scholarly journals An inverse phaseless problem for electrodynamic equations in an anisotropic medium

2019 ◽  
Vol 488 (4) ◽  
pp. 367-371
Author(s):  
V. G. Romanov
Keyword(s):  
Inverse Problem ◽  
Bounded Domain ◽  
Incomplete Data ◽  
Electromagnetic Waves ◽  
Original Problem ◽  
Plane Waves ◽  
Inverse Kinematic ◽  
System Of Equations ◽  
X Ray ◽  
Equations Of Electrodynamics

For the system of equations of electrodynamics which has the anisotropy of the permittivity, an inverse problem of determining the permittivity is studied. It is supposed that the permittivity is characterized by the diagonal matrix = diag (1(x), 1(x), 2(x)) and 1 and 2 are positive constants anywhere outside of a bounded domain 0 3. Periodic in time solutions of the system of Maxwells equations related to two modes of plane waves falled down from infinity on the local non-homogeneity located in 0 is considered. For determining functions 1(x) and 2(x) some information on the module of the vector of the electric strength of two interfered waves is given. It is demonstrated that this information reduces the original problem to two inverse kinematic problems with incomplete data about travel times of the electromagnetic waves. An investigation of the linearized statement for these problems is given. It is shown that in the linear approximation the problem of the determining 1(x) and 2(x) is reduced to two X-ray tomography problems.

scholarly journals Problem of Determining the Anisotropic Conductivity in Electrodynamic Equations

2021 ◽  
Author(s):  
V. G. Romanov
Keyword(s):  
Inverse Problem ◽  
Plane Waves ◽  
Diagonal Matrix ◽  
Anisotropic Conductivity ◽  
Electric Intensity ◽  
X Ray ◽  
Sigma 1

Abstract For a system of electrodynamic equations, the inverse problem of determining an anisotropic conductivity is considered. It is supposed that the conductivity is described by a diagonal matrix σ(x) = $${\text{diag}}({{\sigma }_{1}}(x),{{\sigma }_{2}}(x)$$, σ3(x)) with $$\sigma (x) = 0$$ outside of the domain Ω = $$\{ x \in {{\mathbb{R}}^{3}}|\left| x \right| < R\} $$, $$R > 0$$, and the permittivity ε and the permeability μ of the medium are positive constants everywhere in $${{\mathbb{R}}^{3}}$$. Plane waves coming from infinity and impinging on an inhomogeneity localized in Ω are considered. For the determination of the unknown functions $${{\sigma }_{1}}(x)$$, $${{\sigma }_{2}}(x)$$, and $${{\sigma }_{3}}(x)$$, information related to the vector of electric intensity is given on the boundary S of the domain Ω. It is shown that this information reduces the inverse problem to three identical problems of X-ray tomography.

scholarly journals Scattering of electromagnetic waves by a discrete octahedron from resonant spheres

Radiotekhnika ◽  
2020 ◽  
pp. 181-185
Author(s):  
A.I. Kozar
Keyword(s):  
Electromagnetic Waves ◽  
Nonlocal Boundary ◽  
Scattered Wave ◽  
Nonlocal Boundary Conditions ◽  
Internal Field ◽  
Fredholm Integral Equations ◽  
X Ray ◽  
Equations Of Electrodynamics ◽  
Resonance Properties ◽  
Discrete Convex

A solution is given to the problem of scattering of electromagnetic waves by a discrete convex polyhedron – an octahedron of resonant magnetodielectric spheres based on a complex rhombic crystal lattice. Here we consider a case equivalent to the X-ray optics of crystals, when α / λ՛<<1 and can be α / λg ~ 1; d, h, l / λ՛ ~ 1, where α is the radius of the spheres; λ՛, λg are the lengths of the scattered wave outside and inside the spheres; d, h, l are constant lattices. The solution of the problem is obtained based on the Fredholm integral equations of electrodynamics of the second kind with nonlocal boundary conditions. The expressions found in this work for a metacrystal in the form of an octahedron can be used to study the fields scattered by the crystal in the Fresnel and Fraunhofer zones, as well as to study its internal field. The relations obtained in this work can find application in the study of the scattering of waves of various kinds by convex polyhedrons, the creation on their basis of new types of limited metacrystals, including nanocrystals with resonance properties, and in the study of their behavior in various external media. As well as in the development of methods for modeling electromagnetic phenomena that can occur in real crystals in resonance regions in the optical and X-ray wavelength ranges.

