6.1 The electromagnetic current

It is known that the 3D Chern–Simons interaction describes the scaling limit of a quantum Hall system and predicts edge currents in a sample with boundary, the currents generating a chiral U(1) Kac-Moody algebra. It is no doubt also recognized that, in a somewhat similar way, the 4D BF interaction (with B a two-form, dB the dual *j of the electromagnetic current, and F the electromagnetic field form) describes the scaling limit of a superconductor. We show in this paper that there are edge excitations in this model as well for manifolds with boundaries. They are the modes of a scalar field with invariance under the group of diffeomorphisms (diffeos) of the bounding spatial two-manifold. Not all diffeos of this group seem implementable by operators in quantum theory, the implementable group being a subgroup of volume-preserving diffeos. The BF system in this manner can lead to the w1+∞ algebra and its variants. Lagrangians for fields on the bounding manifold which account for the edge observables on quantization are also presented. They are the analogs of the (1+1)-dimensional massless scalar field Lagrangian describing the edge modes of an Abelian Chern-Simons theory with a disk as the spatial manifold. We argue that the addition of “Maxwell” terms constructed from F∧*F and dB∧*dB does not affect the edge states, and that the augmented Lagrangian has an infinite number of conserved charges—the aforementioned scalar field modes—localized at the edges. This Lagrangian is known to describe London equations and a massive vector field. A (3+1)-dimensional generalization of the Hall effect involving vortices coupled to B is also proposed.

Nonlinear simulation of electromagnetic current diffusive interchange mode turbulence

Plasma Physics and Controlled Fusion ◽

10.1088/0741-3335/39/11/009 ◽

1997 ◽

Vol 39 (11) ◽

pp. 1887-1914 ◽

Cited By ~ 12

Author(s):

M Yagi ◽

S-I Itoh ◽

K Itoh ◽

A Fukuyama

Keyword(s):

Electromagnetic Current ◽

Nonlinear Simulation

OBSERVATION OF DIRECTIONAL WAVE SPECTRA AND REFLECTION COEFFICIENT OF BREAKWATER IN A HARBOR

Coastal Engineering Proceedings ◽

10.9753/icce.v21.3 ◽

1988 ◽

Vol 1 (21) ◽

pp. 3

Author(s):

Tetsunori Ohshimo ◽

Kosuke Kondo ◽

Tsunehiro Sekimoto

Keyword(s):

Reflection Coefficient ◽

Wave Diffraction ◽

Maximum Likelihood Method ◽

Wave Spectrum ◽

Field Investigation ◽

Likelihood Method ◽

Electromagnetic Current ◽

Wave Spectra ◽

Field Investigations ◽

Directional Wave

Field investigations were performed in order to show the effect of wave diffraction by breakwaters through directional wave spectra measurements in a harbor, and to estimate the reflection coefficient by resolving the incident and reflected wave energy in front of a composite type breakwater. Combinations of an ultrasonic wave gage (USW) and an electromagnetic current meter (EMC) were used to measure the synchronized data of the water surface elevation and two horizontal velocities. The EMLM (Extended Maximum Likelihood Method) was applied for the calculation of the directional wave spectrum, and the modified EMLM for an incident and reflection wave field was applied for the estimation of the reflection coefficient. Through the estimated directional wave spectra, the effect of wave diffraction by breakwaters were discussed and the reflection coefficient was estimated at about 0.9. As a result, the applicability of the field investigation method and the modified EMLM were verified.

