scholarly journals Multipole expansions for time-dependent charge and current distributions in quasistatic approximation

2019 ◽  
Vol 34 (02) ◽  
pp. 1950018
Author(s):  
Yuri Krynytskyi ◽  
Andrij Rovenchak
Keyword(s):  
Arbitrary Order ◽  
Multipole Moments ◽  
Full System ◽  
Quasistatic Approximation ◽  
Electric And Magnetic Fields ◽  
Potential Part ◽  
Multipole Expansions ◽  
Definition Of ◽  
Potential Vortex ◽  
The Magnetic Field

We propose a consistent approach to the definition of electric, magnetic and toroidal multipole moments. Electric and magnetic fields are split into potential, vortex and radiative terms, with the latter ones dropped off in the quasistatic approximation. The potential part of the electric field, the vortex parts of the magnetic field and vector potential contain gradients of scalar functions. Formally introducing magnetic and toroidal analogs of the electric charge, we apply multipole expansions for those scalars. Closed-form expressions are derived in an arbitrary order for electric, magnetic and toroidal multipoles, which constitute a full system for expansions of the electromagnetic field.

Transmission line sanitary protective zones. Electromagnetic safety problems

2020 ◽  
pp. 736-736
Author(s):  
N. B. Rubtsova ◽  
A. Y. Tokarskiy
Keyword(s):  
Magnetic Field ◽  
Risk Factor ◽  
Transmission Lines ◽  
General Public ◽  
Field Component ◽  
Regulatory Requirements ◽  
Protection Zones ◽  
Electric And Magnetic Fields ◽  
Health Risk Factor ◽  
The Magnetic Field

The main problems of overhead and cable transmission lines with voltage >=110 kV electric and magnetic fields general public protection are presented. It is shown that it is necessary to develop regulatory requirements for these lines’ sanitary protection zones organization, taking into account the magnetic field component, because its possible health risk factor, up to carcinogenic.

scholarly journals On homogeneous and isotropic universe

2015 ◽  
Vol 30 (34) ◽  
pp. 1550186 ◽  
Author(s):  
M. O. Katanaev
Keyword(s):  
Vector Fields ◽  
Energy Momentum Tensor ◽  
Killing Vector ◽  
Momentum Tensor ◽  
Killing Vector Fields ◽  
Full System ◽  
Independent Functions ◽  
Definition Of ◽  
Usual Scale ◽  
Matter Energy

We give a simple example of spacetime metric, illustrating that homogeneity and isotropy of space slices at all moments of time is not obligatory lifted to a full system of six Killing vector fields in spacetime, thus it cannot be interpreted as a symmetry of a four-dimensional metric. The metric depends on two arbitrary and independent functions of time. One of these functions is the usual scale factor. The second function cannot be removed by coordinate transformations. We prove that it must be equal to zero, if the metric satisfies Einstein’s equations and the matter energy–momentum tensor is homogeneous and isotropic. A new, equivalent, definition of homogeneous and isotropic spacetime is given.

scholarly journals Topology of Coronal Magnetic Fields: Extending the Magnetic Skeleton Using Null-like Points

Solar Physics ◽  
2020 ◽  
Vol 295 (12) ◽  
Author(s):  
Daniel T. Lee ◽  
Daniel S. Brown
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Free Field ◽  
Point Sources ◽  
Topological Features ◽  
Perpendicular Component ◽  
Definition Of ◽  
Magnetic Null ◽  
The Magnetic Field ◽  
Continuous Source

AbstractMany phenomena in the Sun’s atmosphere are magnetic in nature and study of the atmospheric magnetic field plays an important part in understanding these phenomena. Tools to study solar magnetic fields include magnetic topology and features such as magnetic null points, separatrix surfaces, and separators. The theory of these has most robustly been developed under magnetic charge topology, where the sources of the magnetic field are taken to be discrete, but observed magnetic fields are continuously distributed, and reconstructions and numerical simulations typically use continuously distributed magnetic boundary conditions. This article investigates the pitfalls in using continuous-source descriptions, particularly when null points on the $z=0$ z = 0 plane are obscured by the continuous flux distribution through, e.g., the overlap of non-point sources. The idea of null-like points on the boundary is introduced where the parallel requirement on the field $B_{\parallel }=0$ B ∥ = 0 is retained but the requirement on the perpendicular component is relaxed, i.e. $B_{\perp }\ne 0$ B ⊥ ≠ 0 . These allow the definition of separatrix-like surfaces which are shown (through use of a squashing factor) to be a class of quasi-separatrix layer, and separator-like lines which retain the x-line structure of separators. Examples are given that demonstrate that the use of null-like points can reinstate topological features that are eliminated in the transition from discrete to continuous sources, and that their inclusion in more involved cases can enhance understanding of the magnetic structure and even change the resulting conclusions. While the examples in this article use the potential approximation, the definition of null-like points is more general and may be employed in other cases such as force-free field extrapolations and MHD simulations.

