A technique for dielectric measurement of cylindrical objects in arectangular waveguide

In this paper, the inverse scattering problem of a homogeneous dielectric post in a rectangular waveguide is considered. A novel inversion algorithm, based on the method of moments and eigen analysis, for computation of the dielectric constant of the post (ϵ) from the measured voltage reflection coefficient is introduced. In this method the integral equation for the polarization current induced in the dielectric post is cast into a matrix equation, and then the contribution of ϵ to the resulting reflection coefficient is expressed explicitly using the eigen analysis. It is shown that the dielectric constant can be obtained from the solution of a complex polynomial function which in turn can be obtained numerically using the conjugate gradient method. Practical aspects of dielectric measurement using this technique are discussed. The HP-8510 network analyzer is used to measure the reflection coefficient of dielectric posts in an X-band waveguide sample holder. Metallic and known dielectric posts are used to determine the accuracy of the dielectric measurement technique     

Mass transfer in a granular column in the presence of nonequilibrium sorption at the phase interface

The direct and inverse problems of nonequilibrium sorption dynamics are considered for the case of a variable filtration velocity; the direct problem is solved by means of orthogonal polynomials and the inverse problem with the help of statistical moments.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 2, pp. 230–238, February, 1971.     

Recording and Analysis of the Radiation Spectrum in the Infrared Band by Means of Bragg Waveguide Gratings

A method of spatial separation of the spectral components of electromagnetic radiation based on the use of waveguide diffraction gratings is proposed. Optimization of the parameters of the detecting part of a spectrum recorder that employs the proposed method is realized by means of numerical simulation.__________Translated from Izmeritel’naya Tekhnika, No. 4, pp. 37–39, April, 2005.     

Shape identification for water–ice interface within the cylindrical capsule in cold storage system by inverse heat transfer method

In this study, the inverse heat transfer method is applied to shape identification for the ice layer within the cylindrical capsule in cold storage system. The approach is constructed by combining the curvilinear grid generation scheme, the direct problem solver, the conjugate gradient optimization method, and the redistribution method. According to the practical condition of freezing ice, shape identification for the water–ice interface based on the data of the outer surface temperature is attempted. Results show that the profile of the water–ice interface is possible to be identified by using the inverse heat transfer approach and the accuracy of the ice shape identification is dependent on the uncertainty of the outer surface temperature data, the Biot number, the thickness of the ice layer, and the geometric configuration as well.     

Planning a physical experiment on determination of the parameters of a material by using mathematical methods

A method is developed for solving an inverse problem on the determination of thermomechanical parameters of a material that undergoes phase transformations in the process of hardening. The dependence of the error of determination of parameters on the error admissible in direct measurements of physical fields is established.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 61, No. 2, pp. 181–186, August, 1991.     

Comparison of the born iterative method and tarantola's method for an electromagnetic time-domain inverse problem

Two methods of solving the nonlinear two-dimensional electromagnetic inverse scattering problem in the time domain are considered. These are the Born iterative method and the method originally proposed by Tarantola for the seismic reflection inverse problems. The former is based on Born-type iterations on an integral equation, whereby at each iteration the problem is linearized, and its solution is found via a regularized optimization. The latter also uses an iterative method to solve the nonlinear system of equations. Although it linearizes the problem at each stage as well, no optimization is carried out at each iteration; rather the problem as a whole is posed as a (regularized) optimization. Each method is described briefly and its computational complexity is analyzed. Tarantola's method is shown to have a lower numerical complexity compared to the Born iterative method for each iteration, but in the examples considered, required more iterations to converge. Both methods perform well when inverting a smooth profile; however, the Born iterative method gave better results in resolving localized point scatterers.     

Determination of the source in quasilinear equations of the parabolic type

The uniqueness theorem is proven for the solution of the two-dimensional inverse problem for an unknown source function dependent on the solution of the direct problem and on the spatial coordinate.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 3, pp. 419–423, March, 1989.     

A procedure to obtain the complete electromagnetic scattering properties at discontinuities between integrated optical waveguides

Abstract

A method to obtain the complete electromagnetic scattering properties of discontinuities between arbitrary integrated optical waveguides is presented. The method involves a new generalized scattering matrix concept, together with the generalized telegraphist equations formulism and the modal matching technique. Radiation losses, as well as reflection and transmission coefficients between proper modes, can be obtained. Single and multiple discontinuities in planar and channel optical waveguides have been analysed. Numerical results of complex scattering coefficients are given. The possibilities of the method for analysing waveguide photonic crystals, as well as optical devices in waveguide periodic waveguide structures, are demonstrated.     

