Moment Vector Research Articles

Eigenvector Constraint-Based Method for Eliminating Dead Zone in Magnetic Target Localization

Magnetic target localization using the magnetic gradient tensor (MGT) plays a significant role in underwater localization. However, this method inherently has a localization dead zone, which presents challenges for real-world applications. This paper delves into the root cause of this dead zone, identifying the non-invertibility of the MGT when the magnetic moment vector is orthogonal to the position vector from the target to the observation point. To tackle this issue, a method based on the eigenvector constraints is proposed. By constructing an objective function with eigenvector constraints and leveraging the property that its gradient at the observation point is zero, we derive an equivalent expression for the inverse of MGT that always holds and further develop a dead-zone-free localization method. To validate the robustness and efficacy of the proposed localization method, a comparative analysis with other methods is conducted. Simulation results in a 10 m × 10 m area under Gaussian noise demonstrate the proposed method’s capability to eliminate the dead zone and achieve an average localization error of 0.032 m. Experimental results further demonstrate that the proposed method eliminates the localization dead zone and exhibits greater robustness than the dominant method in the normal region. In summation, this paper provides an effective method for eliminating localization dead zone, offering a more stable and reliable method for magnetic target localization in practice.

Chiroptical Properties of Planar Benzobisthiazole-Bridged Squaraine Dimers.

Five chiral squaraine dimers were synthesized by fusing chiral indolenine semisquaraines with three different benzobisthiazole bridges. The thereby created squaraine dimers show a strong splitting of the lowest energy absorption bands caused by exciton coupling. The intensities of the two exciton transitions and the energetic splitting depend on the angle of the two squaraine moieties within the chromophore dimer. The electric circular dichroism spectra of the dimers show intense Cotton effects whose sign depends on the used squaraine chromophores. Sizable anisotropies gabs of up to 2.6 × 10-3 could be obtained. TD-DFT calculations were used to partition the rotational strength into the three Rosenfeld terms where the electric-magnetic coupling turned out to be the dominant contribution while the exciton chirality term is much smaller. This is because the chromophore dimers are essentially planar but the angle between the electric transition dipole moment of one squaraine and the magnetic transition dipole moment of the other squaraine strongly deviates from 90°, which makes the dot product between the two moment vectors and, thus, the rotational strength substantial.

Relative roll control of satellite docking using electromagnetic coils

An electromagnetic coil topology and its control strategy, which can be incorporated into the electromagnetic docking device, have been proposed for the relative roll control of two satellites in space. The target satellite and the chaser satellite are respectively embarked with four and six coils evenly arranged around the docking axis. All the coils on the target satellite are Direct Current (DC) energized, while the currents in the coils of the chaser satellite are regulated to achieve the relative roll control. The electromagnetic force/torque model is built by utilizing the frequently-used far field model. Based on the fundamental components extracted from that model, this paper proposes a real-time magnetic moment vector distribution formula that simply generates a constant roll torque. This paper not only presents an equation for calculating the relative roll angle through the Euler angles of two satellites, but also an equation that converts the roll torque setpoint to the setpoints of the coil currents. A 3-closed-loop positioning controller composed of angle, angular velocity, and current loop is developed. The proposed topology is verified by finite element simulation, and the control strategy is validated by dynamics simulation and ground-based tests.

Magnetocaloric effect and phase transformation of LaFe11.0M0.5Si1.5 (M = Cu, Ni, Mg) alloys

