scholarly journals Boundary Value Problem of an Infinite Array of Loaded Apertures

2015 ◽  
Vol 3 ◽  
pp. 11-15
Author(s):  
Luis Alejandro Iturri-Hinojosa ◽  
Alexander E. Martynyuk ◽  
Mohamed Badaoui
Keyword(s):  
Mathematical Model ◽  
Reflection Coefficient ◽  
Plane Wave ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Incident Plane Wave ◽  
Incident Plane ◽  
Infinite Array ◽  
The Mathematical Model ◽  
Good Agreement

A mathematical model of the scattering by a periodically arranged apertures in conducting plates is presented. The boundary value problem of an infinite array of loaded apertures is formulated for an arbitrary incident plane wave. The reflection coefficient for some array geometries is obtained and the calculated values are in good agreement with the measurements in a previously published researches. All the rectangular apertures in the array are assumed to be identical and infinitesimally thin. The mathematical model is based on Floquet’s theorem that specifies the requirement of periodicity by the electromagnetic fields.

Scattering by a perfectly conducting multislotted cylinder

1992 ◽  
Vol 70 (1) ◽  
pp. 55-61 ◽  
Author(s):  
Mousa I. Hussein ◽  
M. Hamid
Keyword(s):  
Integral Equation ◽  
Circular Cylinder ◽  
Plane Wave ◽  
Method Of Moments ◽  
Boundary Value ◽  
Integral Equation Method ◽  
Equation Method ◽  
Incident Plane Wave ◽  
Incident Plane ◽  
Field Integral

The problem of scattering by a perfectly conducting multislotted circular cylinder excited by a z-polarized incident plane wave is presented. The solution is carried out using two methods of analysis. In the first method, the fields in and around the cylinder are found in terms of the aperture fields, using the boundary value technique. Then Galerkin's method is introduced to solve for the unknown aperture fields. In the second method, the aperture-field integral equation method is employed and the fields in and around the cylinder are found in terms of the aperture fields, while the resulting equations are solved using the method of moments. Results are obtained and presented using the two methods.

scholarly journals The Mathematical Modeling of Metals Mass Transfer in Three Layer Peat Blocks

2015 ◽  
Vol 1 ◽  
pp. 87
Author(s):  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Edmunds Teirumnieks ◽  
Harijs Kalis
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Mathematical Models ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Difference Methods ◽  
The Mathematical Model

The mathematical model for calculation of concentration of metals for 3 layers peat blocks is developed due to solving the 3-D boundary-value problem in multilayered domain-averaging and finite difference methods are considered. As an example, mathematical models for calculation of Fe and Ca concentrations have been analyzed.

scholarly journals Simulation of the process of water purification in multilayered micro porous media

2019 ◽  
pp. 61-63
Author(s):  
Olena Prysiazhniuk ◽  
Andrii Safonyk ◽  
Anna Terebus
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Boundary Value Problem ◽  
Water Purification ◽  
Asymptotic Approximation ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
The Mathematical Model ◽  
Purification Of Water

The mathematical model of the process of adsorption purification of water from impurities in multilayer microporous filters is formulated. An algorithm for numerically-asymptotic approximation of solution of the corresponding nonlinear singularly perturbed boundary value problem is developed. The developed model allows to investigate the distribution of concentration of pollutant inside the filer.

scholarly journals MATHEMATICAL SIMULATION OF THE SYSTEM SEISMIC FLUCTUATIONS, WHICH CONSISTS OF THE TAILINGS DUMP EMBANKMENT DAM, THE MATERIAL OF DEPOSIT (TAILS) AND UNDER BOTTOM GROUND LAYERS

2016 ◽  
Author(s):  
И.Д. Музаев
Keyword(s):  
Mathematical Model ◽  
Wave Propagation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Seismic Wave Propagation ◽  
Contact Boundary ◽  
Embankment Dam ◽  
Seismic Vibrations ◽  
Contact Surfaces ◽  
The Mathematical Model

Разработана математическая модель совместных сейсмических колебаний системы, состоящей из дамбы обвалования хвостохранилища, материала отложения (хвосты) и подподошвенных слоев грунтового массива. Модель представляет собой контактную краевую задачу для дифференциального уравнения сдвигово-вязких поперечных колебаний тела дамбы с материалами отложений, а также для дифференциальных уравнений сдвигово-вязких поперечных колебаний слоев массива грунта. Эти уравнения взаимосвязаны через граничные условия на контактных поверхностях. Краевая задача решена аналитически. Получены расчетные формулы для вычисления перемещений, скорости и ускорения тела дамбы при распространении падающей на систему сейсмической волны в слоях грунта и в теле дамбы The mathematical model of the system seismic vibrations, which consists of the tailings dump embankment dam, the material of deposit (tails) and under botto ground layers is developed. Model is contact boundary-value problem for the differentialequation of the dam body shift- viscous lateral oscillations with the materials of deposits, and also for the differential equations of the shift- viscous lateraloscillations of the ground layers. These equations are interconnected through the boundary conditions on the contact surfaces. Boundary-value problem is solved analytically. Calculation formulas for enumerating of displacements, velocity and acceleration calculation of the dam body with the seismic wave propagation in the ground layers and into in the dam body.

