A numerical method for determining electromagnetic fields in cracked metals

We improve the numerical algorithm of the solution of a three-dimensional hypersingular integral equation of first kind based on the collocation method. The efficiency of the developed approach is shown. We also give some numerical results and their interpretation. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 2, pp. 85–93, March–April, 2007.     

Generalization of the Zgoubi method for ray-tracing to include electric fields

The ray-tracing and spin tracking code Zgoubi, originally dedicated to the numerical integration of Lorentz equation in magnetic fields, has been improved in order to allow ray-tracing in electric and electromagnetic fields. This report describes the method, and presents detailed examples of application, including the achromatic quadrupole.     

An asymptotic-numerical method to compute bifurcating branches

In this paper a new method to compute the bifurcating branches for an elastic structure is presented. The method is based on the asymptotic-numerical method (ANM), that is a perturbation technique to solve problems in non-linear mechanics. Herein, we present a computing strategy to find the bifurcation points and the post-buckling branches in the framework of the ANM. Some examples are also given, which prove the effectiveness of the proposed method. A discussion of the results and of the open problems ends the paper. © 1998 John Wiley & Sons, Ltd.     

On a hybrid method to determine strain fields around propagating cracks

The moving singularity of the crack tip in a plane-stress plate causes a highly dynamic stress field of varying intensity with time, throughout the period of the propagation of the crack. This dynamic stress field results in a considerable change of the mechanical and optical properties of a strain-rate dependent material. An analysis of this varying dynamic stress field was presented in this paper which contradicts assumptions and simplifications introduced in a previous paper [7], referring to the same problem. For the experimental determination of the $\text{K}{}^{\mathrm{d}}{}_{\mathrm{I}}\text{-}\text{factor}$ the optical method of the dynamic caustics was utilized in combination with a high-speed camera and a comparison was sketched between the possibilities of this method and the strain-gauge method used in Ref. [7].     

A finite element method to compute three-dimensional magnetic field distribution in transformer cores

A numerical method is proposed to compute three-dimensional magnetic field distributions in nonlinear nonhomogeneous media, neglecting hysteresis and eddy currents. The magnetic field is derived from a scalar potential satisfying a nonlinear elliptic equation, which is solved by a convergent iterative method. A finite element program has been developed to compute the magnetic field distribution in transformer cores. Some numerical results for a butt and lap corner configuration are discussed.     

A method for applying strong electric fields in electron paramagnetic resonance at low temperatures

A method is described for studying epr spectra in crystals under the action of an external electric field which is applicable to a RE-1301 spectrometer, in the resonator of which a quartz cryostat extension is housed. A viscous electrically insulating grease is used, making it possible to carry out investigations in electric fields up to 700 kV cm^?1 at T = 77 and 4.2 K.     

A method to compute mixed-mode stress intensity factors for nonplanar cracks in three dimensions

Methods to compute the stress intensity factors along a three-dimensional (3D) crack front often display a tenuous rate of convergence under mesh refinement or, worse, do not converge, particularly when applied on unstructured meshes. In this work, we propose an alternative formulation of the interaction integral functional and a method to compute stress intensity factors along the crack front which can be shown to converge. The novelty of our method is the decoupling of the two discretizations: the bulk mesh for the finite element solution and the mesh along the crack front for the numerical stress intensity factors, and hence we term it the multiple mesh interaction integral (MMII) method. Through analysis of the convergence of the functional and method, we find scalings of these two mesh sizes to guarantee convergence of the computed stress intensity factors in a variety of norms, including maximum pointwise error and total variation. We demonstrate the MMII on four examples: a semiinfinite straight crack with the asymptotic displacement fields, the same geometry with a nonuniform stress intensity factor along the crack front, a spherical cap crack in a cylinder under tension, and the elliptical crack under far-field tension and shear.     

A hybrid of finite analytic and multi-grid method for calculating electric field distribution

In this paper, the Finite Analytic concept is introduced for calculating the electric field distribution. To express the relationship between central potential and vertex potentials on a grid, the exponential function is adopted instead of the series function in conventional Finite Analytic Method (FAM). On this consideration, the finite analytic equation for electric field calculation is deduced. And aiming at accelerating the computational convergence, the improved FAM is combined with Multi-grid Method and the body fitting grids are generated at each divided subregion for generating the regular grids and for distinguishing the fine grids and coarse grids.     

A numerical investigation of dopant segregation by modified vertical gradient freezing with moderate magnetic and weak electric fields

The paper numerically investigates melt growth of doped gallium-antimonide (GaSb) semiconductor crystals by the vertical gradient freeze (VGF) method utilizing a submerged heater. Electromagnetic (EM) stirring can be induced in the gallium-antimonide melt just above the crystal growth interface by applying a small radial electric current in the melt together with an axial magnetic field. The transport of any dopant by the stirring can promote better compositional homogeneity. This investigation presents a numerical model for the unsteady transport of a dopant during the VGF process by submerged heater growth with a moderate axial magnetic field and a weak electric field. Numerical predictions of the dopant distributions in the crystal and in the melt at several different stages during growth are presented.     

A numerical method to obtain optimal quadrature formulas

This paper present a numerical method to obtain optimal quadrature formulas of Gauss type and Radau type in the sense of Sard. Using the relation between optimal quadrature formulas and nonospline functions, the optimal quadrature formula can be obtained by solving a set of no-linear simultaneous algebraic equations induced from the interpolatory conditions of the monospline. In attempting to solve this set of non-linear algebraic equations for numbers of knots and degrees of interpolution required in estimation problem applications insurmountable numerical errors were encountered. This paper solves the numerical problem by first reducing the number of unknowns and equations to approximately one half the original number. This is accomplished by showing and then using a symmetry property of the monospline. Second an iteration scheme which partitions the reduced order set of non-linear algebraic equations into a linear subsystem and a non-linear subsystem is developed to numerically solve the equations. This iteration algorithm provides the advantages of reducing the computational complexity, dynamically checking the convergence and explicitly evluating the resulting accuracy.     

