A numerical algorithm for simulation of the electric corona discharge in the triode system

A numerical algorithm is described to calculate the charge density, electric field and corona current distribution in the corona triode. The algorithm employs a hybrid technique based on the Boundary and Finite Element Methods (FEM). FEM is used to determine the electric field because of free space charge produced by the corona discharge. The Boundary Element Method (BEM) is applied for calculating the other component of electric filed as a result of the voltage applied to the electrodes. The Method of Characteristics (MOC) is used to update the space charge density distribution. The characteristic lines are traced backwards from points of the analysed domain to the corona wire. The current density, electric field and space charge density distributions can be controlled by changing the configuration of the system. Results of calculations in a few different cases show the influence of different parameters on the work of the corona triode.     

Thermal-Pulse Tomography of Space-charge and Polarization Distributions in Electret Polymers

A new, non-destructive technique for the analysis of electret materials is presented. Thermal-pulse tomography produces three-dimensional images of space-charge and polarization distributions with a lateral resolution of better than 50 μm and a depth resolution of less than 0.5 μm. A focused-pulsed laser heats a circular spot on the opaque upper electrode. While diffusing through the sample, the thermal pulse causes local changes in the sample geometry or dielectric properties, resulting in a short-circuit current in the presence of space charge or electric dipoles. From the transient current, the distribution of the internal electric field can be reconstructed by means of scale transformation or regularization methods.     

Regularized inversion method for retrieval of aerosol particle size distribution function in W(1,2) space

A determination of the aerosol particle size distribution function by using the particle spectrum extinction equation is an ill-posed integral equation of the first kind. To overcome this, we must incorporate regularization techniques. Most of the literature focuses on the Phillips-Twomey regularization or its variations. However, there are drawbacks for some applications in which the real aerosol distributions have large oscillations in a Junge-type distribution. The reason for this is that the scale matrix based on the norm of the second differences in the Phillips-Twomey regularization is too ill- conditioned to filter the large perturbations induced by the small algebraic spectrum of the kernel matrix and the additive noise. Therefore we reexamine the aerosol particle size distribution function retrieval problem and solve it in W1,2 space. This setting is based on Sobolev's embedding theorem in which the approximate solution best simulates the true particle size distribution functions. For choosing the regularization parameters, we also develop an a posteriori parameter choice method, which is based on the discrepancy principle. Our numerical results are based on the remote sensing data measured by the CE318 sunphotometer in Jia Xiang County, Shan Dong Province, China, and are performed to show the feasibility of the proposed algorithms.     

Influence of Statistical Errors on Size Distributions Obtained from Dynamic Light Scattering Data: Simulation of Experimental Noise in the Intensity Autocorrelation Function

Abstract

In this paper, the statistical error courses in the intensity autocorrelation function are simulated and the influence of these errors on size distribution reproducibility is checked. As a numerical method, the constrained regularization method with the Contin program was used and autocorrelation functions were calculated on the basis of the monomodal Schulz distribution. The influence of the regularization parameter α on the recalculated size distributions has also been checked. It has been found that the reproducibility of original size distributions can be lost because of the existence of slow-frequency components in noisy data.     

Statistical approach to the solution of first-kind integral equations arising in the study of materials and their properties

There are a number of problems arising when studying the properties of materials, which require for their solution the inversion of a Fredholm first-kind integral equation. Examples include the determination of the distribution of adsorption energies on the surface of a solid and the evaluation of the distribution of pore radii of a solid from diffusion data. Such equations are, in practice, notoriously difficult to solve. This paper describes a general methodology for solving equations of this type. The method combines the ideas of regularization with a quadratic programming algorithm for minimizing quadratic expressions subject to non-negativity constraints. The condition of non-negativity is essential if we are to recover distribution functions for physical attributes of a solid. The method proposed is tested on simulated data for which the true solution to the equation is already known and on real data arising in each of the two situations described above. The method is shown to perform well in recovering the true solution for the simulated data and to produce results in the real data situations that are consistent with the data observed and with observations of related physical quantities.     

