On Uniqueness Theorem of a Vector Function

Zhou, Xingling

doi:10.2528/pier06081202

Cited by 21 publications

(12 citation statements)

References 6 publications

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“…According to the Helmholtz decomposition, 4 both electric field components contribute independently to the total electric field. In addition, a hydrodynamic contribution to the potential electric field, which was originally suggested by London,5 has been discussed.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of the electric field in type-II superconducting thin films in perpendicular geometry

Romero-Salazar¹,

Jooß²,

Hernández-Flores

2010

Phys. Rev. B

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The study of electric field distributions induced by flux creep in type-II superconducting films allows for important insight into the mechanism of vortex dynamics, the temporal evolution of flux and current distributions, and the occurrence of local losses. Most studies are based on the assumption that a phenomenological materials law, which has been extracted from macroscopic transport measurements, can be also applied to the local electric field during magnetization decay. We evaluate this ansatz by reconstructing the threedimensional-induced E i and potential E p electric fields from experimentally measured time dependence of the flux density distribution. The results are quantitatively compared with solutions of the nonlinear and nonlocal equation of motion for the flux penetration, where the Maxwell equations as well as a materials law are utilized to obtain a two-dimensional E i,2D and E p,2D . We focus our analysis on the electric field distributions on a partially penetrated magnetized state of an epitaxial YBa 2 Cu 3 O 6.95 film.

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Section: Introductionmentioning

confidence: 99%

Reconstruction of the electric field in type-II superconducting thin films in perpendicular geometry

Romero-Salazar¹,

Jooß²,

Hernández-Flores

2010

Phys. Rev. B

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“…Recently, it caused much attentions and some statements on it is also published [17][18][19]. In this paper, we try to give a rigorous statement on it, which is to some extent different from that in Ref.…”

Section: Introductionmentioning

confidence: 94%

“…Then we obtain the decomposition form of every simply connected domain based on Theorem 1. And then the superposition of decomposition forms is done to obtain (18). Finally, we separate the integral domain of surface integral in (18) into two parts: one part is outside surface S of whole domain V and the other part is the interface between sub-domains.…”

Section: Helmholtz Theorem In Multiply Connected Domainmentioning

confidence: 99%

A Rigorous and Completed Statement on Helmholtz Theorem

Gui¹,

Dou²

2007

PIER

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Abstract-There are some limitations on the statement of classic Helmholtz theorem although it has broad applications. Actually, it only applies to simply connected domain with single boundary surface and does not provide any conclusion about the domain where discontinuities of field function exist. However, discontinuity is often encountered in practice, for example, the location of surface sources or interface of two kinds of medium. Meanwhile, most existing versions of Helmholtz theorem are imprecise and imperfect to some extent. This paper not only tries to present a precise statement and rigorous proof on classic Helmholtz theorem with the accuracy of mathematical language and logical strictness, but also generalizes it to the case of multiply connected domain and obtains a generalized Helmholtz theorem in the sense of Lebesgue measure and Lebesgue integral defined on three-dimensional Euclidean space. Meanwhile, our proof and reasoning are more sufficient and perfect.As an important application of the generalized Helmholtz theorem, the concepts of irrotational and solenoidal vector function are emphasized.The generalized Helmholtz theorem and the present conclusion should have important reference value in disciplines including vector analysis such as electromagnetics.

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“…Consider volume V, surrounded by surface S, the uniqueness theorem [10][11][12] of the Maxwell equations states that the necessary and sufficient conditions for the time-harmonic EM field inside V to be uniquely specified within S. Only one of the following three conditions is needed for the theorem to hold true:…”

Section: The Uniqueness Theorem For the Helmholtz Equationmentioning

confidence: 99%

Theoretical Foundation for the Method of Connected Local Fields

Mu¹,

Chang²

2011

PIER

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Abstract-The method of connected local fields (CLF), developed for computing numerical solutions of the two-dimensional (2-D) Helmholtz equation, is capable of advancing existing frequency-domain finitedifference (FD-FD) methods by reducing the spatial sampling density nearly to the theoretical limit of two points per wavelength. In this paper, we show that the core theory of CLF is the result of applying the uniqueness theorem to local EM waves. Furthermore, the mathematical process for computing the local field expansion (LFE) coefficients from eight adjacent points on a square is similar to that in the theory of discrete Fourier transform. We also present a theoretical analysis of both the local and global errors in the theory of connected local fields and provide closed-form expressions for these errors.

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On Uniqueness Theorem of a Vector Function

Cited by 21 publications

References 6 publications

Reconstruction of the electric field in type-II superconducting thin films in perpendicular geometry

Reconstruction of the electric field in type-II superconducting thin films in perpendicular geometry

A Rigorous and Completed Statement on Helmholtz Theorem

Theoretical Foundation for the Method of Connected Local Fields

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