Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Modeling with Differential Equations

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

Poisson's And Laplace's Equation

Poisson's And Laplace's Equation

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.

Poisson Probability Distribution

Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...

Diffusion

Diffusion

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...

Diffusion

Diffusion

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...

Exponential Equations for Modeling Growth

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is the relative...

You might also read

Related Articles

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

Sort by

Same author

Age-related Eye Disease Studies Supplements and Genetic Risk Score Are Crucial Determinants of Intestinal Microbial Alterations in Advanced Age-Related Macular Degeneration.

Ophthalmology science·2025

Same author

A diet rich in fermentable fiber promotes robust changes in the intestinal microbiota, mitigates intestinal permeability, and attenuates autoimmune uveitis.

Scientific reports·2023

Same author

Swept-source optical coherence tomography objective composite activity score for uveitis.

Acta ophthalmologica·2021

Same author

Learning Coarse-Grained Potentials for Binary Fluids.

Journal of chemical information and modeling·2020

Same author

CRNT4SBML: a Python package for the detection of bistability in biochemical reaction networks.

Bioinformatics (Oxford, England)·2020

Same author

BET bromodomain inhibition blocks the function of a critical AR-independent master regulator network in lethal prostate cancer.

Oncogene·2019

Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

See all related articles

Search research articles

Related Experiment Video

Updated: May 30, 2026

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

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

Published on: September 26, 2016

Multinomial diffusion equation.

Ariel Balter¹, Alexandre M Tartakovsky

¹Pacific Northwest National Laboratory, Richland, Washington 99352, USA. ariel.belter@pnl.gov

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 30, 2011

Summary

This summary is machine-generated.

A new microscopic diffusion model accurately captures particle-level fluctuations, matching Langevin dynamics. This model proves superior to the classical stochastic diffusion equation (SDE) in simulations.

More Related Videos

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

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

Published on: September 5, 2019

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

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

Published on: April 9, 2019

Related Experiment Videos

Last Updated: May 30, 2026

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

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

Published on: September 26, 2016

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

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

Published on: September 5, 2019

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

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

Published on: April 9, 2019

Area of Science:

Physics
Physical Chemistry
Computational Science

Background:

Classical diffusion models assume continuous concentrations, neglecting particle-level behavior.
Stochastic diffusion equations (SDEs) are widely used but may fail at small scales.
Understanding diffusion at the particle level is crucial for various scientific disciplines.

Purpose of the Study:

Introduce a novel microscopic model for diffusion.
Validate the model's equivalence to classical SDEs in the macroscopic limit.
Compare the new model's performance against SDEs and Langevin dynamics.

Main Methods:

Developed a discrete particle-based diffusion model.
Derived the macroscopic limit of the model, showing equivalence to SDEs.
Performed numerical simulations comparing the new model, SDE, and Langevin dynamics.

Main Results:

The microscopic model accurately reproduces diffusion-induced fluctuations at the particle scale.
In the limit of large particle numbers (N→∞), the model converges to the classical SDE.
Simulations demonstrate the new model's superior accuracy in capturing ensemble statistics compared to the classical SDE.

Conclusions:

The proposed microscopic diffusion model offers a more accurate representation of diffusion at small scales.
This model bridges the gap between discrete particle behavior and continuous SDEs.
The findings suggest a revised approach for simulating diffusion processes where particle discreteness is significant.