Some singular equations modeling MEMS

P Laurençot, C Walker - Bulletin of the American Mathematical Society, 2017 - ams.org
In the past fifteen years mathematical models for microelectromechanical systems (MEMS)
have been the subject of several studies, in particular due to the interesting qualitative …

Electrostatically actuated MEMS in the post-touchdown regime: the thin-dielectric limit and a novel reduced-order model for release dynamics

NN Goldberg, OM O'Reilly - International Journal of Solids and Structures, 2022 - Elsevier
Microelectromechanical systems (MEMS) often make use of a type of plate-based
electrostatic actuator that can, under certain conditions, come into contact with a dielectric …

Regularized model of post-touchdown configurations in electrostatic MEMS: Equilibrium analysis

AE Lindsay, J Lega, KB Glasner - Physica D: Nonlinear Phenomena, 2014 - Elsevier
In canonical models of Micro-Electro Mechanical Systems (MEMS), an event called
touchdown whereby the electrical components of the device come into contact, is …

Singular perturbation analysis of a regularized MEMS model

A Iuorio, N Popovic, P Szmolyan - SIAM Journal on Applied Dynamical …, 2019 - SIAM
Micro-Electro Mechanical Systems (MEMS) are defined as very small structures that
combine electrical and mechanical components on a common substrate. Here, the …

Numerical bifurcation analysis of post-contact states in mathematical models of Micro-Electromechanical Systems

CJ Naudet, AE Lindsay - Mathematics and Computers in Simulation, 2024 - Elsevier
This paper is a computational bifurcation analysis of a non-linear partial differential equation
(PDE) characterizing equilibrium configurations in Micro electromechanical Systems …

Regularized model of post-touchdown configurations in electrostatic MEMS: bistability analysis

AE Lindsay - Journal of Engineering Mathematics, 2016 - Springer
This paper considers the problem of stiction in electrostatic–elastic deflections whereby
elastic surfaces adhere to one another after coming into physical contact under attracting …

Monge–Ampére simulation of fourth order PDEs in two dimensions with application to elastic–electrostatic contact problems

KL DiPietro, AE Lindsay - Journal of Computational Physics, 2017 - Elsevier
We present an efficient moving mesh method for the simulation of fourth order nonlinear
partial differential equations (PDEs) in two dimensions using the Parabolic Monge–Ampére …

Heterogeneous dielectric properties in models for microelectromechanical systems

P Laurencot, C Walker - SIAM Journal on Applied Mathematics, 2018 - SIAM
An idealized electrostatically actuated microelectromechanical system involving an elastic
plate with a heterogeneous dielectric material is considered. Starting from the electrostatic …

Adaptive Solution to Two-Dimensional Partial Differential Equations in Curved Domains Using the Monge--Ampére Equation

KL DiPietro, AE Lindsay - SIAM Journal on Scientific Computing, 2019 - SIAM
We present a finite difference method for mesh generation and adaptation with application to
the solution of partial differential equations in curved domains. For mesh generation, we …

Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties

P Laurençot, K Nik, C Walker - Calculus of Variations and Partial …, 2022 - Springer
A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is
studied. It was derived in a previous work as a reinforced limit when the thickness of the …