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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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Protein Diffusion in the Membrane01:24

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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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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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Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
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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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Facilitated Transport01:19

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The chemical and physical properties of plasma membranes cause them to be selectively permeable. Since plasma membranes have both hydrophobic and hydrophilic regions, substances need to be able to transverse both regions. The hydrophobic area of membranes repels substances such as charged ions. Therefore, such substances need special membrane proteins to cross a membrane successfully. In  facilitated transport, also known as facilitated diffusion, molecules and ions travel across a...
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Updated: May 8, 2025

Finite Element Modelling of a Cellular Electric Microenvironment
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Power Levy motion. I. Diffusion.

Iddo Eliazar1

  • 1School of Chemistry, Tel Aviv University, 6997801 Tel Aviv, Israel.

Chaos (Woodbury, N.Y.)
|March 25, 2025
PubMed
Summary
This summary is machine-generated.

Power Levy motion (PLM) is introduced as a generalization of Levy motion, analogous to power Brownian motion (PBM) generalizing Brownian motion. This study constructs PLM, exploring its diffusion properties like anomalous diffusion and aging.

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Area of Science:

  • Stochastic Processes
  • Mathematical Physics
  • Statistical Mechanics

Background:

  • Brownian motion is a fundamental stochastic process, representing the scaling limit of finite-variance random walks.
  • Levy motion, a stable and symmetric Levy process, serves as the infinite-variance counterpart to Brownian motion.
  • Power Brownian motion (PBM) is a recent generalization of Brownian motion exhibiting Markovian properties and anomalous diffusion.

Purpose of the Study:

  • Introduce and construct Power Levy Motion (PLM), a novel stochastic process.
  • Explore the diffusion-related properties of PLM, extending concepts from PBM to the infinite-variance domain.
  • Lay the groundwork for further investigation of PLM from an "evolution perspective" in a companion paper.

Main Methods:

  • Construction of the Power Levy Motion (PLM) process.
  • Analysis of PLM increments and their Fourier structure.
  • Investigation of self-similarity, Hurst exponent, sub-diffusion, super-diffusion, aging, and Holder exponent through a "diffusion perspective".

Main Results:

  • PLM is successfully constructed and its emergence is explained.
  • Key diffusion characteristics of PLM, including anomalous diffusion behaviors (sub- and super-diffusion) and aging/anti-aging properties, are detailed.
  • The Fourier structure of increments and the Holder exponent of PLM are analyzed.

Conclusions:

  • Power Levy Motion (PLM) is established as a significant generalization in the realm of stochastic processes.
  • PLM offers a framework to study anomalous diffusion phenomena in infinite-variance settings.
  • This work provides a comprehensive "diffusion perspective" on PLM, paving the way for future research.