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

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Presentation on theme: "Casimir Rack and Pinion Ramin Golestanian Department of Physics and Astronomy University of Sheffield."— Presentation transcript:

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

2 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

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

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

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

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

7 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)

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

9 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

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

11 Equation of Motion  Relevant parameters:  Uniformly moving rack:

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

13 No Dissipation  Pinion Velocity vs Rack Velocity and initial Offset

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

15 Weak Dissipation  The skipping transition boundary

16 Weak Dissipation  Pinion Velocity vs Rack Velocity and Load

17 Strong Dissipation  Pinion Velocity vs Rack Velocity and Load  Stall Force

18 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)

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

20 Vibrating Rack and Pinion  Basin of attraction for forward motion

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

22 Feasibility  Realistic values for the lateral Casimir force amplitude

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

24 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

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


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