Density Vector Research Articles

Triggered singlet fission via tuning current density vectors (CDV) in the ground-state and excited-state

Diradical and low-lying first triplet excited-state energy E(T1) are served as important elements toward tuning singlet fission (SF) efficiency, necessitating a rational and precise design strategy toward their fabrication. Herein, the tunable current density vectors (CDV) strategy is utilized to identify a series of tunable diradicaloid SF switches between dihydro-tetraaza-acenes isomers. Theoretical calculations indicate that the independent local diatropic CDV (ILD-CDV) on the S0-state and T1-state is the origin of the radical site and transition defect, respectively. Importantly, the diradical parameter y0 related to ground state is adjusted by tuning the discontinuous diatropic CDV on zigzag edge of the sandwiched rings, while low-lying first triplet excited-state energy E(T1) depends on the primary charge-transfer related to delocalized CDV region. Our ultimate goal is to emphasize the CDV analysis method that rationalizes the radical and S0→T1 transition site, which provides new application perspectives for precise designing new material in organic electronics.

Is crystal plasticity non-conservative? Lessons from large deformation continuum dislocation theory

Crystal plasticity for large plastic deformations is usually modeled as volume conserving. However, there is experimental evidence that huge amounts of vacancies are produced during plastic deformation. The only regularly considered mechanism of non-conservative dislocation motion is climb of edge dislocations, but this is supposed to be enabled by high vacancy concentrations rather than producing them. In the current contribution we show that large deformation kinematics applied to evolving fields of geometrically necessary dislocations accounts for kinking and jogging of dislocations when cutting through one another. Therefore, dislocation fields in multiple slip situations will not be confined to slip planes and their motion will necessarily involve non-conservative motion of jogs. Because inelastic volume changes in crystals are only possible in the presence of point defects, we find that large deformation continuum dislocation theory must be coupled to an evolving vacancy concentration. We suggest to treat vacancy diffusion as an independent inelastic deformation mechanism yielding a three-way multiplicative decomposition of the deformation gradient. Small numerical examples are used to illustrate the kinematics of emerging and moving kinks and jogs, and the ensuing production of vacancy concentration. Continuum thermodynamics is used to derive coupled evolution equations for geometrically necessary dislocation density vectors and vacancy concentration. We conclude that large deformation crystal plasticity as an averaged theory of dislocations may not be conservative and that the usual kinematic assumption Lp=∑sγ˙sms⊗ns does not hold in multiple slip deformation.

THE RECIPROCITY PRINCIPLE FOR A NONLINEAR ANISOTROPIC MEDIUM WITHOUT HYSTERESIS: THEORY AND PRACTICE OF APPLICATION

The construction of the correct vector material equations for nonlinear anisotropic soft magnetic materials remains one of the main reserves for increasing the accuracy of mathematical models in solving magnetostatic problems in the field formulation. The aim of the work is to establish asymptotic expressions for the reciprocity principle, which is a fundamental property of reversible magnetization processes of nonlinear anisotropic media, and to use the obtained results to optimize the computational process when constructing the vector magnetization characteristic and differential permeability tensor. The potentiality property of the magnetic flux density vector B in H -space is used. The main result of the paper is an illustration, using concrete examples, of an alternative method for calculating vector magnetization characteristics for one of the orthogonal families. In order to eliminate the instrumental error and ensure maximum accuracy and reliability of the obtained results, the exact characteristics for the components of the vector magnetization characteristic obtained by differentiating a special analytical expression for the potential were used as initial ones. The principle of reciprocity, by virtue of its universal nature, makes a significant contribution to the theory of nonlinear anisotropic media in the hysteresis-free approximation. Asymptotic expressions for the reciprocity principle are obtained for the first time. The performed computational experiments on the construction of vector characteristics based on the known magnetization characteristics in one of the directions confirm almost complete coincidence with the exact values obtained analytically. The use of asymptotic expressions for the reciprocity principle not only greatly simplifies computational processes for determining the orthogonal magnetization characteristics, but also implements the calculation of differential permeability tensors for arbitrary field values. The proposed method can be implemented in applications for calculating the magnetic field in devices with nonlinear anisotropic magnetically soft materials, primarily with cold rolled sheet electrical steels, which are most used in electrical engineering.

