ترغب بنشر مسار تعليمي؟ اضغط هنا

Heterogeneous dielectric properties in MEMS models

164   0   0.0 ( 0 )
 نشر من قبل Philippe Laurencot
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

An idealized electrostatically actuated microelectromechanical system (MEMS) involving an elastic plate with a heterogeneous dielectric material is considered. Starting from the electrostatic and mechanical energies, the governing evolution equations for the electrostatic potential and the plate deflection are derived from the corresponding energy balance. This leads to a free boundary transmission problem due to a jump of the dielectric permittivity across the interface separating elastic plate and free space. Reduced models retaining the influence of the heterogeneity of the elastic plate under suitable assumptions are obtained when either the elastics plate thickness or the aspect ratio of the device vanishes.



قيم البحث

اقرأ أيضاً

A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential threshold is not accompanied by a breakdown of the model, but is recovered by the saturation of the constraint for pulled-in states. It is shown that a maximal stationary solution exists and that saturation only occurs for large potential values. In addition, the existence, uniqueness, and large time behavior of solutions to the evolution equation are studied.
170 - Kin Ming Hui 2010
Let $Omegasubsetmathbb{R}^n$ be a $C^2$ bounded domain and $chi>0$ be a constant. We will prove the existence of constants $lambda_Ngelambda_N^{ast}gelambda^{ast}(1+chiint_{Omega}frac{dx}{1-w_{ast}})^2$ for the nonlocal MEMS equation $-Delta v=lam/(1 -v)^2(1+chiint_{Omega}1/(1-v)dx)^2$ in $Omega$, $v=0$ on $1Omega$, such that a solution exists for any $0lelambda<lambda_N^{ast}$ and no solution exists for any $lambda>lambda_N$ where $lambda^{ast}$ is the pull-in voltage and $w_{ast}$ is the limit of the minimal solution of $-Delta v=lam/(1-v)^2$ in $Omega$ with $v=0$ on $1Omega$ as $lambda earrow lambda^{ast}$. We will prove the existence, uniqueness and asymptotic behaviour of the global solution of the corresponding parabolic nonlocal MEMS equation under various boundedness conditions on $lambda$. We also obtain the quenching behaviour of the solution of the parabolic nonlocal MEMS equation when $lambda$ is large.
The goal of this paper is to derive rigorously macroscopic traffic flow models from microscopic models. More precisely, for the microscopic models, we consider follow-the-leader type models with different types of drivers and vehicles which are distr ibuted randomly on the road. After a rescaling, we show that the cumulative distribution function converge to the solution of a macroscopic model. We also make the link between this macroscopic model and the so-called LWR model.
Energy minimizers to a MEMS model with an insulating layer are shown to converge in its reinforced limit to the minimizer of the limiting model as the thickness of the layer tends to zero. The proof relies on the identification of the $Gamma$-limit of the energy in this limit.
199 - Kin Ming Hui 2008
We prove the local and global existence of solutions of the generalized micro-electromechanical system (MEMS) equation $u_t =Delta u+lambda f(x)/g(u)$, $u<1$, in $Omegatimes (0,infty)$, $u(x,t)=0$ on $partialOmegatimes (0,infty)$, $u(x,0)=u_0$ in $Om ega$, where $OmegasubsetBbb{R}^n$ is a bounded domain, $lambda >0$ is a constant, $0le fin C^{alpha}(overline{Omega})$, $f otequiv 0$, for some constant $0<alpha<1$, $0<gin C^2((-infty,1))$ such that $g(s)le 0$ for any $s<1$ and $u_0in L^1(Omega)$ with $u_0le a<1$ for some constant $a$. We prove that there exists a constant $lambda^{ast}=lambda^{ast}(Omega, f,g)>0$ such that the associated stationary problem has a solution for any $0lelambda<lambda^*$ and has no solution for any $lambda>lambda^*$. We obtain comparison theorems for the generalized MEMS equation. Under a mild assumption on the initial value we prove the convergence of global solutions to the solution of the corresponding stationary elliptic equation as $ttoinfty$ for any $0lelambda<lambda^*$. We also obtain various conditions for the existence of a touchdown time $T>0$ for the solution $u$. That is a time $T>0$ such that $lim_{t earrow T}sup_{Omega}u(cdot,t)=1$.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا