simulation of a vibrated granular system · 2007. 6. 29. · alexis burdeau, lptmc orsay, june 20th...
TRANSCRIPT
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Simulation of a vibrated granular system
quasi equilibrium properties
Alexis Burdeau
advisorPascal Viot
Laboratoire de Physique Théorique de la Matière Condensée
UMR 7600 Université Pierre et Marie Curie/ CNRS
Orsay, June 20th 2007
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Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Motivations of the study
Get a better understanding of these experimental results
Propose a realization of stochastic thermostat for 2d granular gases
Recent experimental studies of vibrated system in the same direction Prevost & al, Phys. Rev. Lett.(2002), Reis & al, Phys. Rev. E (2007)
Retrieve experimental results with a simple simulation model
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Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
The experimental system
Baxter & Olafsen, Nature (2003)
Coverage density c from 0.2 to 0.8
Dimensionless acceleration
Range of frequencies f : 50 to 90 Hz
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Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Experimental results
For a perfect Gaussian distribution Renormalized horizontal velocities distributions
Experimentally for the top layer
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Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Simulation Model
System of viscoelastic rough beads
Damped oscillator for the normal force
Tangential friction
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Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Top layer velocity distribution
Nearly perfect Gaussian distributions
K increases with increasing density
Renormalized horizontal velocities distribution in the top layer
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Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Bottom layer velocity distributionStrongly non Gaussian distribution for the horizontal velocity
In red, Gaussian distribution
Significant correlations with the vibrating plate and the other particles
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Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Interpretation of the Gaussian velocities distributionTYPICAL TRAJECTORY OF A LIGHT PARTICLE ON THE
HORIZONTAL PLANE
Density on the top c = 0.4
Collision with a light bead
The collisions with the first layer beads decorrelate the light beads movements
Collision with a heavy bead
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Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Granular temperature
For a tracer in a Gaussian bath Martin & Piasecki (1999)
with
Extension of the thermodynamic definition to the granular gases
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Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Simulation results for the temperature ratio
Growing influence of the top beads on the first layer
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Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Structure of the top layer
In black, particles twice bigger
Pair distribution fonction
In green, Percus Yevick solution for hard disks at equilibrium
In red, normal system
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Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Conclusions & Prospects
Empirical justification of the use of stochastic thermostat for 2d granular gases
Other interesting features : correlation translation/rotation
Strongly dissipative system exhibiting equilibrium properties
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Alexis Burdeau, LPTMC Orsay, June 20th 2007
Simulation of a vibrated granular system
Vertical velocities distributions
In black, distribution of the bottom layer