Spherical tensor approach to multipole expansions. II. Magnetostatic interactions

1976 ◽  
Vol 54 (5) ◽  
pp. 513-518 ◽  
Author(s):  
C. G. Gray ◽  
P. J. Stiles
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Interaction Energy ◽  
Current Distribution ◽  
Spherical Harmonic ◽  
Magnetostatic Interaction ◽  
Multipole Expansions ◽  
The Magnetic Field ◽  
A Current ◽  
Magnetostatic Interactions

The magnetic field due to a given current distribution, the interaction energy of a current distribution with an arbitrary external magnetic field, and the magnetostatic interaction energy between two current distributions are decomposed into multipolar components using spherical harmonic expansions. Diamagnetic interactions and the spin contributions to the multipole expansions are also discussed.

Local electric and magnetic fields in semicontinuous metal films: Beyond the quasistatic approximation

2000 ◽  
Vol 62 (16) ◽  
pp. 11230-11244 ◽  
Author(s):  
V. A. Shubin ◽  
Andrey K. Sarychev ◽  
J. P. Clerc ◽  
Vladimir M. Shalaev
Keyword(s):  
Magnetic Fields ◽  
Metal Films ◽  
Quasistatic Approximation ◽  
Electric And Magnetic Fields

scholarly journals Twin Subgraphs and Core-Semiperiphery-Periphery Structures

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Ricardo Riaza
Keyword(s):  
Structural Properties ◽  
Network Theory ◽  
World Trade ◽  
Systematic Approach ◽  
Arbitrary Order ◽  
Analytical Framework ◽  
Formal Definition ◽  
Graph Theoretic ◽  
Connection Pattern ◽  
Definition Of

A standard approach to reduce the complexity of very large networks is to group together sets of nodes into clusters according to some criterion which reflects certain structural properties of the network. Beyond the well-known modularity measures defining communities, there are criteria based on the existence of similar or identical connection patterns of a node or sets of nodes to the remainder of the network. A key notion in this context is that of structurally equivalent or twin nodes, displaying exactly the same connection pattern to the remainder of the network. Our first goal is to extend this idea to subgraphs of arbitrary order of a given network, by means of the notions of T-twin and F-twin subgraphs. This research, which leads to graph-theoretic results of independent interest, is motivated by the need to provide a systematic approach to the analysis of core-semiperiphery-periphery (CSP) structures, a notion which is widely used in network theory but that somehow lacks a formal treatment in the literature. The goal is to provide an analytical framework accommodating and extending the idea that the unique (ideal) core-periphery (CP) structure is a 2-partitioned K2, a fact which is here understood to rely on the true and false twin notions for vertices already known in network theory. We provide a formal definition of such CSP structures in terms of core eccentricities and periphery degrees, with semiperiphery vertices acting as intermediaries between both. The T-twin and F-twin notions then make it possible to reduce the large number of resulting structures, paving the way for the decomposition and enumeration of CSP structures. We compute explicitly the resulting CSP structures up to order six. We illustrate the scope of our results by analyzing a subnetwork of the well-known network of metal manufactures trade arising from 1994 world trade statistics.

scholarly journals Magnetotellurics with a remote magnetic reference

Geophysics ◽  
1979 ◽  
Vol 44 (1) ◽  
pp. 53-68 ◽  
Author(s):  
T. D. Gamble ◽  
W. M. Goubau ◽  
J. Clarke
Keyword(s):  
Magnetic Field ◽  
Standard Deviation ◽  
Magnetic Fields ◽  
Apparent Resistivity ◽  
The Other ◽  
Impedance Tensor ◽  
Free Data ◽  
Electric And Magnetic Fields ◽  
Conventional Methods ◽  
The Magnetic Field

