Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations

Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions, exactly characterize the inhomogeneities based on monotonicity properties of either the Neumann-to-Dirichlet map (non-linear) or its Fréchet derivative (linear). We give a comparison of the non-linear and linear approach in the presence of measurement noise, and show numerically that the two methods give essentially the same reconstruction in the unit disk domain. For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method in the unit disk geometry.     

Boundary element analysis of nanoinhomogeneities of arbitrary shapes with surface and interface effects

In this paper, a boundary element method (BEM) is proposed to analyze the stress field in nanoinhomogeneities with surface/interface effect. To consider this effect, the continuity conditions along the internal interfaces between the matrix and inhomogeneities are modeled by the well-known Gurtin–Murdoch constitutive relation. In the numerical analysis, the interface elastic moduli and the geometry of the nanoscale inhomogeneity are varied to show their influence on the induced stress field. The interaction between nanoscale inhomogeneities and the effect of different geometric shapes of inhomogeneities, including ellipse, triangle, and square are also investigated for different interface material parameters. It is shown that the elastic field can be greatly influenced by the interfacial energy and geometry of nanoscale inhomogeneities. The proposed BEM formulation is very general, including the complete Gurtin–Murdoch model and is further convenient for arbitrary shapes of inhomogeneity.     

Experimental and numerical analysis of short-pulse laser interaction with tissue phantoms containing inhomogeneities

The objective is to perform an experimental and numerical study to analyze short-pulse laser propagation through tissue phantoms without and with inhomogeneities embedded in them. For a short-pulse laser the observed optical signal has a distinct temporal shape, and the shape is a function of the medium properties. The scattered temporal transmitted and reflected optical signals are measured experimentally with a streak camera for tissue phantoms irradiated with a short-pulse laser source. A parametric study involving different scattering and absorption coefficients of tissue phantoms and inhomogeneities, as well as the detector positions and orientations, is performed. The temporal and spatial profiles of the scattered optical signals are compared with the numerical modeling results obtained by solving the transient radiative transport equation by using the discrete ordinates technique.     

An integral equation formulation of anti-plane inhomogeneities

In this paper, a boundary integral equation formulation for anti-plane shear inhomogeneous medium is presented to study the interaction between the inhomogeneities and cracks. The proposed boundary integral equation formulation only contains out-of-plane interface displacements and out-of-plane discontinuous displacements over cracks. Numerical implementation is simple since the present formulation has considered the shear equilibrium condition over the interfaces between the matrix and inhomogeneities. Out-of-plane interface displacements and out-of-plane traction integral equations are collocated respectively on the matrix–inhomogeneity interfaces and on one side of the crack surface. Numerical examples are given to show the validity and numerical accuracy of the present method.     

非均质材料与位错交互能的数值等效夹杂算法

工程结构中的夹杂物和位错会极大地影响材料的力学性能和服役寿命。以往的解析解主要关注特定形状(如圆形、椭圆形)夹杂物与位错之间的相互作用。当采用数值方法计算时,由于位错的奇异性,即使是商用有限元软件也会面临处理上的困难。该文基于数值等效夹杂算法并结合快速傅里叶变换,求解了无穷体内夹杂物与刃型位错的交互能,有效地规避了数值奇异性问题。相对误差的范数分析结果表明,在杂质附近所产生的应力扰动对最终结果具有较大影响。该文计算方法能够更加精确地确定应力扰动场,并显示出优越的数值收敛性和稳定性。在求解任意形状杂质与位错相互作用问题中,该文提供了一种便捷且有效的计算方案。     

On the capability of micromechanics models to capture the auxetic behavior of fibers/particles reinforced composite materials

This work investigates the possibility to predict the auxetic behavior of composites consisting of non-auxetic phases by means of micromechanical models based on Eshelby’s inclusion concept. Two specific microstructures have been considered: (i) the three-layered hollow-cored fibers-reinforced composite and (ii) a microstructure imitating the re-entrant honeycomb micro-architecture. The micromechanical analysis is based on kinematic integral equations as a formal solution of the inhomogeneous material problem. The interaction tensors between the inhomogeneities are computed thanks to the Fourier’s transform. The material anisotropy due to the morphological and topological textures of the inhomogeneities was taken into account thanks to the multi-site approximation of these tensors. In both cases, the numerical results show that auxetic behavior cannot be captured by such models at least in the case of elastic and isotropic phases. This conclusion is supported by corresponding finite element investigations of the second microstructure that indicate that auxetic behavior can be recovered by introducing joints between inclusions. Otherwise, favorable issues are only expected with auxetic components.     