La (Fe,Si)13 is a promising magnetic refrigerant material. In this paper, the effects of Cu, Ni and Mg substitution of Fe on the magnetocaloric effect and phase transition properties of LaFe11.5Si1.5 alloys were studied by first-principles calculations combined with experiments. Through scanning electron microscopy–energy-dispersive spectroscopy analysis, it was concluded that after Cu partially replaced Fe, the content of the 1:13 main phase significantly decreased to 61.49%, and the contents of the α-Fe and LaFeSi phases increased. Cu was not conducive to the formation of the main phase. After Mg partially replaced Fe, the content of the 1:13 main phase increased to 99.12%, and Mg promoted the formation of the main phase. The electronic structure of the alloy was reconstructed by density functional theory (DFT), and the effects of the doping atoms on the magnetic properties of the alloys were studied. The calculation results showed that Ni atoms had the same weak magnetism as that in the magnetic moment vector direction of Fe atoms, Cu and Mg atoms had magnetism opposite to that in the magnetic moment vector direction of Fe atoms, and all alloys showed a lower total magnetic moment. According to the Arrott curve and the field dependence method of the magnetocaloric effect (MCE), when Cu = 0.5 and Ni = 0.5, the alloy phase transition changed from a first-order phase transition to a second-order phase transition, and when Mg = 0.5, the alloy still had a first-order phase transition.

How hydrophobicity shapes the architecture of protein assemblies

The interactions that give rise to protein self-assembly are basically electrical and hydrophobic in origin. The electrical interactions are approached in this study as the interaction between electrostatic dipoles originated by the asymmetric distribution of their charged amino acids. However, hydrophobicity is not easily derivable from basic physicochemical principles. Its treatment is carried out here considering a hydrophobic force field originated by “hydrophobic charges”. These charges are indices obtained experimentally from the free energies of transferring amino acids from polar to hydrophobic media. Hydrophobic dipole moments are used here in a manner analogous to electric dipole moments, and an empirical expression of interaction energy between hydrophobic dipoles is derived. This methodology is used with two examples of self-assembly systems of different complexity. It was found that the hydrophobic dipole moments of proteins tend to interact in such a way that they align parallel to each other in a completely analogous way to how phospholipids are oriented in biological membranes to form the well-known double layer. In this biological membrane model (BM model), proteins tend to interact in a similar way, although in this case this alignment is modulated by the tendency of the corresponding electrostatic dipoles to counter-align.Graphical abstractHelical conformation of influenza virus PDBid: 6Z5L. Two monomers are shown in cyan and green. The corresponding dipole moment vectors are shown in red (electric dipoles) and blue (hydrophobic dipoles). From the inset figure, it can be seen that the growth of the helix is due to electrical attraction of the monomers, overcoming a hydrophobic repulsion (see text)

Closure theory for high-collisionality multi-ion plasmas

A general formalism is developed to construct and solve a system of linearized moment equations for parallel and perpendicular closures in high-collisionality plasmas. It is applicable for multiple ion species with arbitrary masses, temperatures, charges, and densities. The convergence of closure coefficients is evaluated by increasing the number of moments from 2 to 32 for scalar, vector, and rank-2 tensor moments. As an example, the complete set of closure coefficients for a deuterium-carbon plasma over the entire Hall parameter range is presented. The closure coefficients at various temperature ratios show that the one-temperature closure coefficients can differ significantly from the two-temperature coefficients.

Product inequalities for multivariate Gaussian, gamma, and positively upper orthant dependent distributions

The Gaussian product inequality is an important conjecture concerning the moments of Gaussian random vectors. While all attempts to prove the Gaussian product inequality in full generality have been unsuccessful to date, numerous partial results have been derived in recent decades and we provide here further results on the problem. Most importantly, we establish a strong version of the Gaussian product inequality for multivariate gamma distributions in the case of nonnegative correlations, thereby extending a result recently derived by Genest and Ouimet (2021). Further, we show that the Gaussian product inequality holds with nonnegative exponents for all random vectors with positive components whenever the underlying vector is positively upper orthant dependent. Finally, we show that the Gaussian product inequality with negative exponents follows directly from the Gaussian correlation inequality.

