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Fig. 8. Central finite difference method applied to the magnetic flux density. The nodal magnetic force is , ,, ∆ 11-13 May 2011, Aix-en-Provence, France (17) where L, in the case considered. The magnetic force acting on each slice of the proof mass is related to the real volume of that portion of graphite. Depending to the number of nodes present on the longitudinal axis of one slice, each nodal force is referred to a small volume centered on the same node. For each graphite portion, it is related to the unit volume by the ratio (18) where is the number of nodes on the longitudinal axis. The magnetic force acting on the -th portion of the proof mass is ∑ , (19) where , is the magnetic force per unit volume calculated in the node , . The total magnetic force acting on the entire proof mass is 2·∑ ∑ , . (20) VII. RESULTS The levitation height was measured by the laser sensor [9] on the configuration with 1, 2, 3, nominal graphite side 10mm and nominal graphite thickness 0.3, 0.5, 0.7, 0.9, 1.0mm; the results, referred to the midplane of the proof mass, are reported in Fig. 9. the experimental levitation distance L, 1.0687mm in the configuration with 1 and 1mm; the measured thickness of the proof mass is 0.9117mm. The half graphite mass was divided in 7 portions ( 1, … ,7) and the coefficient for the volume correction was calculated for every portion. The magnetic force acting on each slice of graphite was calculated and compared to the corresponding value of the gravity force acting on the same portion. The mesh size used was 0.5mm that gives the number of nodes along the longitudinal axis of each portion. The results are listed in Table II. Portion Number of nodes TABLE II NUMERICAL CALCULATION RESULTS Volumetric coeff. (α) Magnetic force [mN] Gravity force [mN] 1 27 0.52 0.211 0.261 0.81 2 23 0.52 0.269 0.221 1.22 3 19 0.53 0.090 0.181 0.50 4 15 0.54 0.106 0.141 0.75 5 11 0.56 0.102 0.100 1.01 6 7 0.60 0.082 0.060 1.37 7 3 1.00 0.016 0.020 0.80 The gravity force acting on the entire graphite mass is 1.970mN. The numerical calculation of the magnetic force was conducted at the levitation height of the graphite mid-plane 1mm L, . Due to the high uncertainty about the magnets coercive force, two values of representative of its range of variability were considered. For 750 kA⁄ m, the total magnetic force results 1.751mN, corresponding to the error with the gravity force of about 11.1%. For 900 kA⁄ m, the total magnetic force results 2.409mN, corresponding to the 22.3% error with the gravity force. Following the first approximation of linear interpolation, the actual value of coercive force for the current magnets is about 800 kA⁄ m In conclusion, the force equilibrium is demonstrated by the discrete model, with relative small errors that are addressable to (a) the experimental error in the evaluation of levitation height, (b) the approximations introduced by the discretization, (c) the uncertainty about the material properties and the magnetization curve of the magnets. Further investigations will provide more detailed results in terms of resolution of the levitation height and material parameters evaluation; different configurations of the levitating system will be considered as well. Fig. 9. Experimental levitation height of the proof mass mid-plane in different configurations: N=1 (◦), N=2 (), N=3 (). The calculation of the magnetic force was conducted at VIII. CONCLUSIONS The numerical model developed and presented in this paper was used to calculate the magnetic force acting on a proof mass of diamagnetic material levitating on permanent magnets in the ‘opposite’ configuration. Starting from the magnetic field distribution obtained with a commercial FEM simulator, the nodal magnetic force on the proof mass was calculated at the vertical position corresponding to the experimental levitation height. The resulting magnetic force was compared to the gravity force acting on the proof mass 101
11-13 May 2011, Aix-en-Provence, France and the vertical equilibrium was verified quite precisely. The relatively small error was attributed to the uncertainties about materials and measurements and to the approximations of the discretized model. REFERENCES [1] W.C. Tang, M.G. Lim, and R.T. Howe, “Electrostatic comb drive levitation and control method,” J. Microelectromech. S., vol. 1, pp. 170-178, 1992. [2] S.W. Chyuan and Y.S. Liao, “Computational study of the effect of finger width and aspect ratios for the electrostatic levitating force of MEMS combdrive,” J. Microelectromech. S., vol. 14, pp. 305- 312, 2005. [3] E.M. Yeatman, “Applications of MEMS in power sources and circuits,” J. Micromech. Microeng., vol. 17, pp. S184-S188, 2007. [4] G. De Pasquale, C. Siyambalapitiya, A. Somà, and J. Wang, “Performances improvement of MEMS sensors and energy scavengers by diamagnetic levitation,” proc. of ICEAA, Torino, Italy, pp. 465-468, 2009. [5] H. Chetouani, B. Delinchant, and G. Reyne, “Efficient modelling approach for optimization of a system based on passive diamagnetic levitation as a platform for bio-medical applications,” in Compel, vol. 26, Emeral Group <strong>Publishing</strong>, 2007, pp. 345-355. [6] F. Barrot, “Acceleration and inclination sensors based on magnetic levitation. Application in the particular case of structural health monitoring in civil engineering,” PhD thesis, EPFL, Lausanne, Switzerland, 2008. [7] C. Elbuken, M.B. Khamesee, and M. Yavuz, “Eddy current damping for magnetic levitation: downscaling from macro- to micro-levitation,” J. Phys. D: Appl. Phys., vol. 39, pp. 3932-3938, 2006. [8] D. Garmire, H. Choo, R. Kant, S. Govindjee, C.H. Séquin, R.S. Muller, and J. Demmel, “Diamagnetically levitated MEMS accelerometers,” proc. of Transducers and Eurosensors, Lyon, France, pp. 1203-1206, 2007. [9] G. De Pasquale, C. Siyambalapitiya, S. Iamoni, and A. Somà, “Characterization of low-stiffness suspensions based on diamagnetic levitation for MEMS energy harvesters,” proc. Power MEMS, Leuven, Belgium, pp. 77-80, 2010. [10] H. Chetouani, V. Haguet, C. Jeandey, C. Pigot, A. Walther, N.M. Dempsey, F. Chatelain, B. Delinchant, and G. Reyne, “Diamagnetic levitation of beads and cells above permanent magnets,” proc. of Transducers and Eurosensors, Lyon, France, pp. 715-718, 2007. [11] M.K. Alqadi, H.M. Al-Khateeb, F.Y. Alzoubi, and N.Y. Ayoub, “Effects of magnet size and geometry on magnetic levitation force,” Chin. Phys. Lett., vol. 24 p. 2664, 2007. 102
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COLLECTION OF PAPERS PRESENTED AT T
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III
