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Related papers: Finite time singularity in a MEMS model revisited

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A moving boundary problem with two free boundaries modeling a two-dimensional idealized MEMS device with pull-in instability is discussed. We use a fixed point argument to show that the model possesses stationary solutions for small source…

Analysis of PDEs · Mathematics 2014-07-15 Martin Kohlmann

In this paper we study the local wellposedness of the solution to a non-linear parabolic-dispersive coupled system which models a Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device has two…

Analysis of PDEs · Mathematics 2023-12-06 Heiko Gimperlein , Runan He , Andrew A. Lacey

We discuss an evolution free boundary problem of mixed type with two free boundaries modeling an idealized electrostatically actuated MEMS device. While the electric potential is the solution of an elliptic equation, the dynamics of the…

Analysis of PDEs · Mathematics 2015-08-11 Martin Kohlmann

This dissertation presents a new coupled electro-mechanical model that is an improvement on the classical parallel-plate approximation. The model employs a hyperbolic function to account for the beam deformed shape and electrostatic field.…

Applied Physics · Physics 2017-08-24 Xi Luo

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 insulating layer covering the bottom plate tends to zero. This…

Analysis of PDEs · Mathematics 2020-04-01 Philippe Laurençot , Katerina Nik , Christoph Walker

Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures with cross-sections of the order of microns ($\mu m$) and lengths of the order of tens or hundreds of microns. These structures are often plates or array of…

Computational Physics · Physics 2007-05-23 N. Majumdar , S. Mukhopadhyay

We consider periodically driven potential impurities coupled to the surface states of a two-dimensional topological insulator. The problem is addressed by means of two models, out which the first model is an effective continuum Hamiltonian…

Strongly Correlated Electrons · Physics 2019-10-02 Saurabh Pradhan , Jonas Fransson

In the current work we study a stochastic parabolic problem. The underlying problem is actually motivated by the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device in the case of random fluctuations of…

Analysis of PDEs · Mathematics 2020-12-22 Ourania Drosinou , Nikos I. Kavallaris , Christos V. Nikolopoulos

In canonical models of Micro-Electro Mechanical Systems (MEMS), an event called touch- down whereby the electrical components of the device come into contact, is characterized by a blow up in the governing equations and a non-physical…

Analysis of PDEs · Mathematics 2013-10-02 A. E. Lindsay , J. Lega , K. B. Glasner

We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…

Analysis of PDEs · Mathematics 2025-12-10 Irina Kmit , Natalya Lyul'ko

Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures (plates or array of thin beams) with cross-sections of the order of microns and lengths of the order of tens or hundreds of microns. Electrostatic forces play…

Computational Physics · Physics 2007-05-23 N. Majumdar , S. Mukhopadhyay

A coupled system consisting of a quasilinear parabolic equation and a semilinear hyperbolic equation is considered. The problem arises as a small aspect ratio limit in the modeling of a MEMS device taking into account the gap width of the…

Analysis of PDEs · Mathematics 2024-04-25 Christoph Walker

This paper proposes a new general methodology for finite-time singularity formation for moving interface problems involving the incompressible Euler equations in the plane. The first problem considered is the two-phase Euler vortex sheets…

Analysis of PDEs · Mathematics 2017-09-04 Daniel Coutand

We study the effect of the parameter $\lambda$, the dimension $N$, the profile $f$ and the geometry of the domain $\Omega \subset\mathbb{R}^N$, on the question of uniqueness of the solutions to the following elliptic boundary value problem…

Analysis of PDEs · Mathematics 2008-10-08 Nassif Ghoussoub , Pierpaolo Esposito

In this note we discuss metastability in a long-but-finite range disordered model for the glass transition. We show that relaxation is dominated by configuration belonging to metastable states and associate an in principle computable…

Statistical Mechanics · Physics 2009-11-11 Silvio Franz

We study periodic solutions of a one-degree of freedom micro-electro-mechanical system (MEMS) with a parallel-plate capacitor under $T$--periodic electrostatic forcing. We obtain analytical results concerning the existence of $T-$ periodic…

Dynamical Systems · Mathematics 2021-12-01 Shirali Kadyrov , Ardak Kashkynbayev , Piotr Skrzypacz , Konstantinos Kaloudis , Anastasios Bountis

The aim of this paper is to deal with multi-physics simulation of micro-electro-mechanical systems (MEMS) based on an advanced numerical methodology. MEMS are very small devices in which electric as well as mechanical and fluid phenomena…

Other Computer Science · Computer Science 2007-11-29 V. Rochus , J. -C. Golinval , C. Louis , C. Mendez , I. Klapka

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 properties they feature. Still most research is devoted to an…

Analysis of PDEs · Mathematics 2017-06-12 Philippe Laurencot , Christoph Walker

The parabolic problem $u_t-\Delta u=\frac{\lambda f(x)}{(1-u)^2}+P$ on a bounded domain $\Omega$ of $R^n$ with Dirichlet boundary condition models the microelectromechanical systems(MEMS) device with an external pressure term. In this…

Analysis of PDEs · Mathematics 2023-09-15 Lingfeng Zhang , Xiaoliu Wang

We investigate the finite time stability property of one-dimensional nonautonomous initial boundary value problems for linear decoupled hyperbolic systems with nonlinear boundary conditions. We establish sufficient and necessary conditions…

Analysis of PDEs · Mathematics 2025-12-10 Irina Kmit