On the capability of micromechanics models to capture the auxetic behavior of fibers/particles reinforced composite materials

This work investigates the possibility to predict the auxetic behavior of composites consisting of non-auxetic phases by means of micromechanical models based on Eshelby’s inclusion concept. Two specific microstructures have been considered: (i) the three-layered hollow-cored fibers-reinforced composite and (ii) a microstructure imitating the re-entrant honeycomb micro-architecture. The micromechanical analysis is based on kinematic integral equations as a formal solution of the inhomogeneous material problem. The interaction tensors between the inhomogeneities are computed thanks to the Fourier’s transform. The material anisotropy due to the morphological and topological textures of the inhomogeneities was taken into account thanks to the multi-site approximation of these tensors. In both cases, the numerical results show that auxetic behavior cannot be captured by such models at least in the case of elastic and isotropic phases. This conclusion is supported by corresponding finite element investigations of the second microstructure that indicate that auxetic behavior can be recovered by introducing joints between inclusions. Otherwise, favorable issues are only expected with auxetic components.     

Light scattering on oceanic turbulence

Turbulent inhomogeneities of fluid flow have the effect of scattering light in near-forward angles, thus providing an opportunity to use optics to quantify turbulence. Here we report measurements of the volume-scattering function in the range of 10(-7) to 10(-3) rad using a wave-front sensing technique. The total scattering coefficient b, due to scattering on turbulent inhomogeneities, is between 1 and 10 m(-1) under typical oceanographic conditions. The numerical calculations of turbulent volume-scattering functions compare well with the laboratory measurement. These results suggest that optical measurements at small angles are affected by turbulence-related scattering, and their effects can be well modeled with numerical calculations.     

Multifrequency near-field acoustic tomography and holography of 3D subbottom inhomogeneities

A method of coherent multifrequency acoustic tomography and holography of spatially localized subbottom inhomogeneities in shallow seas is proposed. This method is based on solving of the near-field inverse scattering problem that makes it possible to realize a subwavelength resolution. It involves the analysis of measurement data obtained by the 2D transversal scanning with the source-receiver system along the sea bottom, over the area of sounded inhomogeneities. The solution begins with the Born approximation, where the original 3D integral equation for the scattered field is reduced to the 1D Fredholm equation of the first kind relative to the depth profile of the lateral spectrum of inhomogeneities. When solving this integral equation for each pair of spectral components, the generalized discrepancy method is in use. Then, corrections to the Born approximation can be obtained in the proposed iterative procedure. For distributed inhomogeneities, the inverse Fourier transform of the retrieved spectrum gives their 3D distribution that can be visualized as tomography images. For solid targets, this spectrum is used to obtain their shape (i.e. to solve the problem of computer holography). Corresponding results of the numerical simulation are presented.     

Thermal energy transfer by plasmon-resonant composite nanoparticles at pulse laser irradiation

Heating of composite plasmon-resonant nanoparticles (spherical gold nanoshells) under pulse laser illumination is considered. The numerical solution of the time-dependent heat conduction equation accounting for spatial inhomogeneities of absorbed laser radiation is performed. Important features of temperature kinetics and thermal flux inside nanoparticles are analyzed. Possible applications of the observed effects in nanotechnology and medicine are discussed.     

Two-dimensional simulation of a high-gain, generalized self-filtering, unstable resonator

The performance of a high-power excimer laser, generalized self-filtering, unstable resonator has been modeled by means of a numerical code. The spectral method and the Rigrod equations are basic to the numerical procedure, which is quite general because it results from an appropriate combination of independent propagation algorithms. The code can be applied to arbitrary resonator geometry and can be used to take account of gain medium inhomogeneities and instability phenomena.     