Ion/molecule reactions to chemically deconvolute the electrospray ionization mass spectra of synthetic polymers

A new approach has been developed to analyze synthetic polymers via electrospray ionization mass spectrometry. Ion/molecule reactions, a unique feature of trapping instruments such as quadrupole ion trap mass spectrometers, can be used to chemically deconvolute the molecular mass distribution of polymers from the charge-state distribution generated by electrospray ionization. The reaction involves stripping charge from multiply charged oligomers to reduce the number of charge states. This reduces or eliminates the overlapping of oligomers from adjacent charge states. 15-Crown-5 was used to strip alkali cations (Na+) from several narrow polydisperse poly(ethylene glycol) standards. The charge-state distribution of each oligomer is reduced to primarily one charge state. Individual oligomers can be resolved, and the average molecular mass and polydispersities can be calculated for the polymers examined here. In most cases, the measured number-average molecular mass values are within 10% of the manufacturers' reported values obtained by gel permeation chromatography. The polydispersity was typically underestimated compared to values reported by the suppliers. Mn values were obtained with 0.5% RSD and are independent, over several orders of magnitude, of the polymer and cation concentration. The distributions that were obtained fit quite well to the Gaussian distribution indicating no high- or low-mass discriminations.     

An adaptive regularization algorithm for recovering the rate constant distribution from biosensor data

We present here the theoretical results and numerical analysis of a regularization method for the inverse problem of determining the rate constant distribution from biosensor data. The rate constant distribution method is a modern technique to study binding equilibrium and kinetics for chemical reactions. Finding a rate constant distribution from biosensor data can be described as a multidimensional Fredholm integral equation of the first kind, which is a typical ill-posed problem in the sense of J. Hadamard. By combining regularization theory and the goal-oriented adaptive discretization technique, we develop an Adaptive Interaction Distribution Algorithm (AIDA) for the reconstruction of rate constant distributions. The mesh refinement criteria are proposed based on the a posteriori error estimation of the finite element approximation. The stability of the obtained approximate solution with respect to data noise is proven. Finally, numerical tests for both synthetic and real data are given to show the robustness of the AIDA.     

Numerical Solution and Experimental Test for Corona Discharge Between Blade and Plate

This paper presents a numerical technique to solve the problem of space charge distribution in a blade-plate electrodes system. The coupled equations are: Poisson equation solved by finite element method (FEM) to determine the distributions of potential, and charge conservation equation solved by the method of characteristics (MOC) to obtain the charge density between the two electrodes. The structured mesh is redefined at each step of the iterative scheme. A simplified injection law at the blade is retained; it allows us to obtain solutions which compare very favorably with experimental results concerning the current density distribution at the plate     

Improved inversion procedure for particle size distribution determination by photon correlation spectroscopy

We propose a minimum variation of solution method to determine the optimal regularization parameter for singular value decomposition for obtaining the initial distribution for a Chahine iterative algorithm used to determine the particle size distribution from photon correlation spectroscopy data. We impose a nonnegativity constraint to make the initial distribution more realistic. The minimum variation of solution is a single constraint method and we show that a better regularization parameter may be obtained by increasing the discrimination between adjacent values. We developed the S-R curve method as a means of determining the modest iterative solution from the Chahine algorithm. The S-R curve method requires a smoothing operator. We have used simulated data to verify our new method and applied it to real data. Both simulated and experimental data show that the method works well and that the first derivative smoothing operator in the S-R curve gives the best results.     

Modeling of electrical field modified by injected space charge

This paper presents the numerical solution of the coupled Poisson equation and charge conservation equation. We present an algorithm to obtain the distributions of electric field and charge density resulting from a corona discharge in the two-dimensional hyperbolic blade-ground plate configuration. We use finite elements method (FEM) to determine the potential distribution, finite volume method (FVM) and method of characteristics (MOC) to determine the distribution of charge density. The structured mesh is redefined at each iteration step to decrease artificial numerical diffusion. For solving the conservation equation, MOC with redefinition of structured mesh appears to be the best technique.     

