magnetic potential
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Sensors ◽  
2022 ◽  
Vol 22 (1) ◽  
pp. 326
Author(s):  
Darko Vasić ◽  
Ivan Rep ◽  
Dorijan Špikić ◽  
Matija Kekelj

Computationally fast electromagnetic models of eddy current sensors are required in model-based measurements, machine interpretation approaches or in the sensor design phase. If a sensor geometry allows it, the analytical approach to the modeling has significant advantages in comparison to numerical methods, most notably less demanding implementation and faster computation. In this paper, we studied an eddy current sensor consisting of a transmitter coil with a finitely long I ferrite core, which was screened with a finitely thick magnetic shield. The sensor was placed above a conductive and magnetic half-layer. We used vector magnetic potential formulation of the problem with a truncated region eigenfunction expansion, and obtained expressions for the transmitter coil impedance and magnetic potential in all subdomains. The modeling results are in excellent agreement with the results using the finite element method. The model was also compared with the impedance measurement in the frequency range from 5 kHz to 100 kHz and the agreement is within 3% for the resistance change due to the presence of the half-layer and 1% for the inductance change. The presented model can be used for measurement of properties of metallic objects, sensor lift-off or nonconductive coating thickness.


2021 ◽  
Author(s):  
Sangwha Yi

In the special relativity theory, we study the gauge theory in the electro-magnetic field theory.Using that the Electro-magnetic potential is 4-vector, we treat the invariant potential. Electro-magnetic field theory’s the gauge theory is expanded


Author(s):  
Richard W. Saltus ◽  
Travis Hudson

In southern Alaska, Wrangellia-type magnetic crustal character extends from the Talkeetna Mountains southwest through the Alaska Range to the Bristol Bay region. Magnetic data analyses in the Talkeetna Mountains showed that there are mid-crustal differences in the magnetic properties of Wrangellia and the Peninsular terrane. After converting total field magnetic anomaly data to magnetic potential, we applied Fourier filtering techniques to remove magnetic responses from deep and shallow sources. The resulting mid-crustal magnetic characterization delineates the regional magnetic potential domains that correspond to the Wrangellia and Peninsular terranes throughout southern Alaska. These magnetic potential domains show that Wrangellia-type crust extends southwest to the Illiamna Lake region and that it overlaps the mapped Peninsular terrane. Upon reconsidering geologic ties between Wrangellia, Peninsular, and Alexander terranes we conclude that Peninsular terrane is part of what we here call Western Wrangellia. Western Wrangellia contains the Lower Jurassic Talkeetna volcanic arc and is similar to Wrangellia of the Vancouver Island area, Canada (Southern Wrangellia) which contains the Lower Jurassic Bonanza volcanic arc. Others have previously made this correlation and proposed that the Talkeetna arc-bearing part of southern Alaska was displaced from the Bonanza arc-bearing part of Canada. We generally agree and propose that about 1000 km of dextral displacement along ancestral Border Ranges fault segments and other faults of south-central Alaska separated Western Wrangellia from Southern Wrangellia. We think this displacement was mostly in the Late Jurassic and earliest Cretaceous, perhaps between about 160 and 130 Ma.


2021 ◽  
Vol 58 ◽  
pp. 18-47
Author(s):  
L.I. Danilov

We prove absolute continuity of the spectrum of a periodic $n$-dimensional Schrödinger operator for $n\geqslant 4$. Certain conditions on the magnetic potential $A$ and the electric potential $V+\sum f_j\delta_{S_j}$ are supposed to be fulfilled. In particular, we can assume that the following conditions are satisfied. (1) The magnetic potential $A\colon{\mathbb{R}}^n\to{\mathbb{R}}^n$ either has an absolutely convergent Fourier series or belongs to the space $H^q_{\mathrm{loc}}({\mathbb{R}}^n;{\mathbb{R}}^n)$, $2q>n-1$, or to the space $C({\mathbb{R}}^n;{\mathbb{R}}^n)\cap H^q_{\mathrm{loc}}({\mathbb{R}}^n;{\mathbb{R}}^n)$, $2q>n-2$. (2) The function $V\colon{\mathbb{R}}^n\to\mathbb{R}$ belongs to Morrey space ${\mathfrak{L}}^{2,p}$, $p\in \big(\frac{n-1}{2},\frac{n}{2}\big]$, of periodic functions (with a given period lattice), and $$\lim\limits_{\tau\to+0}\sup\limits_{0<r\leqslant\tau}\sup\limits_{x\in{\mathbb{R}}^n}r^2\bigg(\big(v(B^n_r)\big)^{-1}\int_{B^n_r(x)}|{\mathcal{V}}(y)|^pdy\bigg)^{1/p}\leqslant C,$$ where $B^n_r(x)$ is a closed ball of radius $r>0$ centered at a point $x\in{\mathbb{R}}^n$, $B^n_r=B^n_r(0)$, $v(B^n_r)$ is volume of the ball $B^n_r$, $C=C(n,p;A)>0$. (3) $\delta_{S_j}$ are $\delta$-functions concentrated on (piecewise) $C^1$-smooth periodic hypersurfaces $S_j$, $f_j\in L^p_{\mathrm{loc}}(S_j)$, $j=1,\ldots,m$. Some additional geometric conditions are imposed on the hypersurfaces $S_j$, and these conditions determine the choice of numbers $p\geqslant n-1$. In particular, let hypersurfaces $S_j$ be $C^2$-smooth, the unit vector $e$ be arbitrarily taken from some dense set of the unit sphere $S^{n-1}$ dependent on the magnetic potential $A$, and the normal curvature of the hypersurfaces $S_j$ in the direction of the unit vector $e$ be nonzero at all points of tangency of the hypersurfaces $S_j$ and the lines $\{x_0+te\colon t\in\mathbb{R}\}$, $x_0\in{\mathbb{R}}^n$. Then we can choose the number $p>\frac{3n}{2}-3$, $n\geqslant 4$.


