A DECOMPOSITION OF L2(Ω)3 AND AN APPLICATION TO MAGNETOSTATIC EQUATIONS

1993 ◽  
Vol 03 (03) ◽  
pp. 289-301 ◽  
Author(s):  
PATRICK CIARLET
Keyword(s):  
Magnetic Field ◽  
Connected Subset ◽  
Field Solution ◽  
The Magnetic Field

The domain Ω considered in the following is an open, bounded and connected subset of R3. The purpose of this paper is to find a decomposition of the space of functions L2(Ω)3 of the form grad P⊕ curl W and then to apply this result to the magnetostatic set of equations. Moreover, we prove that if the spaces P and W are chosen correctly, a function u of L2(Ω)3 can be written as grad p+curl w, p∈P and w∈W being unique (up to a constant for p). In the case of the magnetostatic equations, we provide a characterization of the magnetic field solution of these equations.

scholarly journals Magnetic properties of cobalt microwires measured by piezoresistive cantilever magnetometry

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
G. Tosolini ◽  
J. M. Michalik ◽  
R. Córdoba ◽  
J. M. de Teresa ◽  
F. Pérez-Murano ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Room Temperature ◽  
Signal To Noise Ratio ◽  
Static Deflection ◽  
Magnetic Structures ◽  
Dual Beam ◽  
Piezoresistive Cantilevers ◽  
Good Signal ◽  
The Magnetic Field

AbstractWe present the magnetic characterization of cobalt wires grown by focused electron beam-induced deposition (FEBID) and studied using static piezoresistive cantilever magnetometry. We have used previously developed high force sensitive submicron-thick silicon piezoresistive cantilevers. High quality polycrystalline cobalt microwires have been grown by FEBID onto the free end of the cantilevers using dual beam equipment. In the presence of an external magnetic field, the magnetic cobalt wires become magnetized, which leads to the magnetic field dependent static deflection of the cantilevers. We show that the piezoresistive signal from the cantilevers, corresponding to a maximum force of about 1 nN, can be measured as a function of the applied magnetic field with a good signal to noise ratio at room temperature. The results highlight the flexibility of the FEBID technique for the growth of magnetic structures on specific substrates, in this case piezoresistive cantilevers.

scholarly journals Stochastic Dosimetry for the Assessment of Children Exposure to Uniform 50 Hz Magnetic Field with Uncertain Orientation

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
E. Chiaramello ◽  
S. Fiocchi ◽  
P. Ravazzani ◽  
M. Parazzini
Keyword(s):  
Magnetic Field ◽  
Central Nervous System ◽  
Nervous System ◽  
Electric Field ◽  
Stochastic Model ◽  
Significant Difference ◽  
The Central Nervous System ◽  
Children Exposure ◽  
The Magnetic Field

This study focused on the evaluation of the exposure of children aging from five to fourteen years to 50 Hz homogenous magnetic field uncertain orientation using stochastic dosimetry. Surrogate models allowed assessing how the variation of the orientation of the magnetic field influenced the induced electric field in each tissue of the central nervous system (CNS) and in the peripheral nervous system (PNS) of children. Results showed that the electric field induced in CNS and PNS tissues of children were within the ICNIRP basic restrictions for general public and that no significant difference was found in the level of exposure of children of different ages when considering 10000 possible orientations of the magnetic field. A “mean stochastic model,” useful to estimate the level of exposure in each tissue of a representative child in the range of age from five to fourteen years, was developed. In conclusion, this study was useful to deepen knowledge about the ELF-MF exposure, including the evaluation of variable and uncertain conditions, thus representing a step towards a more realistic characterization of the exposure to EMF.

scholarly journals Characterization of the magnetic field of the Herbig Be star HD 200775★

2008 ◽  
Vol 385 (1) ◽  
pp. 391-403 ◽  
Author(s):  
E. Alecian ◽  
C. Catala ◽  
G. A. Wade ◽  
J.-F. Donati ◽  
P. Petit ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Be Star ◽  
The Magnetic Field

