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Related Concept Videos

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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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...
Assessment of Diffusion and Perfusion01:17

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Understanding and evaluating diffusion and perfusion is critical in assessing a patient's respiratory and circulatory health. These processes play key roles in maintaining the body's internal environment, ensuring that tissues receive adequate oxygen while waste products are efficiently removed.
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Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
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Proteins show rotational as well as lateral diffusion across the membrane. The lateral diffusion of proteins was confirmed through the cell fusion experiment where mouse and human cells were fused, resulting in hybrid cells. When the human and mouse cells fused, the specific membrane proteins on human and mouse cells were marked with the red and green-fluorescent markers, respectively. Initially, the red and green fluorescence was located on the respective hemisphere of the cell. As time...
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Updated: May 11, 2026

Fluorescence Recovery after Merging a Droplet to Measure the Two-dimensional Diffusion of a Phospholipid Monolayer
07:54

Fluorescence Recovery after Merging a Droplet to Measure the Two-dimensional Diffusion of a Phospholipid Monolayer

Published on: October 15, 2015

FRACTIONAL PEARSON DIFFUSIONS.

Nikolai N Leonenko1, Mark M Meerschaert, Alla Sikorskii

  • 1Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4YH, UK, LeonenkoN@cardiff.ac.uk , URL : http://www.cardiff.ac.uk/maths/contactsandpeople/profiles/leonenkoN.html.

Journal of Mathematical Analysis and Applications
|April 30, 2013
PubMed
Summary
This summary is machine-generated.

This study presents explicit strong and stochastic solutions for fractional Pearson diffusions, which model sub-diffusive phenomena. These findings advance the understanding and application of diffusion modeling in complex systems.

Keywords:
Mittag-Leffler functionPearson diffusioneigenfunction expansionfractional derivativehitting timestable process

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Last Updated: May 11, 2026

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Area of Science:

  • Mathematical Physics
  • Stochastic Processes
  • Fractional Calculus

Background:

  • Pearson diffusions model particle movement using polynomial-coefficient diffusion equations.
  • Fractional Pearson diffusions extend these models to sub-diffusive phenomena, crucial for understanding particle sticking and trapping.
  • Existing models often lack explicit solutions for these complex fractional diffusion processes.

Purpose of the Study:

  • To derive explicit strong solutions for fractional Pearson diffusions.
  • To present novel stochastic solutions for these diffusion processes.
  • To provide advanced analytical tools for modeling sub-diffusion.

Main Methods:

  • Spectral methods were employed to obtain explicit strong solutions.
  • A non-Markovian inverse stable time change was utilized to derive stochastic solutions.
  • The study focuses on time-fractional diffusion equations with polynomial coefficients.

Main Results:

  • Explicit strong solutions for fractional Pearson diffusions are provided.
  • Stochastic solutions are successfully derived using advanced time-change techniques.
  • The paper demonstrates the utility of spectral and stochastic methods in this domain.

Conclusions:

  • The study successfully provides explicit and stochastic solutions for fractional Pearson diffusions.
  • These solutions offer new analytical capabilities for modeling sub-diffusive behaviors.
  • The findings contribute to the theoretical framework of fractional diffusion processes.