聚酯薄膜中的热释光与热激电流

同时测量了聚酯薄膜的热释光与热激电流谱，用作者提出的自动分离法对光强或电流与温度的关系进行了分析。发现低温峰（150－250K）具有复杂的能级分布，其分布宽度近似为0．24－0．46eV，受陷载流子的初始浓度分布函数呈近高斯型。将TSC及TL谱中低温宽峰归结为薄膜中－COO－基团的局部运动导致受陷载流子的热释放。     

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.     

Inversion of light-scattering measurements for particle size and optical constants: theoretical study

We invert the Fredholm equation representing the light scattered by a single spherical particle or a distribution of spherical particles to obtain the particle size distribution function and refractive index. We obtain the solution by expanding the distribution function as a linear combination of a set of orthonormal basis functions. The set of orthonormal basis functions is composed of Schmidt-Hilbert eigenfunctions and a set of supplemental basis functions, which have been orthogonalized with respect to the Schmidt-Hilbert eigenfunctions by using the Gram-Schmidt orthogonalization procedure. We use the orthogonality properties of the basis functions and of the eigenvectors of the kernel covariance matrix to obtain the solution that minimizes the residual errors subject to a trial function constraint. The inversion process is described, and results from the inversion of several simulated data sets are presented.     

Fit of first order thermoluminescence glow peaks using the Weibull distribution function

A new thermoluminescence glow curve deconvolution (GCD) function is introduced which accurately describes first order thermoluminescence (TL) curves. The new GCD function is found to be accurate for first order TL peaks with a wide variety of the values of the TL kinetic parameters E and s. The 3-parameter Weibull probability function is used with the function variables being the maximum peak intensity (Im), the temperature of the maximum peak intensity (Tm) and the Weibull width parameter b. An analytical expression is derived from which the activation energy E can be calculated as a function of Tm and the Weibull width parameter b. The accuracy of the Weibull fit was tested using the ten reference glow curves of the GLOCANIN intercomparison program and the Weibull distribution was found to be highly effective in describing both single and complex TL glow curves. The goodness of fit of the Weibull function is described by the Figure of Merit (FOM) which is found to be of comparable accuracy to the best FOM values of the GLOCANIN program. The FOM values are also comparable to the FOM values obtained using the recently published GCD functions of Kitis et al. It is found that the TL kinetic analysis of complex first-order TL glow curves can be performed with high accuracy and speed by using commercially available software packages.     

Optimal distribution of a heat source within a thermopenetrator

Heat conduction within a heater of an arbitrary shape is investigated. A mathematical model is presented as a mixed boundary-value problem for the Poisson equation converted into a Fredholm boundary integral equation of the first kind which is solved numerically. A closed-form solution for the particular case of a rectangular heater is also found. Provided that the temperature and heat flux on the heater's boundary are given, the problem is treated as an inverse problem where the heat source distribution within the heater is the unknown function. The existence of the unique solution of this inverse problem is proved. Finally, the problem is solved numerically for a one-dimensional heat source.     

Characterisation of the thermally stimulated conductivity and thermoluminescence of natural topaz

Thermally stimulated conductivity (TSC) and thermoluminescence (TL) measurements were conducted to investigate the mechanisms of charge transfer and luminescence emission in natural samples of Brazilian topaz irradiated with beta particles from a 90Sr/90Y source or with a 1.75 MeV Van de Graaff electron beam. The luminescence and conductivity were simultaneously monitored during the heating of the samples, allowing direct comparison of the TL and TSC peaks. The results show that the three main TL peaks are accompanied by corresponding TSC peaks, usually shifted to higher temperatures. Comparison of the relative TL/TSC intensities of peaks 2 and 3 indicates that the process of thermal quenching of the luminescence is probably active, which is also supported by TL/TSC measurements at different heating rates. Results on the dose response of TL/TSC peaks also reveal an interesting feature: the TL intensity shows a monotonic increase with dose in the range of study (50 Gy-3 kGy) comprising a linear-supralinear-saturation characteristic, while the TSC peaks exhibit an increase from 50 Gy to 1 kGy, followed by a small decrease for doses greater than 1 kGy. This result is interpreted in terms of a model involving multiple traps and one recombination centre.     

Fredholm integral equation of the Laser Intensity Modulation Method (LIMM): Solution with the polynomial regularization and L-curve methods

The Laser Intensity Modulation Method (LIMM) is widely used for the determination of the spatial distribution of polarization in polar ceramics and polymers, and space charge in non-polar polymers. The analysis of experimental data requires a solution of a Fredholm integral equation of the 1st kind. This is an ill-posed problem that has multiple and very different solutions. One of the more frequently used methods of solution is based upon Tikhonov regularization. A new method, the Polynomial Regularization Method (PRM), was developed for solving the LIMM equation with an 8th degree polynomial using smoothing to achieve a stable and optimal solution. An algorithm based upon the L-curve method (LCM) was used for the prediction of the best regularization parameter. LIMM data were simulated for an arbitrary polarization distribution and were analyzed using PRM and LCM. The calculated distribution function was in good agreement with the simulated polarization distribution. Experimental polarization distributions in a poorly poled sample of polyvinylidene fluoride (PVDF) and in a LiNbO₃ bimorph, and space charge in polyethylene were analyzed. The new techniques were applied to the analysis of 3-dimensional polarization distributions.     

