Analytical Vector Research Articles

Analytical vector generalization of the classical Stoner–Wohlfarth hysteron

In view of the difficulties in using the well-known Stoner–Wohlfarth (SW) ferromagneticsingle-domain particle as a vector hysteresis unit in statistical models of hysteresis like thePreisach-type model or in micromagnetic models, we propose a new description of thesingle-domain ferromagnetic grains by using a vector hysteron (VH) as the 2D and 3Dgeneralization of the rectangular hysteron. The vector hysteron introduced from magneticsymmetry considerations describes analytically the properties of a range of single-domainferromagnetic particles and also provides the physical motivation for the linear form of theenergy barrier used in several dynamic models. In this paper we show the maincharacteristics of the analytical vector hysteron by comparing it with the well-knownStoner–Wohlfarth model. We compare the hysteresis curves, switching fields and energeticproperties of the uniaxial single-domain particles as provided by the two models.

Hysteresis characteristics of an analytical vector hysteron

The analytical way to describe uniaxial single-domain particles, using new symmetry considerations on the magnetic anisotropy, as a vector hysteresis unit (vector hysteron), is presented. The main characteristics of the vector hysteron such as the longitudinal hysteresis loops, transversal hysteresis loops and rotational hysteresis loops are presented. An extension of the vector hysteron and a vector hysteron that can be applied to the ferroelectric hysteresis are also presented.

A new definition of regularity for representation of canonical commutation relations algebras

A new criterion of regularity for the representation of canonical commutation relations algebras is given on the basis of the concept of an analytical vector.

Toward a Lagrangian Vector Field Topology

AbstractIn this paper we present an extended critical point concept which allows us to apply vector field topology in the case of unsteady flow. We propose a measure for unsteadiness which describes the rate of change of the velocities in a fluid element over time. This measure allows us to select particles for which topological properties remain intact inside a finite spatio‐temporal neighborhood. One benefit of this approach is that the classification of critical points based on the eigenvalues of the Jacobian remains meaningful. In the steady case the proposed criterion reduces to the classical definition of critical points. As a first step we show that finding an optimal Galilean frame of reference can be obtained implicitly by analyzing the acceleration field. In a second step we show that this can be extended by switching to the Lagrangian frame of reference. This way the criterion can detect critical points moving along intricate trajectories. We analyze the behavior of the proposed criterion based on two analytical vector fields for which a correct solution is defined by their inherent symmetries and present results for numerical vector fields.

Vectorial structural characteristics of four-petal Gaussian beams in the far field

Based on the vector angular spectrum theory of electromagnetic waves and the method of stationary phase, analytical vector structures of four-petal Gaussian beams (FPGB) in the far field are derived. The energy flux for the TE term, TM term and the whole beam are represented and illustrated with numerical examples. Effects of beam orders and paraxial degrees on energy flux distributions are discussed in detail, and the corresponding analytical explanations are also given. These results may provide a new approach to manipulate other higher-order laser beams in the far field.

Assessment of Useful Life of Lubricants Using Analytical Hierarchy Process (AHP) and Vector Projection Approach (VPA)

Problem statement: In general, engine oil is usually changed as defin ed by car or lubricant manufacturers, which is according to mileage. However, it was found from past researches that, at the predefined mileage or timeframe, most lubricant is still acceptably usable and efficient. Approach: This research aimed to calculate useful life of lubrican t in order to reach its maximum usefulness. The method of study began by collecting data that indic ates deterioration of lubricant by increasing milea ge which includes total base number, viscosity, iron a nd flash point. Then the data was analyzed by means of Analysis Hierarchy Process (AHP). These variables were used to construct a model for calculating appropriate useful life of lubricant by using vecto r projection approach. It was found from this study that the defined mileage for changing lubricant, wh ich is generally at 5,000 km, is not appropriate. Results: Results of the study suggest that the most appropr iate mileage for change of lubricant is at 12,000 km. Conclusion: It could be concluded that collection of data abou t characteristics of lubricant and use of model for calculating useful life of lub ricant can define appropriate interval change of lubricant.

Separatrices and basins of stability from time series data: an application to biodynamics

An approach is presented for identifying separatrices in phase space generated from noisy time series data sets representative of measured experimental data. These separatrices are identified as ridges in the phase space distribution of finite-time Lyapunov exponents, i.e., Lagrangian coherent structures (LCS). As opposed to previous approaches, the LCS is identified using only trajectories since no analytical or data-defined vector field is available. The method is applied to a biological simulation in which the separatrix reveals a basin of stability. These results suggest that the method will be a fruitful approach to time series analysis, particularly in cases where a limited number of trajectories are available as might be encountered in experiments.

