Introduction to Electrodynamics

Griffith, David J.; Ruppeiner, George

doi:10.1119/1.12574

Cited by 440 publications

(716 citation statements)

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“…Similar methods have al- ready proven valuable in electrostatics and fluid flow estimation (Griffith, 1999;Kohlberger et al, 2003). We show the representation can be considered a natural parameterization for both elastic and fluid image registration due to the decoupling of the parameters.…”

Section: Discussionmentioning

confidence: 99%

“…These considerations also holds for the deformation field, u, which we define as the difference from the identity warp, such that ϕ = x + u. We apply the Helmholtz decomposition to the deformation field, using the fact that a vector field, which is twice continuously differentiable and with rapid enough decay at infinity, can be split into a sum of the gradient of a scalar function and the curl of a vector function (Griffith, 1999) …”

Section: Helmholtz Decomposition Of Vector Fields -Introducing Two Nementioning

confidence: 99%

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CURL-GRADIENT IMAGE WARPING - Introducing Deformation Potentials for Medical Image Registration using Helmholtz Decomposition

Hansen

Larsen

Christensen

2009

Proceedings of the Fourth International Conference on Computer Vision Theory and Applications

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Abstract:Image registration is becoming an increasingly important tool in medical image analysis, and the need to understand deformations within and between subjects often requires analysis of obtained deformation fields.The current paper presents a novel representation of the deformation field based on the Helmholtz decomposition of vector fields. The two decomposed potential fields form a curl free field and a divergence free field. The representation has already proven its worth in fluid modelling and electrostatics, and we show it also has desirable features in image registration and morphometry in particular. The potentials are shown to a offer decoupling of the two potential fields in both elastic and fluid image registration. For morphometry applications, we show that when decomposing the deformation field in symmetric and antisymmetric parts, the vector potential alone describes the vorticity, and the scalar gradient potential gives a first-order approximation to the determinant of the Jacobian. We provide some insight into the behavior of curl and divergence representation of the warp field by constructed examples and by a demonstration on real medical image data. Our theoretical findings are readily observable in our empirical experiment, which further illustrates the benefit of the parametrization.

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Section: Discussionmentioning

confidence: 99%

Section: Helmholtz Decomposition Of Vector Fields -Introducing Two Nementioning

confidence: 99%

CURL-GRADIENT IMAGE WARPING - Introducing Deformation Potentials for Medical Image Registration using Helmholtz Decomposition

Hansen

Larsen

Christensen

2009

Proceedings of the Fourth International Conference on Computer Vision Theory and Applications

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“…so the work is indeed stored as the energy of the dipolar field 33 , andμ · L µ ·μ > 0, so Lenz's law is justified.…”

Section: Inductance Due To Spin Currentmentioning

confidence: 99%

“…Consider ideal, classical magnetic monopoles q m in a closed ring, and a electric field pierced through the ring. Time variance of electric flux 33 , Lenz's law can be justified. We stress that this analysis does not apply to the emerged monopoles in spin ice [58][59][60][61] , since the monopoles therein do not modify Maxwell's equations and experience Lorentz force.…”

Section: Inductance Due To Electric Dipole Currentmentioning

confidence: 99%

“…The relation between spin motive force, inductance, and electric flux vector bears a form similar to Faraday's law of induction 32 . The analog of Lenz's law can be deduced from the energy conservation argument 33 , which states that the induced emf always opposes changing of the spin current. Moreover, the electric flux vector is consistent with that defined from quantum interference of magnetic dipoles 27 .…”

Section: Introductionmentioning

confidence: 99%

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Inductance due to spin current

Chen

2014

Journal of Applied Physics

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The inductance of spintronic devices that transport charge neutral spin currents is discussed. It is known that in a media that contains charge neutral spins, a time-varying electric field induces a spin current. We show that since the spin current itself produces an electric field, this implies existence of inductance and electromotive force when the spin current changes with time. The relations between the electromotive force and the corresponding flux, which is a vector calculated by the cross product of electric field and the trajectory of the device, are clarified. The relativistic origin generally renders an extremely small inductance, which indicates the advantage of spin current in building low inductance devices. The same argument also explains the inductance due to electric dipole current, and applies to physical dipoles consist of polarized bound charges.

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CalcDeltaB: An efficient postprocessing tool to calculate ground‐level magnetic perturbations from global magnetosphere simulations

et al. 2014

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Ground magnetic field variations can induce electric currents on long conductor systems such as high‐voltage power transmission systems. The extra electric currents can interfere with normal operation of these conductor systems; and thus, there is a great need for better specification and prediction of the field perturbations. In this publication we present CalcDeltaB, an efficient postprocessing tool to calculate magnetic perturbations ΔB at any position on the ground from snapshots of the current systems that are being produced by first‐principle models of the global magnetosphere‐ionosphere system. This tool was developed during the recent “dB/dt” modeling challenge at the Community Coordinated Modeling Center that compared magnetic perturbations and their derivative with observational results. The calculation tool is separate from each of the magnetosphere models and ensures that the ΔB computation method is uniformly applied, and that validation studies using ΔB compare the performance of the models rather than the combination of each model and a built‐in ΔB computation tool that may exist. Using the tool, magnetic perturbations on the ground are calculated from currents in the magnetosphere, from field‐aligned currents between magnetosphere and ionosphere, and the Hall and Pedersen currents in the ionosphere. The results of the new postprocessing tool are compared with ΔB calculations within the Space Weather Modeling Framework model and are in excellent agreement. We find that a radial resolution of 1/30RE is fine enough to represent the contribution to ΔB from the region of field‐aligned currents.

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Introduction to Electrodynamics

Cited by 440 publications

References 0 publications

CURL-GRADIENT IMAGE WARPING - Introducing Deformation Potentials for Medical Image Registration using Helmholtz Decomposition

CURL-GRADIENT IMAGE WARPING - Introducing Deformation Potentials for Medical Image Registration using Helmholtz Decomposition

Inductance due to spin current

CalcDeltaB: An efficient postprocessing tool to calculate ground‐level magnetic perturbations from global magnetosphere simulations

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