Classification of IR Images of Small Eruptions at the Erebus Volcano, Antarctica, With Zernike Moments and Support Vector Machine

AbstractTo investigate the explosive nature of the Erebus volcano, Antarctica, millions of infrared images of the Ray lava lake were analyzed to identify time and position of non‐explosive small eruptions (NESEs). We developed a new technique based on two steps: (a) feature recognition using Zernike moments of the IR images and (b) classification using Support Vector Machine (SVM) applied to Zernike moments. Measures of the performance score were at least higher than 97% via different metrics for different categorization tasks. We observed distinctly different Zernike spectrums between NESEs and no‐eruption images. In the three months with the best quality images (December 2013, December 2014, and January 2015), out of about one million images per month, 654, 405, and 3,650 NESEs were detected, respectively. Using k‐means clustering three activity regimes emerged: low (≤4 NESEs per hour), intermediate (4 <NESEs per hour <14), and intense (≥14 NESEs per hour). December 2013 and December 2014 were associated with low and medium activity regimes only, while January 2015 had mainly medium and intense activity. The frequency of large eruptions and of NESEs do not show a correlation, supporting the hypothesis of the existence of multiple deep processes at the origin of the gas release. Space analysis of NESEs shows that they emerge over the surface primarily above the conduit, but not isotropically, pointing to complex interaction with the magma lake convection.

Determination of Vibrational Modes of l-Alanine Single Crystals by a Combination of Terahertz Spectroscopy Measurements and Density Functional Calculations.

Density-functional theory may be used to predict both the frequency and the dipole moment of the fundamental oscillations of molecular crystals. Suitably polarized photons at those frequencies excite such oscillations. Thus, in principle, terahertz spectroscopy may confirm the calculated fundamental modes of amino acids. However, reports to date have multiple shortcomings: (a)material of uncertain purity and morphology and diluted in a binder material is employed; (b)consequently, vibrations along all crystal axes are excited simultaneously; (c)data are restricted to room temperature, where resonances are broad and the background dominant; and (d)comparison with theory has been unsatisfactory (in part because the theory assumes zero temperature). Here, we overcome all four obstacles, in reporting detailed low-temperature polarized THz spectra of single-crystal l-alanine, assigning vibrational modes using density-functional theory, and comparing the calculated dipole moment vector direction to the electric field polarization of the measured spectra. Our direct and detailed comparison of theory with experiment corrects previous mode assignments for l-alanine, and reveals unreported modes, previously obscured by closely spaced spectral absorptions. The fundamental modes are thereby determined.

Second Harmonic Generation Signatures of Supramolecular Assemblies Based on Amide Moieties.

Targeting the use of the second harmonic generation (SHG) as a bioimaging technique to unravel the formation of aggregates, the SHG first hyperpolarizabilities ( ) of assemblies of benzene-1,3,5-tricarboxamide derivatives have been evaluated at the density functional theory level. Calculations have revealed that i) the assemblies exhibit SHG responses and the total first hyperpolarizability responses of the aggregates are evolving with their size. The largest aggregation effect is a 18-times increase for of B4 when going from the monomer to the pentamer, that ii) the intrinsic SHG responses described by the hyper-Rayleigh Scattering are enhanced in presence of iodine atoms on the phenyl core, that iii) the side chains affect the relative orientation of the dipole moment and first hyperpolarizability vectors, which impacts more the EFISHG quantities than their moduli, and that iv) the radial component to is dominant for the compounds having the largest responses. These results have been obtained using the sequential molecular dynamics then quantum mechanics approach to account for dynamic structural effects on the SHG responses.

Third-order moment varieties of linear non-Gaussian graphical models

Abstract In this paper, we study linear non-Gaussian graphical models from the perspective of algebraic statistics. These are acyclic causal models in which each variable is a linear combination of its direct causes and independent noise. The underlying directed causal graph can be identified uniquely via the set of second and third-order moments of all random vectors that lie in the corresponding model. Our focus is on finding the algebraic relations among these moments for a given graph. We show that when the graph is a polytree, these relations form a toric ideal. We construct explicit trek-matrices associated to 2-treks and 3-treks in the graph. Their entries are covariances and third-order moments and their $2$-minors define our model set-theoretically. Furthermore, we prove that their 2-minors also generate the vanishing ideal of the model. Finally, we describe the polytopes of third-order moments and the ideals for models with hidden variables.

