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The Assembly and Application of 'Shear Rings': A Novel Endothelial Model for Orbital, Unidirectional and Periodic Fluid Flow and Shear Stress
Published on: October 31, 2016
Thermodynamics of the self-gravitating ring model
Takayuki Tatekawa1, Freddy Bouchet, Thierry Dauxois
1Laboratoire de Physique, UMR-CNRS 5672, ENS Lyon, 46 Allée d'Italie, 69364 Lyon cédex 07, France.
Summary
The self-gravitating-ring (SGR) model reveals distinct thermodynamic behaviors between ensembles, featuring negative specific heat phases and differing phase transition orders. This model serves as a key prototype for 1D self-gravitating systems.
Area of Science:
- Statistical mechanics
- Astrophysical fluid dynamics
- Computational physics
Background:
- Self-gravitating systems exhibit complex thermodynamic properties.
- Understanding ensemble equivalence is crucial in statistical mechanics.
- The self-gravitating-ring (SGR) model provides a simplified yet relevant system for studying these phenomena.
Purpose of the Study:
- To map the phase diagram of the SGR model in both microcanonical and canonical ensembles.
- To investigate ensemble nonequivalence and the presence of negative specific heat phases.
- To identify tricritical points and analyze phase transition orders.
Main Methods:
- Simulating the SGR model with a softening parameter to regularize short-range interactions.
- Analyzing thermodynamic properties across different energy regimes.
- Employing an iterative method, inspired by 2D turbulence, to find stable stationary mass distributions.
Main Results:
- A global entropy maximum exists, ensuring well-defined thermodynamics in the mean-field limit.
- Ensembles are not equivalent; a negative specific heat phase appears in the microcanonical ensemble for small softening parameters.
- Phase transitions shift from second to first order at a tricritical point, with differing locations in each ensemble.
Conclusions:
- The SGR model is an excellent one-dimensional prototype for self-gravitating systems.
- Ensemble nonequivalence and negative specific heat are significant features of this system.
- The iterative method ensures convergence to stable equilibrium states.
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