The Study on the Linking-Up of Free-Form Surface Fiber Placement Track Based on Mesh Creating

When using meshing creating method of FP (fiber placement) track, once the track point falls at some vertex point of mesh element, in the meantime the vertex point happens to be shared by several mesh elements, there needs a reasonable calculation method to select next mesh element which the FP track will pass through. Then it comes to the problem on linking of FP tracks. In order to solve it, in this paper, the author puts forward a new method, in which parallel projection theory is used, project need analytical mesh element and FP reference vector to a sound projective plane, on which the mesh element be selected and the FP track be calculated, then the FP track would be projected back to the placement surface. Program using this method realized a reasonable joint at the shared vertex point of meshing elements, which the FP direction has little change, and the mutation of track doesn’t come forth. So, the correctness of the method, which putted forward in this paper, is proved.

Dynamics of learning near singularities in radial basis function networks

The radial basis function (RBF) networks are one of the most widely used models for function approximation in the regression problem. In the learning paradigm, the best approximation is recursively or iteratively searched for based on observed data (teacher signals). One encounters difficulties in such a process when two component basis functions become identical, or when the magnitude of one component becomes null. In this case, the number of the components reduces by one, and then the reduced component recovers as the learning process proceeds further, provided such a component is necessary for the best approximation. Strange behaviors, especially the plateau phenomena, have been observed in dynamics of learning when such reduction occurs. There exist singularities in the space of parameters, and the above reduction takes place at the singular regions. This paper focuses on a detailed analysis of the dynamical behaviors of learning near the overlap and elimination singularities in RBF networks, based on the averaged learning equation that is applicable to both on-line and batch mode learning. We analyze the stability on the overlap singularity by solving the eigenvalues of the Hessian explicitly. Based on the stability analysis, we plot the analytical dynamic vector fields near the singularity, which are then compared to those real trajectories obtained by a numeric method. We also confirm the existence of the plateaus in both batch and on-line learning by simulation.

Dual-Plane Vector Control of a Five-Phase Induction Machine for an Improved Flux Pattern

A technique to improve the flux pattern within a five-phase induction machine is presented. The technique is developed through dual-plane vector control, with synchronized fluxes. By vector space decomposition, an analytical model and vector control of the machine are accomplished in two orthogonal vector planes,d1-q1 and ds-qs . The magnitude and rotating speed of the associated fluxes (fundamental and third harmonic) can be independently controlled in each vector plane. Synchronization control locks the relative position between the two fluxes. The resultant air-gap flux density is fully controlled, preventing iron saturation. This feature is especially important in reshaping the flux and back EMF waveform of the machine. A quasi-trapezoidal air-gap flux density distribution is achieved for better iron utilization and higher torque density. It is confirmed that compared with sinusoidal fluxing, the quasi-trapezoidal flux pattern will not lead to an oversized power inverter when improving machine torque density. The basic understanding and control scheme can be extended to a multiphase induction machine with a phase number greater than five.

The input-output Linearizing Control Scheme of the Doubly-Fed Induction Machine as a Wind Power Generation

The active and reactive powers control of a doubly fed induction generator - DFIG -connected to the grid utility and driven by a wind turbine is presented. The control scheme is based on the input-output feedback linearization strategy. For this purpose, An appropriate mathematical model of the - DFIM - based on the so-called stator magnetizing current field oriented is detailed. An analytical space vector modulation back-to-back SVPWM three-level converter is used. The paper discusses the operating principles of the power generation scheme. Simulation results show that the input-output linearizing control provides decoupled control and perfect tracking of the generated active and reactive powers.

Reading Nairobi: Place, Space, and Difference at the 2007 World Social Forum

The 2007 World Social Forum (WSF) took place in Nairobi, 20-25 January. Most of the controversies had to do with the character of the space that was produced there and what it signalled about a more global political drift in the WSF. This chapter addresses the challenge of 'reading Nairobi' but, more generally, it seeks to elaborate an approach by which to more adequately analyze the WSF, both as a somewhat coherent global political process while also recognizing the exploding plurality of the WSF as a multi-faceted phenomenon. The critics of ?open space' argue variously that the concept itself is wrong-headed and depoliticizing in its embrace of liberal pluralism; Difference as an analytical vector in reading any specific WSF event or process has to do with the character and scope of diversity in the ?open space' of the forum, its ethos of respect for difference, and its production of transcommunality. Keywords: Nairobi event; open space; World Social Forum (WSF)

Assessing the risk situation of network security for active defense

The risk situation assessment and forecast technique of network security is a basic method of active defense techniques. In order to assess the risk of network security two methods were used to define the index of risk and forecast index in time series, they were analytical hierarchy process (AHP) and support vector regression (SVR). The module framework applied the methods above was also discussed. Experiment results showed the forecast values were so close to actual values and so it proved the approach is correct.

