Related Experiment Video
Updated: Oct 16, 2025
13:02
Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
Published on: February 27, 2016
12.5K
Quantitative kinetic theory of flocking with three-particle closure
Rüdiger Kürsten1, Thomas Ihle1
1Institut für Physik, Universität Greifswald, Felix-Hausdorff-Strasse 6, 17489 Greifswald, Germany.
Physical Review. E
|October 16, 2021
Summary
This study develops a new kinetic theory for self-propelled particles, accurately predicting flocking behavior beyond simple models. The theory shows directional correlations shift flocking transitions toward lower noise levels.
Area of Science:
- Physics
- Statistical Mechanics
- Complex Systems
Background:
- Self-propelled particles exhibit collective behaviors like flocking.
- Existing models often rely on mean-field approximations, limiting accuracy for dense systems.
Purpose of the Study:
- Develop a kinetic theory for aligning self-propelled particles in 2D.
- Accurately predict flocking transitions beyond mean-field approximations.
- Investigate the role of N-particle interactions and correlations.
Main Methods:
- Developed a kinetic theory incorporating full pair correlation functions.
- Utilized a closure relation for three-particle spatial correlations.
- Compared theoretical predictions with agent-based simulations.
Main Results:
- Achieved excellent quantitative agreement for pair correlations in the disordered regime.
- Demonstrated good quantitative agreement for the onset of flocking.
- Found that flocking transitions shift to lower noise due to directional correlations favoring disorder.
Conclusions:
- The developed kinetic theory provides accurate predictions for flocking phenomena.
- N-particle interactions and correlations significantly influence flocking transitions.
- The theory offers an improvement over mean-field approaches and aligns with Landau-kinetic theory.
Related Concept Videos
02:43Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision
35.4K
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.
35.4K
01:18First Law: Particles in Two-dimensional Equilibrium
7.6K
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...
Newton's first law tells us about...
7.6K
01:10First Law: Particles in One-dimensional Equilibrium
7.3K
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...
7.3K
01:23Equilibrium Conditions for a Particle
1.6K
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...
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...
1.6K
01:28Conservation of Linear Momentum for a System of Particles
352
In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
352
01:21Principle of Linear Impulse and Momentum for a System of Particles
382
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...
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...
382