scholarly journals Oxygen chain disorder as the weak scattering source inYBa2Cu3O6.50

2010 ◽  
Vol 82 (13) ◽  
Author(s):  
J. S. Bobowski ◽  
J. C. Baglo ◽  
James Day ◽  
Lynne Semple ◽  
P. Dosanjh ◽  
...  
Keyword(s):  
Weak Scattering ◽  
Oxygen Chain

scholarly journals Electromagnetic scattering beyond the weak regime: Solving the problem of divergent Born perturbation series by Padé approximants

2020 ◽  
Vol 238 ◽  
pp. 06019
Author(s):  
Thomas van der Sijs ◽  
Omar El Gawhary ◽  
Paul Urbach
Keyword(s):  
Inverse Problem ◽  
Multiple Scattering ◽  
Padé Approximants ◽  
Perturbation Approach ◽  
Pade Approximants ◽  
Born Series ◽  
Scattering Effects ◽  
Weak Scattering ◽  
Strong Scattering ◽  
Multiple Scattering Effects

Electromagnetic scattering is the main phenomenon behind all optical measurement methods where one aims to retrieve the shape or physical properties of an unknown object by measuring how it scatters an incident optical field. Such an inverse problem is often approached by solving, several times, the corresponding direct scattering problem and trying to find the best estimate of the object which is compatible with a set of measurements. In the direct scattering problem, two regimes can be distinguished depending on the size of the object and the permittivity contrast: the weak-scattering regime and the strong-scattering regime. Generally, the presence of the scatterer alters the form of the incident field inside the scatterer. If that effect is neglected in the physical model, then one speaks of the so-called single-scattering regime or, more often, the Born approximation. The regime in which this approximation is valid is the weak-scattering regime. The corresponding inverse problem, that aims to retrieve the object from scattering data, becomes linear in this case. Linearizing the problem simplifies the method to solve it, but also introduces limitations to the maximum spatial resolution achievable in the reconstruction of the object. In the strong-scattering regime, multiple-scattering effects are not neglected and the inverse problem is treated in its full non-linear nature, which makes finding its solution a far more challenging task. Despite the existence of numerical methods, a powerful way to solve those direct problems would be to use a perturbation approach where the field is expressed as a series, known as the Born series. The advantage of a perturbation approach stems from the fact that each term of the series has a clear physical meaning and can unveil much more about the scattering process than a purely numerical approach can offer. Unfortunately, the series solution turns out to be strongly divergent in the strong-scattering regime, making it an unpractical approach for problems under these strong-scattering conditions. Thus, despite the fact that multiple scattering could, in principle, allow resolving sub-wavelength details of the unknown object, this possibility is in practice hampered by the divergent nature of the higher-order terms of the Born series. In this work, we show how to solve this problem by employing Padé approximants and how to treat electromagnetic problems well beyond the weak-scattering regime and provide an accurate evaluation of the scattered field even under strong-scattering conditions. Padé approximants are rational functions that can offer improvements in two ways, namely series acceleration of converging series and analytic continuation of a series outside its region of convergence. In the case of a symmetric approximant of order N, the approximant is calculated from 2N + 1 terms in the Born series, therefore incorporating multiple-scattering effects to which these higher-order corrections in the Born series correspond. We apply the method to two scalar scattering problems: that of a one-dimensional slab and that of an infinitely long cylinder, which reduces to a two-dimensional problem under normal incidence. In particular, we treat cases in the strong-scattering regime where the Born series diverges, but where Padé approximation retrieves a valuable result. In Fig. 1 the case of a cylinder is shown which is well beyond the weak-scattering regime, but where the most accurate Padé approximant gives a good result for the field. The presented approach incorporates multiple-scattering effects and can therefore represent an important building block to the application of the Born series to direct and inverse problems, with potential applications in superresolution, optical metrology, and phase retrieval.

Synthesis, crystal structure and properties of a 2-D Cd(II) coordination polymer based on ferrocenecarboxylate and 4,4′-bipyridine ligands

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kai-Long Zhong ◽  
Jing Quan ◽  
Xian-Xiao Pan ◽  
Wei Song ◽  
Bing-Feng Li
Keyword(s):  
Coordination Polymer ◽  
Gravimetric Analysis ◽  
Structure And Properties ◽  
X Ray Diffraction ◽  
Hydrothermal Conditions ◽  
X Ray ◽  
Carboxylate Oxygen ◽  
Oxygen Chain ◽  
Crystal Structural

Abstract A new cadmium(II)-based coordination polymer [Cd3(FcCOO)6(4,4′-bipy)(H2O)2] n (FcCOO = ferrocenecarboxylato and 4,4′-bipy = 4,4′-bipyridine) has been synthesized under hydrothermal conditions and characterized by single-crystal X-ray diffraction. The results of a crystal structural analysis has revealed that the title compound consists of two crystallographically unique CdII centers, one in a general position with a five-coordinated and one on an inversion center with a six-coordinated environment. The CdII centers are connected by FcCOO− units to form a metal carboxylate oxygen chain extending parallel to the [100] direction while the 4,4′-bipy ligands further act as bridging linkers of the CdII centers resulting in a layered polymer. In addition, an X-ray powder diffraction and thermal gravimetric analysis and a cyclo-voltammetric characterization of the complex have also been carried out.