Author(s):  
Shinichi Ishiguri

The purpose of this paper is to demonstrate the existence of an artificial magnetic monopole and to introduce new electromagnetic equations by altering an electric field and a magnetic field vectors.As a principle device, a cylindrical condenser is prepared, and a superconducting loop is inserted into it. By this conduction, radial electric fields take a role as the centripetal force and both counterclockwise and clockwise motions are induced. As a result, a stationery wave is formed in which the nodes take a part in creating a monopole as follows.First, employing the Lorentz conservations and because node of the stationary wave has no phases, the momentum k and the vector potential A vanish and instead a magnetic potential appears in order to maintain the Lorentz conservation. This magnetic potential has relationship with an electric potential, and thus consequently, a dependent relationship is obtained between an electric field and a magnetic field vectors. Using this conclusive dependent relationship, we can derive new Maxwell equation assembly which are created by altering the electric field and the magnetic field vectors. In this process, we derive a divergent equation of magnetic fields which is not zero, i.e., the existence of a magnetic monopole. Employing these newly derived Maxwell equation, an electromagnetic wave is derived whose speed is the same as one the existing Maxwell equations provide. As a monopole configuration, this paper discusses the energy gap of the vacuum, which is a result of the Dirac equation and describes a monopole as pairs between two Cooper pairs (i.e. four electrons) whose interaction is a photon. As mentioned, because the total momenta and phases are zero, this paper defines the wave function as the Dirac function and demonstrate the condensation, employing the Bloch&rsquo;s theorem. Moreover, using the macroscopic basic equations, we retrace the creation of the divergent magnetic field in view of macroscopic phenomenon., which provides results in this paper.In Result section in this paper, we succeeded in demonstrating the distribution of the divergent magnetic field of monopole in terms of both microscopic and macroscopic scales. Furthermore, Discussion section describes properties a magnetic monopole should follow.


2021 ◽  
Author(s):  
Laurent Baratchart ◽  
Christian Gerhards ◽  
Alexander Kegeles ◽  
Peter Menzel
Keyword(s):  

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Zhiwei Liu ◽  
Hui Qi

AbstractAn analytical solution to the anti-plane dynamics problem of semi-space rare earth giant magnetostrictive media with circular cavity defects near the horizontal boundary under the action of SH wave is studied. Based on the Helmholtz theorem and the theory of complex function, the elastic-magnetic dynamic equation of magnetostrictive medium is established, and the semi-space incident wave field is written. In addition, based on the theory of complex function and the method of wave function expansion, the expression of the wave function of the scattered displacement field and the corresponding magnetic potential of the scattered wave under the condition of no stress and magnetic insulation of the horizontal boundary are obtained. Then, based on the conditions of free boundary stress, continuous magnetic induction intensity and continuous magnetic potential around the circular cavity, the infinite linear algebraic equations are established. Finally, the analytical expressions of dynamic stress concentration factor and magnetic field intensity concentration factor around circular cavity in semi-space rare earth giant magnetostrictive medium are obtained. Numerical examples show that the analysis results depend on the following parameters: permeability, dimensional-piezomagnetic coefficient, frequency of the incident wave, incident angle, distance between the circular cavity and horizontal boundary. These results have certain reference value for the study of non-destructive testing and failure analysis of rare earth giant magnetostrictive materials.


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