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Related Concept Videos

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...
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.
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
Theory of Metallic Conduction01:17

Theory of Metallic Conduction

The conduction of free electrons inside a conductor is best described by quantum mechanics. However, a classical model makes predictions close to the results of quantum mechanics. It is called the theory of metallic conduction.
In this theory, Newton's second law of motion is used to determine the acceleration of an electron in the presence of an applied electric field. Then, its velocity is expressed via this acceleration.
An electron moves through the crystal, containing positive ions,...
Genetic Drift03:33

Genetic Drift

Natural selection—probably the most well-known evolutionary mechanism—increases the prevalence of traits that enhance survival and reproduction. However, evolution does not merely propagate favorable traits, nor does it always benefit populations.Life is not fair. A deer grazing contentedly in a field can have her meal cut tragically short by a bolt of lightning. If the doomed doe is one of only three in the population, 1/3 of the population’s gene pool is lost. Random events like this can...
Regression Toward the Mean01:52

Regression Toward the Mean

Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when researchers try to extrapolate results...
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...

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Related Experiment Video

Updated: Jun 6, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Diffusion about the mean drift location in a biased random walk.

Edward A Codling1, Rachel N Bearon, Graeme J Thorn

  • 1Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom. ecodling@essex.ac.uk

Ecology
|November 10, 2010
PubMed
Summary

This study explores biased random walks, modeling animal and cell movement. Diffusion patterns around the average position are typically anisotropic, depending on movement speed and direction choices.

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Related Experiment Videos

Last Updated: Jun 6, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

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Published on: September 26, 2016

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Area of Science:

  • Mathematical modeling
  • Biophysics
  • Animal behavior

Background:

  • Random walks model diverse movements like cell chemotaxis and animal migration.
  • Diffusion in biased random walks depends on angular distribution moments.

Purpose of the Study:

  • Derive diffusion coefficients for 2D biased random walks.
  • Analyze the impact of angular distributions and movement speed on diffusion.
  • Generate long-time spatial probability distributions.

Main Methods:

  • Investigated biased random walks with various angular distributions.
  • Derived analytical expressions for diffusion coefficients (fixed/variable speed).
  • Utilized computer simulations to validate theoretical findings.

Main Results:

  • Diffusion is typically anisotropic around the mean drift position.
  • Derived probability density functions for long-time spatial distributions.
  • Demonstrated dependence of diffusion on angular distribution and speed.

Conclusions:

  • Theoretical and simulation results show anisotropic diffusion in biased random walks.
  • Findings are relevant to understanding microorganism swimming and broader animal movement patterns.
  • Provides a framework for generalizing random walk models to various biological systems.