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.     

Charge Reconfiguration in Isolated Quantum Dot Arrays

A high level of tunability and control over arrays of quantum dots are key ingredients toward the goal of scalable‐based qubit architectures. Increasing array size simultaneously increases the parameter space and therefore the tuning complexity. The electron reconfiguration behavior of quantum dot arrays isolated from the electron reservoirs is studied experimentally. Isolating a quantum dot array from the reservoirs does not only enable a high degree of control over the tunnel couplings but at the same time drastically simplifies the stability diagrams for small numbers of electrons trapped in the array. Experimental results on double, triple, and quadruple quantum dot arrays are presented and complementary model calculations allow the identification of all transitions observed in the experiment. Highly tunable long‐range transitions are observed in isolated triple quantum dots and evidence of higher‐order cotunneling is found for the quadruple quantum dot array.     

Exploring k and ? with R–Equation Model Using Elliptic Relaxation Function

An extended version of the isotropic R?Cequation model accompanied by an elliptic relaxation approach to account for the distinct effects of low-Reynolds number (LRN) and wall proximity is proposed. The turbulent kinetic energy k and the dissipation rate ? are evaluated using the R ( $=k^2/\tilde{\epsilon}$ ) transport equation together with some empirical relations. The eddy viscosity formulation maintains the positivity of normal Reynolds stresses and the Schwarz?? inequality for turbulent shear stresses. The model coefficients/functions preserve the anisotropic characteristics of turbulence in the sense that they are sensitized to rotational and nonequilibrium flows. The model is validated against a few well-documented flow cases, yielding predictions in good agreement with the direct numerical simulation (DNS) and experimental data. Comparisons indicate that the present model offers some improvement over the Spalart?CAllmaras one?Cequation model and competitiveness with the SST k?C?? model.     

An efficient Schottky-varactor frequency multiplier at millimeter waves. Part IV. Quintupler

The multiplication efficiency of a millimeter-wave Schottky-varactor quintupler with fixed idler terminations was studied. The highest efficiency measured was 4.2% at 168 GHz with 10 mW input power and 3.3% with 40 mW input power. Over the range from 165 GHz to 170 GHz the output power was 0.7–1.3 mW withp _in =40 mW.     

A simplified approach to the generalized standard-addition method and its application in electrothermal atomic absorption spectrometry

A simple and general standard-addition method for a single-component determination is presented. The method uses two independent variables for the calculation of the analyte concentration (the amount of sample taken and the amount of analyte added) and one dependent variable, the response. The sensitivity and the response of the blank can also be estimated from the model by changing the amount of the sample and the amount of the analyte addition. In the simples case, a linear equation is assumed to exist between the variables. Geometrically, the model can be expressed by the response plane in the variable-space. The method has all the advantages of the ordinary standard-addition method but also includes automatic blank elimination and versatile matrix-interference control. Two examples of the use of the method are based on graphite-furnace atomic absorption spectrometry of chromium and lead. Standard statistical packages are applied.     

High molar mass ethene/1‐olefin copolymers synthesized with acenaphthyl substituted metallocene catalysts

The influence of ligand structure on copolymerization properties of metallocene catalysts was elucidated with three C₁‐symmetric methylalumoxane (MAO) activated zirconocene dichlorides, ethylene(1‐(7, 9)‐diphenylcyclopenta‐[a]‐acenaphthadienyl‐2‐phenyl‐2‐cyclopentadienyl)ZrCl₂ ( 1 ), ethylene(1‐(7, 9)‐diphenylcyclopenta‐[a]‐acenaphthadienyl‐2‐phenyl‐2‐fluorenyl)ZrCl₂ ( 2 ), and ethylene(1‐(9)‐fluorenyl‐(R)1‐phenyl‐2‐(1‐indenyl)ZrCl2 ( 3 ). Polyethenes produced with 1 /MAO had considerable, ca. 10% amount of trans‐vinylene end groups, resulting from the chain end isomerization prior to the chain termination. When ethene was copolymerized with 1‐hexene or 1‐hexadecene using 1 /MAO, molar mass of the copolymers varied from high to moderate (531–116 kg/mol) depending on the comonomer feed. At 50% comonomer feed, ethene/1‐olefin copolymers with high hexene or hexadecene content (around 10%) were achievable. In the series of catalysts, polyethenes with highest molar mass, up to 985 kg/mol, were obtained with sterically most crowded 2 /MAO, but the catalyst was only moderately active to copolymerize higher olefins. Catalyst 3 /MAO produced polyethenes with extremely small amounts of trans‐vinylene end groups and relatively low molar mass 1‐hexene copolymers (from 157 to 38 kg/mol) with similar comonomer content as 1 . These results indicate that the catalyst structure, which favors chain end isomerization, is also capable to produce high molar mass 1‐olefin copolymers with high comonomer content. In addition, an exceptionally strong synergetic effect of the comonomer on the polymerization activity was observed with catalyst 3 /MAO. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 373–382, 2008