Effect of Pressure on Fluid Damping in MEMS Torsional Resonators with Flow Ranging from Continuum to Molecular Regime

High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However, when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels that may vary from atmospheric to low vacuum. The interaction of the surrounding fluid with the vibrating structure leads to dissipation, thus bringing down the quality factor. Depending on the ambient fluid pressure or the gap between the vibrating and the fixed structure, the fluid motion can range from continuum flow to molecular flow giving a wide range of dissipation. The relevant fluid flow characteristics are determined by the Knudsen number which is the ratio of the mean free path of the gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably big for molecular flow. In this paper, we study the effect of fluid pressure on the quality factor by carrying out experiments on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects and switches. We only vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow, transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different air pressures ranging from 760 Torr to 0.001 Torr. The variation of this pressure over six orders of magnitude ensures required rarefaction to range over all flow conditions. Finally, we get the variation of quality factor with pressure. The result indicates that the quality factor, Q, follows a power law, Q ∝P ^–r , with different values of the exponent r in different flow regimes. In the second part of the paper, we propose the use of effective viscosity for considering velocity slip conditions in solving Navier–Stokes equation numerically. This concept is validated with analytical results for a simple case and then compared with the experimental results presented in this paper. The study shows that the effective viscosity concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h ₀/L<0.01). As this ratio increases, the range of validity decreases.     

Acetyltrimethylsilane mediated synthesis of dihydrophenanthrenes

An easy and efficient synthesis of phenanthrene derivatives through base catalyzed ring transformation of 4-sec-amino-2-oxo-5,6-dihydro-2H-benzo[h]chromene-3-carbonitriles with acetyltrimethylsilane is described in good yields. The advantage of this reaction is the direct transformation of 2-oxobenzo[h]chromene into phenanthrene via C-C insertion from acetyltrimethylsilane.     

On bifurcations in a chaotically stirred excitable medium

We study a one-dimensional filamental model of a chaotically stirred excitable medium. In a numerical simulation we systematically explore its rich bifurcation scenarios involving saddle-nodes, Hopf bifurcations and hysteresis loops. The bifurcations are described in terms of two parameters signifying the excitability of the reacting medium and the strength of the chaotic stirring, respectively. The solution behaviour, in particular at the bifurcation points, is analytically described by means of a nonperturbative variational method. Using this method we reduce the partial differential equations to either algebraic equations for stationary solutions and bifurcations, or to ordinary differential equations in the case of non-stationary solutions and bifurcations. We present numerical simulations corroborating our analytical results.     

Transparent water repellent silica films by sol-gel process

Non-wettable surfaces with high contact angles and facile sliding angle of water droplets have received tremendous attention in recent years. The present paper describes the room temperature (∼27 °C) synthesis of dip coated water repellent silica coatings on glass substrates using iso-butyltrimethoxysilane (iso-BTMS) as a co-precursor. Emphasis is given to the influence of the hydrophobic reagent (iso-BTMS) on the water repellent properties of the silica films. Silica sol was prepared by keeping the molar ratio of tetraethoxysilane (TEOS) precursor, methanol (MeOH) solvent, water (H₂O) constant at 1:16.53:8.26 respectively, with 0.01 M NH₄F throughout the experiment and the molar ratio of iso-BTMS/TEOS (M) was varied from 0 to 0.965. The effect of M on the surface structure and hydrophobicity has been researched. The static water contact angle values of the silica films increased from 65° to 140° and water sliding angle values decreased from 42° to 16° with an increase in the M value from 0 to 0.965. The water repellent silica films are thermally stable up to a temperature of 280 °C and above this temperature the film shows hydrophilic behavior. The water repellent silica films were characterized by the Fourier Transform Infrared (FT-IR) Spectroscopy, Scanning Electron Microscopy (SEM), Atomic Force Microscopy (AFM), % of optical transmission, thermal and chemical aging tests, humidity tests, static and dynamic water contact angle measurements.     

