三维电阻抗成像的体积元方法的数值模拟和分析

电阻抗成像是一类椭圆方程反问题,本文在三维区域上对其进行数值模拟和分析.对于椭圆方程Neumann边值正问题,本文提出了四面体单元上的一类对称体积元格式,并证明了格式的半正定性及解的存在性;引入单元形状矩阵的概念,简化了系数矩阵的计算;提出了对电阻率进行拼接逼近的方法来降低反问题求解规模,使之与正问题的求解规模相匹配;导出了误差泛函的Jacobi矩阵的计算公式,利用体积元格式的对称性和特殊的电流基向量,将每次迭代中需要求解的正问题的个数降到最低.一系列数值实验的结果验证了数学模型的可靠性和算法的可行性.本文所提出的这些方法,已成功应用于三维电阻抗成像的实际数值模拟.     

BIOLUMINESCENCE TOMOGRAPHY： BIOMEDICAL BACKGROUND,MATHEMATICAL THEORY,AND NUMERICAL APPROXIMATION

Over the last couple of years molecular imaging has been rapidly developed to study physiological and pathological processes in vivo at the cellular and molecular levels. Among molecular imaging modalities, optical imaging stands out for its unique advantages, especially performance and cost-effectiveness. Bioluminescence tomography （BLT） is an emerging optical imaging mode with promising biomedical advantages. In this survey paper, we explain the biomedical significance of BLT, summarize theoretical results on the analysis and numerical solution of a diffusion based BLT model, and comment on a few extensions for the study of BLT.     

Travel Time Tomography

We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary rigidity problem is whether we can determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points. The lens rigidity problem problem is to determine a Riemannian metric of a Riemannian manifold with boundary by measuring for every point and direction of entrance of a geodesic the point of exit and direction of exit and its length. The linearization of these two problems is tensor tomography. The question is whether one can determine a symmetric two-tensor from its integrals along geodesics. We emphasize recent results on boundary and lens rigidity and in tensor tomography in the partial data case, with further applications.     

Numerical simulation and analysis of generalized difference method on triangular networks for electrical impedance tomography

Electrical impedance tomography is an inverse problem of elliptic differential equations. Numerical methods based on combining generalized difference method and Levenberg–Marquardt iteration on a planar domain are proposed. Positive semi-definiteness and existence of solution of the generalized difference scheme are proved. Element geometry matrix is introduced to shortcut calculation and standardize computer program. A series of numerical experiments verify the reliability of its mathematical model and the feasibility of the algorithm. A class of electrical current patterns is proposed to minimize the number of direct problems to be solved in each iteration. These methods have been applied successfully in practical simulation of electrical impedance tomography.     

Bergman polynomials on an archipelago: Estimates, zeros and shape reconstruction

Growth estimates of complex orthogonal polynomials with respect to the area measure supported by a disjoint union of planar Jordan domains (called, in short, an archipelago) are obtained by a combination of methods of potential theory and rational approximation theory. The study of the asymptotic behavior of the roots of these polynomials reveals a surprisingly rich geometry, which reflects three characteristics: the relative position of an island in the archipelago, the analytic continuation picture of the Schwarz function of every individual boundary and the singular points of the exterior Green function. By way of explicit example, fine asymptotics are obtained for the lemniscate archipelago |z^m−1|<r^m, 0<r<1, which consists of m islands. The asymptotic analysis of the Christoffel functions associated to the same orthogonal polynomials leads to a very accurate reconstruction algorithm of the shape of the archipelago, knowing only finitely many of its power moments. This work naturally complements a 1969 study by H. Widom of Szegő orthogonal polynomials on an archipelago and the more recent asymptotic analysis of Bergman orthogonal polynomials unveiled by the last two authors and their collaborators.     

An investigation of the accelerated thermal degradation of different epoxy resin composites using X-ray microcomputed tomography and optical coherence tomography

Epoxy resin composites reinforced with hollow glass microspheres, microlight microspheres, 3D parabeam glass, and E-Glass individually were subjected to accelerated thermal degradation conditions. X-ray microcomputed tomography (XμCT) was used to evaluate density changes, reinforcement filler damage, homogeneity, cracks and microcracks in the bulk of the different epoxy resin composites. XμCT 3D images, 2D reconstructed images and voids calculations revealed microspheres damage, filler distributions and showed cracks in all composites with different shapes and volume in response to the thermal degradation conditions. In addition, expansion of air bubbles/voids was observed and recorded in the microsphere and microlight epoxy composite samples. In a complementary way, optical coherence tomography (OCT) was used as a novel optical characterisation technique to study structural changes of the surface and near-surface regions of the composites, uncovering signs of surface shrinkage caused by the thermal treatment. Thus, combining XμCT and OCT proved useful in examining epoxy resin composites' structure, filler-resin interface and surface characteristics.     

Synthesis of [carbonyl-C]acetophenone via the Stille cross-coupling reaction of [1-C]acetyl chloride with tributylphenylstannane mediated by Pd2(dba)3/P(MeNCH2CH2)3N·HCl

The Stille cross-coupling reaction of [1-¹¹C]acetyl chloride with tributylphenylstannane leading to [carbonyl-¹¹C]acetophenone was studied with the goal of developing a new ¹¹C-labeling method for positron emission tomography tracer synthesis. The coupled product [carbonyl-¹¹C]acetophenone was synthesized using the Pd₂(dba)₃/P(MeNCH₂CH₂)₃N·HCl system with a 60-61% radiochemical conversion from [1-¹¹C]acetyl chloride (decay-corrected, n = 3).     

CONTROLLING THE 3D NANOSCALE ORGANIZATION OF BULK HETEROJUNCTION POLYMER SOLAR CELLS

In this study,the three dimensional nanoscale organization in the photoactive layers of poly(3-hexylthiophene) (P3HT) and a methanofullerene derivative (PCBM) is revealed by transmission electron tomography.After annealing treatment,either at elevated temperature or during slow solvent evaporation,nanoscale interpenetrating networks are formed with high crystalline order and favorable concentration gradients of both components through the thickness of the photoactive layer.Such a tailored morphology acco...     

氮化硅陶瓷烧结微结构演化的同步辐射CT实时研究

利用同步辐射CT (SR-CT)技术, 在氮化硅陶瓷样品烧结过程中对其进行实时投影成像, 并应用滤波反投影算法和数字图像处理技术, 得到了样品在整个烧结过程中内部微结构演化的二维和三维重建图像, 实现了对陶瓷固相烧结过程实时、无损的观测. 通过重建图像清晰观测到了陶瓷样品在烧结三个阶段中颗粒接触、烧结颈形成、晶粒和气孔长大、气孔球化并收缩等烧结现象; 统计了样品在不同烧结时刻的孔隙率, 得到了孔隙率随烧结时间对数的变化曲线, 并根据曲线分析了样品在不同烧结时刻致密化速率的变化, 得到了烧结中期孔隙率和时间对数的线性关系. 实验的结果和现有烧结理论相吻合, 并为进一步完善烧结理论提供了有效的实验数据.     

Revealing the Distribution of the Atoms within Individual Bimetallic Catalyst Nanoparticles

To be able to correlate the catalytic properties of nanoparticles with their structure, detailed knowledge about their make‐up on the atomic level is required. Herein, we demonstrate how atom‐probe tomography (APT) can be used to quantitatively determine the three‐dimensional distribution of atoms within a Au@Ag nanoparticle with near‐atomic resolution. We reveal that the elements are not evenly distributed across the surface and that this distribution is related to the surface morphology and residues from the particle synthesis.