Varvec{J}-, M- and varvec{L}-integrals of line charges and line forces

In this work, the varvec{J}-, M- and varvec{L}-integrals of two line charges and two line forces in generalized plane strain are derived in the framework of three-dimensional (3D) electrostatics and three-dimensional compatible linear elasticity, respectively, in order to study the interaction between them. The key point in this derivation is achieved by expressing the varvec{J}-, M- and varvec{L}-integrals of point charges and point forces in three dimensions in terms of the corresponding three-dimensional Green functions, that is, the three-dimensional Green function of the Laplace operator and the three-dimensional Green tensor of the Navier operator, respectively. The major mathematical tool used in deriving the varvec{J}-, M- and L_3-integrals of line charges and line forces from the corresponding varvec{J}-, M- and varvec{L}-integrals of point charges and point forces is the method of embedding or method of descent of Green functions to two dimensions (2D) from the corresponding Green functions in 3D. The analytical expressions of varvec{J}-, M- and L_3-integrals of line charges and line forces in antiplane and plane strain are derived and discussed. The varvec{J}-integral is the electrostatic part of the Lorentz force (electrostatic interaction force) between two line charges in electrostatics and the Cherepanov force between two line forces in elasticity. The M-integral of two line sources (charges or forces) equals half the electrostatic interaction energy in electrostatics and half the elastic interaction energy in elasticity of these two line sources, respectively. The L_3-integral of two line sources (charges or forces) is the z-component of the configurational vector moment or the rotational moment representing the total torque about the z-axis caused by the interaction of the two line sources. An important outcome is that the varvec{J}-integral is twice the negative gradient of the M-integral, leading to the result that the {varvec{J}}-integral for line charges and line forces is a conservative force (with the corresponding interaction energy playing the role of the potential energy) and consequently an irrotational vector field. Finally, the obtained varvec{J}-, M- and L_3-integrals being functions of the distance and of the angle, are able to describe the physical behaviour of the interaction of two line sources (charges and forces), since they represent the fundamental and necessary quantities, that is, the interaction force, interaction energy and total torque produced by the interaction of these two line sources.

Sensitivity of explosive materials to the action of electromagnetic fields

The analysis was done to define the most common methods of detection and disposal of explosive objects. According to the principle of their operation, the methods were subdivided into 4 classes. It was established that physical methods are the most effective, and most of them are based on the use of electromagnetic waves with various parameters. To define the degree of ef-fect of electromagnetic waves on explosive materials it was reasonable to study their electromag-netic properties. It is shown that the main parameter that quantitatively characterizes the degree of sensitivity of explosive materials to the action of electromagnetic fields is the dipole moment of their molecules. The molecular structure of the most common explosive materials, in particular hexogen, pentaerythritol tetranitrate and trinitrotoluene, tetryl, lead trinitroresorcinate, mercu-ryfulminate and lead azide has been analyzed. It is shown that the molecules of these substances have a two-dimensional structure, while the molecules of hexogen, pentaerythritol tetranitrate, and mercury fulminate are symmetrical. It corresponds to the absence of a dipole moment in such molecules. The dipole moments of asymmetric molecules of trinitrotoluene, tetryl, lead trinitrore-sorcinate, and lead azide were calculated using the method of adding force vectors of dipole moments of interatomic bonds. The calculated data showed that the dipole moments of these sub-stances are significant, so the electromagnetic influence on the activation of these explosive mate-rials cannot be neglected. Partially, the high values of the dipole moments of trinitrotoluene (µ(C7H5N3O6)=2,55 D) and tetryl (µ(C7H5N5O8)=9,27 D) can be explained by an increased num-ber of asymmetric bonds with nitrogen that has a high electronegativity. The obtained data can be used for the development of the safety algorithms to provide a safe work of the rescuers during demining of the territory and when using the devices of an active electromagnetic action in order to prevent the uncontrolled detonation of explosive objects

