Three-dimensional MR reconstruction of high-contrast magnetic susceptibility by the variational born iterative method based on the magnetic field volume integral equation

2017 ◽  
Vol 79 (2) ◽  
pp. 923-932 ◽  
Author(s):  
Shengnan Li ◽  
Ronghan Hong ◽  
Na Liu ◽  
Jianhua Zhang ◽  
Lin Chen ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Integral Equation ◽  
Magnetic Susceptibility ◽  
Iterative Method ◽  
Three Dimensional ◽  
High Contrast ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Mr Reconstruction ◽  
The Magnetic Field

scholarly journals Three-Dimensional Volume Integral Equation Method for Solving Isotropic/Anisotropic Inhomogeneity Problems

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1866
Author(s):  
Jungki Lee ◽  
Mingu Han
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Practical Interest ◽  
Integral Equation Method ◽  
Equation Method ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Isotropic Solid ◽  
Anisotropic Inhomogeneity ◽  
Volume Integral Equation Method

In this paper, the volume integral equation method (VIEM) is introduced for the analysis of an unbounded isotropic solid composed of multiple isotropic/anisotropic inhomogeneities. A comprehensive examination of a three-dimensional elastostatic VIEM is introduced for the analysis of an unbounded isotropic solid composed of isotropic/anisotropic inhomogeneity of arbitrary shape. The authors hope that the volume integral equation method can be used to compute critical values of practical interest in realistic models of composites composed of strong anisotropic and/or heterogeneous inhomogeneities of arbitrary shapes.

scholarly journals Paramagnetic and Diamagnetic Susceptibility of Infinite Quantum Well

2020 ◽  
Vol 3 (2) ◽  
pp. 61-67
Author(s):  
Adam Badra Cahaya
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Quantum Well ◽  
Diamagnetic Susceptibility ◽  
Three Dimensional ◽  
Positive Sign ◽  
Basic Physics ◽  
Paramagnetic Materials ◽  
Quantization Formalism ◽  
The Magnetic Field

Paramagnetism and diamagnetism of a material characterized by its magnetic susceptibility. When a material is exposed to an external magnetic field, magnetic susceptibility is defined as the ratio of the induced magnetization and the magnetic field. A paramagnetic material has magnetic susceptibility with positive sign. On the other hand, a diamagnetic material has magnetic susceptibility with negative sign. Atomically, paramagnetic materials consist of atoms that has orbital with unpaired electrons. Theoretical study of paramagnetic susceptibility and diamagnetic susceptibility are well described by Pauli paramagnetism and Landau diamagnetism, respectively. Although paramagnetism and diamagnetism are among the simplest magnetic properties of material that are studied in basic physics, theoretical derivations of Pauli paramagnetic and Landau diamagnetic susceptibility require second quantization formalism of quantum mechanics. We aim to discuss the paramagnetic and diamagnetic susceptibilities for simple three-dimensional quantum well using first quantization formalism.

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