Consistency and variations in optical characteristics of four-layer polymeric waveguides

In the present work, four-layer polymeric waveguides have been fabricated and characterized by interchanging the film layer. Using polyvinyl alcohol (PVA) and styrene acrylonitrile (SAN) polymer it has been shown that polymers do not loose their own property in multilayer structure and better efficiency can be achieved in the form of low propagation losses and mode filtration. Due to high contrast of PVA and SAN films, a broad spectrum of refractive index in four-layer structure has been achieved.     

Synergism in electron gas in crossed fields

An electron gas in crossed electric and magnetic fields of arbitrary strength is considered in the framework of nonequilibrium statistical mechanics. It is known that more than one independent frequency existing in a system, which are of comparable magnitude, can generate coherent synergic radiation. In the present system three independent frequencies exist: viz the synchrotron frequency due to the magnetic field, the hopping frequency due to the electric field, and the plasma frequency. It is shown that all these can combine to generate a new synergic coherent radiation. The results also show the possibility of interpreting the quantum nature of Hall conductance as due to density function alone. Besides these, the solution admits the Schubnikov-de Haas oscillation of the electrical conductivity due to change in the fields.     

Investigation of energetic ion-induced mixing in Bi/Ge system

The present study is carried out for the investigation of energetic ion beam mixing in the Bi/Ge system, induced by electronic excitation. The system Ge/Bi/C was deposited on Si substrate at room temperature in the high vacuum deposition system and irradiated using Au ions of 120?MeV at the fluences 1?×?10¹³, 5?×?10¹³ and 1?×?10¹⁴?ions/cm². The top layer of carbon was deposited as the protecting layer to avoid oxidation. The swift heavy ions (SHI)-induced interface mixing was studied by Rutherford backscattering spectroscopy (RBS) for depth profiles and compositions, grazing incidence X-ray diffraction (GIXRD) for phase identification and atomic force microscopy (AFM) for surface roughness. We have calculated the mixing rate, mixing efficiency and inter-diffusion coefficient for the Bi/Ge system. We observed that the thickness of the mixed region increased with increasing fluence. In the GIXRD pattern, no new crystalline phase formation was observed after irradiation, the mixed region may be in an amorphous form. The mixing effect is explained in the framework of the thermal spike model.     

Time series model for GLWB with surrender benefit and stochastic interest rate: Dynamic withdrawal approach

This study investigates the pricing problem of a variable annuity (VA) contract embedded with a guaranteed lifetime withdrawal benefit (GLWB) rider. VAs are annuities in which the value is linked to a bond and equity sub-account fund. The guaranteed lifetime withdrawal benefit rider regularly provides a series of payments to the policyholder for the term of the policy while he/she is alive, regardless of portfolio performance. At the time of the policyholder's death, the remaining fund value is given to his nominee. Therefore, proper fund modeling is critical in the pricing of VA products. Several writers in the literature used a GBM model in which variance is considered to be constant to represent the fund value in a variable annuity contract. However, on the other hand, the returns on financial assets are non-normally distributed in real life. A bit much Kurtosis, leverage effect, and Non-zero Skewness characterize the returns. The generalized autoregressive conditional heteroscedastic (GARCH) models are also used for presenting a discrete framework for the pricing of GLWB. Still, the interest rate was kept constant without including the surrender benefit and the static withdrawal approach, which keeps the model far from the real scenario. Thus, in this research, the generalized GARCH models are used with surrender benefit and dynamic withdrawal strategy to develop a time series model for the pricing of annuity that overcomes the constraints of previous models. A numerical illustration and sensitivity analysis are used to examine the suggested model.     

Effect of pit formation and surface roughness on size-dependent thermal conductivity of nanometer-thick semiconducting films

In this work, the thermal conductivity variation due to pit formation and surface roughness in nanometer-thick semiconducting films has been studied. It is shown that the thermal conductivity of thin films is reduced due to the presence of these effects in the films. This reduction in thermal conductivity is dependent on film thickness. The present analysis has been done on GaAs nanometer-thick films using the available experimental data.