Mathematical model of magnetic field for a sectorial ferromagnetic cylinder

The solution of the boundary-value problem of magnetostatics for a circular ferromagnetic cylinder with a longitudinal sectorial cutout is described. The external primary magnetic field is orthogonal to the cylinder and directed at arbitrary azimuth relative to the cutout. A system of algebraic equations for finding the amplitudes of azimuthal expansions of the spatial distribution of the secondary field of the outer and sectorial partial regions of the cylinder is obtained by the method of rearrangement of functions.

Characterisation of transient electromagnetic signals during fixed interference sources in tunnel structure

<abstract> <p>The detection effect of the transient electromagnetic method is ambiguous in engineering applications due to the existence of interference sources, so explaining the influence of these fixed interference sources on is crucial. In this paper, the response characterisation of transient electromagnetic signals of fixed interference sources are thoroughly investigated. First, the secondary field generated by these interference sources is analyzed, and a typical fixed interference source is calculated. Then, a sensitivity analysis of the transient electromagnetic response curve is carried out. Finally, the mathematical superposition method for multiple field sources is proposed and verified. The results illustrate that the transient electromagnetic response curve of uniform full-space surrounding rock with a single fixed interference source has an apparent lifting phenomenon in the middle stage and presents an approximate horizontal change rule at the late stage. The transient electromagnetic response curves of multiple field sources separately illustrate the response characterisation of different field sources at different time stages. These research results can provide a valuable reference for the on-site interpretation of detection signals.</p> </abstract>

Estimation and geologic interpretation of regolith chargeability and superparamagnetic susceptibility in airborne electromagnetic data

All available inversion software for airborne electromagnetic (AEM) data can at a minimum fit a nondispersive conductivity model to the observed inductive secondary field responses, whether operating in the time or frequency domain. Quasistatic inductive responses are essentially controlled by the induction number, the product of frequency with conductivity and magnetic permeability. Recent research has permitted the conductivity model to be dispersive, commonly using a single Cole-Cole parameterization of the induced polarization (IP) effect; but this parameterization slows down and destabilizes any inversion, and it does not account for the need for dual or multiple Cole-Cole responses. Little has been published on inverting AEM data affected by frequency-dependent magnetic permeability, or superparamagnetism (SPM), usually characterized by a Chikazumi model. Because the IP and SPM effects are small and are usually only obvious at late delay times, the aim of our research is to determine if these IP and SPM effects can be fitted and stripped from the AEM data after being approximated with simple dispersive models. We are able to successfully automate a thin-sheet model to do this stripping. Stripped data then can be inverted using a nondispersive conductivity model. The IP and SPM parameters fitted independently to each independent measured decay to provide stripping are proven to be spatially coherent, and they are geologically sensible. The results are found to enhance interpretation of the regolith geology, particularly the nature and distribution of transported materials that are not afforded by mapping conductivity/conductance alone.

Lunar secondary craters: Results for secondary sizes across the Moon, and size-velocity distributions of ejected blocks

&lt;p&gt;Planetary impact events eject large volumes of surface material.&amp;#160; Crater excavation processes are difficult to study, and in particular the details of individual ejecta fragments are not well understood.&amp;#160; A related, enduring issue in planetary mapping is whether a given crater resulted from a primary impact (asteroid or comet) or instead is a secondary crater created by an ejecta fragment.&amp;#160; With mapping and statistical analyses of six lunar secondary crater fields we provide three new constraints on these issues: 1) definition of the maximum secondary crater size as a function of distance from a primary crater on the Moon, 2) estimation of the size and velocity of ejecta fragments that formed these secondaries, and 3) estimation of the fragment size ejected at escape velocity.&amp;#160;&lt;/p&gt;&lt;p&gt;We mapped secondary craters around primary craters ranging in size from ~0.83&amp;#8211;660 km in diameter using Lunar Reconnaissance Orbiter Camera (LROC) Narrow and Wide Angle Camera images. &amp;#160;Identification of secondary craters was based on expected secondary crater morphologies (e.g., v-shaped ejecta, clusters or chains, and elongation in the direction radial to the primary, similarity in degradation state across the secondary field) and secondaries were assigned a confidence level (as to whether they were likely a secondary crater) based on the number of expected morphologies they displayed. &amp;#160;Only the most confident features were utilized in this work, as there is no way to capture all secondary craters within a given lunar secondary field. &amp;#160;Scaling from secondary crater sizes to ejecta fragment sizes was carried out using the Housen-Holsapple-Schmidt formulations.&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&lt;/p&gt;&lt;p&gt;The largest secondaries and those made by the highest velocity fragments (up to ~1.4 km/s) were mapped around the Orientale basin.&amp;#160; The estimated size of fragments that could reach the lunar Hill-sphere escape velocity of 2.34 km/s varies by the size of the impact event, but could be as large as ~850 m for Orientale. &amp;#160;Note that these are not necessarily expected to be coherent fragments, they could also be loosely bound collections of smaller fragments. &amp;#160;However, the fragments/clumps mapped here remained in a form that resembles a single fragment in order to form the distinct secondary craters observed. &amp;#160;For low velocity secondaries, surprisingly, we found features that appear to be secondary craters formed from fragments with velocities as small as 50 m/s around the smallest primary. &amp;#160;&lt;/p&gt;&lt;p&gt;Through this analysis, we confirmed and extended a suspected scale-dependent trend in ejecta size-velocity distributions.&amp;#160; Maximum ejecta fragment sizes fall off much more steeply with increasing ejection velocity for larger primary impacts (compared to smaller primary impacts).&amp;#160; Specifically, we characterize the maximum ejecta sizes for a given ejection velocity with a power law, and find the velocity exponent varies between approximately -0.3 and -3 for the range of primary craters investigated here.&amp;#160; Data for the jovian moons Europa and Ganymede confirm similar trends for icy surfaces.&amp;#160; This result is not predicted by analytical theories of formation of Grady-Kipp fragments or spalls during impacts, and suggests that further modeling investigations are warranted to explain this scale-dependent effect.&lt;/p&gt;