THE STABILITY AND FREE VIBRATIONS OF A COLUMN SUBJECTED TO A CONSERVATIVE LOAD GENERATED BY A HEAD WITH A PARABOLIC CONTOUR

2013 ◽  
Vol 13 (07) ◽  
pp. 1340012
Author(s):  
LECH TOMSKI ◽  
SEBASTIAN UZNY
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Free Vibrations ◽  
Specific Load ◽  
Kinetic Criterion ◽  
The Stability ◽  
The Mathematical Model ◽  
First Time ◽  
Roller Radius

The boundary value problem concerning the free vibrations of a slender system subjected to a specific load has been formulated and solved in this work. Heads with parabolic contour have been used to realize the specific load for the first time. The boundary value problem has been formulated using Hamilton's principle. The critical load and the characteristic curves in the plane load–natural frequency have been determined on the basis of the kinetic criterion of stability. Numerical calculations have been assigned to different values of the parameters of the considered system for which the parabolic parameter and the parameter of the roller radius are ranked. The roller is the head of the receiving load. The accuracy of the mathematical model was confirmed on the basis of experimental research based on frequency and modal analysis.

Electromagnetic modelling of 3D periodic structure containing magnetized or polarized ellipsoids

2006 ◽  
Vol 14 (3) ◽  
Author(s):  
M. Koledintseva
Keyword(s):  
Plane Wave ◽  
Incident Wave ◽  
Surrounding Medium ◽  
Boundary Plane ◽  
Angle Of Incidence ◽  
Incident Plane Wave ◽  
Regular Array ◽  
Incident Plane ◽  
Electromagnetic Modelling ◽  
Infinite Array

AbstractCoupling matrix and coupling coefficient concepts are applied to the interaction of an incident plane wave with a regular array of small magnetized or polarized ellipsoids, placed in a homogeneous surrounding medium. In general case, the angle of incidence and polarization of the plane wave upon an array of ellipsoids can be arbitrary. In this model, it is assumed that all the ellipsoids are the same, and the direction of their magnetization is also the same. The direction of magnetization is arbitrary with respect to the direction of the propagation of the incident wave and to the boundary plane between the first medium, where the incident wave comes from, and the array material under study. Any magnetized or polarized ellipsoid is represented as a system of three orthogonal elementary magnetic radiators (EMR) and/or three orthogonal elementary electric radiators (EER). Mutual interactions of individual radiators in the array through the incident plane wave and corresponding scattered electromagnetic fields are taken into account. The electrodynamic characteristics — reflection from the surface of the semi-infinite array (in particular, containing uniaxial hexagonal ferrite resonators), transmission through the array, and absorption are analyzed.

scholarly journals Research of a mathematical model of low-concentrated aqueous polymer solutions

2006 ◽  
Vol 2006 ◽  
pp. 1-27 ◽  
Author(s):  
Mikhail V. Turbin
Keyword(s):  
Mathematical Model ◽  
Weak Solution ◽  
Boundary Value Problem ◽  
Polymer Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Aqueous Polymer ◽  
Initial Boundary Value ◽  
The Mathematical Model

The initial-boundary value problem for the mathematical model of low-concentrated aqueous polymer solutions is considered. For this initial-boundary value problem a concept of a weak solution is introduced and the existence theorem for such solutions is proved.

scholarly journals Core-Shell Nano-Antenna Configurations for Array Formation with More Stability Having Conventional and Non-Conventional Directivity and Propagation Behavior

Nanomaterials ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 99
Author(s):  
Qaisar Hayat ◽  
Junping Geng ◽  
Xianling Liang ◽  
Ronghong Jin ◽  
Sami Ur Rehman ◽  
...  
Keyword(s):  
Plane Wave ◽  
Propagation Direction ◽  
Core Shell ◽  
Incident Plane Wave ◽  
Polarization Direction ◽  
Shell Nanoparticles ◽  
Incident Plane ◽  
Core Shell Nanoparticles ◽  
Coated Nanoparticle ◽  
2D Array

The enhancement of optical characteristics at optical frequencies deviates with the choice of the arrangement of core-shell nanoparticles and their environment. Likewise, the arrangements of core-shell nanoparticles in the air over a substrate or in liquid solution makes them unstable in the atmosphere. This article suggests designing a configuration of an active spherical coated nanoparticle antenna and its extended array in the presence of a passive dielectric, which is proposed to be extendable to construct larger arrays. The issue of instability in the core-shell nanoantenna array models is solved here by inserting the passive dielectric. In addition to this, the inclusion of a dielectric in the array model reports a different directivity behaviour than the conventional array models. We found at first that the combination model of the active coated nanoparticle and passive sphere at the resonant frequency can excite a stronger field with a rotated polarization direction and a propagation direction different from the incident plane-wave. Furthermore, the extended 2D array also rotates the polarization direction and propagation direction for the vertical incident plane-wave. The radiation beam operates strong multipoles in the 2D array plane at resonant frequency (behaving non-conventionally). Nevertheless, it forms a clear main beam in the incident direction when it deviates from the resonance frequency (behaving conventionally). The proposed array model may have possible applications in nano-amplifiers, nano-sensors and other integrated optics.

A New Method and Applications of the Boundary Value Problem of Differential Equation

2014 ◽  
Vol 937 ◽  
pp. 695-699
Author(s):  
Hong E Li ◽  
Xiao Xu Dong ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Cong Yin Fan
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Kernel Function ◽  
Boundary Value ◽  
Outer Boundary ◽  
Seepage Flow ◽  
Petroleum Engineering ◽  
Constructive Method ◽  
Linear Homogeneous Differential Equation ◽  
The Mathematical Model

The similar structure of solution for the boundary value problem of second order linear homogeneous differential equation has been studied. Based on the analysis of the relationship between similar structure of solution, its kernel function, the equation and boundary conditions, similar constructive method (shortened as SCM) of solution is obtained. According to the SCM, the similar structure of solution and its kernel function are constructed for the mathematical model of homogeneous reservoir which considers the influence of bottom-hole storage and skin effect under the infinite outer boundary condition. The SCM is a new and innovative way to solve boundary value problem of differential equation and seepage flow theory, which is especially used in Petroleum Engineering.

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