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Related Concept Videos

Elastic Collisions: Case Study01:15

Elastic 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...
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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...
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Laboratory Drop Towers for the Experimental Simulation of Dust-aggregate Collisions in the Early Solar System
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Published on: June 5, 2014

Chapman-Enskog expansion for multi-particle collision models.

Thomas Ihle1

  • 1Department of Physics, North Dakota State University, P.O. Box 6050, Fargo, ND 58108, USA.

Physical Chemistry Chemical Physics : PCCP
|October 24, 2009
PubMed
Summary

Stochastic rotation dynamics, a particle-based fluid simulation method, allows deriving hydrodynamic equations. This approach incorporates a novel collisional contribution to transport coefficients, enhancing accuracy for fluid flow simulations.

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Setting Limits on Supersymmetry Using Simplified Models
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Last Updated: Jun 19, 2026

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Published on: June 5, 2014

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07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Area of Science:

  • Computational fluid dynamics
  • Statistical mechanics
  • Kinetic theory

Background:

  • Particle-based simulation methods for fluid flow rely on discrete time dynamics involving streaming and collision events.
  • Existing Chapman-Enskog approaches for these models often omit crucial collisional contributions to transport coefficients.

Purpose of the Study:

  • To derive hydrodynamic equations from a particle-based simulation method, specifically stochastic rotation dynamics.
  • To introduce and validate a multi-particle generalization of the Enskog equation within this framework.
  • To incorporate a collisional contribution to transport coefficients absent in previous models.

Main Methods:

  • Derivation of a multi-particle Enskog equation from the Liouville equation in two dimensions.
  • Application of the Chapman-Enskog expansion to obtain macroscopic hydrodynamic equations.
  • Analysis of the collisional contribution to transport coefficients within the derived equations.

Main Results:

  • Successfully derived hydrodynamic equations from stochastic rotation dynamics using a multi-particle Enskog equation generalization.
  • The resulting macroscopic equations include a collisional contribution to transport coefficients.
  • This contribution precisely matches results from established kinetic theories, validating the approach.

Conclusions:

  • Stochastic rotation dynamics provides a systematic and powerful route for deriving hydrodynamic equations from particle-based models.
  • The inclusion of collisional contributions enhances the accuracy and applicability of these models.
  • This methodology is generalizable to more complex systems, including those with active particles.