Approximation of the solution of inverse problem of scattering of electromagnetic waves on plane dielectrics

We propose a method for the determination of the material parameters of dielectric coatings according to the measured values of scattered electromagnetic fields which enables us to introduce an efficient procedure of processing of the data of measurements in the methods of nondestructive testing. As a specific feature of the proposed method for the solution of the formulated inverse problem, we can mention the possibility of reconstruction of piecewise continuous profiles of dielectric permittivity for laminated materials. The procedure of reconstruction is based on the method of integral equations. The solution of the problem is obtained approximately. The measured values of the coefficient of reflection of plane electromagnetic waves are extrapolated to the high-frequency region, which enables us to guarantee higher accuracy of reconstruction of the functions of dielectric permittivity for the analyzed structures.     

Guiding mode expansion of a TE and TM transverse-mode integral equation for dielectric slab waveguides with an abrupt termination.

We propose a rigorous transverse-mode integral equation formulation for analyzing TE and TM electromagnetic radiation fields on the facet of dielectric slab waveguides with an abrupt termination in free space. Both exact waveguide guiding modes and discretized radiation modes are included in the kernels of the integral equation. To reduce the size of the matrix that approximates the exact integral equation, we expand the unknown field at the junctions in terms of guiding modes of a selected waveguide with sufficiently large normalized frequency and core thickness. By direct matrix inversion, we obtain numerical solutions of the scattered fields at the junctions. Our method can be used to study the field distribution as well as the energy reflection and transmission coefficients of dielectric waveguides with multiple step discontinuities.     

Mechanical behaviors of quasi-ordered entangled aluminum alloy wire material

Quasi-ordered entangled aluminum alloy wire materials with nominal porosity of 57–77% have been fabricated by assembling a set of aluminum alloy wires with diameter of 0.28 mm. The as-prepared materials display three-stage stress–strain behavior under uniaxial compressive loading, i.e., initial nonlinear ‘quasi-elastic’ deformation, strain-hardening ‘pseudo-platform’ stage, and the final densifying stage. The experiment indicates that the structural deformation mechanism dominates the initial stress–strain behavior. At the elastic stage, the materials reveal a significant ‘strain-hysteresis effect’. The compressive yield strength and the elastic modulus exhibit a significant dependence of porosity, i.e., both decrease as the porosity increases. The data obey the typical power law relationship suggested by Gibson–Ashby.     

结构影响线识别：反问题可识别性分析与降维贝叶斯不确定性量化

结构影响线识别是移动荷载下既有结构评估的理论基础,其本质上是基于系统输入-输出含噪数据反向对静力系统指定截面的响应函数进行识别。已有研究虽然取得了进展,但它们在以下两个方面存在局限性：缺乏反问题可识别性分析;缺乏不确定性量化。反问题可识别性分析是为了厘清系统识别的参数的解的情况。不确定性量化是基于测量输入-输出含噪数据估计影响线参数的后验概率密度函数。针对上述两个局限性,该文在贝叶斯概率框架的基础上开展关于影响线识别的反问题可识别性分析与贝叶斯不确定性量化。该文进行基于直接参数化的影响线识别,包括系统输入与输出、反问题可识别性分析、参数最优值。经分析得出：一方面,直接参数化无法保证全局模型可识别;另一方面,现有方法即使是全局模型可识别的情况下也无法进行不确定性量化。为保证反问题是全局模型可识别且同时获取参数后验概率密度函数,该文提出基于降维贝叶斯不确定性量化的影响线后验识别,包括系统输入与输出重构、反问题可识别性分析、后验概率密度函数。该文进行模拟数据下新光大桥吊杆拉力影响线识别,与实测及模拟数据下简支梁桥应变影响线识别,验证提出方法的有效性。     

Optical waveguides for imaging applications: Design by an inverse scattering approach

An inverse scattering theory is used to design optical waveguides capable of transmitting spatial images without degradation. The propagation characteristics of N modes each carrying a pixel of the image are specified by a transverse rational reflection coefficient. The Gel'fand-Levitan-Marchenko inverse scattering theory is used to obtain the unique solution of the permittivity profile of the waveguide from the reflection coefficient     

Nondestructive testing of materials using 14 MeV neutrons and a pulse-shape analyzer system