Линии тока и вектор плотности потока энергии при возбуждении колебаний пьезоэлектрическим преобразователем в слоистом фононном кристалле

The use of periodic composite structures has a great potential for improving sensors/actuators and self-adjusting optics, as well as for active vibration suppression and energy storage systems. At the same time, the employment of dielectric elastomers offers even greater possibilities since they provide tools for the active control of wave energy fluxes. The mathematical formulation of the problem considers more general state equations for piezoelectric bodies. Namely, the absence of symmetry in elastic and piezoelectric tensors is taken into account. The present study investigates the features of elastic wave excitation by a surface piezoelectric transducer (generally made of dielectric elastomer) in multi-layered periodic composites or so-called phononic crystals. A hybrid approach is used to solve the boundary value problem, which involves application of the spectral element method and the boundary integral equation method. Employing the energy streamlines and the power density vector, wave phenomena associated with the interaction of a piezoelectric transducer with a layered phononic crystal at frequencies belonging to four frequency ranges (band gaps, pass bands and the frequency ranges, in which only a quasi-transverse or quasi-longitudinal waves propagate without attenuation) are analyzed.

Implementation of annihilation and junction reactions in vector density-based continuum dislocation dynamics

In a continuum dislocation dynamics (CDD) formulation by Xia and El-Azab (2015 Modelling Simul. Mater. Sci. Eng. 23 055009), dislocations are represented by a set of vector density fields, one per crystallographic slip systems. The space-time evolution of these densities is obtained by solving a set of dislocation transport equations coupled with crystal mechanics. Here, we present an approach for incorporating dislocation annihilation and junction reactions into the dislocation transport equations. These reactions consume dislocations and result in nothing as in the annihilation reactions, or produce new dislocations of different types as in the case of junction reactions. Collinear annihilation, glissile junctions, and sessile junctions are particularly emphasized here. A generalized energy-based criterion for junction reactions is established in terms of the dislocation density and Burgers vectors of the reacting species, and the reaction rate terms for junction reactions are formulated in terms of the dislocation densities. In order to illustrate how the dislocation network changes as a result of junction formation and annihilation in a CDD setting, we present some numerical examples focusing on the reactions processes themselves. The results show that our modeling approach is able to capture the respective dislocation network changes associated with dislocation reactions in FCC crystals: dislocations of opposite line directions encountering each other on collinear slip systems annihilate to connect the dislocations on the two slip systems, glissile junctions form on new slip system behave like Frank–Read sources, and sessile junctions form and expand along the intersection of the slip planes of the reacting dislocation species. A collective-dynamics test showing the frequency of occurrence of junctions of different types relative to each other is also presented.

Seismic Response Analysis for Ordinary State-Based Peridynamics in a Linear Isotropic Elastic Material

Earthquakes may induce the failure of soil-structures built with a geo-material. It is therefore a crucially important aspect to study how a crack initiates and propagates in these soil-structures to analyze and improve their earthquake resistance. Peridynamics, although a powerful method for such an analysis, has not been applied to seismic response analysis of soil-structures on a viscous boundary surface that can consider an input seismic wave. To apply seismic response analysis to ordinary state-based peridynamics (OSB-PD), this paper proposed a fictitious viscous boundary layer and Rayleigh damping components constructed with time derivative of force density vectors. OSB-PD was semi-verified through the comparison of calculated response acceleration via the proposed method and via the dynamic finite element method (FEM). The discussions were stressed on the effect of Poisson’s ratio, the frequency, and the Rayleigh damping components relative to the calculated response acceleration in both methods. Moreover, the seismic response acceleration at the top of the analysis model was calculated through the proposed method using an actual seismic acceleration time history, and then the result was compared with that calculated by the dynamic FEM. The results of both methods in the seismic response analysis agreed well with each other. From these results, we verified that the fictitious viscous layer can represent incoming/outgoing acceleration wave from the bottom of the analysis domain, and that Rayleigh damping can be expressed using the time derivative of force density vectors.

Optoelectronic properties of heptacene, its fluorinated derivatives and silole, thiophene analogues

Properties of heptacene, its fluorinated derivatives and its silole and thiophene fused substituted analogues were investigated using DFT calculations. While heptacene can be considered as a p-type semiconductor, replacement of H in heptacene by F atoms yields suitable changes for n-type semiconductor applications. Silole and thiophene analogues exhibit larger reorganization energies and band gaps. While thiophene gives UV light (blue shift), silole has a visible absorption (red shift). Modified compounds suitable for both p-type and n-type semiconductors are identified. Good linear correlations are made between the degree of π-orbitals (DPO) parameters and energetic properties including band gaps, ionization energy and electron affinity, especially for thiophene-acenes. The current density vectors plotted onto the current-induced density (ACID) isosurface show a strong diatropic ring current at the peripheral CC bonds as compared to those of S/Si atoms of the structures designed.

