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Related Concept Videos

Distribution of Molecular Speeds01:27

Distribution of Molecular Speeds

The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
Carrier Transport01:21

Carrier Transport

The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
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Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

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...
Protein Diffusion in the Membrane01:24

Protein Diffusion in the Membrane

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...
Drift Velocity01:19

Drift Velocity

The high speed of electrical signals results from the fact that the force between charges acts rapidly at a distance. Thus, when a free charge is forced into a wire, the incoming charge pushes other charges ahead due to the repulsive force between like charges. These moving charges move the charges farther down the line. The density of charge in a system cannot easily be increased, so the signal is passed on rapidly. The resulting electrical shock wave moves through the system at nearly the...
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Mean free path and Mean free time

Consider the gas molecules in a cylinder. They move in a random motion as they collide with each other and change speed and direction. The average of all the path lengths between collisions is known as the "mean free path."

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Updated: Jun 14, 2026

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

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Published on: September 5, 2019

Velocity correlations and mobility in single-file diffusion.

Ashwani K Tripathi1, Deepak Kumar

  • 1School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

We analyzed velocity correlations for a single particle within a dense, one-dimensional system. The correlation function decays quickly, becomes negative, and shows a power-law decay at long times, influenced by particle density.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Many-Body Systems

Background:

  • Understanding particle dynamics is crucial in statistical mechanics.
  • Velocity correlations reveal fundamental transport properties in interacting systems.
  • One-dimensional systems exhibit unique collective behaviors.

Purpose of the Study:

  • To exactly evaluate the two-time velocity correlation function for a tagged particle.
  • To investigate the influence of particle density on correlation decay.
  • To analyze the system's mobility under external forces.

Main Methods:

  • Exact evaluation of the two-time velocity correlation function.
  • Ensemble averaging over initial conditions.
  • Analysis of system response to constant external forces.

Main Results:

  • The velocity correlation function decays rapidly and becomes negative.
  • Higher particle density accelerates the decay rate.
  • A universal power-law decay (-t^{-3/2}) is observed at large times for all densities.

Conclusions:

  • The study provides an exact solution for velocity correlations in a driven 1D system.
  • Density plays a key role in the dynamics of velocity correlations.
  • The findings offer insights into transport phenomena and fluctuations in interacting particle systems.