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Kinematics, equilibrium, and shape in Hamiltonian systems: the "LAB" effect
1Southeast Applied Analysis Center, School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA. bunimovh@math.gatech.edu
Chaos (Woodbury, N.Y.)
|August 30, 2003
Summary
Particles in typical containers do not fully mix, unlike in simple boxes. This "LAB" effect, observed in laboratory experiments, shows particles remain unevenly distributed even with infinite particles.
Area of Science:
- Statistical Mechanics
- Dynamical Systems Theory
- Computational Physics
Background:
- Ideal gas models often assume complete mixing for simplicity.
- Understanding particle distribution is crucial for thermodynamics and fluid dynamics.
- Previous models focused on idealized container shapes like boxes.
Purpose of the Study:
- To investigate particle distribution in containers with non-ideal shapes.
- To demonstrate incomplete mixing in systems beyond idealized models.
- To explain the "LAB" (look at billiards) effect.
Main Methods:
- Simulations of finite particle systems in containers with "typical" shapes.
- Analysis of steady-state particle distributions.
- Utilizing billiard systems as a transparent model.
Main Results:
- Systems with a finite number of particles in typical containers exhibit incomplete mixing.
- Particles do not occupy all positions equally in the steady state.
- This effect persists even in the limit of infinitely many particles.
Conclusions:
- "Typical" container shapes lead to incomplete particle mixing, contrasting with "box" shapes.
- The observed phenomenon is termed the "LAB" effect, observable in laboratory experiments.
- Billiard systems provide a clear model for understanding this non-mixing behavior.