Density Vector Research Articles

Tightly focusing evolution of the auto-focusing linear polarized circular Pearcey Gaussian vortex beams

Abstract We report tightly focused characteristics of the auto-focusing linear polarized circular Pearcey Gaussian vortex beams (CPeGVBs) with on-axis and off-axis vortex pairs through high numerical aperture in this paper. Compared with the linear polarized Airy beam, we find that the autofocusing linear polarized CPeGVBs are rotating during the tightly focusing progress. We analyse the relationship between the autofocusing and the tightly focusing of CPeGVBs. At the same time, some cases of the flat-top beam and the quasi optical comb mode generated by the linear polarized CPeGVBs are analyzed in detail, and the changing of the focus depth with beam parameters is also discussed. To show the superiority of linear polarization CPeGVBs, we explore the tightly focusing intensity contrasts of the beams, and we characterize the resulting optical polarization singularity using zero-, one- and two-order topological structures. We present the spin density vector and the polarization ellipse distributions of the CPeGVBs in the x − y plane. Furthermore, the CPeGVBs present two kinds of the spin density vector on the optical axis that one is helix shaped and the other one is oscillating in the one axial direction of CPeGVBs by choosing the appropriate factors. Our results have the potential applications in reverse shaping of focal fields and optical trapping control.

Stochastic trophic level index model: A new method for evaluating eutrophication state

The trophic state index (TSI) and trophic level index (TLI) are commonly used methods for evaluating the eutrophication state of lakes and reservoirs. However, they are unable to overcome uncertainties such as calculation errors and spatial heterogeneity of evaluation indicators. To comprehensively evaluate the eutrophication state of a region, we introduce a probability density function and propose the stochastic trophic level index model (STLI). The probability density function of each trophic level is derived through the principle of maximum entropy, and membership vector F (F1, F2, F3, F4, F5) for each trophic level is established to quantify the risk of regional eutrophication. We utilized STLI to evaluate the eutrophication status of Songhua Lake, China, and determined that the method can be used for uncertainty and risk assessment. Our results show that the Jiaohe River backwater area has the highest eutrophication level (light eutropher), with a 0.12 probability of further deterioration to middle eutropher. The eutrophication status of the Main Scenic Area of the Songhua Lake Scenic Resort was shown to be mesotropher, with 0.26 and 0.08 probabilities of further deterioration to light eutropher and middle eutropher, respectively. Finally, the eutrophication status of the Songhua River Three Lakes Reserve Experimental Area was shown to be mesotropher, with a 0.24 probability of further deterioration to light eutropher. Overall, the Songhua River Three Lakes Reserve Experimental Area is the most promising for the lowest level of eutrophication. We recommend that the management department take effective targeted measures against the Jiaohe River backwater area first. The probability density and membership vector of STLI can effectively solve the uncertainties presented by traditional methods for evaluating regional eutrophication status.

Detailed Analytical Approach to Solve the Magnetoacoustic Tomography with Magnetic Induction (MAT-MI) Problem for Three-Layer Objects

This paper is devoted to an analytical approach to the magnetoacoustic tomography with magnetic induction (MAT-MI) problem for three-layer low-conductivity objects. For each layer, we determined closed-form analytical expressions for the eddy current density and Lorentz force vectors based on the separation of variables method. Next, the analytical formulas were validated with numerical solutions obtained with the help of the finite element method (FEM). Based on the acoustic dipole radiation theory, the influence of the transducer reception pattern on MAT-MI was investigated. To obtain acoustic wave patterns, as a system transfer function we proposed the Morlet wavelet. Finally, image reconstruction examples for objects of more complex shapes are presented, and the influence of the MAT-MI scanning resolution and the presence of the noise on the image reconstruction quality was studied in detail.

Thermal Conductivity of Grade UPV-1 Pyrolytic Graphite at 1900–2950 K

The need to account for a misalignment between the heat flux density and temperature gradient vectors when studying thermal conductivity of anisotropic materials was analyzed. A method for measuring thermal conductivity of pyrolytic graphite (grade UPV-1) in the direction parallel to the precipitation plane was proposed. The advantage of the proposed method is the possibility to determine thermal conductivity of pyrolytic graphite in the direction parallel to the precipitation plane while accounting for a misalignment between the heat flux density and temperature gradient vectors. The test samples were shaped as hollow cylinders with the pyrolytic graphite precipitation plane located along the radius of the cylinder. The heat flux density was determined based on the radiation heat flux emitted from the outer surface of the sample, and the temperature gradient was calculated along the radius, which made it possible to maintain the alignment between the heat flux density and temperature gradient vectors. A comparative analysis of the thermal conductivity values obtained in this study (parallel to the precipitation plane) and those reported in the reference sources was performed. The studied temperature range was extended into the higher temperature region by 450 K and constitutes 1900–2950 K.

