Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

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

28.7K
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...
28.7K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

72
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
72
Mean free path and Mean free time01:22

Mean free path and Mean free time

3.4K
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."
3.4K
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

2.7K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
2.7K
Carrier Transport01:21

Carrier Transport

416
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:
416
Theory of Metallic Conduction01:17

Theory of Metallic Conduction

1.3K
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,...
1.3K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Natural microcosms in ecology: fulfilling the promise of model systems?

Philosophical transactions of the Royal Society of London. Series B, Biological sciences·2026
Same author

Tracking Dynamics of Superspreading Through Contacts, Exposures, and Transmissions in Edge-Based Network Epidemics.

Bulletin of mathematical biology·2026
Same author

Linking species local trends from assemblage monitoring to global extinction risk.

Nature communications·2026
Same author

Biomedical open source software: Crucial packages and hidden heroes.

PLoS computational biology·2026
Same author

Ethical Frameworks for Conducting Social Challenge Studies.

Journal of empirical research on human research ethics : JERHRE·2026
Same author

Biodiversity Trends Show an Excess of Both Near Stasis and of Very Large Change.

Ecology letters·2026
Same journal

Poisoning the Genome: Targeted Backdoor Attacks on DNA Foundation Models.

ArXiv·2026
Same journal

Mechanistic mathematical model of the in vitro infection dynamics of Bunyamwera and Batai viruses including MOI-dependent shortening of the eclipse phase.

ArXiv·2026
Same journal

AI-Driven Lumped-Element Modeling of Human Respiratory System for Studying Voice Mechanics.

ArXiv·2026
Same journal

Beyond Algorithms: Conceptual Innovation in Medical Imaging AI.

ArXiv·2026
Same journal

Feynman Kac Reweighted Schrödinger Bridge Matching for Surface-Based Tau PET Harmonization.

ArXiv·2026
Same journal

Agentic Discovery of Non-Canonical Antimicrobial Peptides with AMPGAN v3.

ArXiv·2026
See all related articles

Related Experiment Video

Updated: Jun 15, 2025

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
00:10

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

Published on: September 5, 2019

8.2K

Stochastic diffusion using mean-field limits to approximate master equations.

Laurent Hébert-Dufresne, Matthew M Kling, Samuel F Rosenblatt

    Arxiv
    |August 26, 2024
    PubMed
    Summary
    This summary is machine-generated.

    New mean-FLAME models accurately simulate stochastic diffusion, crucial for predicting epidemic spread and species range shifts. These tools capture uncertainty in heterogeneous environments, improving forecasts and interventions.

    More Related Videos

    Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
    12:15

    Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy

    Published on: April 9, 2019

    8.7K
    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

    7.9K

    Related Experiment Videos

    Last Updated: Jun 15, 2025

    Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
    00:10

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

    Published on: September 5, 2019

    8.2K
    Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
    12:15

    Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy

    Published on: April 9, 2019

    8.7K
    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

    7.9K

    Area of Science:

    • Ecology
    • Epidemiology
    • Computational Biology

    Background:

    • Stochastic diffusion models the dispersal of epidemics and species, vital for pandemic preparedness and climate change adaptation.
    • Current deterministic models and simulations inadequately capture dispersal randomness and spatial heterogeneity.
    • Marginal areas, like species range edges or small populations, require precise modeling of low numbers, which averages miss.

    Purpose of the Study:

    • Introduce novel "mean-FLAME" models for accurate stochastic dispersion simulation.
    • Address limitations of deterministic tools in modeling heterogeneous environments and nonlinear dynamics.
    • Improve forecasting and intervention strategies for phenomena like epidemics and shifting species ranges.

    Main Methods:

    • Develop approximate master equations to track probability distributions across all possible states.
    • Incorporate mean-field approximations for highly active states.
    • Allow for exact local tracking or collapse to deterministic models based on state tracking depth.

    Main Results:

    • Demonstrate mean-FLAME models' ability to capture uncertainty in nonlinear dynamical processes.
    • Highlight the failure of deterministic tools in marginal or heterogeneous areas.
    • Showcase improved accuracy for edge-of-range species dispersal and small-population epidemics.

    Conclusions:

    • Mean-FLAME models offer a significant advancement in simulating stochastic diffusion.
    • Accurate modeling of uncertainty in marginal areas is critical for reliable predictions.
    • These tools enhance our capacity for effective pandemic preparedness and ecological management.