Density Vector Research Articles

Size effects in wedge indentation predicted by a gradient-enhanced crystal-plasticity model

A recently developed gradient-enhanced crystal-plasticity model is applied to predict the size effects in wedge indentation. In the model, the internal length scale is defined through standard quantities that appear in the underlying non-gradient hardening law. A careful calibration of the non-gradient hardening law is thus performed, and the model is validated against published experimental results. To this end, a comprehensive computational study of wedge indentation into a nickel single crystal is performed, and the obtained results show a good agreement with the experiment in terms of the load–penetration depth curves for three wedge angles, as well as in terms of the distributions of lattice rotation, GND density, and net Burgers vector. For the indentation depth of about 200 μm, as employed in the experiment, the predicted size effects are insignificant. Accordingly, the size effects are next studied for the indentation depth varied between 200 μm and 1 μm. As an intermediate result, apparently not published to date, the general 3D crystal plasticity model with anisotropic hardening is consistently reduced to a 2D plane-strain model in which plastic deformation is realized by three effective in-plane slip systems, each representing two crystallographic slip systems.

Noise robust and rotation invariant framework for texture analysis and classification

Texture feature extraction is an important task in image processing and computer vision. Typical applications include automated inspection, image retrieval or medical analysis. In this paper we propose a noise robust and rotation invariant approach to texture feature analysis and classification. The proposed framework is based on a simple texture feature extraction step which decomposes the image structures by means of a family of orientated filters. The output is an orientation density vector which is called Orientation Feature Vector (OFV). The OFV can be used as the input feature vector to a texture classifier, and in addition, by using an interpolation step it is possible to extract the main orientations of the texture from the OFD, providing additional high level features for image analysis. In this work, three families of filters have been studied in the texture feature extraction step. The experimental results show the ability of the proposed framework in classification problems, improving more than 20% the results of other state-of-the-art methods when a high level of Gaussian noise is considered.

Magnetism of automotive wheels with pneumatic radial tires

This paper shows enhancement of knowledge about magnetic flux density of automotive wheels with radial pneumatic tires equipped with ferromagnetic belt made of tangled steel wires. The investigations were focused on the measurement of magnetic flux density vector (B) over tire’s tread using sensor ability to measure 3 Cartesian projections of B. The other aim of the article is to introduce the prototype of a measuring device as well as measurement technique the purpose of which is to obtain a single or a collection of so called magnetic profiles. Circumferential and crosswise to the tread magnetic profiles and scans over tread surface were presented and analyzed. Moreover, magnetic profile’s parameters were proposed in order to quantitatively characterize magnetic flux density changes in circumferential profiles. Usefulness of them was analyzed and discussed in the context of the measurement technique and the practical utilization. The results revealed that the magnetic flux density is not uniform over tire’s tread surface and the “magnetic surface” is not anisotropic but highly directional. What is more, there are preferred sensor’s locations and measurement directions. The Authors also pointed out some potential application of gained knowledge in domain of vehicle state measurement such as speed, distance and wheel slip.

Scrolling text detection based on region characteristic analysis for frame rate up-conversion

This paper proposes a new scrolling text detection method for frame rate up-conversion, which uses a text edge detector and motion vector distribution analysis of the detected text. Existing methods use either edge or motion vector information of an image for scrolling text detection. Thus, when text begins or ends scrolling at the frame boundary, they have difficulty in detecting the text. Moreover, these methods use a fixed threshold to detect text edges. This makes their detection accuracy dependent on the local characteristic of an image. To overcome these drawbacks, the proposed algorithm uses both text edge detector and motion vector distribution analysis. The proposed method consists of the following three steps. In the first step, a text map is generated by the text edge detector based on region-adaptive thresholding for luminance change. Then, an initial scrolling text map is generated by calculating the difference between the previous and current text maps. Finally, the scrolling text is refined by analyzing the region characteristic of the detected text, including density, structure, and motion vector distribution. Compared with the state-of-the-art method, the experimental results show that the proposed method increases the detection accuracy by up to 17.6%. In addition, when the proposed algorithm is used for scrolling text detection, the frame rate up-conversion algorithm can generate high quality interpolated images for the scrolling text regions.