Determining the initial distribution in space-fractional diffusion by a negative exponential regularization method

In this paper, we consider the backward problem for diffusion equation with space fractional Laplacian, i.e. determining the initial distribution from the final value measurement data. In order to overcome the ill-posedness of the backward problem, we present a so-called negative exponential regularization method to deal with it. Based on the conditional stability estimate and an a posteriori regularization parameter choice rule, the convergence rate estimate are established under a-priori bound assumption for the exact solution. Finally, several numerical examples are proposed to show that the numerical methods are effective.     

A comparison of different methods to solve inverse biharmonic boundary value problems

The Boundary Element Method (BEM) is applied to solve numerically some inverse boundary value problems associated to the biharmonic equation which involve over‐ and under‐specified boundary portions of the solution domain. The resulting ill‐conditioned system of linear equations is solved using the regularization and the minimal energy methods, followed by a further application of the Singular Value Decomposition Method (SVD). The regularization method incorporates a smoothing effect into the least squares functional, whilst the minimal energy method is based on minimizing the energy functional for the Laplace equation subject to the linear constraints generated by the BEM discretization of the biharmonic equation. The numerical results are compared with known analytical solutions and the stability of the numerical solution is investigated by introducing noise into the input data. Copyright © 1999 John Wiley & Sons, Ltd.     

An Analytical Method for Computing the One-Dimensional Backward Wave Problem

The present paper reveals a new computational method for the illposed backward wave problem. The Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown initial data of velocity. Then, we consider a direct regularization to obtain a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us to obtain an analytical solution of regularization type. The sufficient condition of the data for the existence and uniqueness of solution is derived. The error estimate of the regularization solution is provided. Some numerical results illustrate the performance of the new method.     

Dielectric properties and spatial distribution of polarization of ceramic + polymer composite sensors

Thin films ceramic + polymer composite sensors with mixed connectivities possess high values of piezo- and pyroelectric coefficients and the formability and flexibility which are not attainable in a single-phase ferroelectric material, i. e., an electroceramic or a polymer. The efficiency and the piezo- and pyroelectric figure of merit (FOM) are influenced by the temperature dependence of the dielectric properties and the nature of the spatial distribution of polarization of the composite material. We report the results of a study of dielectric properties of calcium – modified lead titanate (PTCa) and a polar copolymer, polyvinylidene fluoride and trifluoroethylene P(VDF-TrFE) and PTCa and epoxy in a wide frequency range. Each of the two composites was fabricated with two different volume fractions of the constituent phases. Furthermore, the spatial distribution of polarization was determined by the laser intensity modulation method (LIMM) for each composite sensor in order to assess the polarization distribution of the sensors. These results are also reported in this work. Received: 6 November 2000 / Reviewed and accepted: 7 November 2000     

Boundary knot method for some inverse problems associated with the Helmholtz equation

The boundary knot method is an inherently meshless, integration‐free, boundary‐type, radial basis function collocation technique for the solution of partial differential equations. In this paper, the method is applied to the solution of some inverse problems for the Helmholtz equation, including the highly ill‐posed Cauchy problem. Since the resulting matrix equation is badly ill‐conditioned, a regularized solution is obtained by employing truncated singular value decomposition, while the regularization parameter for the regularization method is provided by the L‐curve method. Numerical results are presented for both smooth and piecewise smooth geometry. The stability of the method with respect to the noise in the data is investigated by using simulated noisy data. The results show that the method is highly accurate, computationally efficient and stable, and can be a competitive alternative to existing methods for the numerical solution of the problems. Copyright © 2005 John Wiley & Sons, Ltd.     

Liquid crystalline texture and hydrogen bond on the thermal conductivities of intrinsic thermal conductive polymer films

Polymer-dispersed liquid crystal(PDLC)films comprising polyvinyl alcohol(PVA)and liquid crystal monomer(LCM)were successfully obtained by the method of solution casting&thermal compress-ing.LCM was distributed orderly in PVA matrix by hydrogen bond interaction,to form PVA-LCM interpenetrating-layered networks.When the mass fraction of LCM was up to 35 wt％,the corresponding in-plane thermal conductivity coefficient(λ∥)of PDLC film was significantly increased to 1.41 W m-1 K-1,about 10.8 times that of neat PVA(0.13 W m-1 K-1).High intrinsic λ//values of PDLC films were mainly attributed to the formed microscopic-ordered structures from ordered stacking of LCM,ordered arrangement of PVA chains,and their hydrogen bond interaction.This work would offer a new way to design and prepare novel intrinsic high thermal conductive polymers.     

