Non-equilibrium external flows including wall-catalysis effects by adaptive upwind finite elements

Conclusion Quasi second-order upwind finite-volume approximations have been extended to construct implicit algorithms for the computation of hypersonic non-equilibrium inviscid or viscous flows over adapted unstructured grids.The Navier-Stokes computations have shown great sensitivity to the modelling of the transport terms and to the degree of wall catalysis. Thus an accurate prediction of the wall heat flux would require taking into account a more appropriate model of the gas-surface interaction.Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 53–62, April, 1993.     

Numerical simulation of laminar flames at low Mach number by adaptive finite elements

We present an adaptive finite-element method for the simulation of reactive flows in general domains including reliable error control for quantities of physical interest. On the basis of computable a posteriori error bounds the mesh is locally adjusted by a hierarchical feedback process yielding economical mesh-size distributions for a prescribed maximum number of cells. The key feature is the computational evaluation of the sensitivity of the error with respect to the local residuals by solving an associated global dual problem. This general approach is applied for computing three examples of flames in two dimensions with an increasing degree of complexity, namely a simple diffusion flame described by the flame-sheet model, an ozone decomposition flame and a methane flame in a complex burner geometry using a detailed reaction mechanism.     

利用荧光CT实现生物医学样品内元素分布的无损成像

荧光CT是一种可无损重建元素空间分布的发射型断层成像技术,对生物医学研究具有重要意义.同步辐射的高通量、高准直和能量可调等特性使荧光CT的生物医学应用成为可能.文章通过优化设计,在上海同步辐射光源建立了一套用于生物医学样品微量元素分析的荧光CT成像系统.通过对实验装置的优化,提高了系统的数据采集速度和空间分辨率.将极大...     

Performance evaluation of adaptive meshing algorithms for fluorescence diffuse optical tomography using experimental data

Fluorescence diffuse optical tomography (FDOT) is a computationally demanding imaging problem. The discretizations of FDOT forward and inverse problems pose a trade-off between the accuracy and the computational efficiency of the image reconstruction. To address this trade-off, we analyzed the effect of discretization on the accuracy of FDOT imaging and proposed novel adaptive meshing algorithms for FDOT in a series of studies. In this Letter, we apply these new adaptive meshing algorithms to FDOT imaging using real data from a phantom experiment to demonstrate the practical advantages of our algorithms in FDOT image reconstruction.     

BECOOL: Ballooning eigensolver with COOL finite elements

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ballooning Eigensolver using COOL finite elements) with second order Legendre polynomials recovers precisely the eigenvalues computed by the VVBAL shooting code. Timing runs reveal the need to determine an optimal lower order case. Eigenvalue convergence runs show that cubic Legendre polynomials construct the optimal ballooning mode equation for intensive computations.     

Full-wavelet approach for fluorescence diffuse optical tomography with structured illumination

We present a fast reconstruction method for fluorescence optical tomography with structured illumination. Our approach is based on the exploitation of the wavelet transform of the measurements acquired after wavelet-patterned illuminations. This method, validated on experimental data, enables us to significantly reduce the acquisition and computation times with respect to the classical scanning approach. Therefore, it could be particularly suited for in vivo applications.     

A three-dimensional finite elements approach for the coupled radiative transfer equation and diffusion approximation modeling in fluorescence imaging

During the last few years a quite large number of fluorescence molecular imaging applications have been reported in the literature, as one of the most challenging aspects in medical imaging is to “see” a tumor embedded into tissue, which is a turbid medium, by using fluorescent probes for tumor labeling. However, the forward solvers, required for the successful convergence of the inverse problem, are still lacking accuracy and time feasibility. Moreover, initialization of these solvers may be proven even more difficult than solving the inverse problem itself. This paper describes in depth a coupled radiative transfer equation and diffusion approximation model for solving the forward problem in fluorescence imaging. The theoretical confrontation of these solvers comprises the model deployment, its Galerkin finite elements approximation and the domain discretization scheme. Finally, a new optical properties mapping algorithm, based on super-ellipsoid models, is implemented, providing a fully automated simulation target construction within feasible time.     