Lump soliton wave solutions for the (2+1)-dimensional Konopelchenko–Dubrovsky equation and KdV equation

2019 ◽  
Vol 33 (18) ◽  
pp. 1950199 ◽  
Author(s):  
Mostafa M. A. Khater ◽  
Dianchen Lu ◽  
Raghda A. M. Attia
Keyword(s):  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Auxiliary Equation ◽  
Wave Solutions ◽  
All Solutions ◽  
Long Range Interactions ◽  
Weak Scattering ◽  
Novel Method ◽  
Soliton Wave Solutions

This paper studies (2+1)-dimensional Konopelchenko–Dubrovsky equation and (2+1)-dimensional KdV equation via a modified auxiliary equation technique. These two systems describe the connection between the nonlinear weaves with a weak scattering and long-range interactions between the tropical, mid-latitude troposphere, the interaction of equatorial and mid-latitude Rossby waves, respectively. We implement a novel technique to these systems to find analytical traveling wave solutions. The performance of this novel method shows its ability for applying on various nonlinear partial differential equations. All solutions obtained are checked by the Maple software system and verified for its high fidelity.

scholarly journals Anomalous forward scattering of gain-assisted dielectric shell-coated metallic core spherical particles

Nanophotonics ◽  
2016 ◽  
Vol 6 (5) ◽  
pp. 1063-1072 ◽  
Author(s):  
Fei Shen ◽  
Ning An ◽  
Yifei Tao ◽  
Hongping Zhou ◽  
Zhaoneng Jiang ◽  
...  
Keyword(s):  
Forward Direction ◽  
Mie Scattering ◽  
Forward Scattering ◽  
Spherical Particles ◽  
Optical Antennas ◽  
Core Shell ◽  
Shell Nanoparticles ◽  
Dielectric Shell ◽  
Weak Scattering ◽  
Order Of Magnitude

AbstractWe have investigated the scattering properties of an individual core-shell nanoparticle using the Mie theory, which can be tuned to support both electric and magnetic modes simultaneously. In general, the suppression of forward scattering can be realized by the second Kerker condition. Here, a novel mechanism has to be adopted to explain zero-forward scattering, which originates from the complex interactions between dipolar and quadrupolar modes. However, for lossy and lossless core-shell spherical nanoparticles, zero-forward scattering can never be achieved because the real parts of Mie expansion coefficients are always positive. By adding proper gain in dielectric shell, zero-forward scattering can be found at certain incident wavelengths, which means that all electric and magnetic responses in Mie scattering can be counteracted totally in the forward direction. In addition, if the absolute values of dipolar and quadrupolar terms are in the same order of magnitude, the local scattering minimum and maximum can be produced away from the forward and backward directions due to the interacting effect between the dipolar and quadrupolar terms. Furthermore, by adding suitable gain in shell, super-forward scattering can also be realized at certain incident wavelengths. We also demonstrated that anomalously weak scattering or superscattering could be obtained for the core-shell nanoparticles with suitable gain in shell. In particular, for such a choice of suitable gain in shell, we can obtain zero-forward scattering and anomalously weak scattering at the same wavelength as well as super-forward scattering at another wavelength. These features may provide new opportunities for cloaking, plasmonic lasers, optical antennas, and so on.

Finite-frequency traveltime tomography using the Generalized Rytov approximation

2020 ◽  
Vol 221 (2) ◽  
pp. 1412-1426 ◽  
Author(s):  
B Feng ◽  
W Xu ◽  
R S Wu ◽  
X B Xie ◽  
H Wang
Keyword(s):  
Convergence Rate ◽  
Large Scale ◽  
Frequency Theory ◽  
Seismic Exploration ◽  
Finite Frequency ◽  
Traveltime Tomography ◽  
Sensitivity Kernel ◽  
Rytov Approximation ◽  
Weak Scattering ◽  
Small Phase

SUMMARY Wave-equation-based traveltime tomography has been extensively applied in both global tomography and seismic exploration. Typically, the traveltime Fréchet derivative is obtained using the first-order Born approximation, which is only satisfied for weak velocity perturbations and small phase shifts (i.e. the weak-scattering assumption). Although the small phase-shift restriction can be handled with the Rytov approximation, the weak velocity-perturbation assumption is still a major limitation. The recently developed generalized Rytov approximation (GRA) method can achieve an improved phase accuracy of the forward-scattered wavefield, in the presence of large-scale and strong velocity perturbations. In this paper, we combine GRA with the classical finite-frequency theory and propose a GRA-based traveltime sensitivity kernel (GRA-TSK), which overcomes the weak-scattering limitation of the conventional finite-frequency methods. Numerical examples demonstrate that the accumulated time delay of forward-scattered waves caused by large-scale smooth perturbations can be correctly handled by the GRA-TSK, regardless of the magnitude of the velocity perturbations. Then, we apply the new sensitivity kernel to solve the traveltime inverse problem, and we propose a matrix-free Gauss–Newton method that has a faster convergence rate compared with the gradient-based method. Numerical tests show that, compared with the conventional adjoint traveltime tomography, the proposed GRA-based traveltime tomography can obtain a more accurate model with a faster convergence rate, making it more suited for recovering the large-intermediate scale of the velocity model, even for strong-perturbation and complex subsurface structures.

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