An Investigation on Optimal Initial Self-Stress Design of Tensegrity Grid Structures

To achieve the optimal feasible force density vector of a given geometry configuration tensegrity grid structure, an efficient procedure is presented for optimal initial self-stress design of tensegrity grid structures by consecutively solving two linear homogeneous systems in conjunction with a minimization problem. The nonlinear constrained optimization algorithm, known as the Interior-Point Method (I-PM), is utilized to obtain the minimal solution, leading to a set of force densities which guarantee the non-degeneracy condition of the force density matrix. The evaluation of the eigenvalues of tangent stiffness matrix is also introduced to check the geometric stability of the tensegrity grid structures. Finally, three numerical examples have been investigated comprehensively to prove the capability of the proposed method in optimal initial self-stress design of tensegrities. Furthermore, division of number of member group has been discussed in detail for the purpose of demonstrating the efficiency of the proposed method in seeking initial force densities of tensegrity grid structures.

Study of local currents in low dimension materials using complex injecting potentials

A complex potential is constructed to inject electrons into the conduction band, mimicking electron currents in nanoscale systems. The injected electrons are time propagated until a steady state is reached. The local current density can then be calculated to show the path of the conducting electrons on an atomistic level. The method allows for the calculation of the current density vectors within the medium as a function of energy of the conducting electron. Using this method, we investigate the electron pathway of graphene nanoribbons in various structures, molecular junctions, and black phosphorus nanoribbons. By analyzing the current flow through the structures, we find strong dependence on the structural geometry and the energy of the injected electrons. This method may be of general use in the study of nano-electronic materials and interfaces.

Motion Compensation for Industrial Computed Tomography

X-ray computed tomography (CT) is a powerful tool for industrial inspection. However, the harsh conditions encountered in some production environments make accurate motion control difficult, leading to motion artifacts in CT applications. A technique is demonstrated that removes motion artifacts by using an iterative-solver CT reconstruction method that includes a bulk Radon transform shifting step to align radiographic data before reconstruction. The paper uses log scanning in a sawmill as an example application. We show how for a known nominal object density distribution (circular prismatic in the case of a log), the geometric center and radius of the log may be approximated from its radiographs and any motion compensated for. This may then be fed into a previously developed iterative reconstruction CT scheme based on a polar voxel geometry and useful for describing logs. The method is validated by taking the known density distribution of a physical phantom and producing synthetic radiographs in which the axis of object rotation does not coincide with the center of field of view for a hypothetical scanner geometry. Reconstructions could then be made on radiographs that had been corrected and compared to those that had not. This was done for progressively larger offsets between these two axes and the reduction in voxel density vector error studied. For CT applications in industrial settings in which precise motion control is impractical or too costly, radiographic data shifting and scaling based on predictive models for the Radon transform appears to be a simple but effective technique.

Transverse spin in the scattering of focused radially and azimuthally polarized vector beams

We study the effect of focusing of the radially and azimuthally polarized vector beams on the spin angular momentum (SAM) density and Poynting vector of scattered waves from a Mie particle. Remarkably, the study reveals that the SAM density of the scattered field is solely transverse in nature for radially and azimuthally polarized incident vector beams; however the Poynting vector shows usual longitudinal character. We also demonstrate that the transverse SAM density can further be tuned with wavelength and focusing of the incident beam by exploiting the interference of different scattering modes. These results may stimulate further experimental technique of detecting the transverse spin and Belinfante's spin-momentum densities.

Current density tensors.

It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.

2D analytical model for heteropolar active magnetic bearings considering eccentricity

This study presents a 2D analytical model for heteropolar active magnetic bearings. In this method, the problem is divided in to three subdomains: slots, slot-openings and air-gap regions. Initially, the radial and tangential components of the flux density vector are analytically presented in the absence of eccentricity. Then the impact of various amounts of eccentricity is investigated. Finally, the magnetic local traction and magnetic forces exerted to the rotor along x and y directions are calculated. The comparison between the proposed analytical model and the finite-element method shows the efficacy of the model.

