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

Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

470
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
470
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

465
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
465
Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models00:57

Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models

175
Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
175
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

1.9K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
1.9K
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

959
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
959
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.6K
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.
3.6K

You might also read

Related Articles

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

Sort by
Same author

Ferrostatin-1 inhibits ferroptosis and alleviates organophosphate nerve agent-induced cognitive deficits by regulating ACSL4/GPX4 and NCOA4/FTH1 pathways in the hippocampus of guinea pigs.

Ecotoxicology and environmental safety·2026
Same author

Association between the advanced lung cancer inflammation index and all-cause mortality in critically ill patients with atrial fibrillation.

Medicine·2026
Same author

Pathogen spectrum of pulmonary infections in kidney transplant recipients and the diagnostic value of mNGS: a sputum and BALF study based on clinical decision-making.

Frontiers in cellular and infection microbiology·2026
Same author

Expert-Guided Cross-View Fusion With Self-Derived Lesion Proposals for Multi-View Diabetic Retinopathy Grading.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same author

3D Single-Virus Tracking: Advances in Methodology and Labeling Strategies Towards Probing the Virus-Epithelium Interaction.

Viruses·2026
Same author

Equilibrium-distribution-function-based mesoscopic finite-difference methods for partial differential equations: Modeling and analysis.

Physical review. E·2026
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles

Related Experiment Video

Updated: Oct 23, 2025

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates
10:33

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

Published on: February 23, 2018

25.6K

Multiple-relaxation-time lattice Boltzmann model-based four-level finite-difference scheme for one-dimensional

Yuxin Lin1, Ning Hong2, Baochang Shi1,3

  • 1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.

Physical Review. E
|August 20, 2021
PubMed
Summary
This summary is machine-generated.

A new multiple-relaxation-time lattice Boltzmann (MRT-LB) model for diffusion equations was developed. This model yields an unconditionally stable, sixth-order accurate finite-difference scheme, confirmed by numerical simulations.

More Related Videos

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

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

Published on: September 5, 2019

8.4K
The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

8.8K

Related Experiment Videos

Last Updated: Oct 23, 2025

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates
10:33

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

Published on: February 23, 2018

25.6K
Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

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

Published on: September 5, 2019

8.4K
The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

8.8K

Area of Science:

  • Computational physics
  • Numerical analysis

Background:

  • The one-dimensional diffusion equation is a fundamental model in various scientific fields.
  • Developing accurate and stable numerical methods is crucial for solving such equations.

Purpose of the Study:

  • To introduce a novel multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the one-dimensional diffusion equation.
  • To derive and analyze an explicit finite-difference scheme from the proposed MRT-LB model.

Main Methods:

  • Development of a multiple-relaxation-time lattice Boltzmann (MRT-LB) model using the D1Q3 lattice structure.
  • Theoretical derivation of a four-level finite-difference scheme from the MRT-LB model.
  • Analysis of the stability and accuracy of the derived finite-difference scheme.

Main Results:

  • The derived four-level finite-difference scheme is unconditionally stable.
  • The scheme achieves sixth-order accuracy in space by adjusting specific parameters (ω₀, s₁, s₂).
  • Numerical simulations confirm the theoretical findings and demonstrate the scheme's effectiveness.

Conclusions:

  • The proposed MRT-LB model effectively leads to a highly accurate and stable numerical scheme.
  • The developed finite-difference method offers a robust tool for solving one-dimensional diffusion equations.
  • This work contributes to advancing numerical techniques in computational physics and applied mathematics.