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

First Law: Particles in Two-dimensional Equilibrium

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...

Molecular and Ionic Solids

Molecular and Ionic Solids

Crystalline solids are divided into four types: molecular, ionic, metallic, and covalent network based on the type of constituent units and their interparticle interactions.
Molecular Solids
Molecular crystalline solids, such as ice, sucrose (table sugar), and iodine, are solids that are composed of neutral molecules as their constituent units. These molecules are held together by weak intermolecular forces such as London dispersion forces, dipole-dipole interactions, or hydrogen bonds, which...

First Law: Particles in One-dimensional Equilibrium

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...

Structures of Solids

Structures of Solids

Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...

Dimensionless Groups in Fluid Mechanics

Dimensionless Groups in Fluid Mechanics

Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...

Principle of Linear Impulse and Momentum for a Single Particle

Principle of Linear Impulse and Momentum for a Single Particle

Linear momentum is a fundamental concept in physics that describes the motion of an object. It is a vector quantity, having a magnitude equal to the product of its mass and its velocity, and direction along the object's velocity. On the other hand, linear impulse, also known as momentum impulse, is a concept in physics related to the change in the linear momentum of an object. Impulse is a vector quantity defined as the product of force and the time over which the force is applied.
Delving into...

You might also read

Related Articles

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

Sort by

Same author

Trends in lung cancer survival: superior outcomes in US veterans compared to general population.

JNCI cancer spectrum·2026

Same author

Trends in Smoldering Myeloma Incidence in the United States From Cancer Registries, 2012-2022.

American journal of hematology·2026

Same author

Risk factors for anticoagulant-related bleeding in cancer: traditional and cancer-specific factors.

Blood vessels, thrombosis & hemostasis·2025

Same author

Smoldering multiple myeloma in the United States: a population-based analysis.

Blood advances·2025

Same author

Nonreciprocal field theory for decision-making in multi-agent control systems.

Nature communications·2025

Same author

Breakdown of stochastic resonance in complex networks.

Physical review. E·2025

Search research articles

Related Experiment Video

Updated: Jul 2, 2026

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

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

Published on: December 4, 2017

Coarse-grained single-particle dynamics in two-dimensional solids and liquids.

Jörg R Silbermann¹, Martin Schoen, Sabine H L Klapp

¹Stranski-Laboratorium für Physikalische und Theoretische Chemie, Sekretariat C7, Technische Universität Berlin, Strasse des 17, Juni 115, Berlin, Germany. joerg.silbermann@fluids.tu-berlin.de

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

|September 4, 2008

Summary

This study validates the generalized Langevin equation (GLE) for describing single-particle dynamics in a 2D Lennard-Jones system. The GLE accurately models particle motion, even in high-temperature liquid phases where harmonic approximations fail.

More Related Videos

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

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

Published on: September 17, 2021

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

Related Experiment Videos

Last Updated: Jul 2, 2026

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

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

Published on: December 4, 2017

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

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

Published on: September 17, 2021

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

Area of Science:

Condensed Matter Physics
Statistical Mechanics
Computational Physics

Background:

The Mori-Zwanzig projection operator formalism enables describing single-particle dynamics via a generalized Langevin equation (GLE).
This GLE is exact for low-temperature solids under the harmonic approximation.
The validity of the GLE beyond the harmonic approximation is not well-established.

Purpose of the Study:

To investigate the accuracy of the generalized Langevin equation (GLE) for describing single-particle dynamics.
To evaluate the GLE's performance under thermodynamic conditions where harmonic approximations are invalid.
To compare GLE predictions with molecular dynamics simulations in a 2D Lennard-Jones system.

Main Methods:

Molecular dynamics (MD) simulations of a 2D system with Lennard-Jones interactions.
Computation of characteristic time autocorrelation functions for a tagged particle in MD simulations.
Solving the generalized Langevin equation (GLE) and comparing its results with MD data.

Main Results:

Excellent agreement between GLE predictions and MD simulations was observed at low temperatures.
Deviations between GLE and MD results emerge at higher temperatures.
These deviations remain surprisingly small even in the high-temperature liquid phase.

Conclusions:

The generalized Langevin equation (GLE) provides a robust description of single-particle dynamics in 2D Lennard-Jones systems.
The GLE retains significant accuracy beyond the harmonic approximation, extending its applicability to liquid phases.
This work validates the GLE as a powerful tool for studying complex particle dynamics in condensed matter systems.