Numerical and analytical modelling of trapped gas in micromechanical squeeze-film dampers

Damping in air gaps of micromechanical devices that vibrate out-of-plane is studied at frequencies where the acoustic wavelength is comparable with the air gap dimensions. A FEM study with a viscoacoustic solver shows that above a certain frequency, closed damper borders can be assumed in the approximate analysis of the squeeze-film damper, regardless of the practical border conditions. Here, this closed-border (trapped gas) problem is solved analytically from the linearized Navier–Stokes equations in 1D. This results in a compact model for the mechanical impedance that accounts for damping, inertial and spring forces as well as thermal behaviour and slip border conditions. The model produces the gas resonances in the air gap when the wavelength of the acoustic wave is smaller than the gap dimensions. Due to the slip conditions, the model is valid in modeling micromechanical oscillating structures with small air gaps.     

Eigenvalue Asymptotics for Locally Perturbed Second-Order Differential Operators

We consider the appearance of discrete spectrum in spectralgaps of magnetic Schrödinger operators with electric backgroundfield under strong, localised perturbations. We show that forcompactly supported perturbations the asymptotics of the countingfunction of the occurring eigenvalues in the limit of a strongperturbation does not depend on the magnetic field nor on thebackground field.     

The Limit Distribution of the Largest Interpoint Distance from a Symmetric Kotz Sample

Generalizing recent work of P. C. Matthews and A. L. Rukhin (Ann. Appl. Probab.3(1993), 454–466), we obtain the limit law of the largest interpoint Euclidean distance for a spherically symmetric multivariate sample of the Kotz distribution. While going through the proof, some errors in the reasoning given by Matthews and Rukhin are pointed out and corrected.     

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms

In this paper, we introduce optimal control algorithm for the design of pulse sequences in NMR spectroscopy. This methodology is used for designing pulse sequences that maximize the coherence transfer between coupled spins in a given specified time, minimize the relaxation effects in a given coherence transfer step or minimize the time required to produce a given unitary propagator, as desired. The application of these pulse engineering methods to design pulse sequences that are robust to experimentally important parameter variations, such as chemical shift dispersion or radiofrequency (rf) variations due to imperfections such as rf inhomogeneity is also explained.