Electromagnetic modelling with topography on regular grids with equivalent materials

SUMMARY Maxwell’s equations are valid regardless of the choice of the coordinate system. By this property a change of coordinates can be equivalently expressed as a change of the material parameters. This idea opens a new approach to the problem of accurate electromagnetic modelling in the vicinity of steep topography or bathymetry. Via a change of coordinates, any earth model with complicated layer interfaces can be represented by an equivalent model where those interfaces are flat, but with its materials correspondingly altered. This new model could then be discretized on a regular mesh and fields could be computed by an appropriate finite difference or integral equation code. Unfortunately, this is not straightforward because both the new electric and magnetic materials are fully anisotropic. By instead applying a finite element secondary field approach to the equivalent model, we can completely account for the topography interface in the planar layered background model. The only modification required to existing finite element formulations is a slightly more complicated right-hand side of the linear system of equations, whereas the system matrix is unchanged in any coordinate system. In a numerical modelling experiment we confirm that our technique gives increased accuracy when compared with a recently published technique for dealing with topography in a secondary field formulation for the case of a magnetotelluric source field. In turn, in the vicinity of conductivity anomalies, accuracy can also be negatively affected.

Rectify the effect of measurement in survival probability of the ground vibrational state in diatomic molecule

We have proposed a methodology that uses secondary electromagnetic field to overcome the effect of measurement on quantum dynamics. Our aim is also to find out some characteristics of the used secondary (recovery) field. We have applied the methodology to reduce the quantum Zeno effect (ZE), a consequence of repeated measurements in survival probability of ground vibrational state. As the model systems, we choose HBr[Formula: see text] and HI. The study is done with variation in frequency, pulse shape and other parameters of the secondary field. In all cases, suitable secondary field for which the Zeno effect is minimum is found near 0 [Formula: see text] 1 vibrational transition frequency. Suitable time gap between the measurement and the application of secondary field depends on the shape of the secondary field. When the secondary field is optimized, the recovery is more than 90% which almost nullify the Zeno effect.

Inductive localization accuracy of a passive 3-D coil in an Industry 4.0 environment

In this paper a localization system of a passive 3-D coil is proposed and signal uncertainties due to the 3-D coil's arbitrary orientation are analyzed. The 3-D coil is excited by an alternating primary magnetic field. Geometrically distributed pick-up coils measure the 3-D coil's secondary field. By means of a simulated look-up table that assigns expected voltages from the pick-up coils to the positions of the 3-D coil, the position of the 3-D coil is deduced by a least-squares approach. A basic assumption is that the secondary field is invariant to the orientation of the 3-D coil. This allows a reduction of the computational effort for the look-up table generation and the table search during the localization phase since for each position the field distribution for only one orientation has to be calculated. However, the assumption of invariance to rotation is only valid for a dipole model. In this paper we investigate the localization error introduced by this assumption when using 3-D coils with a geometric extent in an inhomogeneous primary field. Optimized localization methods that decrease the statistical error are proposed. The theoretical results are verified with measurements conducted on a laboratory system.