Binormal schrodinger system of Heisenberg ferromagnetic equation in the normal direction with Q-HATM approach

In this paper, we first study the applications of the wave propagation flow in the normal direction, which is assumed to be the path of the propagated light radiated by Heisenberg ferromagnetic equation. Then the Coriolis phase is mainly used to demonstrate the relationship between the geometric magnetic phase and parallel transportation of the wave propagation field of the evolving light radiating in the normal orientation with Heisenberg ferromagnetic equation. Moreover, we investigate the geometric magnetic interpretation of the binormal evolution of the wave propagation field in the normal direction by considering the nonlinear fractional system with the repulsive type. Finally, we obtain numerical fractional solutions for the nonlinear fractional systems with the repulsive type by using the [Formula: see text]-Homotopy analysis transform ([Formula: see text]-HATM) method.

Scanning Magnetic Microscope Using a Gradiometric Configuration for Characterization of Rock Samples

Scanning magnetic microscopy is a tool that has been used to map magnetic fields with good spatial resolution and field sensitivity. This technology has great advantages over other instruments; for example, its operation does not require cryogenic technology, which reduces its operational cost and complexity. Here, we presented a spatial domain technique based on an equivalent layer approach for processing the data set produced by magnetic microscopy. This approach estimated a magnetic moment distribution over a fictitious layer composed by a set of dipoles located below the observation plane. For this purpose, we formulated a linear inverse problem for calculating the magnetic vector and its amplitude. Vector field maps are valuable tools for the magnetic interpretation of samples with a high spatial variability of magnetization. These maps could provide comprehensive information regarding the spatial distribution of magnetic carriers. In addition, this approach might be useful for characterizing isolated areas over samples or investigating the spatial magnetization distribution of bulk samples at the micro and millimeter scales. This technique could be useful for many applications that require samples that need to be mapped without a magnetic field at room temperature, including rock magnetism.

Numerical evaluation of active source magnetics as a method for imaging high-resolution near-surface magnetic heterogeneity

We have evaluated a geophysical method that uses a low-frequency magnetic source to image subsurface magnetic heterogeneity. This active source approach can be used to image magnetic features at higher resolutions than the conventional passive geomagnetic method. Importantly, this frequency-domain active source approach is independent of the effects of remanent magnetization, which complicates the interpretation of geomagnetic data. We carried out forward modeling of frequency-domain electromagnetic (EM) data and we found that, at frequencies of a few hertz, the magnetostatic response due to the induced magnetization dominates the EM induction response. The result suggests that it is possible to make magnetic interpretation of low-frequency EM data without having to consider the conductivity structure and the corresponding EM induction effect. We compare the anomalous magnetic responses with magnetic noise components and find that the proposed active source magnetic (ASM) method has a depth of investigation of approximately 300 m. Free-space field and inductive noise are considered as the most important issues affecting the depth of investigation. We also determine the potential for linear interpretation of magnetic heterogeneity under 0.1 SI by showing that the low-frequency magnetic response can be approximated by a linear magnetic response. In our synthetic experiments, inversion of the ASM data shows a marked enhancement in resolution, with no effect of the remanent magnetization, in contrast to geomagnetic inversion. These results show that the ASM method is a useful geophysical tool, especially when high-resolution imaging of magnetic susceptibility is required or where strong remanent magnetization complicates the magnetic interpretation.