恒压下树脂在双尺度多孔介质中的流动特性

基于复合材料液态模塑(LCM)工艺过程中存在半饱和区域的实验现象以及对预制体双尺度效应的逐步认识, 一些学者提出用沉浸模型来研究双尺度多孔介质的不饱和流动。通过体积均匀化方法描述了双尺度多孔介质复合材料液态模塑工艺模型的特征, 得到含有沉浸项的双尺度多孔介质的质量守恒方程, 并采用有限元法对方程进行数值求解, 通过具体算例计算了考虑双尺度效应时恒压树脂注射下不同时段的压力分布状态, 得到树脂在填充过程中流动前沿半饱和区域从出现到消失的过程, 采用不同注射压力进行模拟并比较。结果表明, 与单尺度多孔介质模型不同, 双尺度多孔介质模型更能反映实际树脂填充过程中出现的半饱和区域现象。     

Determination of ionisation energies and attempt-to-escape factors using thermally stimulated conductivity

A procedure for determining an arbitrary distribution of activation energies (E) and attempt-to-escape frequencies (s) from overlapping contributions to thermoluminescence (TL) or thermally stimulated conductivity (TSC) is described. For the case of no retrapping, i.e. first order kinetics, the glow curve can be described by a two-dimensional Fredholm equation representing a superposition of Randall-Wilkins first-order peak shapes. The solution to this equation gives the distribution of trapping energies and attempt-to-escape-frequency factors necessary to obtain the TL or TSC peak shape. Analysis of simulated TL/TSC data for trap distributions distributed in both E and s demonstrates that the arbitrary E and s values can be determined from the solution of the Fredholm equation. The procedure is demonstrated for experimental TSC data from gamma-irradiated Al2O3:C.     

Mie light-scattering granulometer with adaptive numerical filtering. I. Theory

A search procedure based on a least-squares method including a regularization scheme constructed from numerical filtering is presented. This method, with the addition of a nephelometer, can be used to determine the particle-size distributions of various scattering media (aerosols, fogs, rocket exhausts, motor plumes) from angular static light-scattering measurements. For retrieval of the distribution function, the experimental data are matched with theoretical patterns derived from Mie theory. The method is numerically investigated with simulated data, and the performance of the inverse procedure is evaluated. The results show that the retrieved distribution function is quite reliable, even for strong levels of noise.     

Solution of the time‐harmonic viscoelastic inverse problem with interior data in two dimensions

We consider the problem of determining the distribution of the complex‐valued shear modulus for an incompressible linear viscoelastic material undergoing infinitesimal time‐harmonic deformation, given the knowledge of the displacement field in its interior. In particular, we focus on the two‐dimensional problems of anti‐plane shear and plane stress. These problems are motivated by applications in biomechanical imaging, where the material modulus distributions are used to detect and/or diagnose cancerous tumors. We analyze the well‐posedness of the strong form of these problems and conclude that for the solution to exist, the measured displacement field is required to satisfy rather restrictive compatibility conditions. We propose a weak, or a variational formulation, and prove the existence and uniqueness of solutions under milder conditions on measured data. This formulation is derived by weighting the original PDE for the shear modulus by the adjoint operator acting on the complex‐conjugate of the weighting functions. For this reason, we refer to it as the complex adjoint weighted equation (CAWE). We consider a straightforward finite element discretization of these equations with total variation regularization, and test its performance with synthetically generated and experimentally measured data. We find that the CAWE method is, in general, less diffusive than a corresponding least squares solution, and that the total variation regularization significantly improves its performance in the presence of noise. Copyright © 2012 John Wiley & Sons, Ltd.