A Two-Dimensional Electrostatic Model of Interdigitated Comb Drive in Longitudinal Mode

Abstract

A periodic homogenization model of the electrostatic equation is constructed for a comb drive with a large number of fingers and whose mode of operation is in-plane and longitudinal. The model is obtained in the case where the distance between the rotor and the stator is of an order ε α , α ≥ 2, where ε denotes the period of distribution of the fingers. The model derivation uses the two-scale convergence technique. Strong convergences are also established. This allows us to find, after a proper scaling, the limit of the electrostatic force applied to the rotor in the longitudinal direction.

Homogenization of a modified bidomain model involving imperfect transmission

“…We point out again that our model generalizes the modified bidomain one with diffusive inclusions and perfect transmission conditions considered in [21,22], the original model being recovered by suitably rearranging the parameters appearing in equation (2.20). We, finally, remark that homogenization techniques can be applied to improve the design of biomedical devices used in heart problems (see [24] and the references therein).…”

Homogenization of a Locally Periodic Oscillating Boundary

“…The transmission condition (34) means here that the trace of u 0 + on each connected component of the sections Y (x) for x ∈ − is equal to the trace of u 0 − . That is, zero jump condition into each branch from below.…”

“…There are many works on homogenization in periodically oscillating domains with pillar type oscillations of fixed amplitude where the cross-section of each pillar is constant in the vertical direction. For the literature on pillar type oscillations, we refer to [31,34,35,49] and the references therein. Oscillating boundary domains with nonuniform cylindrical pillars, that is when the cross-sections of the pillars are varying in the vertical direction, have been considered in [1,32,42,45].…”

Homogenization of a modified bidomain model involving imperfect transmission

“…We point out again that our model generalizes the modified bidomain one with diffusive inclusions and perfect transmission conditions considered in [21,22], the original model being recovered by suitably rearranging the parameters appearing in equation (2.20). We, finally, remark that homogenization techniques can be applied to improve the design of biomedical devices used in heart problems ( [24] and the references therein).…”