Abstract. We study a reaction-diffusion equation in a bounded domain in the plane, which is a mathematical model of an idealized electrostatically actuated microelectromechanical system (MEMS). A relevant feature in these systems is the "pull-in" or "jump-to contact" instability, which arises when applied voltages are increased beyond a critical value. In this situation, there is no longer a steady state configuration of the device where mechanical members of the device remain separate. It may present a limitation on the stable operation regime, as with a micropump, or it may be used to create contact, as with a microvalve. The applied voltage appears in the equation as a parameter. We prove that this parameter controls the dynamics in the sense that before a critical value the solution evolves to a steady state configuration, while for larger values of the parameter, the "pullin" instability or "touchdown" appears. We estimate the touchdown time. In one dimension, we prove that the touchdown is self-similar and determine the asymptotic rate of touchdown. The same type of results are obtained in a disk. We also present numerical simulations in some two-dimensional domains which allow an estimate of the critical voltage and of the touchdown time. This information is relevant in the design of the devices.
A mathematical model of an idealized electrostatically actuated MEMS or NEMS device is presented for the purpose of studying the dynamics of the so-called "pull-in" instability. This arises when applied voltages are increased beyond a certain critical voltage where steady-state solutions cease to exist. A reduced onedimensional nonlinear reaction-diffusion equation representing an idealized electrostatic structure is derived and analyzed. The coefficient tuning the nonlinear part determines existence of steady-state solutions. Questions about where, when, and how touchdown occurs are answered. A summary of new findings is presented and formal analytical results are compared with numerical approximations.
Perhaps the most widely known nonlinear phenomena in nano- and 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 present a limitation on the stable range of operation, as with a micropump, or may be utilized to create contact, as with a microvalve. Here, a mathematical model of an idealized electrostatically actuated MEMS or NEMS device is constructed for the purpose of studying the dynamics and touchdown behavior of systems operated in the pull-in regime. The model is analyzed in the viscosity dominated limit. This gives rise to a non-linear parabolic equation of reaction-diffusion type. The model is studied using a combination of analytical and numerical techniques.
An artificial neural network (ANN) has been designed to obtain neutron doses using only the count rates of a Bonner spheres spectrometer (BSS). Ambient, personal and effective neutron doses were included. One hundred and eighty-one neutron spectra were utilised to calculate the Bonner count rates and the neutron doses. The spectra were transformed from lethargy to energy distribution and were re-binned to 31 energy groups using the MCNP 4C code. Re-binned spectra, UTA4 response matrix and fluence-to-dose coefficients were used to calculate the count rates in the BSS and the doses. Count rates were used as input and the respective doses were used as output during neural network training. Training and testing were carried out in the MATLAB environment. The impact of uncertainties in BSS count rates upon the dose quantities calculated with the ANN was investigated by modifying by +/-5% the BSS count rates used in the training set. The use of ANNs in neutron dosimetry is an alternative procedure that overcomes the drawbacks associated with this ill-conditioned problem.
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