Closed-form approximation of symmetric thin-film multi-layer plasmonic dispersion equation solutions

This study is devoted to the design of an elastic polymer thin film-based capacitive wind-pressure sensor to meet the anticipated use for real-time monitoring of structural wind pressure in civil engineering. This sensor is composed of four basic units: lateral elastic deflection unit of a wind-driven circular polymer thin film, parallel plate capacitor with a movable circular electrode plate, spring-driven return unit of the movable electrode plate, and dielectric materials between electrode plates. The capacitance of the capacitor varies with the parallel move of the movable electrode plate which is first driven by the lateral elastic deflection of the wind-driven film and then is, after the wind pressure is reduced or eliminated, returned quickly by the drive springs. The closed-form solution for the contact problem between the wind-driven thin film and the spring-driven movable electrode plate is presented, and its reliability is proved by the experiment conducted. The numerical examples conducted show that it is workable that by using the numerical calibration based on the presented closed-form solution the proposed sensor is designed into a nonlinear sensor with larger pressure-monitoring range and faster response speed than the linear sensor usually based on experimental calibration.

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Indentation Technique to Investigate Elastic Moduli of Thin Films on Substrates

MRS Proceedings ◽

10.1557/proc-130-105 ◽

1988 ◽

Vol 130 ◽

Cited By ~ 1

Author(s):

D. S. Stone ◽

T. W. Wu ◽

P.-S. Alexopoulos ◽

W. R. Lafontaine

Keyword(s):

Thin Film ◽

Experimental Data ◽

Thin Films ◽

Closed Form ◽

Elastic Moduli ◽

Depth Sensing ◽

Indentation Technique ◽

Average Displacement ◽

Elasticity Solutions ◽

Poor Adhesion

AbstractClosed-form elasticity solutions are introduced, that predict the average displacement beneath square and triangular, uniformly loaded areas at the surface of a bilayer. The solutions aid in the application of depth-sensing indentation techniques for measuring thin film elastic moduli. The elasticity solutions agree closely with experimental data of Al, Si, 1 μm Al on Si, and 2 μm Cr on Si. The case of poor adhesion between the film and substrate is briefly examined.

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Closed Form Approximation of Swap Exposures

SSRN Electronic Journal ◽

10.2139/ssrn.2334393 ◽

2013 ◽

Author(s):

Heikki Sepppll ◽

Ser-Huang Poon ◽

Thomas Schrrder

Keyword(s):

Closed Form ◽

Closed Form Approximation

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Economic Capital Modeling Closed Form Approximation for Real-Time Applications

SSRN Electronic Journal ◽

10.2139/ssrn.2444549 ◽

2014 ◽

Author(s):

Thomas Ribarits ◽

Axel Clement ◽

Heikki Sepppll ◽

Hua Bai ◽

Ser-Huang Poon

Keyword(s):

Closed Form ◽

Real Time ◽

Economic Capital ◽

Real Time Applications ◽

Closed Form Approximation

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A simple closed form dispersion equation for shear types of surface waves propagating in periodic structures

IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control ◽

10.1109/58.251293 ◽

1993 ◽

Vol 40 (4) ◽

pp. 421-423 ◽

Cited By ~ 4

Author(s):

V.P. Plessky

Keyword(s):

Surface Waves ◽

Closed Form ◽

Dispersion Equation ◽

Periodic Structures

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A Closed-Form Approximation to the Distribution for the Sum of Independent Non-identically Generalized Gamma Variates and Applications

Mathematical Modelling and Engineering Problems ◽

10.18280/mmep.080104 ◽

2021 ◽

Vol 8 (1) ◽

pp. 33-44

Author(s):

Toufik Chaayra ◽

Hussain Ben-azza ◽

Faissal El Bouanani

Keyword(s):

Closed Form ◽

Fading Channels ◽

Performance Metrics ◽

Approximate Expression ◽

Maximal Ratio Combining ◽

Generalized Gamma ◽

The Moment ◽

Probability Density Function Pdf ◽

Closed Form Approximation ◽

Fox’S H Function

Evaluating the sum of independent and not necessarily identically distributed (i.n.i.d) random variables (RVs) is essential to study different variables linked to various scientific fields, particularly, in wireless communication channels. However, it is difficult to evaluate the distribution of this sum when the number of RVs increases. Consequently, the complex contour integral will be difficult to determine. Considering this issue, a more accurate approximation of the distribution function is required. By assuming the probability density function (PDF) of a generalized gamma (GG) RV evaluated in terms of a proper subset H1,0 1,1 class of Fox’s H-function (FHF) and the moment-based approximation to estimate the FHF parameters, a closed-form tight approximate expression for the distribution of the sum of i.n.i.d GG RVs and a sufficient condition for the convergence are investigated. The proposed approximate may be an analytical useful tool for analyzing the performance of certain numbers branch maximal-ratio combining receivers subject to GG fading channels. Hence, various closed-form performance metrics are derived and examined in terms of FHF. Numerical simulations are carried out to illustrate the theoretical results.

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