Capturing strain localization in dense sands with random density

This paper presents a three‐invariant constitutive framework suitable for the numerical analyses of localization instabilities in granular materials exhibiting unstructured random density. A recently proposed elastoplastic model for sands based on critical state plasticity is enhanced with the third stress invariant to capture the difference in the compressive and extensional yield strengths commonly observed in geomaterials undergoing plastic deformation. The new three‐invariant constitutive model, similar to its two‐invariant predecessor, is capable of accounting for meso‐scale inhomogeneities as well as material and geometric nonlinearities. Details regarding the numerical implementation of the model into a fully nonlinear finite element framework are presented and a closed‐form expression for the consistent tangent operator, whose spectral form is used in the strain localization analyses, is derived. An algorithm based on the spectral form of the so‐called acoustic tensor is proposed to search for the necessary conditions for deformation bands to develop. The aforementioned framework is utilized in a series of boundary‐value problems on dense sand specimens whose density fields are modelled as exponentially distributed unstructured random fields to account for the effect of inhomogeneities at the meso‐scale and the intrinsic uncertainty associated with them. Copyright © 2006 John Wiley & Sons, Ltd.     

Determining the geometric parameters of diffuse scattering objects

A spectral-correlation diagnostic method has been used for determining the linear dimensions of inhomogeneities with diffuse scattering surfaces in optical media. Experimental data are in good agreement with the results of numerical simulations and are consistent with theoretical notions. It is shown that the proposed method can be implemented on a simple technical basis and used is practice.     

The Newtonian potential inhomogeneity problem: non-uniform eigenstrains in cylinders of non-elliptical cross section

Understanding the fields that are set up in and around inhomogeneities is of great importance in order to predict the manner in which heterogeneous media behave when subjected to applied loads or other fields, e.g., magnetic, electric, thermal, etc. The classical inhomogeneity problem of an ellipsoid embedded in an unbounded host or matrix medium has long been studied but is perhaps most associated with the name of Eshelby due to his seminal work in 1957, where in the context of the linear elasticity problem, he showed that for imposed far fields that correspond to uniform strains, the strain field induced inside the ellipsoid is also uniform. In Eshelby’s language, this corresponds to requiring a uniform eigenstrain in order to account for the presence of the ellipsoidal inhomogeneity, and the so-called Eshelby tensor arises, which is also uniform for ellipsoids. Since then, the Eshelby tensor has been determined by many authors for inhomogeneities of various shapes, but almost always for the case of uniform eigenstrains. In many application areas in fact, the case of non-uniform eigenstrains is of more physical significance, particularly when the inhomogeneity is non-ellipsoidal. In this article, a method is introduced, which approximates the Eshelby tensor for a variety of shaped inhomogeneities in the case of more complex eigenstrains by employing local polynomial expansions of both the eigenstrain and the resulting Eshelby tensor, in the case of the potential problem in two dimensions.     

MODELING THE INFLUENCE OF INITIAL MATERIAL INHOMOGENEITIES ON THE FATIGUE LIFE OF NOTCHED COMPONENTS

This paper summarizes a fracture mechanics analysis developed to study the effect of initial size and spatial distribution of inherent material inhomogeneities on fatigue life. Calculations were performed for a set of experiments conducted previously to determine the influence of microporosity size and frequency on the fatigue life of notched 7050-T7451 aluminum specimens. The favorable comparison between the numerical and experimental results indicates the analysis method could be used to predict the benefits to fatigue life obtained by reducing the size and distribution of initial inhomogeneities such as those due to microporosity.     

Optimum parametric synthesis of broadband matched junctions

A method of synthesizing of smooth, broadband matched junctions is proposed that is based on numerical integration of a differential equation for the coefficient of wave reflection from inhomogeneities. Optimum profiles of the wave impedance and frequency dependences of the power reflection coefficient are obtained and analyzed. It is shown that the proposed method allows solution of the synthesis problem to be significantly optimized due to minimization of computation time.     

Chromatic Refraction with Global Ozone Monitoring by Occultation of Stars. II. Statistical Properties of Scintillations

The statistical properties of stellar scintillations are discussed with special attention to correcting the atmospheric transmittance data for scintillations in measurements made with the Global Ozone Monitoring by Occultation of Stars (GOMOS) instrument. Both anisotropic and isotropic turbulent inhomogeneities are taken into account. Calculated rms scintillation reaches several percent for altitudes of 30-35 km, an amplitude comparable with the expected absorbing features. Estimates of cross-correlation functions show that the GOMOS correction procedure can be applied efficiently for scintillations caused by anisotropic inhomogeneities, in contrast to the isotropic case. Some recommendations are given for conditions of observations with which to make better corrections of scintillations.