Analytical solutions to the advection-diffusion equation with Atangana-Baleanu time-fractional derivative and a concentrated loading

In this communication we have studied well known physical process of two-dimensional advection–diffusion phenomena. The advection–diffusion equation is time-fractionalized by exploiting Atangana-Baleanu fractional derivative operator. This fractionalization is achieved in the generalized constitutive equation of the mass flux density vector. The fractionalized two-dimensional advection–diffusion equation turns out to be a two-dimensional nonlinear fractional partial differential equation. This partial differential equation is considered under the hypothesis of an initial concentrated loading and Robin type boundary conditions. The analytical expression of the solution is determined for this boundary value problem by employing the integral transforms method, namely, the Laplace transform, sine-Fourier transform and finite sine–cosine Fourier transform. The effects of fractional parameter α on the concentration obtained from the analytical solution, for various parameters of interest, are illustrated graphically with the help of software Mathcad. The graphs illustrate that the memory effects are remarkable for small values of time and ordinary for large values of the time.

The source of lattice rotation in rotating lattice single (RLS) crystals

Laser heating can be used to produce single crystal architectures in glass with a lattice that rotates at a constant rate. Such metamaterials can offer properties that are disallowed by conventional crystal structures. To establish the mechanism of this lattice rotation, we used transmission electron microscopy (TEM) to directly observe and characterize dislocations in Sb2S3 crystal lines fabricated in Sb-S-I glass as a model system. The lattice rotation calculated from the density and Burgers vectors of edge dislocations agrees with lattice rotation values experimentally determined by electron backscatter diffraction (EBSD) and selected area diffraction patterns (SADP). These results provide the first direct proof of the dislocation mechanism of lattice rotation in rotating lattice single (RLS) crystals, and very likely other forms of growth actuated bending, twisting and noncrystallographic branching as seen in spherulites.

System of porous medium equations

We investigate the evolution of population density vector, u=(u1,⋯,uk), of k-species whose diffusion is controlled by its absolute value |u|. More precisely, we study the properties and asymptotic large time behaviour of solution u=(u1,⋯,uk) of degenerate parabolic system(ui)t=∇⋅(|u|m−1∇ui)for m>1 and i=1,⋯,k. Under some regularity assumptions, we prove that the component ui which describes the population density of i-th species with population Mi converges to Mi|M|B|M| in space with two different approaches where B|M| is the Barenblatt solution of the standard porous medium equation with L1 mass |M|=M12+⋯+Mk2.As an application of the asymptotic behaviour, we establish a suitable Harnack type inequality which makes the spatial average of ui under control by the value of ui at one point. We also find 1-directional travelling wave type solutions and the properties of solutions which has travelling wave behaviour at infinity.

The Source of Lattice Rotation in Rotating Lattice Single (RLS) Crystals

Laser heating can be used to produce single crystal architectures in glass with a lattice that rotates at a constant rate. Such metamaterials can offer properties that are disallowed by conventional crystal structures. To establish the mechanism of this lattice rotation, we used transmission electron microscopy (TEM) to directly observe and characterize dislocations in Sb2S3 crystal lines fabricated in Sb-S-I glass as a model system. The lattice rotation calculated from the density and Burgers vectors of edge dislocations agrees with lattice rotation values experimentally determined by electron backscatter diffraction (EBSD) and selected area diffraction patterns (SADP). These results provide the first direct proof of the dislocation mechanism of lattice rotation in rotating lattice single (RLS) crystals, and very likely other forms of growth actuated bending, twisting and noncrystallographic branching as seen in spherulites.

Three-Axis Attitude Determination with Pseudo-Bias Estimation from Gravity/Magnetic Vector Observations

This paper revisits the stationary alignment problem of attitude and heading reference systems (AHRSs). The investigation is initiated from the three-axis attitude determination (TRIAD)–based method, purposely chosen to use nonunitary/nonorthogonal observations of the local gravity and Earth’s magnetic flux density vectors. For the simplifying assumption of body and navigation frames aligned, a comprehensive error analysis is developed, providing additional insight into the problem. Closed-form formulas for the residual normality and orthogonality errors are used to devise innovative pseudo-bias estimation (PBE) algorithms for the - and -axis magnetometer biases, as well as for the -axis accelerometer bias. As a direct consequence of applying the latter, and also figuring as the main contribution of this paper, an improved (more accurate) AHRS stationary alignment approach is obtained, herein called TRIAD-PBE. The error analysis is extended to representative state-of-the-art attitude determination techniques, confirming the relevance of TRIAD-PBE, especially in the presence of hard-iron magnetism. Results from simulated and experimental tests confirm the adequacy of the outlined verifications.

