Analytical Methods in Wave Scattering and Diffraction, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 28 February 2025 | Viewed by 4616

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School of Informatics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Interests: applied mathematics; wave propagation and scattering theory; partial differential equations; integral equations; mathematical modeling
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Special Issue Information

Dear Colleagues,

Boundary-value problems (BVPs) pertaining to scattering and radiation by devices supporting novel wave phenomena are of primary importance in Applied and Computational Mathematics, Computational Physics and Engineering. Modeling such BVPs with analytical or semi-analytical techniques is essential to obtain solutions with controllable accuracy and in small execution time. These solutions can be considered as significant benchmarks and starting points for optimizing efficiently the devices parameters in order to achieve specific near- or far-field variations. The purpose of this special issue is to gather contributions from experts on analytical and semi-analytical techniques with application domains including but not limited to single- or multiple-particle scattering, metamaterials, direct and inverse scattering by inclusions in layered media, propagation in waveguides, resonators, and analysis of periodic, layered or complex media. The techniques applied for the analytical modeling are expected to span from integral-equation/differential-equation based methodologies to generalized separation of variables and Fourier-series expansions as well as to Galerkin and eigenfunction series techniques. Contributions with main emphasis on numerical methods for wave phenomena are also welcome provided that they exploit analytical means at certain stages of the procedures employed for the derivations of the solutions.

Dr. Nikolaos L. Tsitsas
Guest Editor

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Keywords

  • waves
  • scattering
  • diffraction
  • radiation
  • integral equation techniques
  • asymptotic analysis
  • metamaterials and periodic structures
  • electromagnetics
  • photonics
  • acoustic waves
  • elastic waves

Published Papers (3 papers)

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Research

23 pages, 675 KiB  
Article
Fourier Transform of the Lippmann-Schwinger Equation: Solving Vectorial Electromagnetic Scattering by Arbitrary Shapes
by Frederic Gruy, Victor Rabiet and Mathias Perrin
Mathematics 2023, 11(22), 4691; https://doi.org/10.3390/math11224691 - 18 Nov 2023
Viewed by 1034
Abstract
In Electromagnetics, the field scattered by an ensemble of particles—of arbitrary size, shape, and material—can be obtained by solving the Lippmann–Schwinger equation. This singular vectorial integral equation is generally formulated in the direct space Rn (typically n=2 or [...] Read more.
In Electromagnetics, the field scattered by an ensemble of particles—of arbitrary size, shape, and material—can be obtained by solving the Lippmann–Schwinger equation. This singular vectorial integral equation is generally formulated in the direct space Rn (typically n=2 or n=3). In the article, we rigorously computed the Fourier transform of the vectorial Lippmann–Schwinger equation in the space of tempered distributions, S(R3), splitting it in a singular and a regular contribution. One eventually obtains a simple equation for the scattered field in the Fourier space. This permits to draw an explicit link between the shape of the scatterer and the field through the Fourier Transform of the body indicator function. We compare our results with accurate calculations based on the T-matrix method and find a good agreement. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction, 2nd Edition)
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14 pages, 2183 KiB  
Article
Wave Scattering through Step Down Cascading Junctions
by Hadia Ali, Mahmood-ul-Hassan, Ali Akgül and Ali Saleh Alshomrani
Mathematics 2023, 11(9), 2027; https://doi.org/10.3390/math11092027 - 24 Apr 2023
Viewed by 1132
Abstract
In this paper, we present the scattering of plane waves through two junctions with step-down cascading discontinuities. The solutions in the form of trapped modes corresponding to discrete eigen values are also presented. We illustrate the matching of continuity of pressure and velocity [...] Read more.
In this paper, we present the scattering of plane waves through two junctions with step-down cascading discontinuities. The solutions in the form of trapped modes corresponding to discrete eigen values are also presented. We illustrate the matching of continuity of pressure and velocity at the edges, conservation of energy, convergence/error of reflection, and reflection and transmission of the incident wave that go through the wider region. We discuss the reflection and transmission amplitudes by varying dimensions of wave-guide structure against wave number. We plot the surface and contour plots along with absolute potential solutions at different frequencies where extrema of field amplitudes occur. We also derive the results of extra ordinary acoustic transmission (EAT) for existing models. We apply the Mode Matching Method (MMM) to tackle the problem. Our model would be beneficial to structure the old and new models containing cavities and junctions. However, these structure models cannot retrieve our proposed geometrical model. The results will be helpful to model the practical exhaust system in noise reduction theory. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction, 2nd Edition)
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17 pages, 3867 KiB  
Article
Graphene Twistronics: Tuning the Absorption Spectrum and Achieving Metamaterial Properties
by Ammar Armghan, Meshari Alsharari, Khaled Aliqab, Osamah Alsalman, Juveriya Parmar and Shobhit K. Patel
Mathematics 2023, 11(7), 1579; https://doi.org/10.3390/math11071579 - 24 Mar 2023
Cited by 5 | Viewed by 1687
Abstract
Graphene twistronics using multilayer graphene is presented in such a way that it provides a metamaterial effect. This manuscript also analyzes the prediction of behavior using machine learning. The metamaterial effect is achieved by twisting the graphene layers. Graphene twistronics is a new [...] Read more.
Graphene twistronics using multilayer graphene is presented in such a way that it provides a metamaterial effect. This manuscript also analyzes the prediction of behavior using machine learning. The metamaterial effect is achieved by twisting the graphene layers. Graphene twistronics is a new concept for changing the electrical and optical properties of bilayer graphene by applying a small angle twist between the layers. The angle twists of 5°, 10°, and 15° are analyzed for the proposed graphene twistronics design. Tuning in the absorption spectrum is achieved by applying small twists to the angles of the bilayer graphene. Results in the form of absorption, conductivity, permeability, permittivity, and impedance are presented for different twist angles. The twisted graphene layers also demonstrate negative permittivity and negative permeability, similar to metamaterials. These negative refraction properties of graphene twistronics provide flexibility and transparency, which can be applied in photovoltaic applications. Machine-learning-based regression models are used to reduce the simulation time and resources. The results show that a regression model can reliably estimate intermediate wavelength absorption values with an R2 of 0.9999. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction, 2nd Edition)
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