Higher order Markov chain models for monsoon rainfall over West Bengal, India

39-44 Two-state Markov chain models of different orders have been used to simulate the pattern of rainfall during the monsoon season (June-September) over Gangetic West Bengal (India). The analysis is based on the relevant data for 31-year period (1970-2000) for four major meteorological stations in the region. The determination of the proper order of the Markov chain that best describes the rainfall pattern is an interesting problem and Bayesian information criterion has been used for the purpose. Bayesian information criterion (BIC) reveals that third order Markov chain model best describes the rainfall pattern in general except for one station. This is verified and it is found that third/fourth order chain simulates the observed data more closely than the chains of other orders using the classical goodness of fit test. The time independent behaviour of the chain has also been studied with the help of steady state probabilities. The theoretical and observed values of the mean recurrence time have been found to be in close agreement. </smarttagtype

Squeeze Film Effect in Surface Micromachined Nano Ultrasonic Sensor for Different Diaphragm Displacement Profiles

In the present paper, we have analytically explored the small variations of the local pressure in the trapped air film of both sides of the clamped circular capacitive micromachined ultrasonic transducer (CMUT), which consists of a thin movable membrane of silicon nitride (Si3N4). This time-independent pressure profile has been investigated thoroughly by solving the associated linear Reynold's equation in the framework of three analytical models, viz. membrane model, plate model, and non-local plate model. The solution involves Bessel functions of the first kind. The Landau-Lifschitz fringing technique has been assimilated to engrave the edge effects in estimation of the capacitance of CMUT, which should be considered in the micrometer or lesser dimension. To divulge the dimension-based efficacy of the considered analytical models, various statistical methods have been employed. Our use of contour plots of absolute quadratic deviation revealed a very satisfactory solution in this direction. Though the analytical expression of the pressure profile is very cumbersome in various models, the analysis of these outputs exhibits that the pressure profile follows the displacement profile in all the cases indicating no viscous damping. A finite element model (FEM) has been used to validate the systematic analyses of displacement profiles for several radii and thicknesses of the CMUT's diaphragm. The FEM result is further corroborated by published experimental results bearing excellent outcome