Electron-Electron Cross-Relaxation and Spectral Diffusion during Dynamic Nuclear Polarization Experiments on Solids.

Recently it has been shown that experimental electron-electron double resonance (ELDOR) spectra of amorphous glasses containing free radicals with inhomogeneously broadened electron paramagnetic resonance (EPR) spectra can be analyzed using a set of coupled rate equations for the electron polarizations of frequency bins composing these spectra, named the eSD (electron spectral diffusion) model. The rate matrix defining these equations has elements depending on the microwave, the spin-lattice relaxation rates and on eSD rate constants responsible for polarization exchange. In this study, we show that in addition to the static dipolar flip-flop terms in the Hamiltonian a zero-quantum electron cross-relaxation mechanism can be responsible for the polarization exchange process in our samples. This conclusion was reached by calculating the EPR lineshapes of a system of 11 coupled electrons exposed to microwave irradiation using an eigenstate population rate equation derived from the spin density vector rate equation in Liouville space. These equations involve all terms of the Hamiltonian and in addition rate constants representing longitudinal relaxation and cross-relaxation mechanisms as well as MW irradiation. The results of these calculations are compared with the results obtained from the eSD model.

Helicons in uniform fields. I. Wave diagnostics with hodograms

The wave equation for whistler waves is well known and has been solved in Cartesian and cylindrical coordinates, yielding plane waves and cylindrical waves. In space plasmas, waves are usually assumed to be plane waves; in small laboratory plasmas, they are often assumed to be cylindrical “helicon” eigenmodes. Experimental observations fall in between both models. Real waves are usually bounded and may rotate like helicons. Such helicons are studied experimentally in a large laboratory plasma which is essentially a uniform, unbounded plasma. The waves are excited by loop antennas whose properties determine the field rotation and transverse dimensions. Both m = 0 and m = 1 helicon modes are produced and analyzed by measuring the wave magnetic field in three dimensional space and time. From Ampère's law and Ohm's law, the current density and electric field vectors are obtained. Hodograms for these vectors are produced. The sign ambiguity of the hodogram normal with respect to the direction of wave propagation is demonstrated. In general, electric and magnetic hodograms differ but both together yield the wave vector direction unambiguously. Vector fields of the hodogram normal yield the phase flow including phase rotation for helicons. Some helicons can have locally a linear polarization which is identified by the hodogram ellipticity. Alternatively the amplitude oscillation in time yields a measure for the wave polarization. It is shown that wave interference produces linear polarization. These observations emphasize that single point hodogram measurements are inadequate to determine the wave topology unless assuming plane waves. Observations of linear polarization indicate wave packets but not plane waves. A simple qualitative diagnostics for the wave polarization is the measurement of the magnetic field magnitude in time. Circular polarization has a constant amplitude; linear polarization results in amplitude modulations.

Challenges in the determination of the interstellar flow longitude from the pickup ion cutoff

