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S-PA meeting @ APCTP, April. 3rd. 2024

Brownian motors and adiabatic pistons:

simple models exhibiting self-propulsion induced by the force imbalance in microscopic kinetics.

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Smoluchowski-Feynman ratchet

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Brownian motor

[Van den Broeck, Kawai, Meurs, PRL (2004)]

 

compartments

 

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Overview

[Van den Broeck, Kawai, Meurs, PRL (2004)]

 

 

Leading order equation

 

 

Next leading order equation

 

 

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Adiabatic piston

[Meurs, Van den Broeck, Garcia, PRE (2004)]

 

 

 

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Frictional Granular Motor

[Talbot, Wildman, Viot, PRL (2011)]

 

angular velocity

damping coefficient

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Brownian motor with a friction

[Gnoli, Petri, Dalton, Pontuale, Gradenigo, Sarracino, Puglishi, PRL (2013)]

angular velocity

 

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Adiabatic piston with a friction

[Sano and Hayakawa, PRE (2014)]

friction constant

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Brownian motor with a driving

[JS Lee, J-M Park, J D Noh, H Park and Hayakawa, PRR (2021)]

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Boltzmann-Master equation

[Meurs, Van den Broeck, Garcia, PRE (2004)]

 

 

 

 

 

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Kramers-Moyal expansion

[Meurs, Van den Broeck, Garcia, PRE (2004)]

 

Taking the Tayler expansion

 

 

 

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Equations for moments

[Meurs, Van den Broeck, Garcia, PRE (2004)]

 

 

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Transition rate for each compartments

[Meurs, Van den Broeck, Garcia, PRE (2004)]

 

 

 

 

 

 

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Transition rate

[Meurs, Van den Broeck, Garcia, PRE (2004)]

 

 

 

Equilibrium Boltzmann distribution

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Transition rate

[Meurs, Van den Broeck, Garcia, PRE (2004)]

 

 

conservation laws of the energy and momentums

 

 

 

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Transition rate

[Meurs, Van den Broeck, Garcia, PRE (2004)]

 

 

 

 

 

 

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Fraction of the surface orientation

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Equation of motions

 

 

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Equation of motions

 

 

 

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