Discontinuous Galerkin method for the forward modelling in optical diffusion tomography

We propose a discontinuous Galerkin discretization scheme for the forward modelling in optical diffusion tomography in highly scattering media to facilitate dynamic mesh adaptation for complex domains. In addition, the numerical method is also shown to effectively deal with inhomogeneities in optical properties and refractive index mismatch at material interfaces. The accuracy of the method is demonstrated over a model concentric spherical layers problem where the discontinuous Galerkin method is compared against an analytical solution. Copyright © 2010 John Wiley & Sons, Ltd.     

3D elastodynamic fields of non-uniformly coated obstacles: Notion of eigenstress and eigenbody-force fields

Based on wave-function expansion, the time harmonic wave scattered by a circular and spherical inhomogeneity has been studied by numerous investigators. This method has also been employed to axisymmetrically coated circular and spherical inhomogeneities by some authors. When the geometry of the obstacle is not axisymmetric, the wave-function expansion is no longer applicable. In this paper, it is proposed to employ the dynamic equivalent inclusion method (DEIM) which is more general than the methods presented in the literature. It will be seen that DEIM may be used to treat a wide range of situations in a unified manner and is not bound to certain symmetries. The DEIM was first proposed by Fu and Mura [Fu, L.S., Mura, T., 1983. The determination of elastodynamic fields of an ellipsoidal inhomogeneity. ASME J. Appl. Mech. 50, 390–396], and no further developments have been done on it ever since. Its original formulation has some shortcomings with regard to the concept of homogenizing eigenstrains, and for usage of polynomial eigenstrains. Moreover, it is limited to single ellipsoidal inhomogeneity without coating. The new viewpoints of homogenizing eigenstress and eigenbody-force fields which are compatible with the physics of the problem are given. Expressing the eigenstress, eigenbody-force fields and the Green’s function associated with the governing Helmholtz equation in terms of the spherical wave-functions is the natural choice and is very effective. Another important task is the development of the three dimensional DEIM for inhomogeneities having homogeneous or functionally graded (FG) coating with variable thickness, which eliminates any possible symmetries.     

Equivalent inclusion approach and effective medium approximations for the effective conductivity of isotropic multicomponent materials

Most effective medium approximations for isotropic inhomogeneous materials are based on dilute solutions of some typical inclusions in an infinite matrix medium, while the simplest approximations are those for the composites with spherical and circular inclusions. Practical particulate composites often involve inhomogeneities of more complicated geometry than that of the spherical (or circular) one. In our approach, those inhomogeneities are supposed to be substituted by simple equivalent spherical (circular) inclusions from a comparison of their respective dilute solution results. Then the available simple approximations for the equivalent spherical (circular) inclusion material can be used to estimate the effective conductivity of the original composite. Numerical illustrations of the approach are performed on some 2D and 3D geometries involving elliptical and ellipsoidal inclusions.     

Sinusoidal pumping of groundwater near cylindrical inhomogeneities

A new analytic-element solution is presented for a well with a sinusoidal discharge pumping near cylindrical inhomogeneities. Both the transmissivity and the storage coefficient may be different inside each cylinder. The solution consists of separate series solutions inside and outside each cylinder; asymptotic expansions are presented for cases where the sinusoidal period is small and the radius and transmissivity of the cylinder are large. The complex coefficients in the series solutions are determined by requiring continuity of head and normal flow across the boundary of each cylinder resulting in a linear system of complex equations that may be solved with standard methods. The solution represents one of the few analytic solutions for two-dimensional transient groundwater flow in an aquifer with inhomogeneities. Computer implementation requires truncation of the series; machine accuracy may be reached when enough terms are used in the series solutions. The effect of cylindrical inhomogeneities on the amplitude and phase of the head are investigated. The complex behavior suggests it may be difficult to determine location and properties of cylindrical inhomogeneities from pump tests, which confirms reported difficulties of interpreting pump test results from heterogeneous aquifers.     

Propagation of diffuse light in a turbid medium with multiple spherical inhomogeneities

We develop a fast and accurate solver for the forward problem of diffusion tomography in the case of several spherical inhomogeneities. The approach allows one to take into account multiple scattering of diffuse waves between different inhomogeneities. Theoretical results are illustrated with numerical examples; excellent numerical convergence and efficiency are demonstrated. The method is generalized for the case of additional planar diffuse-nondiffuse interfaces and is therefore applicable to the half-space and slab imaging geometries.     

Microscopic Charge Inhomogeneities in Underdoped La2?xSrxCuO4: Local Structural Evidence

We present local structural evidence for the existence of charge inhomogeneities at low temperature in underdoped and optimally doped La_2–x Sr _x CuO₄. The inhomogeneities disappear for x 0.2. The evidence for the charge inhomogeneities comes from an anomalous increase in the inplane Cu–O bond length distribution in the underdoped samples as well as evidence for CuO₆ octahedral tilt inhomogeneities in the intermediate range structure. Preliminary analysis of the temperature dependence of this phenomenon indicates that the inhomogeneities set in at temperatures in the range 60 K < T _co < 130 K, which depends on doping.     

