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Aims: In this research work, a design method and a comparative of a touch mode capacitive pressure sensor (TMCPS) using poly-dimethyl-siloxane (PDMS) and poly-methyl methacrylate (PMMA) is the done. A novel method is proposed to linear the output characteristics of the sensor because planer type capacitive sensors are non-linear. Study Design: This method uses a mechanical coupler to convert the deflection of the diaphragm into a linear displacement that helps to linear the output characteristics. The mathematical model of the sensor is designed and simulated the 3D model to validate the mathematically calculated values. Place and Duration of Study: This study is done in the Department of Electronics and Communication Engineering, Rajiv Gandhi University, Arunachal Pradesh at COMSOL Simulation Laboratory during 2021 to 2023. Methodology: The mechanical and electrostatic components of the sensor are represented mathematically model in two separate parts. For this study, a square diaphragm was used since it exhibits greater deflection than circular or rectangular diaphragms. In order to validate the model equation, a 3D model of a sensor is created in the COMSOL Multiphysics simulator and simulated. For the pressure range of 0.1 [MPa] to 10.1 [MPa], the identical 3D model of the sensor construction with a square diaphragm thickness of 20 µm is simulated for PDMS and PMMA. The different elements influencing the sensor's sensitivity are discovered, and the effects of the materials PDMS and PMMA on the output characteristic are discussed. Results: The simulated and calculated sensitivity of the sensors based on PDMS are 0.03685 [fF/MPa] and 0.03467 [fF/MPa] respectively. And the simulated and calculated sensitivity of the sensors based on PMMA are 0.03929 [fF/MPa] and 0.03748 [fF/MPa] respectively. It is observed that the PDMS based TMCPS has more sensitivity then the PMMA based TMCPS. Conclusion: The PMMA based TMCPS has higher sensitivity than the PDMS based TMCPS. The various parameters that affect the sensitivity of the sensor are diaphragm shape, size, Poisson’s ratio and Young’s modulus, area covered by the dielectric material, dielectric constant of the polymers dielectric and surface are of the electrode plate. Future Scope: Future research for TMCPS can be conducted using composite polymer dielectric materials and new polymer dielectric materials to improve the sensitivity. One can optimize the sensor using different tools as the mathematical model is developed.

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Aims: The main aim of this research work is: To design a mathematical model of the sensor and validate with the 3D model simulation of the sensor in COMSOL Multiphysics simulator and To optimize the sensor for maximizing its sensitivity. Study Design: In the methodology, we design and utilizePZT-5A piezoelectric in shear mode as the piezoelectric is attached on a cantilever structure. The various factors affecting the sensitivity of the sensor are investigated after validating the mathematical model with the simulated values. Place and Duration of Study: This study is done in the Department of Electronics and Communication Engineering, Rajiv Gandhi University, Arunachal Pradesh at COMSOL Simulation Laboratory during 2022 to 2023. Methodology: In this study, a cantilever structure is considered for the mechanical structure. The stress distribution on the structure is calculated for the applied pressure range from 0 to 1000 Pa. Later, the output voltage of the sensor is calculated. This mathematical model is validated with the COMSOL multiphysics simulator. The optimization of the sensor is done in mathematical tool with maximizing function after providing the conditions.  Results: The maximum stress on the sensor structure occurred near the clamped part of the cantilever. The calculated and simulated output sensitivities of the PZT-5A piezoelectric based pressure sensor are-1.6021 mV/kPa and -1.046887 mV/kPa respectively. Conclusion: We conclude that the PZT-5A piezoelectric based pressure sensor has a linear output with negative gradient as the stress induced on the structure is tensile stress. The various parameters that affect the sensitivity of the sensor arefound to depend on the shape and size of the cantilever structure, Poisson’s ratio and Young’s modulus, piezoelectric voltage coefficient and piezoelectric material thickness. Future Scope:  In future, this study can be extended by taking different shape and size of the cantilever. The different modes of piezoelectric and different materials may be another future scope of this study.

In modified gravity, we investigate the universe’s accelerating expansion in a vacuum. We obtain a highly nonlinear differential equation from the variation of Einstein–Hilbert action with the consideration of a Robertson–Walker metric. Because the differential equations have non-analytic solutions, the expansion phase of the Friedmann–Robertson–Walker universe is studied using numerical approaches. We analyzed the acceleration phases of the cosmos for different periods, cosmic jerk and snap parameters, and their dependencies on the initial values and coupling parameters involved in various [Formula: see text] gravity models. Using a parametric technique, we also give the values of the jerk and snap parameters in different accelerating stages of the universe. Finally, the behavior of the dark energy component is addressed for [Formula: see text] models.