Electro-elastic dislocations in piezoelectric materials

ABSTRACTIn this paper, dislocations in piezoelectric materials are studied in the framework of linear incompatible theory of piezoelectricity with eigendistortion and eigenelectric field. We consider that both field variables, the displacement vector and the electrostatic potential ϕ, possess a jump discontinuity at the dislocation surface. This leads to the appearance of two eigenfields, the eigendistortion or plastic distortion tensor and the eigenelectric field vector providing the terminology of electro-elastic dislocations. These two eigenfields give rise to the well-known concept of dislocation density tensor and the new-introduced concept of the electric dislocation density vector, respectively, completing the basic framework of the mathematical modelling of electro-elastic dislocations in piezoelectric materials. Material balance (or broken conservation) laws which correspond to translation, scaling and rotation groups of transformations are derived for piezoelectric materials with electro-elastic dislocations considering additionally inhomogeneities, body forces and body charges. The terms breaking the translational, scaling and rotational symmetries, that is, the configurational or material forces (electro-elastic Peach–Koehler force, Cherepanov force, electrostatic part of the Lorentz force, piezoelectric inhomogeneity force or Eshelby force), the corresponding total configurational work and total configurational vector moment which give rise to the non-conserved -, M- and -integrals, respectively, are obtained.

Flux Density of the Umov Electromagnetic Energy during Uniform Motion of an Extended Electron

Abstract—The flux density vector of the electromagnetic energy in the Poynting form and the problem of the electron electromagnetic momentum, associated with this definition, are considered. The alternative flux density definition, i.e., the Umov vector whose value is identical to the Poynting vector only for empty space, is also analyzed. For qualitative comparison of differential and integral values of these two vectors in the case of non-empty space, the model of the extended electron whose charge density is inversely proportional to the quartic distance from the symmetry center is studied. It is shown that the Umov vector in this case appears more universal, since the corresponding energy conservation law does not contain a term responsible for the electromagnetic energy conversion to other energy types.

Assamese Handwritten Character Recognition using Supervised Fuzzy Logic

This paper presents a state of the art supervised fuzzy pattern recognition system for recognition of Assamese handwritten characters. The fuzzy classifier is well suited for applications with ambiguities and handwritten character recognition is such a task. The dataset used in this experiment is taken from ISI Kolkata. After preprocessing images are normalized into uniform size 42x32 and then two features namely distance vector and density vector have been extracted. The experiment has two stages, training and testing. In first stage we extract distance vector and density features from uniform zones of the binary images for training classes and estimate the mean and variance for each class. In second stage we use this mean and variance to calculate the membership values for each unknown character of the testing set of data. An exponential fuzzy membership function is used for this purpose. Finally we recognize an unknown test character as that class for which it gives highest membership value. Finally result is stored in editable document. The highest recognition accuracy achieved in the experiment is 88.29%, 86.55% and 82.74% for numerals, vowels and consonants respectively.

Generation of Spiral Spin Density Vectors With A Circularly Polarized, Vortex Beam

Spiral spin density vectors refer to the spiral trajectory of the spin density vectors in three dimensional (3D) space, and similar to the polarization Mobius strip, polarization knots and photonic wheel, are also special polarization structures in 3D optical field and only exist in three dimensions. In this article, we propose a new way to generate the spiral spin density vectors with a long spiral range. This is realized by strongly focusing a circularly polarized beam with one off-axis vortex. In this field, the spiral interval of spin density vectors theoretically always exists on the propagation axis, and its position can be controlled by the beam size parameter $f/w_0$ . The polarization variation and the spiral spin density vectors are discussed analytically along the propagation direction. It is found that the spiral shape and spiral ‘speed’ can be adjusted by the off-axis distance of the vortex and the semi-aperture angle of the focusing system respectively. A special spiral behavior of the spin density vector at the geometrical focus is also observed in this focused field. The spiral spin density vectors supply a new rotational degree of freedom in 3D optical field and our finding may have applications in optical micro-manipulations.

