Nanomechanical motion transducers for miniaturized mechanical systems

Reliable operation of a miniaturized mechanical system requires that nanomechanical motion be transduced into electrical signals (and vice versa) with high fidelity and in a robust manner. Progress in transducer technologies is expected to impact numerous emerging and future applications of micro- and, especially, nanoelectromechanical systems (MEMS and NEMS); furthermore, high-precision measurements of nanomechanical motion are broadly used to study fundamental phenomena in physics and biology. Therefore, development of nanomechanical motion transducers with high sensitivity and bandwidth has been a central research thrust in the fields of MEMS and NEMS. Here, we will review recent progress in this rapidly-advancing area. © 2017 by the authors

Inertial imaging with nanomechanical systems

Mass sensing with nanoelectromechanical systems has advanced significantly during the last decade. With nanoelectromechanical systems sensors it is now possible to carry out ultrasensitive detection of gaseous analytes, to achieve atomic-scale mass resolution and to perform mass spectrometry on single proteins. Here, we demonstrate that the spatial distribution of mass within an individual analyte can be imaged - in real time and at the molecular scale - when it adsorbs onto a nanomechanical resonator. Each single-molecule adsorption event induces discrete, time-correlated perturbations to all modal frequencies of the device. We show that by continuously monitoring a multiplicity of vibrational modes, the spatial moments of mass distribution can be deduced for individual analytes, one-by-one, as they adsorb. We validate this method for inertial imaging, using both experimental measurements of multimode frequency shifts and numerical simulations, to analyse the inertial mass, position of adsorption and the size and shape of individual analytes. Unlike conventional imaging, the minimum analyte size detectable through nanomechanical inertial imaging is not limited by wavelength-dependent diffraction phenomena. Instead, frequency fluctuation processes determine the ultimate attainable resolution. Advanced nanoelectromechanical devices appear capable of resolving molecular-scale analytes. © 2015 Macmillan Publishers Limited. All rights reserved

Numerical Analysis of Multi-Domain Systems: Coupled Nonlinear PDEs & DAEs with Noise

We present a numerical modeling and simulation paradigm for multi-domain, multi-physics systems with components modeled both in a lumped and distributed manner. The lumped components are modeled with a system of differential-algebraic equations (DAEs), whereas the possibly nonlinear distributed components that may belong to different physical domains are modeled using partial differential equations (PDEs) with associated boundary conditions (BCs). We address a comprehensive suite of problems for nonlinear coupled DAE-PDE systems including (i) transient simulation, (ii) periodic steady-state (PSS) analysis formulated as a mixed boundary value problem that is solved with a hierarchical spectral collocation technique based on a joint Fourier-Chebyshev representation, for both forced and autonomous systems, (iii) Floquet theory and analysis for coupled linear periodically time-varying (LPTV) DAE-PDE systems, (iv) phase noise analysis for multi-domain oscillators, (v) efficient parameter sweeps for PSS and noise analyses based on first-order and pseudo-arclength continuation schemes. All of these techniques, implemented in a prototype simulator, are applied to a substantial case study: A multi-domain feedback oscillator composed of distributed and lumped components in two physical domains, namely, a nano-mechanical beam resonator operating in the nonlinear regime, an electrical delay line, an electronic amplifier and a sensor-actuator for the transduction between the two physical domains. IEE