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

Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

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
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
Maxwell's Equation Of Electromagnetism01:29

Maxwell's Equation Of Electromagnetism

James Clerk Maxwell (1831–1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major contributions to the development of the kinetic theory of gases, to the understanding of color vision, and to understanding the nature of Saturn's rings. He is probably best known for having combined existing knowledge on the laws of electricity and magnetism with his insights into a complete overarching electromagnetic theory, which is represented by...
Maxwell's Thermodynamic Relations01:23

Maxwell's Thermodynamic Relations

Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...
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...
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.

You might also read

Related Articles

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

Sort by
Same author

Mitigating polarization in flat-sheet membrane distillation through CFD-driven spacer design.

Scientific reports·2026
Same author

Machine Learning Allowed Interpreting Toxicity of a Fe-Doped CuO NM Library Large Data Set─An Environmental In Vivo Case Study.

ACS applied materials & interfaces·2024
Same author

Enhancing ReaxFF for molecular dynamics simulations of lithium-ion batteries: an interactive reparameterization protocol.

Scientific reports·2024
Same author

Mesoscopic Modeling and Experimental Validation of Thermal and Mechanical Properties of Polypropylene Nanocomposites Reinforced By Graphene-Based Fillers.

Macromolecules·2024
Same author

Method for predicting the wettability of micro-structured surfaces by continuum phase-field modelling.

MethodsX·2023
Same author

Atomistic to Mesoscopic Modelling of Thermophysical Properties of Graphene-Reinforced Epoxy Nanocomposites.

Nanomaterials (Basel, Switzerland)·2023

Related Experiment Video

Updated: Jun 23, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

Generalized Maxwell state and H theorem for computing fluid flows using the lattice Boltzmann method.

Pietro Asinari1, Ilya V Karlin

  • 1Department of Energetics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 28, 2009
PubMed
Summary
This summary is machine-generated.

A generalized Maxwell distribution function was analytically derived for lattice Boltzmann (LB) methods, unifying existing equilibria and enabling new multiple relaxation-time models.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment
10:23

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment

Published on: December 1, 2023

Related Experiment Videos

Last Updated: Jun 23, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment
10:23

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment

Published on: December 1, 2023

Area of Science:

  • Computational fluid dynamics
  • Statistical mechanics
  • Numerical methods

Background:

  • The lattice Boltzmann (LB) method is a powerful numerical technique for simulating fluid dynamics.
  • Existing equilibrium distribution functions in LB methods have limitations.
  • A unified theoretical framework for LB equilibria is needed.

Purpose of the Study:

  • To derive a generalized Maxwell distribution function for the lattice Boltzmann method.
  • To demonstrate that previously introduced LB equilibria are special cases of this new function.
  • To develop new multiple relaxation-time LB models and prove their stability.

Main Methods:

  • Analytical derivation of the generalized Maxwell distribution function.
  • Demonstration of existing LB equilibria as special cases.
  • Development of novel multiple relaxation-time LB models.
  • Proof of the H theorem for the new models.

Main Results:

  • The generalized Maxwell distribution function was successfully derived analytically.
  • All previously known LB equilibria were shown to be special cases of the generalized Maxwellian.
  • A new class of multiple relaxation-time LB models was introduced.
  • The H theorem was proven for these new models, ensuring thermodynamic consistency.

Conclusions:

  • The generalized Maxwell distribution provides a unified theoretical foundation for LB equilibria.
  • This work opens avenues for developing more accurate and versatile LB models.
  • The proven H theorem guarantees the stability and physical realism of the new models.