Tight-focusing properties of linearly polarized circular Airy Gaussian vortex beam

We show the tight-focusing properties of a linearly polarized circular Airy Gaussian vortex beam (CAiGVB) with a high-numerical-aperture objective lens; the light intensity distributions exhibit diversity with different positions of the vortex pairs (on-axis or off-axis vortex pairs). By choosing different optical distribution factors, the CAiGVB turns into a circular Airy vortex beam or Gaussian vortex beam, and the depth of focus can also be controlled. It is known that the vortex beam possesses both orbital and spin angular momentum. The spin density vector changes its direction in three-dimensional space during beam propagation, as long as it is not purely transverse or longitudinal, which would cause 3D polarization ellipse topologies. In contrast, the polarization topologies degenerate into 2D when the spin density vector is purely transverse or longitudinal. Furthermore, the direction of the spin density vector is closely related to the Gouy phase difference between longitudinal and transverse electric field components of the vectorial beam.

Study of underexpanded sonic jets from square convergent micro nozzles

Numerical simulations using the RANS with the SSTk-ω turbulence model are performed to understand the flow feature of an underexpanded sonic jet from a convergent nozzle with a square cross-section of 1 mm × 1 mm at the nozzle exit. The nozzle pressure ratio, which is the ratio of the plenum pressure upstream of the nozzle to back pressure, is held constant at 4.0 and the Reynolds number based upon the flow properties and the height at the nozzle exit is 5.94 × 104. The near-field shock structure in shock-containing square jets is demonstrated with the three-dimensional representations of the magnitudes of the density and pressure gradient vectors.

Analysis of a model for longitudinal electromagnetic stirring in the continuous casting of steel

A recent three-dimensional (3D) model that revisited earlier theoretical work for longitudinal electromagnetic stirring in the continuous casting of steel blooms is analyzed further to explore how the bloom width interacts with the pole pitch of the stirrer to affect the magnetic flux density. Whereas the first work indicated the presence of a boundary layer in the steel near the interface with the stirrer, with all three components of the magnetic flux density vector being coupled to each other, in the analysis presented here we find that the component along the direction of the travelling wave decouples from those in the other two directions and can even be determined analytically in the form of a series solution. Moreover, it is found that the remaining two components can be found via a two-dimensional computation, but that it is not possible in general to determine these components without taking into account the surrounding air. The validity of the asymptotically reduced model solution is confirmed by comparing it with the results of 3D numerical computations. Moreover, the asymptotic approach provides a way to compute the time-averaged Lorentz force components that requires two orders of magnitude less computational time than the fully 3D approach.

대규모 군집을 위한 3 차원 경로계획 알고리즘에 대한 연구

In this paper, we propose a three-dimensional path planning algorithm for a large-scale swarm. The proposed algorithm is based on the Eulerian approach that controls spatial characteristics which is an agent density vector. This algorithm has three phases, which are environment abstraction, optimal transport, and collision avoidance, respectively. The algorithm can be applied to a largescale swarm of 1000 agents or more, and it guarantees collision avoidance between obstacles existing in the given flight environment and the surrounding agents. We carried out simulation using two scenarios, and as a result, it was confirmed that the proposed algorithm is suitable for three-dimensional path planning for a large-scale swarm.

A Volume PEEC Formulation Based on the Cell Method for Electromagnetic Problems From Low to High Frequency

A new and general partial element equivalent circuit (PEEC) formulation based on electric and magnetic vector potentials and the cell method is presented. The purpose of this paper is manifold. First, a comprehensive review of well-established PEEC method is given and the state-of-the-art of the method with focus on the inclusion of magnetic media in the formulation is discussed. Then, a new and general formulation of the PEEC method based on integral equations is proposed. The formulation is valid for conductive, dielectric, and magnetic media and its advantages with respect to the state-of-the-art PEEC formulations are underlined. Unlike the existing PEEC methods, this novel formulation, thanks to the reinterpretation of PEEC in the context of integral equation methods, allows for maintaining a circuit interpretation for both electric and magnetic media. Thus, a standard Spice-like solver can in principle be adopted for the solution of electromagnetic (EM) problems also when magnetic media are involved. The imposition of the divergence condition for the current density vectors is guaranteed and also the case of inhomogeneous and anisotropic media is considered. A thorough discussion on the suitability of the method for the study of both low- and high-frequency EM problems is also presented. Finally, the case study of a near-field communication antenna is considered as an example of the applicability of the formulation to problems of industrial interest. Comparisons with commercial softwares, measurements, and the state-of-the-art PEEC method are given in order to demonstrate the accuracy and the advantages of the proposed PEEC formulation.

