Related Experiment Video
Updated: Aug 6, 2026
10:09
Operation of the Collaborative Composite Manufacturing (CCM) System
Published on: October 1, 2019
First Order Non-Instantaneous Corrections in Collisional Kinetic Alignment Models
Laura Kanzler1, Carmela Moschella2,3, Christian Schmeiser2
1Sorbonne Université, UMR CNRS 7598, Université de Paris Cité, Laboratoire Jacques-Louis Lions, 75005 Paris, France.
Journal of Statistical Physics
|July 26, 2026
Summary
This study introduces a new kinetic theory model for non-instantaneous collisions, improving accuracy beyond the standard instantaneous assumption. The findings offer a more precise approach to modeling particle interactions in physics and chemistry.
Area of Science:
- Physics
- Kinetic Theory
- Statistical Mechanics
Background:
- Standard kinetic theory relies on the assumption of instantaneous collisions.
- This simplification may limit accuracy in certain physical phenomena.
- Modeling particle interactions requires precise collision dynamics.
Purpose of the Study:
- To develop and analyze a kinetic theory model that accounts for non-instantaneous collisions.
- To investigate higher-order effects in collision alignment.
- To derive an accurate approximation for short collision durations.
Main Methods:
- Developed a mathematical model for non-instantaneous alignment collisions.
- Studied the model in the asymptotic regime of short collision duration.
- Derived a first-order accurate approximative model as a correction to the instantaneous limit.
- Proved rigorous results on well-posedness and the instantaneous limit.
Main Results:
- A first-order accurate approximative model was derived.
- The model consists of a system of two equations.
- Rigorous mathematical proofs confirm the model's validity and its convergence to the instantaneous limit.
- An equally accurate scalar approximation was also suggested.
Conclusions:
- The proposed model offers a more accurate description of particle collisions than the standard instantaneous assumption.
- This work provides a rigorous mathematical foundation for non-instantaneous collision models.
- The derived approximative model and scalar approximation can be applied in various kinetic theory applications.
Related Concept Videos
01:00Elastic Collisions: Introduction
An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...
01:15Elastic Collisions: Case Study
Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...
01:12Reduced Mass Coordinates: Isolated Two-body Problem
In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
01:17Kinematic Equations - II
The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
01:04Types Of Collisions - I
When two objects come in direct contact with each other, it is called a collision. During a collision, two or more objects exert forces on each other in a relatively short amount of time. A collision can be categorized as either an elastic or inelastic collision. If two or more objects approach each other, collide and then bounce off, moving away from each other with the same relative speed at which they approached each other, the total kinetic energy of the system is said to be conserved. This...
01:18Kinematic Equations - III
The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
Using the kinematic equations,...
Using the kinematic equations,...