Isoparametric,finite element,variational solution of integral equations for three-dimensional fields

An improved numerical method, based on a variational approach with isoparametric finite elements, is presented for the solution of the boundary integral equation formulation of three-dimensional fields. The technique provides higher-order approximation of the unknown function over a bounding surface described by two-parameter, non-planar elements. The integral equation is discretized through the Rayleigh–Ritz procedure. Convergence to the solution for operators having a positive-definite component is guaranteed. Kernel singularities are treated by removing them from the relevant integrals and dealing with them analytically. A successive element iterative process, which produces the solution of the large dense matrix of the complete structure, is described. The discretization and equation solution take place one element at a time resulting in storage and computational savings. Results obtained for classical test models, involving scalar electrostatic potential and vector elastostatic displacement fields, demonstrate the technique for the solution of the Fredholm integral equation of the first kind. Solution of the Fredholm equation of the second kind is to be reported subsequently.     

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.     

Simultaneous Thermoluminescence and Thermally Stimulated Current in Polyamide

We have obtained simultaneous thermoluminescence (TL) and thermally Stimulated current (TSC) spectra in two types of polyamide film, such as nylons 6 and 11 under study of electron detrapping and recombination. There are three main relaxation peaks or regions, designated γ,β and α in order of increasing temperature in the TSC spectra, in contrast, a high temperature relaxation peak in TL spectra disappears. The centers or peaks of these relaxation regions are located at near 180, 230 and 310 K, respectively, deviating±10 K. However. we also observed two anomalous phenomena: first, a very large, short-circuited, thermally stimulated discharge current (TSDC) up to 10-8 A, but reversible in direction for non-polarized nylons 6 and 11, even after several times repeatedly; secondly, no TL signal except for non-polarized nylon 6 film.     

Microdosimetric interpretation of the photon energy response of LiF:Mg,Ti detectors

Photon energy response of MTS-N (LiF:Mg,Ti) detectors (TLD Poland) and of MTS-N detectors sensitised with 200 Gy of 60Co gamma rays, followed by UV irradiation (sMTS-N), has been determined using X rays with narrow energy spectra, in the energy range from 20 to 300 keV. The over-response of LiF:Mg,Ti detectors for X rays (relative TL efficiency eta = 1.1) can be explained as an ionisation density effect. Low energy X rays produce short electron tracks, which locally deposit a high radiation dose and, consequently, lead to an enhanced (supralinear) response. This over-response has not been observed in sensitised MTS-N where supralinearity in the response after gamma ray doses above 1 Gy is not seen. Using the dose-response curves measured for MTS-N detectors after 137Cs gamma ray irradiation and local doses calculated using Monte Carlo generated electron tracks, it was possible to predict the relative TL effectiveness for different X ray energies. The calculation procedure can be applied to predict the photon energy response of LiF:Mg,Ti detectors in an arbitrary photon field.     

Joint estimation of E–N curves and their scatter using evolutionary algorithms

We present an approach for estimating E–N curves and their scatter. The scatter of a number of load cycles to failure at an arbitrary amplitude-strain level is modelled using a two-parametric Weibull distribution with the constant shape parameter β and the scale parameter η dependent on the strain amplitude by the Coffin–Manson equation. In this way the E–N curve and its scatter can be described using five parameters: the four parameters of the Coffin–Manson equation for the scale parameter of the Weibull distribution and the shape parameter of the Weibull distribution. The objective was to estimate these five parameters, which are generally unknown (since the data from the literature are manly known only for the median E–N curves), on the basis of the known fatigue-life data to obtain not only the trend of the E–N curve, but also its scatter. In order to estimate these parameters on the basis of the fatigue-life data, two evolutionary algorithms were applied: a real-valued genetic algorithm (GA) and the differential ant-stigmergy algorithm (DASA). In the article a mathematical background of the approach is presented and applied to 27 test cases of simulated fatigue-life data and one real case of experimentally obtained fatigue-life data. The results are analysed and discussed.     

Thermal stresses near a penny-shaped crack in an elastic sphere embedded in an infinite elastic space

This paper gives an analysis of the distribution of thermal stresses in a sphere which is bonded to an infinite elastic medium. The thermal and the elastic properties of the sphere and the elastic infinite medium are assumed to be different. The penny-shaped crack lies on the diametral plane of the sphere and the centre of the crack is the centre of the sphere. By making a suitable representation of the temperature function, the heat conduction problem is reduced to the solution of a Fredholm integral equation of the second kind. Using suitable solution of the thermoelastic displacement differential equation, the problem is then reduced to the solution of a Fredholm integral equation, in which the solution of the earlier integral equation arising from heat conduction problem occurs as a known function. Numerical solutions of these two Fredholm integral equations are obtained. These solutions are used to evaluate numerical values for the stress intensity factors. These values are displayed graphically.     

