure dictates condensation, with different behaviors for gamma > 3 and gamma <= 3.

Conclusions:

  • Scale-free network structure induces diverse condensation phenomena in CA models, contrasting with regular lattices.
  • The interplay between mass diffusion and network topology is key to understanding emergent behaviors.
  • Findings provide insights into aggregation processes in complex interconnected systems.