Context. The interstellar flow longitude corresponds to the Sun’s direction of movement relative to the local interstellar medium. Thus, it constitutes a fundamental parameter for our understanding of the heliosphere and, in particular, its interaction with its surroundings, which is currently investigated by the Interstellar Boundary EXplorer (IBEX). One possibility to derive this parameter is based on pickup ions (PUIs) that are former neutral ions that have been ionized in the inner heliosphere. The neutrals enter the heliosphere as an interstellar wind from the direction of the Sun’s movement against the partially ionized interstellar medium. PUIs carry information about the spatial variation of their neutral parent population (density and flow vector field) in their velocity distribution function. From the symmetry of the longitudinal flow velocity distribution, the interstellar flow longitude can be derived.Aim. The aim of this paper is to identify and eliminate systematic errors that are connected to this approach of measuring the interstellar flow longitude; we want to minimize any systematic influences on the result of this analysis and give a reasonable estimate for the uncertainty.Methods. We use He+ data measured by the PLAsma and SupraThermal Ion Composition (PLASTIC) sensor on the Solar TErrestrial RElations Observatory Ahead (STEREO A) spacecraft. We analyze a recent approach, identify sources of systematic errors, and propose solutions to eliminate them. Furthermore, a method is introduced to estimate the error associated with this approach. Additionally, we investigate how the selection of interplanetary magnetic field angles, which is closely connected to the pickup ion velocity distribution function, affects the result for the interstellar flow longitude.Results. We find that the revised analysis used to address part of the expected systematic effects obtains significantly different results than presented in the previous study. In particular, the derived uncertainties are considerably larger. Furthermore, an unexpected systematic trend of the resulting interstellar flow longitude with the selection of interplanetary magnetic field orientation is uncovered.

One Solution of the Forward Problem of DC Resistivity Well Logging by the Method of Volume Integral Equations with Allowance for Induced Polarization

For theoretically studying the intensity of the influence exerted by the polarization of the rocks on the results of direct current (DC) well logging, a solution is suggested for the direct inner problem of the DC electric logging in the polarizable model of plane-layered medium containing a heterogeneity by the example of the three-layer model of the hosting medium. Initially, the solution is presented in the form of a traditional vector volume-integral equation of the second kind (IE2) for the electric current density vector. The vector IE2 is solved by the modified iteration–dissipation method. By the transformations, the initial IE2 is reduced to the equation with the contraction integral operator for an axisymmetric model of electrical well-logging of the three-layer polarizable medium intersected by an infinitely long circular cylinder. The latter simulates the borehole with a zone of penetration where the sought vector consists of the radial Jr and Jz axial (relative to the cylinder’s axis) components. The decomposition of the obtained vector IE2 into scalar components and the discretization in the coordinates r and z lead to a heterogeneous system of linear algebraic equations with a block matrix of the coefficients representing 2x2 matrices whose elements are the triple integrals of the mixed derivatives of the second-order Green’s function with respect to the parameters r, z, r', and z'. With the use of the analytical transformations and standard integrals, the integrals over the areas of the partition cells and azimuthal coordinate are reduced to single integrals (with respect to the variable t = cos ϕ on the interval [−1, 1]) calculated by the Gauss method for numerical integration. For estimating the effective coefficient of polarization of the complex medium, it is suggested to use the Siegel–Komarov formula.

Imaging and Variability Studies of CTA 102 during the 2016 January γ-ray Flare

Abstract The γ-ray-bright blazar CTA 102 is studied using imaging (new 15 GHz and archival 43 GHz Very Long Baseline Array, VLBA data) and time variable optical flux density, polarization degree, and electric vector position angle (EVPA) spanning between 2015 June 1 and 2016 October 1, covering a prominent γ-ray flare during 2016 January. The pc-scale jet indicates expansion with oscillatory features up to 17 mas. Component proper motions are in the range 0.04–0.33 mas yr−1 with acceleration up to 1.2 mas followed by a slowing down beyond 1.5 mas. A jet bulk Lorentz factor ≥17.5, position angle of 128.°3, inclination angle ≤6.°6 and intrinsic half opening angle ≤1.°8 are derived from the VLBA data. These inferences are employed in a helical jet model to infer long-term variability in flux density, polarization degree, EVPA, and a rotation of the Stokes Q and U parameters. A core distance of r core,43 GHz = 22.9 pc, and a magnetic field strength at 1 pc and the core location of 1.57 G and 0.07 G, respectively, are inferred using the core-shift method. The study is useful in the context of estimating jet parameters and in offering clues to distinguish mechanisms responsible for variability over different timescales.