FOLMS-AMDCNet: an automatic recognition scheme for multiple-antenna OFDM systems

The existing recognition algorithms of space-time block code (STBC) for multi-antenna (MA) orthogonal frequency-division multiplexing (OFDM) systems use feature extraction and hypothesis testing to identify the signal types in a complex communication environment. However, owing to the restrictions on the prior information and channel conditions, these existing algorithms cannot perform well under strong interference and noncooperative communication conditions. To overcome these defects, this study introduces deep learning into the STBC-OFDM signal recognition field and proposes a recognition method based on the fourth-order lag moment spectrum (FOLMS) and attention-guided multi-scale dilated convolution network (AMDCNet). The fourth-order lag moment vectors of the received signals are calculated, and vectors are stitched to form two-dimensional FOLMS, which is used as the input of the deep learning-based model. Then, the multi-scale dilated convolution is used to extract the details of images at different scales, and a convolutional block attention module (CBAM) is introduced to construct the attention-guided multi-scale dilated convolution module (AMDCM) to make the network be more focused on the target area and obtian the multi-scale guided features. Finally, the concatenate fusion, residual block and fully-connected layers are applied to acquire the STBC-OFDM signal types. Simulation experiments show that the average recognition probability of the proposed method at −12 dB is higher than 98%. Compared with the existing algorithms, the recognition performance of the proposed method is significantly improved and has good adaptability to environments with strong disturbances. In addition, the proposed deep learning-based model can directly identify the pre-processed FOLMS samples without a priori information on channel and noise, which is more suitable for non-cooperative communication systems than the existing algorithms.

Effect of Terminal Fluorination on Chiroptical Properties of Carbo[5-8]helicenes: A Systematic Computational Study at the RI-ADC(2) Level.

In this article, effects of di-, tetra-, and octafluorination on the structural and chiroptical properties of carbo[5-8]helicenes are reported. Three fluorinated derivatives are designed from each parent carbohelicene by substituting either one, two, or four hydrogens at each terminal ring with fluorine atoms. Excited states properties such as UV-vis and CD spectra of all the six fluorinated carbohelicenes are computed at the ADC(2)/def2-TZVP level, and the results are compared against the results of their respective parent carbohelicene. In addition, CPL properties are also computed at the same level of theory. In the case of carbo[5]helicene (5H), gCPL decreases with an increase in the degree of fluorination. A similar observation is made in carbo[6]helicene (6H) too, although the value for tetrafluorinated 6H is slightly larger than for difluorinated 6H. Di- and tetrafluorination in carbo[7]helicene (7H), and all types of considered fluorination in carbo[8]helicene (8H) produce improved gCPL results. Results for fluorescence rate constants are also shown. Results are analyzed in terms of the transition dipole moment vectors and the angles between those.

On the Conical Hull of Moment Vectors

On the Conical Hull of Moment Vectors

Dipolar effects on the work function of an alkali-iodide overlayer (XI, X = Li, Na, K, Rb, and Cs) on tungsten surfaces

A first-principles approach was used to investigate the effects of alkali metal iodide XI (X = Li, Na, K, Rb, and Cs) adsorption on the work functions of (100), (110), and (111) surfaces of W. For the most energetically stable structures, work functions and their corresponding electric dipole moment vectors were calculated. In agreement with available experimental measurements, it was verified that the formation of XI dipoles on the W surface causes the work function to decrease significantly. It was shown that the calculated XI dipoles are tilted with respect to the W surface for all systems. This contradicts earlier published suggestions that the surface electrostatic energy of the dipoles prevented them from being aligned along the surface and were instead normal to the surface. In our work it is shown that the orientations (tilt) and strengths of the dipole moments can be explained in terms of the internal strain caused by the alkali metal’s different atomic sizes and available surface area. What matters for the decrease in the work function is the component of the dipolar moment perpendicular to the surface. For all systems, the work function reduction was shown to be directly proportional to the normal component of the electric field created by these XI dipoles.