The complete discretization of the dual mixed method for the heat diffusion equation in a polygonal domain

The purpose of this paper is to prove a priori error estimates for the completely discretized problem of the dual mixed method for the non-stationary heat diffusion equation in a polygonal domain of R2. Due to the geometric singularities of the domain, the exact solution is not regular in the context of classical Sobolev spaces. Instead, one must use weighted Sobolev spaces in our analysis. To obtain optimal convergence rates of the discrete solutions, it is necessary to refine adequately the considered meshings near the reentrant corners of the polygonal domain. In a previous work, using the Raviart–Thomas vectorfields of degree 0 for the discretization of the heat flux density vector, we have obtained a priori error estimates of order 1 for the semi-discrete solutions of this problem. In our actual paper, we complete the discretization of the problem in time by using Euler’s implicit scheme, and we obtain optimal error estimates of order 1, in time and space. Numerical results are given to illustrate this improvement of the convergence orders.

Vibration transmission and power flow of laminated composite plates with inerter-based suppression configurations

This paper investigates the vibration transmission and power flow behaviour of harmonically excited laminated composite plates attached with different inerter-based suppression configurations. The substructure approach based on analytical and numerical methods is employed to obtain the steady-state dynamic response. Power flow analysis is carried out to determine the time-averaged power flow input and transmission as well as the kinetic energy of the plate. The power flow density vector is used to show explicitly the vibration transmission paths within the composite plate. It is shown that the fibre orientation and stacking sequences can have significant effects on the time-averaged power flow characteristics as well as the dominant vibration transmission paths. It is also shown that passive spring, damper and inerter elements may be attached to the plate to modify its vibration response and transmission according to specific design requirements. The proposed inerter-based suppression device with two different configurations can reduce the vibration level over a wide frequency range for vibration suppression. The findings may provide insights for the enhanced dynamic designs of laminated composite plates, and the suppression of their vibrations using inerter-based devices.

Plane strain deformation by slip in FCC crystals

Deformation studies of a metal or alloy single crystal under plane strain boundary conditions have proved valuable for providing information on the deformation behavior of such materials under multiaxial states of stress and strain. Examples include the initiation and propagation of cracks during brittle fracture and the development of deformation textures in metal forming operations. Restrictions imposed by plane strain boundary conditions on the values of global strain components and on active slip systems by the principle of maximum plastic work confine slip to subsets of physically possible crystallographic slip system (CSS). Such ensembles produce components of global strain that independently satisfy plane strain constraints. This leads to the definition of Pseudo Slip Systems (PSS) having basis vectors formed from the resultants of corresponding basis vectors in participating CSS. Nye’s State of Dislocation tensor applied at both macro- and micro-structural scales describes global and local lattice rotations resulting from the geometrically necessary dislocation (GND) content. Local Nye Tensors (LNT) for each active CSS are dyadic products of their Burgers vector and a Dislocation Density Vector (DDV) describing the GND population. This vector, lying in the slip plane, has a magnitude equal to that of the local GND, and a direction given by the character of the resultant population. The Global Nye Tensor (GNT), A, is the sum of LNTs for each active CSS and expresses in global specimen coordinates the resultant Burgers vector flux from all active CSS. We demonstrate these relationships by analyzing plane strain deformation in a Ni single crystal caused by wedge indentation along a 〈110〉 direction.

Patterns in Random Permutations

Every k entries in a permutation can have one of k! different relative orders, called patterns. How many times does each pattern occur in a large random permutation of size n?The distribution of this k!-dimensional vector of pattern densities was studied by Janson, Nakamura, and Zeilberger (2015). Their analysis showed that some component of this vector is asymptotically multi-normal of order \(1/\sqrt n \), while the orthogonal component is smaller.Using representations of the symmetric group, and the theory of U-statistics, we refine the analysis of this distribution. We show that it decomposes into k asymptotically uncorrelated components of different orders in n, that correspond to Sk-representations.Some combinations of pattern densities that arise in this decomposition have interpretations as practical nonparametric statistical tests.

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.

3-D adaptive FEA with weighted node density technique

PurposeThis paper aims to propose a method to create 3-D finite element meshes automatically using the Delaunay tetrahedralization with the weighted node density technique. Using this method, the adaptive finite element analysis (FEA) was carried out for the calculation of the magnetic field of an eddy current verification model to clarify the usefulness of the method. Moreover, the error evaluation function for the adaptive FEA was also discussed.Design/methodology/approachThe method to create the 3-D finite element meshes using the Delaunay tetrahedralization is realized by the weighted node density technique, and Zienkiewicz-Zhu’s error estimator is used as the error evaluation function of the adaptive FEA.FindingsThe magnetic flux density vectors on the node in the error evaluation function for the adaptive FEA should be calculated with the weighted average by the reciprocal of the volume of elements.Originality/valueThis paper describes the method to create 3-D finite element meshes and the comparison among calculation methods of the magnetic flux density vectors on the node for the error estimator.

