scholarly journals Cloaking Using the Anisotropic Multilayer Sphere

Photonics ◽  
2020 ◽  
Vol 7 (3) ◽  
pp. 52 ◽  
Author(s):  
Sidra Batool ◽  
Mehwish Nisar ◽  
Fabrizio Frezza ◽  
Fabio Mangini
Keyword(s):  
Mathematical Model ◽  
Arbitrary Number ◽  
Static Approximation ◽  
Quasi Static Approximation ◽  
Number Of Layers ◽  
Multilayer Sphere ◽  
Tangential Directions

We studied a Spherically Radially Anisotropic (SRA) multilayer sphere with an arbitrary number of layers. Within each layer permittivity components are different from each other in radial and tangential directions. Under the quasi-static approximation, we developed a more generalized mathematical model that can be used to calculate polarizability of the SRA multilayer sphere with any arbitrary number of layers. Moreover, the functionality of the SRA multilayer sphere as a cloak has been investigated. It has been shown that by choosing a suitable contrast between components of the permittivity, the SRA multilayer sphere can achieve threshold required for invisibility cloaking.

scholarly journals Analytical expressions for electrodynamic parameters of the shielded microstrip line

2021 ◽  
Vol 9 (4) ◽  
pp. 68-76
Author(s):  
A. N. Kovalenko ◽  
A. D. Yarlykov
Keyword(s):  
Mathematical Model ◽  
Power Series ◽  
Projection Method ◽  
Microstrip Line ◽  
Wave Resistance ◽  
Strip Conductor ◽  
Static Approximation ◽  
Quasi Static Approximation ◽  
Wide Range ◽  
Analytical Expressions

On the basis of an electrodynamic model of a screened microstrip line, built on the basis of the projection method using the Chebyshev basis, which explicitly takes into account the edge features of the field, a mathematical model of a microstrip line with a strip conductor was developed. The line width does not exceed the height of the substrate. In this case, the current density on the strip conductor is approximated by only one basis function. Analytical expressions are presented in the form of a sum of slowly and rapidly converging series to determine the main electrodynamic parameters of the line – wave resistance and deceleration coefficient. Due to logarithmic features, slowly converging series are summed up and transformed into rapidly converging power series. In addition, limit expressions in the form of improper integrals are given for the main electrodynamic parameters of an open microstrip line in the quasi-static approximation. Due to the logarithmic features, these integrals are also converted to rapidly converging power series. As a result, simple approximate formulas were obtained. They allow calculating the deceleration coefficient and wave impedance of the line with an error not exceeding 1%, when the width of the strip conductor is less than twice the thickness of the substrate. The results of calculating the electrodynamic parameters obtained on the basis of the developed mathematical model and on the basis of the projection method with an accuracy of up to 5 significant digits are presented. These results make it possible to establish the limits of applicability of the quasi-static approximation and to determine the error in calculating the deceleration coefficient and wave resistance using the obtained analytical expressions. The error does not exceed 0.1%, if the width of the strip conductor is less than twice the thickness of the substrate in a wide range of changes in the substrate dielectric constant and frequency.

A Ternary, Two-Phase, Mathematical Model of Oil Recovery With Surfactant Systems

1984 ◽  
Vol 24 (06) ◽  
pp. 606-616 ◽  
Author(s):  
Charles P. Thomas ◽  
Paul D. Fleming ◽  
William K. Winter
Keyword(s):  
Mathematical Model ◽  
Oil Recovery ◽  
Arbitrary Number ◽  
The Other ◽  
Phase System ◽  
Chemical Flooding ◽  
Two Phase ◽  
Oil Displacement ◽  
Surfactant Systems ◽  
And Diffusion

Abstract A mathematical model describing one-dimensional (1D), isothermal flow of a ternary, two-phase surfactant system in isotropic porous media is presented along with numerical solutions of special cases. These solutions exhibit oil recovery profiles similar to those observed in laboratory tests of oil displacement by surfactant systems in cores. The model includes the effects of surfactant transfer between aqueous and hydrocarbon phases and both reversible and irreversible surfactant adsorption by the porous medium. The effects of capillary pressure and diffusion are ignored, however. The model is based on relative permeability concepts and employs a family of relative permeability curves that incorporate the effects of surfactant concentration on interfacial tension (IFT), the viscosity of the phases, and the volumetric flow rate. A numerical procedure was developed that results in two finite difference equations that are accurate to second order in the timestep size and first order in the spacestep size and allows explicit calculation of phase saturations and surfactant concentrations as a function of space and time variables. Numerical dispersion (truncation error) present in the two equations tends to mimic the neglected present in the two equations tends to mimic the neglected effects of capillary pressure and diffusion. The effective diffusion constants associated with this effect are proportional to the spacestep size. proportional to the spacestep size. Introduction In a previous paper we presented a system of differential equations that can be used to model oil recovery by chemical flooding. The general system allows for an arbitrary number of components as well as an arbitrary number of phases in an isothermal system. For a binary, two-phase system, the equations reduced to those of the Buckley-Leverett theory under the usual assumptions of incompressibility and each phase containing only a single component, as well as in the more general case where both phases have significant concentrations of both components, but the phases are incompressible and the concentration in one phase is a very weak function of the pressure of the other phase at a given temperature. pressure of the other phase at a given temperature. For a ternary, two-phase system a set of three differential equations was obtained. These equations are applicable to chemical flooding with surfactant, polymer, etc. In this paper, we present a numerical solution to these equations paper, we present a numerical solution to these equations for I D flow in the absence of gravity. Our purpose is to develop a model that includes the physical phenomena influencing oil displacement by surfactant systems and bridges the gap between laboratory displacement tests and reservoir simulation. It also should be of value in defining experiments to elucidate the mechanisms involved in oil displacement by surfactant systems and ultimately reduce the number of experiments necessary to optimize a given surfactant system.

The role of advection in the quasi-static approximation

1994 ◽  
Vol 432 ◽  
pp. 302 ◽  
Author(s):  
Shlomi Pistinner ◽  
Giora Shaviv
Keyword(s):  
Static Approximation ◽  
Quasi Static Approximation

Sources of Fatigue in Random-Vibration Durability of Surface Mount Interconnects

2009 ◽  
Author(s):  
Y. Zhou ◽  
M. Al-Bassyiouni ◽  
A. Dasgupta
Keyword(s):  
Accumulation Rate ◽  
Random Excitation ◽  
Additional Stress ◽  
Dynamic Mode ◽  
Dynamic Prediction ◽  
Element Analysis ◽  
Static Approximation ◽  
Quasi Static Approximation ◽  
Dynamic Movement ◽  
Resonant Modes

The transient response of a PBGA256 assembly to random excitation is explored with quasi-static and transient finite element analysis, as well as with experiments. The quasi-static approximation is based on the first modal contribution to the measured PWB response. The dynamic prediction for solder strain and resulting damage accumulation rate are found to be significantly larger than in the quasi-static approximation. The quasi-static model is clearly missing additional stress drivers such as the dynamic movement of the component relative to the PWB and higher resonant modes of PWB flexure. The dynamic mode of the component is verified in this paper with two accelerometers placed on the component and on the PWB. Investigation of the higher modes of the PWB is deferred to a future study.

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