Finite Element Analysis and Modeling of Three-Phase Induction Motor

As mentioned in this paper that three-dimensional and two-dimensional model of the motor is established and three-dimensional structure of the motor is proposed. The finite element structure of the two-dimensional motor is analyzed by using the two-dimensional finite element analysis method combined with a motor example. The finite element parameters of the motor are designed, and the state parameters of the motor involving flux diagram, magnetic line diagram, magnetic density vector diagram and magnetic density cloud diagram are obtained.

Anisotropic surface phonon dispersion of a deuterium-terminated Si(110)-(1 × 1) surface studied by high-resolution electron-energy-loss spectroscopy and first-principles calculations: Isotope effect

The surface phonon dispersion of a deuterium-terminated Si(110)-(1 × 1) surface [D:Si(110)-(1 × 1)] is investigated by using high-resolution electron-energy-loss spectroscopy (HREELS) and first-principles calculations based on the density functional theory (DFT) with the local density approximation (LDA). The characteristics of D:Si(110)-(1 × 1) are unique compared to those of H:Si(110)-(1 × 1) (Matsushita et al., 2015) in terms of the resolved vibrational modes. By the HREELS, one-dimensional surface phonons consisting of D–Si stretching vibrations are observed above the bulk-phonon band energy edge of 64.5 meV. Ten modes are observed below this value, classified as surface, surface resonant, and bulk phonons according to the calculated energy dispersion as well as the depth profile of spectral density and displacement vectors. In particular, five D–Si bending modes are observed out of the seven theoretically predicted modes. The bending modes are strongly coupled with the displacements across the D and five Si layers. The DFT-LDA surface phonon dispersion is in good agreement with the experimental results except a few frequency/dispersion mismatches, as the structure optimized by DFT-LDA mismatches with the previous scanning tunneling microscopy (STM) results (Matsushita et al., 2015). D:Si(110)-(1 × 1) elucidates the nature of covalently bonded phonons and their characteristics both experimentally and theoretically.

Numerical Studies of Electromagnetic Processes in Segmented Heavy-Gage Current-Carrying Conductors

The resistance of heavy-gage current-carrying conductors to alternating current of industrial frequency increases due to the skin effect and proximity effect, which leads to increasing heat loss during transmission of electrical energy. When power cables for a voltage of 110 kV or more are fabricated, segmented Milliken-type current-carrying conductors are used, which make it possible to reduce the resistance to alternating current. The objective of this work is to carry out a numerical study of electromagnetic processes in heavy-gage Milliken-type current-carrying conductors using mathematical simulation. For this purpose, a geometric model is constructed that takes into account the complex spatial structure of current-carrying conductors. For comparison, a geometric model is considered in which the wires are arranged parallel to each other. The electromagnetic processes in the current-carrying conductors are described by differential equations for the complex amplitude of vector magnetic potential derived from Maxwell’s equations. The proposed set of differential equations is supplemented with corresponding boundary conditions. The given problem was solved numerically on the basis of the ANSYS Maxwell software package constructed based on the finite element method. As a result of calculations, the fields of vector magnetic potential in the whole volume under study and the distributions of the current density vector in conductors were obtained, from which the resistances of current-carrying conductors as a whole and of each wire separately were calculated. The calculation results revealed that using Milliken-type current-carrying conductors makes it possible to reduce the conductor resistance by equalizing the current density distribution over the cross sections of wires when a segment of them is twisted.

The evolutions of spin density and energy flux of strongly focused standard full Poincaré beams

Nonzero transverse spin density, which describes phenomenon in which the electromagnetic fields of localized light spin in a plane containing its wavenumber vector, has gained enormous interest recently because of its useful applications like spin-direction coupling and routing. In this Letter, using the Richards–Wolf vectorial method for standard full Poincaré beams, we present an analytical model for the high-numerical-aperture focusing system to calculate all components of the electric and magnetic field strength vectors as well as spin density and Poynting vector. The role and contribution of the optical degrees of freedom including ellipticity, handedness, and orientation when the transverse spin density is present, are revealed based on this analytical model. Ellipticity affects the localization and magnitude of the transverse spin density for both transverse and longitudinal components. In contrast, handedness only affects the longitudinal component whereas orientation only affects the transverse component. Furthermore, the energy flux in the focal plane are also studied in detail for the standard full Poincaré beams. These findings may be help in spin-controlled directive coupling and optical tweezers.