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Symmetry-breaking instability in a prototypical driven granular gas
Evgeniy Khain1, Baruch Meerson
1Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
Summary
A granular gas strip state becomes unstable, breaking symmetry. This instability is independent of driving conditions in large systems, with density changes localized at the wall opposite the heat source.
Area of Science:
- Physics
- Nonlinear Dynamics
- Statistical Mechanics
Background:
- Granular gases, systems of macroscopic particles interacting via collisions, exhibit complex behaviors distinct from molecular gases.
- Understanding the stability and dynamics of particle clusters in driven granular systems is crucial for various applications.
- Previous studies have explored instabilities in granular systems, but the specific case of a laterally uniform strip state requires further investigation.
Purpose of the Study:
- To investigate the symmetry-breaking instability of a laterally uniform granular cluster (strip state) in a prototypical driven granular gas.
- To analyze the influence of system size and boundary conditions on the stability of the strip state.
- To explore the physical mechanisms underlying the observed symmetry-breaking instability.
Main Methods:
- Utilized a theoretical approach based on granular hydrodynamics with Jenkins-Richman constitutive relations for nearly elastic particle collisions.
- Employed marginal stability analysis to predict the onset and nature of instabilities.
- Investigated a two-dimensional system of smooth hard disks driven by a thermal wall in a box, considering zero gravity.
Main Results:
- Predicted a spontaneous symmetry-breaking instability of the strip state, consistent with recent findings for different constitutive relations.
- Demonstrated that in sufficiently large systems, the marginal stability curve becomes independent of the driving wall's boundary conditions.
- Observed that density perturbations are exponentially localized at the wall opposite the thermal driving wall in this large system regime.
- Derived analytical expressions for the short- and long-wavelength asymptotics of the marginal stability curves in the dilute limit.
Conclusions:
- The strip state in a driven granular gas is susceptible to symmetry-breaking instabilities.
- System size plays a critical role in determining the universality of stability criteria, decoupling them from specific boundary conditions.
- The localized nature of density perturbations provides insight into the physics driving the instability.
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