The Oriented and Flux-Weighted Current Density Stagnation Graph of LiH

A scheme is introduced to quantitatively analyze the magnetically induced molecular current density vector field $\mathbf{J}$. After determining the set of zero points of $\mathbf{J}$, which is called its {\em stagnation graph} (SG), the line integrals $\Phi_{\ell_i}=-\frac{1}{\mu_0} \int_{\ell_i} \mathbf{B}_\mathrm{ind}\cdot\mathrm{d}\mathbf{l}$ along all edges $\ell_i$ of the connected subset of the SG are determined. The edges $\ell_i$ are oriented such that all $\Phi_{\ell_i}$ are non-negative and they are weighted with $\Phi_{\ell_i}$. An oriented flux-weighted (current density) stagnation graph (OFW-SG) is obtained. Since $\mathbf{J}$ is in the exact theoretical limit divergence free and due to the topological characteristics of such vector fields the flux of all separate vortices and neighbouring vortex combinations can be determined by adding the weights of cyclic subsets of edges of the OFW-SG. The procedure is exemplified by the case of LiH for a perpendicular and weak homogeneous external magnetic field $\mathbf{B}$}

Diurnal Dynamics of the Umov Kinetic Energy Density Vector in the Atmospheric Boundary Layer from Minisodar Measurements

The diurnal hourly dynamics of the kinetic energy flux density vector, called the Umov vector, and the mean and turbulent components of the kinetic energy are estimated from minisodar measurements of wind vector components and their variances in the lower 200-meter layer of the atmosphere. During a 24-hour period of continuous minisodar observations, it was established that the mean kinetic energy density dominated in the surface atmospheric layer at altitudes below ~50 m. At altitudes from 50 to 100 m, the relative contributions of the mean and turbulent wind kinetic energy densities depended on the time of the day and the sounding altitude. At altitudes below 100 m, the contribution of the turbulent kinetic energy component is small, and the ratio of the turbulent to mean wind kinetic energy components was in the range 0.01–10. At altitudes above 100 m, the turbulent kinetic energy density sharply increased, and the ratio reached its maximum equal to 100–1000 at altitudes of 150–200 m. A particular importance of the direction and magnitude of the wind effect, that is, of the direction and magnitude of the Umov vector at different altitudes was established. The diurnal behavior of the Umov vector depended both on the time of the day and the sounding altitude. Three layers were clearly distinguished: a near-surface layer at altitudes of 5–15 m, an intermediate layer at altitudes from 15 m to 150 m, and the layer of enhanced turbulence above. The feasibility is illustrated of detecting times and altitudes of maximal and minimal wing kinetic energy flux densities, that is, time periods and altitude ranges most and least favorable for flights of unmanned aerial vehicles. The proposed novel method of determining the spatiotemporal dynamics of the Umov vector from minisodar measurements can also be used to estimate the effect of wind on high-rise buildings and the energy potential of wind turbines.

Stability of current density impedance imaging II

<p style='text-indent:20px;'>This paper is a continuation of the authors earlier work on stability of Current Density Impedance Imaging (CDII) [R. Lopez, A. Moradifam, Stability of Current Density Impedance Imaging, SIAM J. Math. Anal. (2020).] We show that CDII is stable with respect to errors in both measurement of the magnitude of the current density vector field in the interior and the measurement of the voltage potential on the boundary. This completes the authors study of the stability of Current Density Independence Imaging which was previously shown only by numerical simulations.</p>

Analysis of vector hysteresis models in comparison to anhysteretic magnetization model

The design of electrical machines and magnetic actuators requires accurate models to represent hysteresis effects in ferromagnetic materials. The magnetic nonlinearity of the iron core is usually considered by an anhysteretic magnetization curve. With this assumption, hysteresis’ effects in the field computation are completely neglected. This paper presents a comparative study of different hysteresis models, particularly Pragmatic Algebraic Model (PAM) and vector stop model, with regard to a vector anhysteretic anisotropic model. The PAM turns out to be an efficient model implemented with one mathematical equation. The multi cells stop model relies on a consistent thermodynamic formulation, whose dissipation corresponds to a dry friction-like element. Both models implement a constitutive relationship, in which the magnetic flux density vector as independent input and magnetic field strength as output. With a rotational single sheet tester (RSST), various tests for a sample of material FeSi24-50A (FeSi) with a silicon proportion of 2.4 wt% can be proceeded under the application of relevant field distribution. The obtained measured data are applied to parameterize and validate the models. Following numerical experiments the results are compared with those obtained by means of an anhysteretic anisotropic model.

