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Origin of the hydrodynamic Lyapunov modes
1Centre Européen de Calcul Atomique et Moléculaire, Ecole Normale Supérieure de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
Summary
New conservation laws during hard sphere fluid collisions create novel hydrodynamic fields. These fields, analogous to established ones, are explored via kinetic theory, revealing partial but promising insights.
Area of Science:
- Statistical Mechanics
- Fluid Dynamics
- Kinetic Theory
Background:
- Lyapunov spectrum analysis reveals "hydrodynamic" exponents in hard sphere fluids.
- These exponents correspond to collective perturbations in phase space.
Purpose of the Study:
- To investigate the origin of collective perturbations in hard sphere fluids.
- To develop a kinetic theory for newly discovered hydrodynamic fields.
Main Methods:
- Analysis of Lyapunov spectrum in hard sphere fluid dynamics.
- Construction of a kinetic theory model for new hydrodynamic fields.
Main Results:
- Collective perturbations arise from new conservation laws during collisions.
- A kinetic theory approach was used to model these new hydrodynamic fields.
- The developed theory partially predicts the properties of the hydrodynamic modes.
Conclusions:
- New conservation laws during collisions are responsible for novel hydrodynamic fields in hard sphere fluids.
- The kinetic theory provides a foundational understanding but requires further elaboration.
- Hydrodynamic exponents do not exhibit a simple correlation with transport coefficients.