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V
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Table of Contents Wednesday 11 May
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PANEL DISCUSSION TEXTILE MICROSYSTE
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Friday 13 May SESSION C4: APPLICATI
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SPECIAL SESSION OF BIO-MEMS/NEMS a
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11-13 May 2011, Aix-en-Provence, Fr
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suspended membrane can be pulled to
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most likely due to not yet consider
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that detectors may measure the diff
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2) Cavity width effect To verify th
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Fig.9. Capacitive sensor output, Va
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The anode and cathode are connected
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! TABLE 3 SUMMARY OF SELECTIVITIES
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The fabrication of optical Cap-Wafe
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the glass is polished down in a cos
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In recent years, the pipe flow moni
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As the speed of the rotor increases
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inches silicon wafers which have th
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samples tested in different vacuum
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l c 11-13 May 2011, Aix-en-Provence
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Vp (V) 3,5 3,0 2,5 2,0 1,5 1,0 0,5
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II. MATHEMATICAL MODEL AND NUMERICA
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fluids travel along a curved channe
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measured mixing indices are depicte
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length, which enables them to focus
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however, a rotation for coincidence
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excludes the nature of the fixed bo
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Using the radial and tangential mid
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Now the challenge in data handling
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value of every active channel. Ther
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electrocardiogram. • The heart be
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In our work, we proposed an innovat
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Fig. 8 Concept of the in-home perso
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found that the early-stage diagnosi
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Power monitoring data detected by w
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device consisted of a bimorph canti
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where C others is the capacitance o
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operation, the pressure inside the
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increased. 11-13 May 2011, Aix-en-
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coefficient compatible with the mic
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Variable Description Value Crab-leg
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Membrane weight (mg) Fig. 4. Struct
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So far, the expected major contribu
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al. used a modified LIGA (German ac
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REFERENCES [1] G. Mehta, J. Lee, W.
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followed by titanium (Ti) which sho
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exposure dose, post exposure bake t
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#### ##/&### 3 # #
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*5%6,+/.,-,7-, ,+.,1/21* %
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B. Energy Applications Society is f
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Presently, the microfabrication pro
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[6] C. Richard, A. Renaudin, V. Aim
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NA sinθ c 11-13 May 2011, Aix-en-
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the waveguide on the fused silica,
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microphone diaphragm. The chosen CM
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TABLE V MICROPHONE CHARACTERISTICS
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Figure 7b shows the effect of a par
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over the temperature range (i.e. th
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given. This allows a CTM model to b
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the magic-Tee, and the coherent sig
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After analyzing the two conditions
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IV. MICRO FABRICATION For fabricati
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IV. A. Simulation and Sensitivity A
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grown to sub-confluence were washed
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Clamps rotation [21] Clamps transla
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Layout Total dimensions of the grip
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focusing increased both as the stre
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Time of diffusion (hr) 1200 1000 80
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Chip Magnet Light source Hot plate
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above, they would move to upward an
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This phenomenon is now reaching the
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C. Proof mass displacement Moreover
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The VerilogA block code is : 11-13
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Author Index Abi-Saab D. 81 Aimez V
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Nussbaum Dominic 273 O’Hara T. 35
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