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Sensors and Sensing Techniques
Published in Stanislaw Zurek, Characterisation of Soft Magnetic Materials Under Rotational Magnetisation, 2017
Of course, the excitation must also be applied in a non-enwrapping way. An example is shown in Figure 3.30, where a single layer of conductors effectively creates a ‘current sheet’. The current is returned in ‘remote bundles’.
On the limitations of magneto-frictional relaxation
Published in Geophysical & Astrophysical Fluid Dynamics, 2022
A more significant limitation of MF without pressure is that it fails to respect conservation of unsigned magnetic flux, which would follow from the ideal induction equation (5d) provided that remains smooth. The problem is that does not remain smooth for any of the forms of MF in common use. When , our one-dimensional problem reduces to a linear diffusion equation. When ν is constant, or becomes constant near to a null point, then is initially smooth but this breaks down at a finite time. In itself, we would argue (in contrast to Low 2013) that this formation of discontinuous current sheets is not a problem, since the state of minimum magnetic energy when fluid pressure is neglected is a discontinuous one (section 2.2). However, the ensuing weak solution obtained does not conserve unsigned flux, so does not evolve toward this expected solution. For one-dimensional configurations such as that investigated here, Craig and Litvinenko (2005) show that adding plasma pressure can also prevent the formation of a discontinuous current sheet, and hence also the breakdown of flux conservation.
An Open Boundary Condition for High-order Solutions of Magnetohydrodynamics on Unstructured Grids
Published in International Journal of Computational Fluid Dynamics, 2020
Xiaoliang Zhang, Chunlei Liang
The initial conditions employed in this simulation is the classical Harris current sheet with small perturbations by setting where is the ratio of plasma pressure (p) to the magnetic pressure (), and is the ratio of specific heats. Finally, is Mach number, is initial magnitude of magnetic field, is the half width of current sheet, is the perturbation amplitude, is the domain length along and directions, respectively. The grid spacing in both directions was set to The fourth-order FR scheme was adopted along with the aforementioned Runge–Kutta method using a time step size of The domain size along x direction was sufficiently enlarged to ensure the boundary conditions over direction has little influence on reconnection region. Open boundary conditions along direction is set while periodic and symmetric boundary conditions were used along and z directions, respectively. Three different sets of resistivity coefficients were investigated, i.e. corresponding to Lundquist numbers respectively. The Lundquist number was defined as where
Achieving polarization control by utilizing electromagnetically induced transparency based on metasurface
Published in Waves in Random and Complex Media, 2022
Cheng-Jing Gao, Yuan-Zhe Sun, Han-Qing Dong, Hai-Feng Zhang
Furthermore, to better quantitatively analyze the EIT behavior, a classical two harmonic oscillator model is employed in this work [64]. The two oscillators (bright mode (x1) and quasi-dark mode (x2)) can interact with the incident electric field E = E0ejωt. And the interaction is described as follows:[64] where, the parameters (x1, x2) and (γ1, γ2) respectively are the resonant amplitude and the damping of the two oscillators. δ is the detuning factor between the intrinsic oscillation frequency of the ‘bright mode’ resonator and the ‘quasi-dark mode’ resonator. Ω is the coupling strength between the two oscillators. g is represented the coupling strength during the bright mode oscillator and the external field. With the approximation of ω12–ω2 ≈ −2ω1(ω–ω1) and the employment of the displacements vectors that are written as xn = cnejωt (n = 1, 2), the transmission can be expressed as below: [64] where the Re stands for the real part. Here the scattering parameters of an electric current sheet and the relation of T = 1 – R can be utilized [65]. We have employed Matlab software to fit the transmission curves of the above EIT structure. Moreover, the curve most consistent with the simulated transmission curve is selected as the theoretical analysis curve. After corresponding fitting, the comparison of the simulated curves with the theoretical analysis results under the double-harmonic oscillator for TE and TM waves are shown in Figure 15. The pivotal fitting parameters of the TE wave are set as γ1 = 0.170, γ2 = 0.025, Ω = 0.180, g = 0.308, and ω0 = 1.278. As for the TM wave, the optimal fitting parameters are selected as γ1 = 0.172, γ2 = 0.020, Ω = 0.181, g = 0.305, and ω0 = 1.385. From Figure 15, it can be noted that the simulated results of the TE and TM waves are in good consistency with the theoretical results, displaying the validity of the two harmonic oscillator model in this work. However, we figure out that there are some local mismatches between the simulated transmission curves and theoretical results under the double-harmonic oscillator, which is caused by the complexity of coupling and a certain loss in the presented structure.