Natural convection flows of Prabhakar-like fractional Maxwell fluids with generalized thermal transport

Natural convective flows of Prabhakar-like fractional viscoelastic fluids over an infinite vertical heated wall are studied by introducing the generalized fractional constitutive equations for the stress-shear rate and thermal flux density vector. The generalized memory effects are described by the time-fractional Prabhakar derivative. Closed-form solutions for the non-dimensional velocity and temperature fields are determined using the method of integral transform. The velocity and heat transfer of Prabhakar-like fractional Maxwell fluids with generalized thermal transport are compared with ordinary Maxwell fluids with generalized thermal transport and with the ordinary viscoelastic fluids with classical Fourier thermal flux. Solutions of the generalized model are particularized into solutions corresponding to flows and heat transfer with Caputo memory, respectively, to flows of the ordinary fluids with ordinary heat transfer. The use of Prabhakar operators shows the possibility of a convenient choice of fractional parameters such that to have a very good fitting between theoretical and experimental data.

Pemetaan Resistensi Nyamuk Aedes sp Terhadap Malation dan Kepadatan Vektor Demam Berdarah Dengue (DBD) di Sulawesi Utara

The event of mosquito immunity or resistance to malation is one of the main inhibitors of chemical eradication of vectors with insecticides. Vector resistance to insecticides is a global phenomenon, especially for managers of vector-borne control programs in Indonesia. The aims of this study was to map the resistance of Aedes sp mosquitoes to the malation and vector density of Dengue Hemorrhagic Fever (Aedes sp) in North Sulawesi Province in 2019. This research was descriptive in order to obtain a description of pre-adult vector density and to map the status of Dengue Hemorrhagic Fever vector resistance (Aedes sp) against malation. Resistance status data using data from 2015-2018 research. The population in this study are houses in North Minahasa Regency, Minahasa Regency, Tomohon City, Bitung City and Manado City. The sample for vector density is a larva survey of 100 resident houses which includes case houses and houses around DHF cases. North Minahasa Regency (Wautumou Village), Minahasa Regency (Papakelan Village), Tomohon City (Rurukan Village), Bitung City (Girian Permai Village), Manado City (Malalayang Village 2). Determination of the sample based on the highest case in each district in the city during the DHF vector resistance test in 2015-2018. The results showed that the average density of HI vectors (31.%), BI (17.5) and CI (34.8%) with resistance status in the four districts of the mosquito vector city of DHF were resistant and one district (North Minahasa) with a vulnerable status. Resistance and density vectors are digitally mapped.

Time-dependent relaxed magnetohydrodynamics: Inclusion of cross helicity constraint using phase-space action

A phase-space version of the ideal magnetohydrodynamic (MHD) Lagrangian is derived from first principles and shown to give a relabeling transformation when a cross-helicity constraint is added in Hamilton's Action Principle. A new formulation of time-dependent “relaxed” magnetohydrodynamics is derived using microscopic conservation of mass and macroscopic constraints on total magnetic helicity, cross helicity, and entropy under variations of density, pressure, fluid velocity, and magnetic vector potential. This gives Euler–Lagrange equations consistent with previous work on both ideal and relaxed MHD equilibria with flow, but generalizes the relaxation concept from statics to dynamics. The application of the new dynamical formalism is illustrated for short-wavelength linear waves, and the interface connection conditions for Multiregion Relaxed MHD (MRxMHD) are derived. The issue of whether E+u×B=0 should be a constraint is discussed.

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.

A New Method Based on Coding Sequence Density to Cluster Bacteria.

Bacterial evolution is an important study field, biological sequences are often used to construct phylogenetic relationships. Multiple sequence alignment is very time-consuming and cannot deal with large scales of bacterial genome sequences in a reasonable time. Hence, a new mathematical method, joining density vector method, is proposed to cluster bacteria, which characterizes the features of coding sequence (CDS) in a DNA sequence. Coding sequences carry genetic information that can synthesize proteins. The correspondence between a genomic sequence and its joining density vector (JDV) is one-to-one. JDV reflects the statistical characteristics of genomic sequence and large amounts of data can be analyzed using this new approach. We apply the novel method to do phylogenetic analysis on four bacterial data sets at hierarchies of genus and species. The phylogenetic trees prove that our new method accurately describes the evolutionary relationships of bacterial coding sequences, and is faster than ClustalW and the existing alignment-free methods.