Boundary-integral equation analysis of cracked anisotropic plates

A numerical procedure based on the boundary-integral equation method, is formulated using the fundamental solution (Green's function) for an infinite anisotropic plate containing an exact crack. The boundary-integral equation developed can be solved numerically for the mode 1 and mode 2 stress intensity factors by approximating boundary data on the surface of an arbitrary body, excluding the crack surface. Thus the efficiency and generality of the boundary-integral equation method and the precision of exact crack model analyses are combined in a direct manner. The numerical results reported herein are as accurate as previously published isotropic results. The effects of material anisotropy are reported for center and double-edge cracked geometries. A path independent integral for obtaining mode 1 and mode 2 stress intensity factors directly for arbitrary loading is reported.     

Mutually constrained partial differential and integral equations for an exterior field problem

A new implementation of the mutually constrained partial differential and integral equation method for the exterior 2-dimensional field problem is described. It is shown, that the method is applicable to exterior problems in an inhomogeneous medium. The inhomogeneity is considered in the finite element procedure and in boundary element method, where an adequate Green's function is applied. The temperature distribution around a three-cable system is then computed as an illustration. The eddy-current losses in the cable sheaths are calculated using the Fredholm integral equation of the second kind.     

Trapping centers and their distribution in Tl2InGaSe4 single crystals by thermally stimulated luminescence

Thermoluminescence (TL) measurements in Tl₂InGaSe₄-layered single crystals have been carried out in the temperature range of 10–200 K at various heating rates (0.2–1.0 K s^?1) to get information about the characteristics of traps. Two TL overlapping glow peaks related to defect levels have been clearly observed. Thermal cleaning procedure was applied to the glow curves to separate overlapped peaks. Initial rise, peak shape, and heating rate methods were used to calculate the activation energies of the revealed traps. The energy values of 5 and 28 meV were evaluated for the peaks observed at low and high temperatures, respectively. Moreover, heating rate dependence and traps distribution analysis were also investigated on the curve obtained after thermal cleaning. The activation energies of the distributed trapping centers were found to be increasing from 29 to 151 meV with increasing the illumination temperature from 42 to 80 K.     

Computational methods for solving static field and eddy current problems via Fredholm integral equations

Two-dimensional static field problems can be solved by a method based on Fredholm integral equations (equations of the second kind). This has numerical advantages over the mote commonly used integral equation of the first kind. The method is applicable to both magnetostatic and electrostatic problems formulated in terms of either vector or scalar potentials. It has been extended to the solution of eddy current problems with sinusoidal driving functions. The application of the classical Fredholm equation has been extended to problems containing boundary conditions: 1) potential value, 2) normal derivative value, and 3) an interface condition, all in the same problem. The solutions to the Fredholm equations are single or double (dipole) layers of sources on the problem boundaries and interfaces. This method has been developed into computer codes which use piecewise quadratic approximations to the solutions to the integral equations. Exact integrations are used to replace the integral equations by a matrix equation. The solution to this matrix equation can then be used to directly calculate the field anywhere.     

Effect of interaction between deep impurity traps on thermally stimulated currents in semiconductors

We demonstrate that the problem of determining the concentrations of free and trapped charge carriers in wide-gap semiconductors from their thermally stimulated current (TSC) curves for m interacting levels in an implicit difference scheme for numerically solving differential rate equations of TSCs reduces to finding the roots of an algebraic equation of degree m + 1. For two interacting trap levels of the same nature (electron or hole traps), we present an algorithm for numerically solving differential rate equations of TSCs which allows the concentrations of free and trapped charge carriers to be determined. TSC curves can be divided into four types according to their shape (dependent on trap parameters and experimental conditions): “splitting” (two well-resolved peaks separated by a temperature range), “saddle” (a well-defined minimum between two peaks), shoulder (on the high- or low-energy side), and “coalescence-absorption” (one peak). The modeling results are used to interpret an experimental TSC curve for semiconducting InSe and to demonstrate that, to adequately interpret experimental TSC data, one should use a model for the interaction between levels.     

A numerical method of solving Fredholm integral equations applied to current distribution and inductance in parallel conductors

If the resistance of a conductor is negligible compared with the reactance and if radiation effects are ignored the inductance and current distribution may be obtained by using perfectly-conducting models. In this paper the distribution of current in a system of infinitely-long, perfectly-conducting straight conductors of arbitrary cross-section is shown to satisfy an integral equation of Fredholm type and a general digital procedure for solving this equation, and hence for determining inductance, is given. The relative advantages of stepped, piecewise-linear and piecewise quadratic approximations to the current distribution are studied using arrangements of strip conductors and of isolated rectangular conductors having known current distributions. The advantageous effect of varying the width of the sections used in the computation is also established. It is shown that inductance estimates accurate to within 0·1 per cent can be obtained with a relatively small number of sections and that for a large number of sections the inductance converges on the theoretical value. The paper also examines current distribution and inductance for ‘go-and return’ systems of rectangular conductors, as well as for two paralleled conductors with remote return, and compares the inductances obtained with previous derivations.