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Hydrodynamics of probabilistic ballistic annihilation
François Coppex1, Michel Droz, Emmanuel Trizac
1Department of Theoretical Physics, University of Genève, CH-1211 Genève 4, Switzerland.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
Summary
This study analyzes a hard sphere gas model where particles can annihilate or scatter. We derived hydrodynamic equations and analyzed stability, finding conditions for system stability.
Area of Science:
- Statistical Mechanics
- Kinetic Theory
- Fluid Dynamics
Background:
- Investigates a dilute gas of hard spheres in d>=2 dimensions.
- Particles interact via annihilation (probability p) or elastic scattering (1-p).
- Key quantities like mass, momentum, and energy are not conserved.
Purpose of the Study:
- Establish hydrodynamic equations from the Boltzmann equation.
- Determine transport coefficients up to Navier-Stokes order.
- Analyze linear stability and conditions for local field stability.
Main Methods:
- Utilizes the Boltzmann equation framework.
- Applies the Chapman-Enskog expansion.
- Performs linear stability analysis.
Main Results:
- Derives hydrodynamic equations for density, momentum, and kinetic temperature.
- Calculates transport coefficients.
- Identifies conditions for the stability of hydrodynamic fields.
Conclusions:
- Provides a closed set of hydrodynamic equations for the described system.
- Offers insights into the stability of non-conserving systems.
- Contributes to understanding complex gas dynamics.