Special features of electromagnetic energy accumulation at regular surface inhomogeneities on a dielectric sphere

Evaporation of a water drop with ~1-mm diameter under the action of laser radiation with 10.6-μm wavelength and power-flux density within (4–12) × 10⁵ W/m² is shown to be determined by the optical properties of regular inhomogeneities occurring on the spherical surface of the liquid.     

The scattering of electro-elastic waves by a spherical piezoelectric particle in a polymer matrix

This paper is devoted to the study of scattering of plane harmonic waves by a piezoelectric sphere with spherical isotropy embedded in an unbounded isotropic polymer matrix. The scattered displacement field and the electric potential in the matrix are expressed in terms of spherical vector wave functions and spherical harmonic functions, respectively. For the field points inside the inhomogeneity, new displacement functions are introduced. Expansion of the new displacement functions and the electric potential in terms of spherical harmonic functions, the equations of motion and electrostatic lead to four second order ordinary differential equations (odes), where three of them are coupled. The coupled system of odes is solved by the generalized Frobenius series. This approach is readily used to handle low and high frequencies. Three different types of piezoelectric inhomogeneities, PZT-4, PZT-5H, and BaTiO₃ are considered and the associated piezoelectric effects on the electro-mechanical fields, differential and total scattering cross-sections are addressed.     

Schwedler网壳结构强震作用下的动力强度破坏研究

对Schwedler单层球面网壳结构进行了强震作用下的动力全过程分析,研究了结构的失效机理。对40m跨的Schwedler理想网壳结构和考虑初始缺陷的网壳结构进行了全过程动力时程分析,考查了此类型网壳结构的动力性能和破坏形式,采用一致缺陷模态法处理初始缺陷,分析了初始缺陷对Schwedler网壳结构动力性能的影响;对具有初始缺陷的网壳结构进行了参数影响分析,分别考查了地震作用、杆件截面和屋面荷载三种因素对结构动力性能的影响;将研究结果与其它球面网壳结构进行了比较,验证了文献[6]提出的理论框架的合理性和实用性。     

Inverse acoustic scattering by solid obstacles: topological sensitivity and its preliminary application

A to pological sensitivity approach is developed for the imaging of penetrable solid obstacles embedded in a fluid background medium by way of inverse acoustic scattering. To this end, an asymptotic form for the scattered field caused by a nucleating spherical solid obstacle in the reference fluid medium is derived within the boundary integral equation framework, where the required limiting behaviour of the acceleration field inside the perturbation is established based on solutions of two simplified fluid–solid interaction problems. With this result, the equivalence of acoustic scattering by fluid and solid scatterers in terms of asymptotic behaviour is observed and numerically validated. The direct and adjoint-field topological sensitivity expressions for transient and time-harmonic excitations are obtained accordingly. The utility of the proposed method as a tool for preliminary obstacle reconstruction and bulk modulus characterization is illustrated through numerical examples and an exploratory experimental study. On the basis of adjusted topological sensitivity formulas for fluid reference domains containing pre-existing solid inhomogeneities, an iterative 3D obstacle reconstruction approach is established and its performance with synthetic data is demonstrated.     

The problem of thermal conduction for two ellipsoidal inhomogeneities in an anisotropic medium and its relevance to composite materials

Summary We consider the problem of thermal conduction for an unbounded medium containing two ellipsoidal inhomogeneities subjected to a remote homogeneous boundary condition of temperature. The constituents are anisotropic and the ellipsoids could be at arbitrary orientations. In the formulation we first introduce some appropriate transformations into the heterogeneous medium and transform the problem into an isotropic matrix consisting of two analogous ellipsoidal inhomogeneities. Next, we replace the effect of inhomogeneities by some polynomial types of equivalent eigen-intensities by the concept of equivalent inclusion. These procedures allow us to write the local fields in terms of harmonic potentials and their derivatives. Numerical results show that linear approximations of eigen-fields yield accurate results in comparison with existing solutions by Honein et al. [2] for moderately separated inhomogeneities. Solutions of this type are used to estimate the overall thermal conductivity of composites with periodic microstructure. Finally, we present results for composites consisting of spherical inclusions with body-centered cubic, face-centered cubic, body-centered orthorhombic, and face-centered orthorhombic arrays.     

Search for Signature of Charge Inhomogeneities in the Phonons of YBa2Cu3O7−x

Copper-oxygen bond-stretching phonons as well as copper-oxygen bond bending phonons were studied in YBa₂Cu₃O_7–x by single-crystal inelastic neutron scattering with the hope to find signatures of dynamic charge inhomogeneities. Marked anomalies were observed in branches associated with copper- in plane oxygen bond-stretching vibrations, whereas the bond-bending modes were found to show normal behavior. The anomalies are more pronounced in optimally YBa₂Cu₃O_6.93 than in underdoped YBa₂Cu₃O_6.6. The displacement pattern of the most anomalous phonons is consistent with dynamic charge stripe formation. However, temperature effects on raising the temperature above T _c or even further up to room temperature were found to be small. Moreover, an interpretation of the data as evidence of a dynamic stripe phase cannot be reconciled with the magnetic fluctuations reported in the literature.     

