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Diffusion01:21

Diffusion

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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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Diffusion01:12

Diffusion

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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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Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models00:57

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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...
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Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

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Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
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Passive Diffusion: Overview and Kinetics01:17

Passive Diffusion: Overview and Kinetics

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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.
When administered orally, drugs establish a substantial concentration gradient between the gastrointestinal (GI) lumen and the bloodstream, expediting...
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Reynolds Transport Theorem01:24

Reynolds Transport Theorem

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The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit...
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  1. Home
  2. Diffusion Properties Of Small-scale Fractional Transport Models.
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  2. Diffusion Properties Of Small-scale Fractional Transport Models.

Related Experiment Video

The Diffusion of Passive Tracers in Laminar Shear Flow
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Diffusion Properties of Small-Scale Fractional Transport Models.

Paolo Cifani1, Franco Flandoli1

  • 1Department of Mathematics, Scuola Normale Superiore, Piazza dei Cavalieri, 7, Pisa, Italy.

Journal of Statistical Physics
|October 31, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

Stochastic transport in complex velocity fields was studied. Mixing spatial structures with persistent Fractional Gaussian Noises (FGN) result in Brownian diffusion for passive particles.

Keywords:
Fractional Brownian MotionHurst ExponentOrnstein-UhlenbeckStochastic Fluid ParticlesStochastic Transport

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Area of Science:

  • Physics
  • Applied Mathematics
  • Complex Systems

Background:

  • Stochastic transport phenomena are crucial in various scientific fields.
  • Understanding particle dynamics in complex, turbulent-like velocity fields remains a challenge.
  • Fractional Gaussian Noises (FGN) offer a way to model persistent random processes.

Purpose of the Study:

  • To numerically investigate stochastic transport in velocity fields driven by FGN.
  • To develop a unified model for comparing different space-time structures in stochastic transport.
  • To analyze the influence of FGN persistence on particle diffusion.

Main Methods:

  • Numerical investigation of stochastic transport.
  • Modeling velocity fields using superposition of divergence-free vector fields activated by FGN.
  • Utilizing an Ornstein-Uhlenbeck approximation and taking the white noise limit for model comparison.
  • Analyzing Fourier components to understand the role of spatial structures and FGN memory.
  • Main Results:

    • A model was established to compare diverse space-time structures on equal footing by normalizing kinetic energy.
    • A key finding is that mixing spatial structures combined with persistent FGN lead to classical Brownian diffusion.
    • The diffusion coefficient is determined, and the memory of FGN is shown to be lost within the velocity field's spatial complexity.

    Conclusions:

    • The study provides a framework for analyzing stochastic transport in complex velocity fields.
    • It demonstrates that spatial complexity can effectively homogenize persistent temporal correlations, leading to simple diffusion.
    • This research contributes to understanding anomalous diffusion and the emergence of Brownian motion from complex dynamics.