Characterization of an Analytical Theta-Pinch Plasma Generated with a Unidirectional Capacitive Discharge

1988 ◽  
Vol 42 (1) ◽  
pp. 77-83 ◽  
Author(s):  
E. T. Johnson ◽  
R. D. Sacks
Keyword(s):  
Magnetic Field ◽  
Discharge Current ◽  
Discharge Circuit ◽  
Radiative Properties ◽  
Plasma Properties ◽  
Capacitive Discharge ◽  
Zero Crossings ◽  
Theta Pinch ◽  
The Magnetic Field

The plasma produced by a high-current capacitive discharge through a graphite fiber bundle is compressed by a magnetic field coaxial with the plasma. The magnetic field is generated by the plasma current in a large coil surrounding the plasma. The field induces an azimuthal (theta) current in the plasma. This current couples with the external magnetic field and produces a radial Lorentz force which reduces the rate of plasma expansion. A diode shunt in the capacitive discharge circuit is used for the generation of a unidirectional discharge current. This arrangement eliminates zero-crossings of the discharge current and thus increases the effectiveness of the magnetic field in controlling the radiative properties of the plasma. Design features of the discharge circuit are presented, as well as a comparison of the plasma properties with oscillatory and unidirectional discharge current waveforms.

scholarly journals Harmonic generation in the interaction of laser with a magnetized overdense plasma

2021 ◽  
Vol 87 (5) ◽  
Author(s):  
Srimanta Maity ◽  
Devshree Mandal ◽  
Ayushi Vashistha ◽  
Laxman Prasad Goswami ◽  
Amita Das
Keyword(s):  
Magnetic Field ◽  
Harmonic Generation ◽  
Laser Energy ◽  
Magnetized Plasma ◽  
Plasma Region ◽  
Particle In Cell ◽  
Incident Laser Intensity ◽  
Overdense Plasma ◽  
The Magnetic Field

The mechanism of harmonic generation in both O- and X-mode configurations for a magnetized plasma has been explored here in detail with the help of particle-in-cell simulations. A detailed characterization of both the reflected and transmitted electromagnetic radiation propagating in the bulk of the plasma has been carried out for this purpose. The efficiency of harmonic generation is shown to increase with the incident laser intensity. A dependency of harmonic efficiency has also been found on magnetic field strength. This work demonstrates that there is an optimum value of the magnetic field at which the efficiency of harmonic generation maximizes. The observations are in agreement with theoretical analysis. For the O-mode configuration, this is compelling as the harmonic generation provides for a mechanism by which laser energy can propagate inside an overdense plasma region.

scholarly journals Magnetoelectric, magnetodielectric and magneto-impedance couplings in Bi1−xNdxFe0.99Co0.01O3 compounds

2021 ◽  
Vol 10 (14) ◽  
pp. e470101422189
Author(s):  
Anuar José Mincache ◽  
Odair Gonçalves de Oliveira ◽  
Lilian Felipe da Silva Tupan ◽  
Daniel Matos Silva ◽  
Ivair Aparecido dos Santos ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Electrical Impedance ◽  
Structural Refinement ◽  
Relative Variation ◽  
Dc Magnetic Field ◽  
Magnetoelectric Coefficient ◽  
Impedance Characterization ◽  
The Magnetic Field ◽  
Rhombohedral Symmetry

In this work Bi1−xNdxFe0.99Co0.01O3 ceramics compositions were synthesized for x = 0.05, 0.20 and, y = 0.01. Structural refinement results show that most of the samples crystallized in a rhombohedral symmetry with R3c. Measurements magnetoelectric coefficient, show that the magnetoelectric coefficients are of second order. The electrical impedance characterization of in function external magnetic fields, has a relative variation of the real dielectric response, the loss tangent and the electrical impedance. The systems, as the DC magnetic field strength increased a gain in both the values of the dielectric constant variation, as well as the variation of the electrical impedance. In other words, the greater the intensity of the magnetic field, the greater your response. There were also significant variations with of the magnetic field AC.  

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