Electromagnetic waves

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Plane Wave ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Plane Waves ◽  
Geometrical Optics ◽  
Particle Detection ◽  
Spatial Coordinates ◽  
A Charge

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.

scholarly journals Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 910
Author(s):  
Andrey Kovtanyuk ◽  
Alexander Chebotarev ◽  
Varvara Turova ◽  
Irina Sidorenko ◽  
Renée Lampe
Keyword(s):  
Inverse Problem ◽  
Oxygen Transport ◽  
Model Parameters ◽  
Cerebral Oxygen ◽  
System Of Equations ◽  
Blood Oxygen ◽  
Stationary Model ◽  
Average Oxygen Concentration ◽  
The Right ◽  
The Brain

An inverse problem for a system of equations modeling oxygen transport in the brain is studied. The problem consists of finding the right-hand side of the equation for the blood oxygen transport, which is a linear combination of given functionals describing the average oxygen concentration in the neighborhoods of the ends of arterioles and venules. The overdetermination condition is determined by the values of these functionals evaluated on the solution. The unique solvability of the problem is proven without any smallness assumptions on the model parameters.

An inversion formula for the transport equation in ℝ3 using complex analysis in several variables

2019 ◽  
Vol 27 (3) ◽  
pp. 341-352
Author(s):  
Seyed Majid Saberi Fathi
Keyword(s):  
Inverse Problem ◽  
Transport Equation ◽  
Inversion Formula ◽  
Complex Analysis ◽  
Three Dimensional ◽  
Analytical Continuation ◽  
Radon Transforms ◽  
Photon Transport ◽  
X Ray ◽  
Several Variables

Abstract In this paper, the stationary photon transport equation has been extended by analytical continuation from {\mathbb{R}^{3}} to {\mathbb{C}^{3}} . A solution to the inverse problem posed by this equation is obtained on a hyper-sphere and a hyper-cylinder as X-ray and Radon transforms, respectively. We show that these results can be transformed into each other, and they agree with known results. Numerical reconstructions of a three-dimensional Shepp–Logan head phantom using the obtained inverse formula illustrate the analytical results obtained in this manuscript.

Manufacturing Metamaterials Using Synchrotron Lithography

2010 ◽  
Vol 75 ◽  
pp. 230-239
Author(s):  
Herbert O. Moser ◽  
Linke Jian ◽  
Shenbaga M.P. Kalaiselvi ◽  
Selven Virasawmy ◽  
Sivakumar M. Maniam ◽  
...  
Keyword(s):  
Electromagnetic Waves ◽  
Cost Effective ◽  
Pattern Generation ◽  
Geometrical Parameters ◽  
X Ray ◽  
Spectral Bands ◽  
Left Handed ◽  
Aspect Ratios ◽  
Multi Level ◽  
Primary Pattern

The function of metamaterials relies on their resonant response to electromagnetic waves in characteristic spectral bands. To make metamaterials homogeneous, the size of the basic resonant element should be less than 10% of the wavelength. For the THz range up to the visible, structure details of 50 nm to 30 μm are required as are high aspect ratios, tall heights, and large areas. For such specifications, lithography, in particular, synchrotron radiation deep X-ray lithography, is the method of choice. X-ray masks are made via primary pattern generation by means of electron or laser writing. Several different X-ray masks and accurate mask-substrate alignment are necessary for architectures requiring multi-level lithography. Lithography is commonly followed by electroplating of metallic replica. The process can also yield mould inserts for cost-effective manufacture by plastic moulding. We made metamaterials based on rod-split-rings, split-cylinders, S-string bi-layer chips, and S-string meta-foils. Left-handed resonance bands range from 2.4 to 216 THz. Latest is the all-metal self-supported flexible meta-foil with pass-bands of 45% up to 70% transmission at 3.4 to 4.5 THz depending on geometrical parameters.

scholarly journals Local and electronic structure around Ga in CdTe: evidence of DX- and A-centers

2012 ◽  
Vol 20 (1) ◽  
pp. 166-171
Author(s):  
Vasil Koteski ◽  
Jelena Belošević-Čavor ◽  
Petro Fochuk ◽  
Heinz-Eberhard Mahnke
Keyword(s):  
Density Functional ◽  
Plane Waves ◽  
Lattice Relaxation ◽  
Defect Structures ◽  
Functional Theory ◽  
Edge Structure ◽  
X Ray ◽  
First Time ◽  
X Ray Absorption ◽  
Good Agreement

The lattice relaxation around Ga in CdTe is investigated by means of extended X-ray absorption spectroscopy (EXAFS) and density functional theory (DFT) calculations using the linear augmented plane waves plus local orbitals (LAPW+lo) method. In addition to the substitutional position, the calculations are performed for DX- and A-centers of Ga in CdTe. The results of the calculations are in good agreement with the experimental data, as obtained from EXAFS and X-ray absorption near-edge structure (XANES). They allow the experimental identification of several defect structures in CdTe. In particular, direct experimental evidence for the existence of DX-centers in CdTe is provided, and for the first time the local bond lengths of this defect are measured directly.

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