scholarly journals Migration transformation of two-dimensional magnetic vector and tensor fields

2012 ◽  
Vol 189 (3) ◽  
pp. 1361-1368 ◽  
Author(s):  
Michael S. Zhdanov ◽  
Hongzhu Cai ◽  
Glenn A. Wilson
Keyword(s):  
Two Dimensional ◽  
Magnetic Vector ◽  
Tensor Fields

scholarly journals Global weak solutions to the stochastic Ericksen–Leslie system in dimension two

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hengrong Du ◽  
Changyou Wang
Keyword(s):  
System Modeling ◽  
Energy Estimates ◽  
Bounded Domains ◽  
Two Dimensional ◽  
Global Weak Solutions ◽  
Tensor Fields ◽  
Ginzburg Landau ◽  
Wiener Type ◽  
Leslie System ◽  
Martingale Solutions

<p style='text-indent:20px;'>We establish the global existence of weak martingale solutions to the simplified stochastic Ericksen–Leslie system modeling the nematic liquid crystal flow driven by Wiener-type noises on the two-dimensional bounded domains. The construction of solutions is based on the convergence of Ginzburg–Landau approximations. To achieve such a convergence, we first utilize the concentration-cancellation method for the Ericksen stress tensor fields based on a Pohozaev type argument, and then the Skorokhod compactness theorem, which is built upon uniform energy estimates.</p>

IN‐SITU DETERMINATION OF THE REMANENT MAGNETIC VECTOR OF TWO‐DIMENSIONAL TABULAR BODIES

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 949-962 ◽  
Author(s):  
H. P. Ross ◽  
P. M. Lavin
Keyword(s):  
Remanent Magnetization ◽  
Natural Remanent Magnetization ◽  
Potential Fields ◽  
Small Samples ◽  
Magnetic Survey ◽  
Two Dimensional ◽  
Magnetic Vector ◽  
Gravity And Magnetic

Recent studies have shown that many rocks of the earth’s crust have a substantial component of remanent magnetization. Extensive sampling is required to determine adequately the remanent vector from small samples. A field technique has been developed (and tested on model data) for the in‐situ determination of the resultant (induced+remanent) magnetic vector of bulk volumes of rock, using a combined analysis of the gravity and magnetic fields of a disturbing body (Poisson’s Theorem). The potential fields are sampled adequately at a limited expenditure of time and effort in the field by utilizing the geometry of two‐dimensional bodies. The major limitation to the analysis is the removal of regional gradients and the estimation of the base levels of anomalies. Combined gravity and magnetic surveys were conducted over six diabase bodies in the Triassic Basin of Pennsylvania. The results of these surveys indicate a resultant direction of magnetization given approximately by: declination 2° W, inclination 41 degrees below the horizon. The corresponding direction of natural remanent magnetization has a declination of 1° W and an inclination of 28 degrees. The ratio of remanent to induced magnetization for the diabase is approximately two. These results have been used to provide a better interpretation of magnetic survey data over a magnetite deposit in the Triassic Basin.

NUMERICAL ANALYSIS OF HYSTERETIC LOSSES IN BSCCO/AG TAPES DUE TO TRANSPORT CURRENT AND EXTERNAL MAGNETIC FIELD

2000 ◽  
Vol 14 (25n27) ◽  
pp. 3165-3170 ◽  
Author(s):  
P. LA CASCIA ◽  
L. BIGONI ◽  
E. CEREDA ◽  
F. NEGRINI ◽  
V. OTTOBONI ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Experimental Data ◽  
External Magnetic Field ◽  
Time Dependence ◽  
Transport Current ◽  
Magnetic Vector Potential ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Magnetic Vector ◽  
Transport Losses

A model to calculate hysteretic and transport losses in multifilamentary BSCCO/Ag tapes is described. The model considers a rectilinear infinitely long tape and is based on the two-dimensional Poisson equation for the magnetic vector potential. The equation is numerically solved by means of the finite element method. The contribution of both transport current and external magnetic field with any orientation with respect to the normal to the wide side of the tape is taken into account. A sinusoidal time dependence of the transport current and of the external magnetic field is considered but the model can analyze any time dependence of both quantities. A comparison between the calculated and experimental data is reported and discussed.

scholarly journals Photoelectric Measurements of Sunspot Magnetic Fields

1971 ◽  
Vol 43 ◽  
pp. 190-191
Author(s):  
F.-L. Deubner ◽  
R. Göhring
Keyword(s):  
Magnetic Field ◽  
Vector Field ◽  
Magnetic Fields ◽  
Linear Polarization ◽  
Field Vector ◽  
Two Dimensional ◽  
Magnetic Vector ◽  
Umbral Dots ◽  
Photoelectric Measurements ◽  
The Magnetic Field

Photoelectric polarization measurements in a stable sunspot (type H) with a particularly dark umbra, where ‘umbral dots’ were virtually lacking, have been carried out with the Capri magnetograph. The measurements were evaluated in terms of Unno's theory to give the value and direction of the magnetic field vector. The parameters η0 = 5, β0 = 2.5 and ΔλD = 40mÅ have been adopted for the Fe I 5250 line. Taking the configuration of the sunspot into account as well as simple conditions of steadiness of the distributions to be obtained, it is possible to derive the magnetic vector field from two-dimensional records of circular and linear polarization without ambiguities.

scholarly journals Killing Tensor Fields of Third Rank on a Two-Dimensional Riemannian Torus

2021 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Vladimir A. Sharafutdinov
Keyword(s):  
Tensor Field ◽  
Killing Vector ◽  
First Integral ◽  
Symmetric Tensor ◽  
Two Dimensional ◽  
Killing Tensor ◽  
Tensor Fields ◽  
Killing Field ◽  
Quadratic Equations ◽  
Isothermal Coordinates

A rank m symmetric tensor field on a Riemannian manifold is called a Killing field if the symmetric part of its covariant derivative is equal to zero. Such a field determines the first integral of the geodesic flow which is a degree m homogeneous polynomial in velocities. There exist global isothermal coordinates on a two-dimensional Riemannian torus such that the metric is of the form ds^2= &lambda;(z)|dz|^2 in the coordinates. The torus admits a third rank Killing tensor field if and only if the function &lambda; satisfies the equation R(&part;/&part;z（&lambda;(c∆^-1&lambda;_zz+a))= 0 with some complex constants a and c&ne;0. The latter equation is equivalent to some system of quadratic equations relating Fourier coefficients of the function &lambda;. If the functions &lambda; and &lambda; + &lambda;_0 satisfy the equation for a real constant &lambda;0, 0, then there exists a non-zero Killing vector field on the torus.

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