Touchdown is the Only Finite Time Singularity in a Three-Dimensional MEMS Model

Finite time singularity in a free boundary problem modeling MEMS

An idealized electostatically actuated microelectromechanical system (MEMS) consists of a fixed horizontal ground plate held at zero potential above which an elastic membrane held at potential V is suspended. A Coulomb force is generated by the potential difference across the device and results in a deformation of the membrane, thereby converting electrostatic energy into mechanical energy, see...

A scenario for finite-time singularity in the quasigeostrophic model

A possible route to finite-time singularity in the quasigeostrophic system, via a cascade of filament instabilities of geometrically decreasing spatial and temporal scales, is investigated numerically using a high-resolution hybrid contour dynamical algorithm. A number of initial temperature distributions are considered, of varying degrees of continuity. In all cases, primary, secondary, and te...

Lee-Yang edge singularity in the three-dimensional Gross-Neveu model at finite temperature

We discuss the relevance of the Lee-Yang edge singularity to the finite-temperature Z2-symmetry restoration transition of the Gross-Neveu model in three dimensions. We present an explicit result for its large-N free-energy density in terms of ζ(3) and the absolute maximum of Clausen’s function. The Gross-Neveu model in d = 3 dimensions provides a remarkable example of a second order temperature...

Similarity and singularity in adhesive elastohydrodynamic touchdown

Dynamics and Touchdown in Electrostatic MEMS

Perhaps the most widely known nonlinear phenomena in nanoand microelectromechanical systems is the “pull-in” or “jump-to-contact” instability. In this instability, when applied voltages are increased beyond a certain critical voltage there is no longer a steady-state configuration of the device where mechanical members remain separate. This instability affects the design of many devices. It may...