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Casimir Rack and Pinion Ramin Golestanian Department of Physics and Astronomy University of Sheffield

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Significance of Casimir Force Tiny at Micron-scale It took 50 years to be verified! Dominant at Nano-scale Strongest distance dependence unwanted effects: stiction harnessed for good use: novel NEMS

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Geometry Challenge Practical Aspect Realistic ``machine parts’’ Fundamental Aspect Pair-wise summation?

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Geometry Challenge Expansion in Dielectric Contrast R. Golestanian, Phys. Rev. Lett. 95, (2005) Not so easy …

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Geometry Challenge Convergence properties R. Golestanian, Phys. Rev. Lett. 95, (2005) CM:

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Normal Casimir Force Is it practical in making nano-mechanical devices? Not really … Repulsive Casimir Force: does it exist? Alchemy of nano-mechanics …

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Lateral Casimir Force Theoretical Prediction ``Josephson-like’’ force between corrugated surfaces R. Golestanian & M. Kardar, Phys. Rev. Lett. 78, 3421 (1997) T. Emig, A. Hanke, R. Golestanian & M. Kardar, Phys. Rev. A 67, (2003)

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Lateral Casimir Force Experimental Verification F. Chen, U. Mohideen, G. L. Klimchitskaya, & V. M. Mostepanenko, Phys. Rev. Lett. 88, (2002)

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Rack and Pinion A. Ashourvan, M.F. Miri, & R. Golestanian, Phys. Rev. Lett. 98, (2007) Powered by Quantum Vacuum Force transduction with no contact could potentially solve wear problem in nano-mechanical systems

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Equation of Motion R x =R y W H y x

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Equation of Motion Relevant parameters: Uniformly moving rack:

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No Dissipation The equation is integrable: nonlinear pendulum Skipping Velocity:

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No Dissipation Pinion Velocity vs Rack Velocity and initial Offset

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No Dissipation The effect of external load on the skipping transition similar to solid friction

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Weak Dissipation The skipping transition boundary

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Weak Dissipation Pinion Velocity vs Rack Velocity and Load

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Strong Dissipation Pinion Velocity vs Rack Velocity and Load Stall Force

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Vibrating Rack and Pinion A. Ashourvan, M.F. Miri, & R. Golestanian, Phys. Rev. E 75, (R)(2007) Is it possible to rectify a symmetric oscillatory motion? See also: T. Emig, Phys. Rev. Lett. 98, (2007)

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Vibrating Rack and Pinion Equation of motion: Pinion Velocity: Solution:

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Vibrating Rack and Pinion Basin of attraction for forward motion

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Vibrating Rack and Pinion Parameter values for forward motion Stall Force:

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Feasibility Realistic values for the lateral Casimir force amplitude

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Feasibility Realistic values for skipping velocity Not so small after all …

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Conclusion Casimir forces are dominant at nano-scale ☺ Knowledge of Casimir forces can be used to avoid unwanted effects in NEMS They can be used to design nano-mechanical devices: mechanical engineering with quantum vacuum fluctuation forces! Non-contact lateral force transduction can solve the wear problem Despite expectation, the Casimir grip can be strong

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THANK YOU Collaborators: A. Ashourvan (IASBS, Zanjan) M.F. Miri (IASBS, Zanjan) Acknowledgement:

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