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Significance of Casimir Force

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

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Significance of Casimir Force

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  1. Casimir Rack and PinionRamin GolestanianDepartment of Physics and AstronomyUniversity 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 Not so easy … R. Golestanian, Phys. Rev. Lett. 95, 230601 (2005)

  5. Geometry Challenge • Convergence properties CM: R. Golestanian, Phys. Rev. Lett. 95, 230601 (2005)

  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, 022114 (2003)

  8. Lateral Casimir Force • Experimental Verification F. Chen, U. Mohideen, G. L. Klimchitskaya, & V. M. Mostepanenko, Phys. Rev. Lett. 88, 101801 (2002)

  9. Rack and Pinion • Powered by Quantum Vacuum • Force transduction with no contact could potentially solve wear problem in nano-mechanical systems A. Ashourvan, M.F. Miri, & R. Golestanian, Phys. Rev. Lett. 98, 140801 (2007)

  10. y l H x=Rq y x q R W Equation of Motion

  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 • Is it possible to rectify a symmetric oscillatory motion? A. Ashourvan, M.F. Miri, & R. Golestanian, Phys. Rev. E 75, 040103 (R)(2007) • See also: T. Emig, Phys. Rev. Lett. 98, 160801 (2007)

  19. Vibrating Rack and Pinion • Equation of motion: • Solution: • Pinion Velocity:

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

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