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

Principle of Linear Impulse and Momentum for a System of Particles01:21

Principle of Linear Impulse and Momentum for a System of Particles

529
In the context of a system of particles moving relative to an inertial frame of reference, the equation of motion is a crucial tool for understanding the dynamics of the system. This equation, which accounts for external forces acting on each particle, plays a fundamental role in describing the system's behavior.
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...
529
Equation of Motion: Center of Mass01:14

Equation of Motion: Center of Mass

568
The equation of motion for a single particle can be expanded to encompass a system of particles consisting of n particles. For any arbitrarily chosen particle within this system, the net force acting upon it is the aggregate of both internal and external forces. Extending this principle to all particles within the system results in the equation of motion for the entire assembly.
Internal forces between any pair of particles manifest as collinear pairs of equal magnitude but opposite directions,...
568
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

7.8K
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...
7.8K
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

13.9K
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...
13.9K
Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

2.0K
When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
2.0K
Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision02:43

Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

37.2K
The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For example, Charles’ law states that volume and temperature are directly related. Gases, therefore, expand when heated at constant pressure. Although gas laws explain how the macroscopic properties change relative to one another, it does not explain the rationale behind it.
37.2K

You might also read

Related Articles

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

Sort by
Same author

Spectral Insights into Active Matter: Exceptional Points and the Mathieu Equation.

Entropy (Basel, Switzerland)·2026
Same author

Reduced density fluctuations via antialigning in active matter.

Physical review. E·2026
Same author

Nonreciprocal antialigning active mixtures: Deriving the exact Boltzmann collision operator.

Physical review. E·2025
Same author

Emergent flocking in mixtures of antialigning self-propelled particles.

Physical review. E·2025
Same author

Kinetic Theory of Self-Propelled Particles with Nematic Alignment.

Entropy (Basel, Switzerland)·2025
Same author

Comment on 'When low-order expansions fail and all higher-order contributions matter-basic example of the mean squared displacement for Brownian motion'.

The European physical journal. E, Soft matter·2023

Related Experiment Video

Updated: Dec 26, 2025

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy
09:16

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy

Published on: January 9, 2017

14.8K

Multiple Particle Correlation Analysis of Many-Particle Systems: Formalism and Application to Active Matter.

Rüdiger Kürsten1, Sven Stroteich1, Martín Zumaya Hernández2,3

  • 1Institut für Physik, Universität Greifswald, Felix-Hausdorff-Str. 6, 17489 Greifswald, Germany.

Physical Review Letters
|March 14, 2020
PubMed
Summary

We developed a new spatial analysis method for multiparticle correlations in systems with many identical particles. This technique simplifies phase transition detection and reveals the importance of correlations in disordered systems.

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

8.9K
Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.6K

Related Experiment Videos

Last Updated: Dec 26, 2025

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy
09:16

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy

Published on: January 9, 2017

14.8K
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

8.9K
Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.6K

Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Mean-field theories often simplify systems by assuming limited correlations.
  • Understanding multiparticle correlations is crucial for accurately modeling complex systems.
  • The Vicsek model is a standard for studying self-propelled particle dynamics and phase transitions.

Purpose of the Study:

  • Introduce a novel, fast spatial point pattern analysis technique.
  • Quantify the significance of multiparticle correlations in various system states.
  • Develop a unified order parameter for detecting phase transitions in the Vicsek model.

Main Methods:

  • Developed a spatial point pattern analysis for arbitrary-order multiparticle correlations.
  • Applied the technique to the Vicsek model of self-propelled particles.
  • Generated a phase space correlation map up to ten-particle correlations.

Main Results:

  • Identified that multiparticle correlations are significant even in large portions of the disordered phase.
  • Demonstrated that a single two-particle correlation parameter effectively identifies both phase transitions.
  • Showed the limitations of mean-field assumptions in regions with high correlation orders.

Conclusions:

  • The new analysis technique offers a powerful tool for studying complex particle systems.
  • The findings challenge the applicability of simplified correlation assumptions in certain regimes.
  • A unified two-particle correlation parameter simplifies the characterization of Vicsek model phase transitions.