We analyze the nonlinear elliptic problem ∆u = λf(x) (1+u)2 on a bounded domain Ω of R with Dirichlet boundary conditions. This equation models a simple electrostatic Micro-Electromechanical System (MEMS) device consisting of a thin dielectric elastic membrane with boundary supported at 0 above a rigid ground plate located at −1. When a voltage –represented here by λ– is applied, the membrane d...

This paper is a continuation of [9], where we analyzed steady-states of the nonlinear parabolic problem ut = ∆u− λf(x) (1+u)2 on a bounded domain Ω of R with Dirichlet boundary conditions. This equation models a simple electrostatic Micro-Electromechanical System (MEMS) device consisting of a thin dielectric elastic membrane with boundary supported at 0 above a rigid ground plate located at −1....

Abstract The adequate modeling of the micro/nano arc resonators' dynamics is vital for their successful implementation. Here, a size-dependent model, wherein material structure, porosity, and micro-rotation effects grains are considered, derived by combining couple stress theory, multi-phase classical Euler–Bernoulli beam aiming to characterize frequency tunability resonators as monitoring eith...

We present a theoretical study of the Rayleigh-like, "pearling", instability recently observed in tubular vesicles of bilayer membranes under the action of optical tweezers. The tweezers are argued to pull the membrane into their operation zone, thereby inducing a tension m it. Consequently, the membrane can respond in a Rayleigh-like instability, m which its area decreases. Our approach is bas...

Postural instability is a disabling feature of Parkinson's disease (PD), contributing to recurrent falls and fall-related injuries. The retropulsion test is widely regarded as the gold standard to evaluate postural instability, and is therefore a key component of the neurological examination in PD. Many variants exist, which confuses both clinical practice and research. Here, we evaluate the me...