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.

This study analyzes the grid-connected PV system performances over a 10-year period under temperate continental conditions in Niš. Based on the experimental results, we found the following: the 10-year yearly average values of PV system efficiency, Yf, CF, and PR are 10.49%, 1178.51 kWh/kWp, 13.45%, and 0.87, respectively. The yearly average value of PV performances for a 10-year measurement indicates that the behavior of the given PV system over 10 years does not change significantly. Besides, a mathematical prediction model was obtained through regression analysis, and ANOVA was applied for testing the model’s validity. It is shown that the obtained model is statistically significant and enables prediction better than a simple average, the mean values of PV electricity are not changed statistically significantly over the 10 observed years, and there is a statistically significant difference in POA mean radiation during the months over 10 years. Based on the obtained model and POA radiation values, a prediction of the PV system output can be made for similar PV installations. The analysis presented in this study significantly impacts energy prediction, PV energy modeling, and the economics and profitability of the grid-connected PV system utilization, as well as the PV systems’ operation planning and maintenance.

In this paper, the homotopy perturbation method (HPM) is applied to the coupled set of Schrödinger–Poisson (SP) equations in inversion layer problem for obtaining the approximate analytical solution. Inversion layer of n-type is considered, and the electric quantum limit is assumed. By introducing some dimensionless quantities, the SP system has been turned into one which can be solved along the infinite interval. After some appropriate transformations, the infinite interval has been reduced to finite one ( 0 , 1 ) $(0,1)$ , and recurrence series of the HPM approximate solutions of the coupled SP system have been obtained. The existence and convergence of obtained HPM approximate solutions have been formally proved. Moreover, these solutions show relative simple mathematical form, as well as high degree of accuracy what is desirable for semiconductor device modelling.

Modeling of the electrostatic potential for fully depleted (FD) silicon-on-insulator (SOI) metal-oxide-semiconductor field effect transistor (MOSFET) is presented in this article. The modeling is based on the analytical solution of two-dimensional Poisson’s equation obtained by using the homotopy perturbation method (HPM). The HPM with suitable boundary conditions results in the so-called HPM solution in general and closed-form, independent of the surface potential. The HPM solution has been applied in modeling the output characteristics of the FDSOI MOSFET, which show good agreement compared with the numerical results.