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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Maxwell and very-hard-particle models for probabilistic ballistic annihilation: hydrodynamic description
François Coppex1, Michel Droz, Emmanuel Trizac
1Department of Theoretical Physics, University of Genève, CH-1211 Genève 4, Switzerland.
Summary
Simplified models like Maxwell and very-hard-particle (VHP) provide bounds for probabilistic ballistic annihilation dynamics. This kinetic modeling approach helps understand far-from-equilibrium systems and the role of dissipation.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Thermodynamics
- Kinetic Theory
Background:
- Probabilistic ballistic annihilation lacks conservation laws, posing a challenge for hydrodynamic descriptions.
- Hard spherelike dynamics in these systems prevent exact analytical solutions.
Purpose of the Study:
- To test simplified kinetic models (Maxwell, VHP) for describing far-from-equilibrium dynamics.
- To analytically compute bounds for key quantities in probabilistic ballistic annihilation.
- To assess the relevance of singular features and approximations in the original model.
Main Methods:
- Analytical computation of upper and lower bounds using Maxwell and VHP models.
- Derivation of scaling exponents from the Boltzmann equation and comparison with Monte Carlo simulations.
- Application of the Chapman-Enskog method to derive constitutive relations and transport coefficients.
- Derivation of Navier-Stokes equations for hydrodynamic fields.
- Linear stability analysis of the homogeneous solution.
Main Results:
- Scaling exponents were obtained from the Boltzmann equation and validated against simulations.
- Constitutive relations and transport coefficients were derived for Maxwell and VHP models.
- Navier-Stokes equations were established for the hydrodynamic fields.
- Linear stability analysis highlighted the role of dissipation in spatial inhomogeneity development.
Conclusions:
- Simplified kinetic models can provide valuable insights and bounds for complex non-equilibrium systems.
- The study validates the use of approximations and kinetic models for understanding systems without conservation laws.
- Dissipation plays a crucial role in the emergence of spatial structures in these systems.
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