Determination of Core Losses in Open-Core Power Voltage Transformers

Power voltage transformers (PVTs) are becoming increasingly present in different substation solutions on a world scale. Such units that are based on the open-core concept introduce several advantages in terms of transformer performance and reliability. This paper provides context for distinct open-core losses, expanding in detail on a measurement-based method for determining both total and specific losses in the open core. The approach is demonstrated on several core model configurations with varying parameters. Apart from loss measurement, the presented core configurations were used to determine and verify the distribution and magnitude of all flux density vector components. The proposed approach is validated by various accompanying measurements but also through comparison with loss measurements performed on several PVT units intended for commercial application.

Evolution of intense laser pulse spot size propagating in collisional plasma embedded in magnetic field with variable direction

In this study, propagation of an intense laser pulse through collisional, homogenous, magnetized plasma has been investigated. The plasma is embedded in an external magnetic field with the amplitude and variable direction being constant. The complex dispersion relation of the plasma medium has been obtained that predicates the Faraday rotation effect. The paraxial wave equation has been used for the study of propagation of laser pulse in plasma. The nonlinear current density vector as a source of wave equation is obtained by motion equation and continuity equation of plasma free electrons. Using the source dependent expansion method, the evolution of laser pulse spot size has been investigated. It is shown that the spot size of the laser pulse is dependent on the strength and direction of the external magnetic field significantly. The effect of collision frequency on the evolution of spot size has been studied. The space damping rate of laser pulse power along the propagation length due to collision is obtained. Results show that the increase in the external magnetic field strength increases the rate of laser energy loss.

Magnetic Structure of Density Matrices.

The spin structure of wave functions is reflected in the magnetic structure of the one-particle density matrix. Indeed, for single determinants we can use either one to determine the other. In this work we discuss how one can simply examine the one-particle density matrix to faithfully determine whether the spin magnetization density vector field is collinear, coplanar, or noncoplanar. For single determinants, this test suffices to distinguish collinear determinants which are eigenfunctions of Ŝn̂ from noncollinear determinants which are not. We also point out the close relationship between noncoplanar magnetism on the one hand and complex conjugation symmetry breaking on the other. Finally, we use these ideas to classify the various ways single determinant wave functions break and respect symmetries of the Hamiltonian in terms of their one-particle density matrix.

Uniqueness of minimizers of weighted least gradient problems arising in hybrid inverse problems

We study the question of uniqueness of minimizers of the weighted least gradient problem $$\begin{aligned} \min \left\{ \int _{\Omega }|Dv|_a : v\in BV_{loc}(\Omega {\setminus } S),\; v|_{\partial \Omega }= f \right\} , \end{aligned}$$ where $$\int _{\Omega }|Dv|_a$$ is the total variation with respect to the weight function a and S is the set of zeros of the function a. In contrast with previous results, which assume that the weight $$a\in C^{1,1}(\Omega )$$ and is bounded away from zero, here a is only assumed to be continuous, and is allowed to vanish and also be discontinuous in certain subsets of $$\Omega $$ . We assume instead existence of a $$C^1$$ minimizer. This problem arises naturally in the hybrid inverse problem of imaging electric conductivity from interior knowledge of the magnitude of one current density vector field, where existence of a $$C^1$$ minimizer is known a priori.

Revisit of non-ordinary state-based peridynamics

The force density vector in the Non-Ordinary State-Based (NOSB) PeriDynamics (PD) replaces the internal force vector derived from the divergence of the stress tensor in the classical (local) stress equilibrium equations. It involves only the non-local form of the first order derivatives of stress and displacement components. Inherent in the NOSB PD formulation is the presence of oscillations especially in the regions of steep displacement gradients. This study introduces an alternative form of the force density vector by considering the internal force vector derived directly from the displacement equilibrium equations. It involves only the non-local form of the second-order derivatives of the displacement components. The numerical results from this form of the force density vector do not present any oscillations. Therefore, it is referred to as the Refined NOSB (RNOSB) – PD. The simulations concern the comparisons of NOSB and RNOSB PD predictions for an isotropic plate with or without a notch or a crack under quasi-static and dynamic tensile loading. The RNOSB PD proves to be effective and accurate for cracking and fracture analysis without any numerical instability.