A numerical analysis of time-dependent two-dimensional magnetic fields

The nonlinear diffusion equation as applied to two-dimensional time-dependent magnetic fields is solved with a finite element algorithm. This algorithm permits the analysis of problems possessing complex geometries, induced eddy currents, permanent magnets, and nonperiodic excitation currents. The numerical procedure utilizes implicit time stepping with an iterative scheme to solve the resulting set of equations. Two examples of applications of this program are presented.     

The PHI2 method: a way to compute time-variant reliability

Time-variant reliability problems appear in the engineering practice when (a) the material properties of the structure deteriorate in time or (b) random loading modelled as random processes is involved. This paper presents a method called PHI2 which is based on the outcrossing approach and allows to solve such problems using classical time-invariant reliability tools such as FORM/SORM methods. The PHI2 method is first presented. Then it is benchmarked with the well-established ‘asymptotic methods’ [Stochast. Process. Appl. 13 (1988) 195; J. Offshore Mech. Arctic Engng 113 (1991) 241; Probab. Engng Mech. 10 (1995) 53; J. Struct. Engng 25 (1998) 1] on three examples dealing with scalar or vector processes and linear or non-linear limit state functions. The PHI2 method appears more accurate in all cases. As an application example, the method is finally applied on a case representing a mechanical system (a beam) placed in an environment that can have exceptional configuration.     

A numerical method of regenerator

A numerical method for regenerators is introduced in this paper. It is not only suitable for the regenerators in cryocoolers and Stirling engines, but also suitable for the stacks in acoustic engines and the pulse tubes in pulse tube refrigerators. The numerical model is one dimensional periodic unsteady flow model. The numerical method is based on the control volume concept with the implicitly solve method. The iteration acceleration method, which considers the one-dimensional periodic unsteady problem as the steady two-dimensional problem, is used for decreasing the calculation time. By this method, the regenerator in an inertance tube pulse tube refrigerator was simulated. The result is useful for understanding how the inefficiency of the regenerator changes with the inertance effect.     

How single conjugated polymer molecules respond to electric fields

Conjugated polymers find applications in a range of devices such as light-emitting diodes, field-effect transistors and solar cells. The elementary electronic response of these semiconductors to electric fields is understood in terms of nanoscale perturbations of charge density. We demonstrate a general breaking of spatial charge symmetry by considering the linear Stark effect in the emission of single chromophores on individual chains. Spectral shifts of several nanometres occur due to effective dipoles exceeding 10 D. Although the electric field does not ionize the exciton, some molecules exhibit field-induced intensity modulations. This quenching illustrates the equivalence of charge symmetry breaking and polaron-pair or charge-transfer-state formation, and provides a microscopic picture of permanent charging, which leads to doping and exciton dissociation in actual devices. In addition to using this tuneable emission in single-photon electro-optic modulators, hysteresis in the Stark shift suggests a route to designing nanoscale memory elements such as molecular switches.     

A hybrid AI optimization method applied to industrial processes

A hybrid artificial intelligent optimization (HAIO) method, which combines traditional classification pattern recognition (CPR) with artificial neural networks (ANN), applied to industrial processes is presented. This new method includes the fuzzy membership function of sample class, the center cluster of class, a hopeful region, inverse mapping, independent neural network modeling of classified analogy, CPR-ANN, GA (genetic algorithm)-ANN and network-based expert system etc. Some applications of the HAIO are shown.     

Measurement procedure to assess exposure to extremely low-frequency fields: a primary school case study

How to correctly measure the exposure of general public to extremely low-frequency (ELF) radiation is a key issue for ELF epidemiological studies. This paper proposes a measurement procedure to accurately assess the exposure of people to electric and magnetic field in the frequency band from 5 Hz to 100 kHz in buildings and their premises. As ELF radiation could be particularly harmful to children, the measurement procedure is focused on exposure to ELF in schools. Thus, the students' exposure to ELF fields can be assessed by correlating the ELF measurements to the hours of school activity. In this paper, the measurement protocol was applied to study the ELF exposure on students from García Quintana primary school in Valladolid, Spain. The campaign of measurements for ELF exposure assessment in this primary school was of great interest for the Regional Council of Public Health because of the social alarm generated by the presence of a significant number cancer cases in children.     

A hybrid boundary node method

A new variational formulation for boundary node method (BNM) using a hybrid displacement functional is presented here. The formulation is expressed in terms of domain and boundary variables, and the domain variables are interpolated by classical fundamental solution; while the boundary variables are interpolated by moving least squares (MLS). The main idea is to retain the dimensionality advantages of the BNM, and get a truly meshless method, which does not require a ‘boundary element mesh’, either for the purpose of interpolation of the solution variables, or for the integration of the ‘energy’. All integrals can be easily evaluated over regular shaped domains (in general, semi‐sphere in the 3‐D problem) and their boundaries. Numerical examples presented in this paper for the solution of Laplace's equation in 2‐D show that high rates of convergence with mesh refinement are achievable, and the computational results for unknown variables are most accurate. No further integrations are required to compute the unknown variables inside the domain as in the conventional BEM and BNM. Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical inversion of a Laplace transform using a Fourier series to compute nonstationary temperature fields in layered structures

An algorithm is examined for the selection and assignment of the parameter a of a numerical inversion of a Laplace transform with the use of Fourier series.Translated from Inzhernerno-fizicheskii Zhurnal, Vol. 61, No. 5, pp. 804–807, November, 1991.