In this paper we present a mathematical model for the dynamics of an electrostatically actuated micro-cantilever. For the common case of cantilevers excited by a periodic voltage, we show that the underlying linearized dynamics are those of a periodic system described by a Mathieu equation. We present experimental results that confirm the validity of the model, and in particular illustrate that...

In this study a possible application of time-dependent canonical perturbation theory to a fast nonlinear time-periodic Hamiltonian with strong internal excitation is considered. It is shown that if the time-periodic unperturbed part is quadratic. the Hamiltonian may be canonically transformed to an equivalent form in which the new unperturbed part is time-invariant so that the time-dependent ca...

It is shown that the complete localization of eigenvectors for the almost Mathieu operator entails the absence of Cantor spectrum for this operator.

In this paper, considering symmetric collapse mode for hybrid tubes, and using Tsai-Hill fracture criterion to take into account the off-axis strength of an orthotropic lamina, an analytical model is extended and an expression is derived for mean crushing load and fold lengths of circular hybrid tubes. In this model, the influences of the geometrical dimensions including diameter, thickness of ...

Vibration frequencies and modes for the thickness-shear vibrations of infinite partially-electroded circular AT-cut quartz plates are obtained by solving the two-dimensional (2D) scalar differential equation derived by Tiersten and Smythe. The Mathieu and modified Mathieu equations are derived from the governing equation using the coordinate transform and the collocation method is used to deal ...

Title: MORBIDITY AND MORTALITY RELATED TO PNEUMONIA AND TRACHEOBRONCHITIS IN ICU AFTER LUNG TRANSPLANTATION Authors: Sébastien TANAKA ([email protected]) Claire GENEVE ([email protected]) Gianpiero TEBANO ([email protected]) Nathalie GRALL ([email protected]) Pascale PIEDNOIR ([email protected]) Régis BRONCHARD ([email protected]) Mathieu GODEMENT (mathi...

We show that the complex PT -symmetric periodic potential V (x) = −(iξ sin 2x+ N)2, where ξ is real and N is a positive integer, is quasi-exactly solvable. For odd values of N ≥ 3, it may lead to exceptional points depending upon the strength of the coupling parameter ξ. The corresponding Schrödinger equation is also shown to go over to the Mathieu equation asymptotically. The limiting value of...

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they res...