Gauge invariance and the electromagnetic current of composite pions

10.2172/10184895 ◽

1993 ◽

Author(s):

M.R. Frank ◽

P.C. Tandy

Keyword(s):

Gauge Invariance ◽

Electromagnetic Current

STORM INDUCED PERIODICITIES OF SUSPENDED SAND MOVEMENT

Coastal Engineering Proceedings ◽

10.9753/icce.v16.105 ◽

1978 ◽

Vol 1 (16) ◽

pp. 105 ◽

Cited By ~ 2

Author(s):

Jay E. Leonard ◽

Benno M. Brenninkmeyer

Keyword(s):

Surf Zone ◽

Normal Wave ◽

Low Frequency ◽

Sediment Concentration ◽

Frequency Component ◽

High Frequency Component ◽

Computational Technique ◽

Electromagnetic Current ◽

Discrete Fourier Analysis ◽

Sediment Movement

An array of electronic sensors was installed on Nauset Light Beach, Cape Cod, Massachusetts, U.S.A., in order to provide a description of the sediment movement during storm conditions. These sensors included two sediment concentration indicators (almometers) which monitor sediment movement as a function of elevation and time, one bidirectional electromagnetic current meter, and a resistive wave staff. Prior field studies performed during "normal" conditions have indicated that surf-zone suspended sediment movement is a low-frequency phenomenon, with the relatively high-frequency component (normal wave period) contributing little to the amount of total sediment transported. Development of a computational technique based upon discrete Fourier analysis and digital filtering called Spectrally Filtered Integration (SFI) provides the calculation and filtering of true units of sediment change in grams-per-liter. Moreover, the SFI technique eliminates the possibility spurious sediment information created by the presence of air bubbles in the water column. Generally, higher-frequency sediment movement is more common during storm conditions than during normal non-storm conditions. This movement is controlled not by the prevailing wave and swell periods, but by a longer period which may be due to water interactions below the surface.

An electromagnetic current meter-based system for application in unsteady flows

IEEE Journal of Oceanic Engineering ◽

10.1109/48.103533 ◽

1990 ◽

Vol 15 (4) ◽

pp. 373-379 ◽

Cited By ~ 2

Author(s):

F.Y. Sorrell ◽

T.B. Curtin ◽

M.D. Feezor

Keyword(s):

Unsteady Flows ◽

Electromagnetic Current

Design and Analysis of PCB Rogowski Coil Current Transformer

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.672-674.984 ◽

2014 ◽

Vol 672-674 ◽

pp. 984-988

Author(s):

Biao Su ◽

Li Xue Li ◽

Yi Hui Zheng ◽

Xin Wang ◽

Yan Liu ◽

...

Keyword(s):

Power System ◽

High Sensitivity ◽

Current Transformer ◽

Rogowski Coil ◽

Electromagnetic Current ◽

Current Transformers ◽

Coil Current ◽

Electronic Current ◽

Rogowski Coils ◽

Electronic Current Transformers

Electronic current transformers are more suitable for the development of power system compared with traditional electromagnetic current transformers. Rogowski coil current transformer is one of three electric current transformers. According to the measurement principle of Rogowski coils, the equivalent circuit of PCB Rogowski coils is analyzed. By using four PCB Rogowski coils combined, a PCB Rogowski coil current transformer is designed and tested. The results show that the designed PCB Rogowski coil transformer has good linearity and high sensitivity and measurement accuracy and it can meet the requirement of power system.

Pair term in the electromagnetic current within the Front-Form dynamics: spin-0 case

Nuclear Physics A ◽

10.1016/s0375-9474(02)00990-9 ◽

2002 ◽

Vol 707 (3-4) ◽

pp. 399-424 ◽

Cited By ~ 58

Author(s):

J.P.B.C. de Melo ◽

T. Frederico ◽

E. Pace ◽

G. Salmè

Keyword(s):

Electromagnetic Current ◽

Front Form

New short-range electromagnetic current in the deuteron

Physics of Atomic Nuclei ◽

10.1134/s1063778807020020 ◽

2007 ◽

Vol 70 (2) ◽

pp. 215-230 ◽

Cited By ~ 2

Author(s):

V. I. Kukulin ◽

I. T. Obukhovsky ◽

V. N. Pomerantsev ◽

P. Grabmayr ◽

A. Faessler

Keyword(s):

Short Range ◽

Electromagnetic Current