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Stochastic Simulation of a Casimir Oscillator

[+] Author Affiliations
Farbod Khoshnoud

University of British Columbia, Vancouver, BC, Canada; California Institute of Technology, Pasadena, CA

Houman Owhadi

California Institute of Technology, Pasadena, CA

Clarence W. de Silva

University of British Columbia, Vancouver, BC, Canada

Paper No. IMECE2010-39746, pp. 635-644; 10 pages
doi:10.1115/IMECE2010-39746
From:
  • ASME 2010 International Mechanical Engineering Congress and Exposition
  • Volume 10: Micro and Nano Systems
  • Vancouver, British Columbia, Canada, November 12–18, 2010
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4447-2
  • Copyright © 2010 by ASME

abstract

Stochastic simulation of a Casimir Oscillator is presented in this paper. This oscillator is composed of a flat boundary of semiconducting oscillator parallel to a fixed plate separated by vacuum. In this system the oscillating surface is attracted to the fixed plate by the Casimir effect, due to quantum fluctuations in the zero point electromagnetic field. Motion of the oscillating boundary is opposed by a spring. The stored potential energy in the spring is converted into kinetic energy when the spring force exceeds the Casimir force, which generates an oscillatory motion of the moving plate. Casimir Oscillators are used as micro-mechanical switches, sensors and actuators. In the present paper, a stochastic simulation of a Casimir oscillator is presented for the first time. In this simulation, Stochastic Variational Integrators using a Langevin equation, which describes Brownian motion, is considered. Formulations for Symplectic Euler, Constrained Symplectic Euler, Stormer-Verlet and RATTLE integrators are obtained and the Symplectic Euler case is solved numerically. When the moving parts in a micro/nano system travel in the vicinity of 10 nanometers to 1 micrometer range relative to other parts of the system, the Casimir phenomenon is in effect and should be considered in analysis and design of such system. The simulation in this paper considers modeling such uncertainties as friction, effect of surface roughness on the Casimir force, and change in environmental conditions such as ambient temperature. In this manner the paper explores a realistic model of the Casimir Oscillator. Furthermore, the presented study of this system provides a deeper understanding of the nature of the Casimir force.

Copyright © 2010 by ASME
Topics: Simulation

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