Magnetotelluric measurements were performed simultaneously at two sites 4.8 km apart near Hollister, California. SQUID magnetometers were used to measure fluctuations in two orthogonal horizontal components of the magnetic field. The data obtained at each site were analyzed using the magnetic fields at the other site as a remote reference. In this technique, one multiplies the equations relating the Fourier components of the electric and magnetic fields by a component of magnetic field from the remote reference. By averaging the various crossproducts, estimates of the impedance tensor not biased by noise are obtained, provided there are no correlations between the noises in the remote channels and noises in the local channels. For some data, conventional methods of analysis yielded estimates of apparent resistivities that were biased by noise by as much as two orders of magnitude. Nevertheless, estimates of the apparent resistivity obtained from these same data, using the remote reference technique, were consistent with apparent resistivities calculated from relatively noise‐free data at adjacent periods. The estimated standard deviation for periods shorter than 3 sec was less than 5 percent, and for 87 percent of the data, was less than 2 percent. Where data bands overlapped between periods of 0.33 sec and 1 sec, the average discrepancy between the apparent resistivities was 1.8 percent.

Elastic Constants of Nematic Liquid Crystals

1972 ◽  
Vol 27 (6) ◽  
pp. 966-976 ◽  
Author(s):  
Hans Gruler ◽  
Terry J. Scheffer ◽  
Gerhard Meier
Keyword(s):  
Magnetic Fields ◽  
Electric Fields ◽  
Detailed Comparison ◽  
Theoretical Treatment ◽  
Electrical Capacitance ◽  
Normal Deformation ◽  
Electric And Magnetic Fields ◽  
The Magnetic Field ◽  
Dynamic Phenomena ◽  
Good Agreement

Abstract We present a theoretical treatment and give experimental observations of the deformation that occurs in a nematic liquid crystal when electric or magnetic fields are applied. We consider only normal deformations in the nematic material where fluid flow and other dynamic phenomena play no role. Three important sample geometries are considered in the magnetic field, and the experimentally observed deformations are in good agreement with theory. The normal deformation induced by electric fields is of interest from a device standpoint, and we give a solution for the deformation that is valid even for large dielectric anisotropics. This solution has been experimentally verified. We give a detailed comparison of the distortions produced by electric and magnetic fields and show that the deformations are of a similar form even though the field is nonuniform in the electric case. The change in birefringence and electrical capacitance as a function of distortion is discussed as a means of observing the deformation.

scholarly journals A definition of the "reactive power" concept

2021 ◽  
pp. 47-51
Author(s):  
Yevgen Honcharov ◽  
Nataliya Kruykova ◽  
Vladyslav Markov ◽  
Igor Polyakov
Keyword(s):  
Electric Fields ◽  
Physical Meaning ◽  
Reactive Power ◽  
Electrical Energy ◽  
Alternating Current ◽  
Active Power ◽  
Electrostatic Fields ◽  
Definition Of ◽  
The Magnetic Field ◽  
Power Concept

A definition of the "reactive power" concept needs to be clarified, since in the literature it is often given extremely vaguely, which causes difficulties in students' perception and is not entirely clear to the general public. Analysis of numerous sources shows that the physical meaning of this concept almost escapes the definitions given in these sources. Moreover, the formula by which the reactive power is calculated raises no objections. However, it does not explain the physical meaning of the concept. The need for a capacious definition that reflects the physical meaning is long overdue. Analysis of literature sources allows us to conclude that reactive power corresponds to the energy that goes from the source to the consumer and returns back, moreover, the process of circulation of this energy proceeds without dissipation. This energy is stored in inductors, keeping the current constant, and in capacitors, because they charge and discharge, keeping the voltage constant. The inductance and capacitance of the circuit consume and return reactive power. The power transferred to the inductor is stored in the magnetic field when the field expands and returns to the source when the field collapses. The power supplied to the capacitor is stored in an electrostatic field when the capacitor is charged and returned to the source when the capacitor is discharged. This power supplied to the circuit by the source is not consumed. It all returns to the source. Thus, the active power, which is the consumed power, is zero. We know that alternating current is constantly changing; thus, cycles of expansion and collapse of magnetic and electrostatic fields constantly occur. The following definition is proposed: non-dissipated electrical energy of alternating current, which excites the magnetic or electric fields, respectively, in inductive and capacitive elements and, coming from them back to the network, is called reactive power.

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