Analysis of the Rotational Motion of a Solid Body in the Presence of External Moments

PurposeIn this work, the vibrating motion of a dynamically symmetric solid body with an elastic string, around a fixed point, as a new model, is investigated.HypothesesThe body spins as a result of external moments along the body’s principal axes, such as perturbing, restoring, and gyrostatic moments. It has been supposed that this body has a rapid angular velocity at the beginning of motion in the direction of its symmetry dynamic axis.MethodsThe averaging approach is employed to transform the governing system of motion into another appropriate averaging one to gain the asymptotic solutions of this system.ConclusionThese solutions are graphed and discussed in different plots depending on the numerical values of the body’s physical properties. The positive effects of the gyrostatic moment vector on the motion are examined in some cases. Furthermore, the obtained results generalize the previously related studies.ApplicationsThe importance of the investigated dynamical system is due to its applications in a variety of domains, including physics and engineering.

Distributed functional-group polarizabilities in polypeptides and peptide clusters toward accurate prediction of electro-optical properties of biomacromolecules.

Aiming at accurately predicting electro-optical properties of biomolecules, this work presents distributed atomic and functional-group polarizability tensors for a series of polypeptides and peptide clusters constructed from glycine and its residuals. By partitioning the electron density using the quantum theory of atoms in molecules, we demonstrated a very good transferability of the group polarizabilities. We were able to identify and extract the most efficient functional groups capable of generating the largest electrical susceptibility in condensed phases. Both the isotropic polarizability and its anisotropy were used to understand the way functional groups act as sources of linear optical responses, how they interact with each other reinforcing the macroscopic optical behavior within the material, and how covalent bonds and non-covalent interactions, such as hydrogen bonds, determine refractive indices and birefringence. Particular attention is devoted to the peptide bonds as they provide links to build biomacromolecules or polymers. An adequate quantum-mechanical treatment of at least the first interaction sphere of a given functional group is required to properly describe the effects of mutual polarization, but we identified optimum cluster size and shape to better estimate polarizabilities and dipole moments of larger molecules or molecular aggregates from the knowledge of the electron density of a central molecule or amino acid residual that is representative of the bulk. The strategy outlined here is a fast yet effective tool for estimating the optical properties of proteins but could eventually find application in the rational design of optical organic materials as well. Electronic-structure calculations were performed on the Gaussin16 program at the DFT level using the CAMB3LYP functional and the double-ζ quality Dunning basis set aug-cc-pVDZ. Electron density partitioning followed the concepts of the Quantum Theory of Atoms and Molecules (QTAIM) and was performed using the AIMAll program. The locally developed Polaber routine was applied to calculate dipole moment vectors and polarizability tensors. It was amended to include the effects of the local field on a given central molecule by means of a modified Atom-Dipole Interaction Model (ADIM).

Dynamic correction in manipulator control systems based on intelligent linear motion mechatronic module

Robotic complexes and robotic manipulators are widely used in the management of various objects and processes of control systems; their performance is directly related to the execution element. Electromagnetic actuators of multi-function control systems are structurally created separately for each adjustment body and lead to system complexity. To solve these problems, improve the executive system's weight-gauge indicators, and simplify the structural schemes, implementing intelligent mechatronic modules that perform linear and rotational movements in space coordinates is one of the urgent tasks. In this article, dynamic correction in manipulator control systems built based on an intelligent linear motion mechatronic module is considered. In manipulator control systems, the use of intelligent mechatronic modules in dynamic correction for manual and semi-automatic control manipulation systems that do not have a feedback channel for forces and moments and the relevance of the handle movement and manipulation objects with such a selection of the forces and moments vector m developed by them was seen. The article presents mathematical models for calculating vector components based on the current values of the generalized coordinates of the manipulator, their speed and acceleration, and the selection of the vector of forces and moments m developed by the intelligent mechatronic modules of the manipulator.