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Related Concept Videos

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

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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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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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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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Theories of Dissolution: Diffusion Layer Model01:15

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Dissolution, the process by which drug particles dissolve in a solvent, is explained by the diffusion layer model, a theoretical framework that simulates the absorption of oral drugs and allows us to analyze experimental data.
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Electrostatic Boundary Conditions01:16

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Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
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Related Experiment Video

Updated: May 7, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Everlasting effect of initial conditions on single-file diffusion.

N Leibovich1, E Barkai

  • 1Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 16, 2013
PubMed
Summary
This summary is machine-generated.

Initial conditions significantly impact tagged particle dynamics in single-file systems. The system

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Area of Science:

  • Statistical Mechanics
  • Soft Matter Physics
  • Complex Systems

Background:

  • Single-file systems, characterized by one-dimensional transport where particles cannot overtake each other, exhibit unique dynamic behaviors.
  • Understanding the influence of initial particle configurations is crucial for predicting system evolution and transport properties.
  • The Einstein relation typically describes equilibrium dynamics, but its applicability in non-equilibrium or memory-dependent systems requires investigation.

Purpose of the Study:

  • To investigate how different initial conditions affect the dynamics of a tagged particle in a one-dimensional single-file system.
  • To analyze the impact of initial particle arrangements on transport coefficients and the validity of the Einstein relation.
  • To explore the long-time behavior and memory effects within the single-file model.

Main Methods:

  • Simulation of a tagged particle interacting with point Brownian particles with hard-core potentials in an infinite 1D channel.
  • Comparison of two distinct initial conditions: equal inter-particle spacing and uniform density distribution.
  • Analysis of mean-square displacement, correlation functions, and transport coefficients, including diffusivity, using methods like the Jepsen line.

Main Results:

  • Distinct initial conditions lead to measurable differences in the mean-square displacement and correlation functions of the tagged particle.
  • The violation of the Einstein relation is observed and shown to be dependent on the specific initial state and averaging method (time vs. ensemble).
  • Transport coefficients, such as diffusivity, are demonstrated to be state-dependent, influenced by the initial configuration.

Conclusions:

  • Initial conditions play a deterministic role in the long-time dynamics of single-file systems, imparting a form of 'system memory'.
  • Unlike equilibrium thermal systems, single-file models do not necessarily forget their initial state, highlighting non-ergodic behavior.
  • The study underscores the importance of considering initial state preparation when characterizing transport phenomena in confined, interacting particle systems.