A 14 MeV neutron generator and fast neutron spectrometer consisting of an organic scintillation detector and a pulse-shape analyzer are used for the nondestructive testing of materials. The 14.6 MeV peak (in the 12.7–15.7 MeV region) is observed to change as a function of both the kind of testing material and the defect condition inside the material. The number of neutron counts under the 14.6 MeV peak for lighter testing materials (e.g., plastic, brass, and aluminum) with a defect will increase, as compared to the number of neutron counts under the same peak region of an identical testing material but with no defect. For heavier testing materials (e.g., steel and lead), the inverse is observed. The method is feasible even with defects of size 0.25 cm³ (i.e., a cylindrical cavity 0.4 cm in diameter and 2.0 cm in length), although quantitative evaluation of the size of the defect as a function of the change of the number of neutron counts under the 14.6 MeV peak region is difficult due to instability of the 14 MeV neutron output.     

Inverse Identification of Temperature-Dependent Volumetric Heat Capacity by Neural Networks

An artificial neural network (NN)-based solution of the inverse heat conduction problem of identifying the temperature-dependent volumetric heat capacity function of a solid material is presented in this paper. The inverse problem was defined according to the evaluation of the BICOND thermophysical property measurement method. The volumetric heat capacity versus temperature function is to be determined using the measured transient temperature history of a single sensor. In this study, noiseless and noisy artificial measurements were generated by the numerical solution of the corresponding direct heat conduction problem. The inverse problem was solved by back-propagation and radial basis function type neural networks applying the whole history mapping approach. The numerical tests included the comparison of two different data representations of the network inputs (i.e., temperature vs. time and time vs. temperature) and accuracy analysis of the two network types with noiseless and noisy inputs. Based on the results presented, it can be stated that feed-forward NNs are powerful tools in a non-iterative solution of function estimation inverse heat conduction problems and they are likely to be very effective in evaluation of real measured temperature histories to determine the volumetric heat capacity as an arbitrary function of temperature.     

Third-order theory of the Risley-prism-based beam steering system

Nonparaxial ray tracing is performed to investigate the field scanned out by a single beam through two rotatable thick prisms with different parameters, and a general solution is obtained and then expanded into a power series to establish the third-order theory for Risley prisms that paves the way to investigate topics of interest such as optical distortions in the scan pattern and an analytical solution of the inverse problem of a Risley-prism-based laser beam steering system; i.e., the problem is concerned with how to direct a laser beam to any specified direction within the angular range of the system.     

Thermal Method for Measuring the Space Distribution of Optical-Radiation Intensity

A thermal method for measuring the space distribution of optical radiation is described, in which is solved the inverse heat conduction problem, i.e., restoration of the heat-source distribution from the temperature distribution in a heated body.     

Application of inverse first-order reliability method for probabilistic fatigue life prediction

A general probabilistic life prediction methodology for accurate and efficient fatigue prognosis is proposed in this paper. The proposed methodology is based-on an inverse first-order reliability method (IFORM) to evaluate the fatigue life at an arbitrary reliability level. This formulation is different from the forward reliability problem, which aims to calculate the failure probability at a fixed time instant. The variables in the fatigue prognosis problem are separated into two categories, i.e., random variables and index variables. An efficient searching algorithm for fatigue life prediction is developed to find the corresponding index variable at a certain confidence level. Numerical examples using direct Monte Carlo simulation and the proposed IFORM method are compared for algorithm verification. Following this, various experimental data for metallic materials are used for model prediction validation.     

The optimal control of fracture and stress parameters in a piezoceramic halfspace with cracks

An approach to the determination of the optimal control of fracture and strength parameters in a piezoceramic halfspace with cracks under antiplane deformation conditions is proposed. The distribution over certain part of the halfspace boundary, harmonically changing with time under the influence of axial forces or electric charges is analyzed as a control interaction. The solution of the inverse problem in fracture mechanics is obtained from the solution of the corresponding direct boundary value problem; in this case, the optimization problem is reduced to the momentum problem. The solution of the direct electroelastic problem using the method of the boundary integral equations is obtained. Various control functions permitting to realize the optimal process of control, i.e. the minimal energetic expenses, are given.     

Solution of the nonlinear inverse problem for a generalized heat-conduction equation in a region with moving boundaries

In an analysis of the numerical solution of the nonlinear inverse heat-conduction problem in a region with moving boundaries, a regularization method is used to construct an algorithm for smoothing the experimental data in a compilation of the input data for the inverse problem.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 29, No. 1, pp. 151–158, July, 1975.