Transfer of spin angular momentum to a dielectric particle

We show here that in the sharp focus of a linearly polarized laser beam the spin vector flux has only transverse components (the effect of photonic wheels or photonic helicopter). For a linearly polarized optical vortex, the orbit-spin conversion leads to the appearance of both longitudinal and transverse components of the spin density vector in the focus. Spin-orbit conversion is experimentally demonstrated for a circularly polarized Gaussian beam when a transverse energy flux (orbital angular momentum) arises in the focus, which is transmitted to a microparticle and makes it rotate. Switching the handedness of circular polarization (from left to right) switches the microparticle rotation direction. It is also shown here that an azimuthally polarized vortex beam with an arbitrary integer topological charge generates in the focus a spin density vector that only has an axial component (pure magnetization), while the transverse spin flux is absent.

Derivation of the full current density vector in the Earth's ionosphere low- and mid-latitude F region using ESA's Swarm satellites

&lt;p&gt;A new multi-spacecraft method to recover estimates of the average three-dimensional current density in the Earth's ionosphere is presented. It is demonstrated using the ESA's Swarm satellite constellation and by taking advantage of the favorable geometrical configurations during the early phase of the mission. The current density vector is calculated inside prisms whose vortices are defined by the satellite positions. The mathematical formalism differs from previous approaches such as the one known as the &amp;#8221;curlometer&amp;#8221;. It makes use of the well-known curl-B technique and involves an inverse problem which allows for error propagation through the calculation. Data from the vector field magnetometers of the three satellites are used and special care is taken to characterize the errors on these data. The method is applied in the low- and mid-latitude F-region on 15 February 2014. It provides latitudinal profiles of the full current density vector together with the associated error bars in the morning and evening sectors. We observe several dynamical features such as clear signatures of field-aligned interhemispheric currents, potential signatures of the wind dynamo current system as well as mid-latitude east-west currents.&lt;/p&gt;

Direct imaging of an inhomogeneous electric current distribution using the trajectory of magnetic half-skyrmions

The direct imaging of current density vector distributions in thin films has remained a daring challenge. Here, we report that an inhomogeneous current distribution can be mapped directly by the trajectories of magnetic half-skyrmions driven by an electrical current in Pt/Co/Ta trilayer, using polar magneto-optical Kerr microscopy. The half-skyrmion carries a topological charge of 0.5 due to the presence of Dzyaloshinskii-Moriya interaction, which leads to the half-skyrmion Hall effect. The Hall angle of half-skyrmions is independent of current density and can be reduced to as small as 4° by tuning the thickness of the Co layer. The Hall angle is so small that the elongation path of half-skyrmion approximately delineates the invisible current flow as demonstrated in both a continuous film and a curved track. Our work provides a practical technique to directly map inhomogeneous current distribution even in complex geometries for both fundamental research and industrial applications.

Electro-plastic metal cutting

In the process of cutting of steels, high strength and heat-resistant alloys a strong warming-up of the cutting instrument takes place, necessitating its cooling by special emulsions and resulting in quick wear and increase of products cost. It was determined by experiment, that during a metal with current cutting, an electro-plastic effect arises. During the lector-plastic cutting, the plastic deformation of a metal under pulse current effect becomes easier, making the friction force between the metal chips and the cutting instrument front edge lower. The electro-plastic metal cutting method accounting the current polarity, current density vector directions, as well as pulse current parameters, can considerably improve the cut surface microstructure and increase the instrument service life. At that, the thermal regime of the cutting can be lowered due to cutting force lowering and heating zone shifting inside the piece or the instrument due to Thomson effect. It was shown, that during the electro-plastic metal cutting the friction force can decrease by 25–30% at the favorable current density vector orientation, as it takes place during electro-static metal drawing and rolling. The current plasticizing action results in decreasing friction force and the chips twisting radius, which can be confluent even for cast iron. At the example of metal drilling with the pulse current, the important current effects on the cutting mechanical parameters revealed. The conditions of metal electro-plastic cutting stated. Results of the experiment study of metal electro-plastic cutting quoted for the processes of steel and cast iron drilling.

Finding Possible Precursors for the 2015 Cotopaxi Volcano Eruption Using Unsupervised Machine Learning Techniques

Cotopaxi Volcano showed an increased activity since April 2015 and evolved into its eventual mild eruption in August 2015. In this work we use records from a broadband seismic station located at less than 4 km from the vent that encompass data from April to December of 2015, to detect and study low-frequency seismic events. We applied unsupervised learning schemes to group and identify possible premonitory low-frequency seismic families. To find these families we applied a two-stage process in which the events were first separated by their frequency content by applying the k-means algorithm to the spectral density vector of the signals and then were further separated by their waveform by applying Correntropy and Dynamic Time Warping. As a result, we found a particular family related to the volcano’s state of activity by exploring its time distribution and estimating its events’ locations.