Microstructure of Ion-Selective Plasticized PVC Membranes Studied by Small-Angle Neutron Scattering

The microstructure of plasticized PVC membranes in the dry state and during the process of soaking in heavy water has been studied by small-angle neutron scattering. In the dry membrane, inhomogeneities were found. The membrane structure is well described by a polydisperse hard-sphere model. The mean diameter of the dispersed spherical inhomogeneities is ～6 nm, which is smaller than the estimated dimension of a single statistically curled PVC polymer chain in the membrane. The values of the best-fit parameters and their change with membrane composition suggest that the particles consist of unplasticized PVC, probably in the crystalline state. The type of plasticizer, the plasticizer content, and the addition of a lipophilic salt were found to influence the water uptake significantly. Water uptake did not change the microstructure due to the original (i.e., dry state) inhomogeneities in the membranes.     

Some features of stress and strain distribution in solids with inhomogeneities under dynamic loading

Results are presented for experimental studies of the effect of material inhomogeneity and curvature of the wave front connected with it on the development of strain and stress localization, and the effect of accumulation in an elastoplastic body with dynamic loading. It is established that propagation of elastoplastic and shock waves in a material with macro- and microinhomogeneity is accompanied by redistribution of stresses and strains, and their amplitude and the distance between them depend not only on the distribution of inhomogeneities, but also on load intensity and on distance from these inhomogeneities.Translated from Problemy Prochnosti, No. 7, pp. 64–67, July, 1991.     

基于六步法的球形台灯减量化包装设计

目的以易碎品球形台灯为包装对象,基于六步法对其进行创新包装设计,为减量化包装提供参考案例。方法确定物流环境条件,为后续验证试验提供评价依据;分析被包装对象的特性和脆值,为包装设计提供依据;进行减量化包装结构设计;对包装设计进行优化;通过验证试验确保方案的可靠性。结果自由跌落试验的角跌落峰值加速度为94.3g,显著小于产品脆值(110.5g);试验验证产品无损伤,功能正常,包装具有良好缓冲性能。定频振动试验后验证产品功能正常,包装具有良好的防振性能。结论基于六步法设计的球形台灯减量化包装具有足够的安全性、可观的经济性和良好的消费者体验。     

Features of laser diagnostics of laminar spherical and annular inhomogeneities

The direct problem of refraction by a laser plane in a medium with nonmonotone radial profile of the index of refraction is solved. The possibility of solving the inverse problem on the basis of the Abel integral is analyzed. A computer simulation of the direct problem for models of hot and cold layers in a liquid in the presence, or absence, of an inhomogeneity core, is conducted. A technique for diagnosis of transparent spherical and cylindrical inhomogeneities based on a combined laser-computer refraction method is proposed. __________ Translated from Izmeritel’naya Tekhnika, No. 1, pp. 34–37, January, 2007.     

Localization of Ultra-Cold Particles over Rough Substrates

Localization and diffusion parameters are calculated for particles adsorbed over inhomogeneous substrates for discrete and quasicontinuous spectra of the adsorbed states. The results are expressed via the angular harmonics of the correlation function of surface roughness. The problem is solved analytically in the limiting cases of longwave particles and large correlation radii of surface inhomogeneities. Elsewhere, the problem is solved numerically for Gaussian correlation of inhomogeneities. Applications to electrons on helium films, mobile adsorbed hydrogen atoms and molecules, ultra-cold neutrons in gravitational or magnetic field, etc., are discussed.     

Ballistic Particles in Helium Systems

Ballistic motion of (quasi-)particles in helium systems with quantized and quasi-continuous spectrum is discussed under conditions when the mean free path is restricted by scattering on random surface inhomogeneities. The transport equation is derived for particles with arbitrary form of energy spectrum and without model assumptions on the structure of surface scattering operator. The results can be applied to quasiparticles in liquid helium systems with quadratic and linear spectra, spectrum with a gap, etc. The transport equation is relatively simple except for the case when the distance between quantized energy levels is comparable to the surface collision frequency. In three limiting cases the diffusion coefficient is calculated analytically for arbitrary correlations of surface inhomogeneities, and elsewhere - numerically for Gaussian correlations. The interwall correlation of surface inhomogeneities affects particle diffusion in a non-trivial way; sometimes, the effect of interwall correlations persists even in the quasiclassical limit.     

Percolation, Fractal Behavior, and High-Tc Superconductivity

Hole suppliers like Sr in doped La₂CuO₄ are mainly randomly distributed. Assuming that the holes are dislocated over a few lattice constants away from the Sr atom, the conducting areas form randomly distributed circles in the CuO₂ layer planes. Conductivity and also superconductivity can occur only when these circles touch each other and form percolation clusters. Mobile holes are accompanied by diffusing d-electrons. Their spin direction is no longer localized on distinct places, and antiferromagnetism breaks down. The phase diagram of high-T _c superconductors is discussed on the basis of a modified continuum percolation model for which the centers of each circle are located on lattice points. The inhomogeneities due to the random hole distributions lead to broad peaks instead of sharp singularities in the static and dynamic response functions.