Kinematic Characterization of Chip Lateral-Curl—The Third Pattern of Chip Curl in Machining

Two patterns of chip curl, namely up- and side-curl, have been widely recognized in machining operations. This paper presents the third pattern of chip curl that is called lateral-curl. The rotating axis of chip lateral-curl is perpendicular to the rotating axes of up- and side-curl. The essential differences are illustrated between the chip lateral-curl concept and the “chip-twisting” concept presented in other related studies. Based on an analytical vector analysis, a new kinematic characterization is presented for the natural (or born) lateral-curl of the chip that is associated with flat-faced tool machining. It is demonstrated that chip forms (or shapes) can be determined by four governing variables: the chip up-, lateral-, and side-curl radii and the chip side-flow angle. A method to indirectly measure the chip lateral-curl radius is presented. The effect of chip lateral-curl on chip forms is investigated through cutting tests, theoretical analysis, and computer simulations.

The iterative calculation of the Cartesian geometry of general non-Cartesian structures

This paper describes an iterative scheme for the calculation of the Cartesian coordinates of the nodes of any rigid structure from a knowledge of internodal distances and angles. Since internodal distances can be determined accurately by laser interferometry, it is possible to derive coordinates to very high precision. The techniques constitute analytical vector and matrix methods which have been programmed in a general way to provide generic software capable of finding iteratively the Cartesian geometry of complex structures such as non-Cartesian machines. It has proved possible to include certain constraints such that specified nodes should not move in certain Cartesian directions and specified connecting lines should remain horizontal or vertical, etc. The method requires an initial estimate of the Cartesian coordinates of the nodes and then adjusts the coordinates until calculated internodal distances and angles are within tolerance. No reprogramming is necessary to analyse a new structure. Full details of the mathematical derivations are included, as are details and results of the application of the method to the Stewart platform.

Time-domain vector representation of monopole transient electromagnetic radiation using Maple software

The analytical time-domain vector representation of the transient electromagnetic radiation of a monopole antenna is computed using the Maple software package. This simulation originates directly from the rigorous formulation of the problem via Maxwell's equations. A ramp-function approximation of the antenna excitation current (of arbitrary waveform) is employed. Using the capabilities of Maple, the problem is easily transformed into a compact Maple code. Maple computing enables analytical time-domain three-dimensional vector expressions for the transient radiation field. The fundamental properties of transient radiation are thus characterized qualitatively and quantitatively, assisting with physical interpretation of the results.

Symbolic vector analysis in plasma physics

Many problems in plasma physics involve substantial amounts of analytical vector calculation. The complexity usually originates from both the vector operations themselves and the underlying coordinate systems. A computer algebra package for symbolic vector analysis in general coordinate systems, GeneralVectorAnalysis (GVA), is developed using Mathematica. The modern viewpoint for 3D vector calculus, differential forms on 3-manifolds, is adopted to unify and systematize the vector calculus operations in general coordinate systems. Besides the basic vector analysis functions, the package provides asymptotic capabilities, 2D vector analysis notation, and a simple interface for users to define their own coordinate systems. These features will benefit physicists and applied mathematicians in their research where complicated vector analysis in complicated coordinate systems is required. Several applications of this symbolic vector analysis package to plasma physics are also given.

A stochastic perturbation method for studying inverse problems of dynamics

In this paper we introduce a method for the local reconstruciton of an analytical vector field ƒ in ℝn from a set of observations about the asymptotics of n different brownian motions driven by ƒ. The case n = 2 is studied in details and an inversion algorithm is proposed. Although such algorithm turns out to be unstable, it can be a starting point for the quantitative analysis of some inverse problems in dissipative dynamics.

Ground effects on induced voltages from nearby lightning

The lightning induced voltage on overhead lines from return strokes and it's dependency of a lossy ground is analyzed using a new, analytical vector potential formulation. Norton's (1937) approximation and the surface impedance approach are used to take loss effects into account. The surface impedance method predicts in general induced voltages in good agreement with Norton's approximation, but the accuracy of the method is dependent on the variation of the current along the lightning channel. Norton's method is compared with the exact Sommerfeld solution, showing a deviation <10% even for low conducting grounds and distances from 100-1000 m. The effect of stroke location and line termination is also analyzed, showing that a line terminated by it's characteristic impedance and excited by a return stroke at the prolongation of the line is especially sensitive to lossy ground effects. Strokes near the mid-point of an overhead line gives less loss effect than strokes at the end of the line. The surface impedance approximation is derived from Norton's method and the necessary assumptions are outlined.

Structural Stability of Planar Homogeneous Polynomial Vector Fields: Applications to Critical Points and to Infinity

LetHmbe the space of planar homogeneous polynomial vector fields of degreemendowed with the coefficient topology. We characterize the setΩmof the vector fields ofHmthat are structurally stable with respect to perturbations inHmand we determine the exact number of the topological equivalence classes inΩm. The study of structurally stable homogeneous polynomial vector fields is very useful for understanding some interesting features of inhomogeneous vector fields. Thus, by using this characterization we can do first an extension of the Hartman–Grobman Theorem which allows us to study the critical points of planar analytical vector fields whosek-jets are zero for allk<munder generic assumptions and second the study of the flows of the planar polynomial vector fields in a neighborhood of the infinity also under generic assumptions.