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The Kinetic Model of Gases01:24

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The kinetic model of gases explains the properties of a perfect gas using three main assumptions: molecules move in ceaseless random motion, their size is negligible compared to the distances between them, and they do not interact except during perfectly elastic collisions. The total energy of a gas is the sum of the kinetic energies of all its constituent molecules. The pressure exerted by the gas arises from the continual bombardment of the container walls by billions of colliding molecules.
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Driven inelastic Maxwell gases.

V V Prasad1, Sanjib Sabhapandit1, Abhishek Dhar2

  • 1Raman Research Institute, Bangalore 560080, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 24, 2015
PubMed
Summary
This summary is machine-generated.

The inelastic Maxwell model with specific driving reaches a steady state for most parameters, unlike purely diffusive systems. This finding is crucial for understanding particle dynamics in driven systems.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Systems
  • Kinetic Theory

Background:

  • The inelastic Maxwell model describes particle systems with velocity-dependent interactions and external driving.
  • Understanding steady-state properties is key in non-equilibrium statistical mechanics.

Purpose of the Study:

  • To analyze the steady-state behavior of the inelastic Maxwell model under specific driving conditions.
  • To derive exact solutions for the velocity distribution and variance.

Main Methods:

  • Analysis of the joint evolution equations for variance and two-particle velocity correlations.
  • Derivation of an exact formula for the variance.
  • Investigation of the system's behavior for different coefficients of restitution and driving parameters.

Main Results:

  • The system achieves a steady state when the driving parameter r(w) is not equal to -1.
  • An exact formula for the variance and the tail of the velocity distribution in the steady state were obtained.
  • The system fails to reach a steady state for r(w) = -1 or under purely diffusive driving (Γ=0).

Conclusions:

  • The inelastic Maxwell model exhibits steady-state behavior dependent on the nature of the external driving.
  • The derived exact solutions provide insights into the statistical properties of driven granular gases and similar systems.