自由枝晶生长相场模型的自适应有限元法模拟

采用自适应有限元方法求解了相场模型的控制方程,利用自适应有限元法在求解效率和精度上的优势,模拟了计算域较大,界面层厚度较薄的情况下镍过冷熔体中单个完整等轴晶的演化过程,使相场模型模拟结果更接近于真实物理模型,并探讨了二次枝晶臂的演化机理.模拟结果表明,二次枝晶臂的演化主要由热扩散控制,并受随机扰动影响,在四个象限内呈现出不对称生长.同时,受枝晶臂生长时排出的潜热积聚作用,同一侧的枝晶臂对新的二次枝晶臂的产生有促进作用.此外,二次枝晶臂出现合并、缩颈熔断、轴向熔化和径向熔化等四种粗化方式. 关键词： 自由枝晶生长 相场 自适应有限元法     

Stochastic resonance in finite arrays of bistable elements with local coupling

In this article, we investigate the stochastic resonance (SR) effect in a finite array of noisy bistable systems with nearest-neighbor coupling driven by a weak time-periodic driving force. The array is characterized by a collective variable. By means of numerical simulations, the signal-to-noise ratio (SNR) and the gain are estimated as functions of the noise and the interaction coupling strength. A strong enhancement of the SR phenomenon for this collective variable in comparison with SR in single unit bistable systems is observed. Gains larger than unity are obtained for some parameter values and multi-frequency driving forces, indicating that the system is operating in a non-linear regime albeit the smallness of the driving amplitude. The large SNR values observed are basically due to the fact that the output fluctuations are small and short lived, in comparison with their typical values in a linear regime. A non-monotonic behavior of the SNR with the coupling strength is also obtained.     

分层校正自适应光学系统相位层析技术

假定大气湍流集中在两薄层内，借助分层大气相关长度与整个大气层相关长度的关系，给出待求相位分布与测量结果相关的超定方程组，进而构造残差方程组，并按最小二乘法原理导出正则方程组，通过求解这组正则方程，首次得到原超定方程组的最小二乘解。     

Full-field time-resolved fluorescence tomography of small animals

In this experimental investigation, we explore the feasibility of using wide-field illumination for time-resolved fluorescence molecular tomography. The performance of wide-field patterns with a time-resolved imaging platform is investigated in vitro and in a small animal model. A Monte Carlo-based forward model is employed to reconstruct fluorescence yield based on time-gated datasets. An improvement in resolution and quantification when using the time-gate data type compared to the commonly used cw data type is demonstrated in vitro. Furthermore, the feasibility of wide-field strategies for fluorescence preclinical applications is established by an accurate localization of a fluorescent inclusion implanted in the chest cavity of a murine model.     

Linear scheme for time-domain fluorescence molecular tomography

Based on the generalized pulse spectrum technique that was previously developed for time-domain diffuse optical tomography, we propose a linear framework of time-domain fluorescence molecular tomography for simultaneous reconstruction of both the yield and lifetime of multi-fluorophores. The methodology is exemplified for mono-component case and validated with simulated data.     

A splitting extrapolation for solving nonlinear elliptic equations with d-quadratic finite elements

Nonlinear elliptic partial differential equations are important to many large scale engineering and science problems. For this kind of equations, this article discusses a splitting extrapolation which possesses a high order of accuracy, a high degree of parallelism, less computational complexity and more flexibility than Richardson extrapolation. According to the problems, some domain decompositions are constructed and some independent mesh parameters are designed. Multi-parameter asymptotic expansions are proved for the errors of approximations. Based on the expansions, splitting extrapolation formulas are developed to compute approximations with high order of accuracy on a globally fine grid. Because these formulas only require us to solve a set of smaller discrete subproblems on different coarser grids in parallel instead of on the globally fine grid, a large scale multidimensional problem is turned into a set of smaller discrete subproblems. Additionally, this method is efficient for solving interface problems.     

Spectral finite elements for vibrating rods and beams with random field properties

The classical stochastic Helmholtz equation grasps, through the random field of the refraction index, the spatial variability in the mass density but not the variability in elastic moduli or geometric parameters. In contradistinction to this restriction, the present analysis accounts for the spatial randomness of mass density as well as those of elastic properties and cross-sectional geometric properties of rods undergoing longitudinal vibrations and of Timoshenko beams in flexural vibrations. All the material variabilities are described here by random Fourier series with a typical (average) characteristic size of inhomogeneity d, which is either smaller, comparable to, or larger than the wavelength. The third length scale entering the problem, but kept constant, is the rod or beam length. We investigate the relative effects of random noises in all the material parameters on the spectral stiffness matrices associated with rods and beams for a very wide range of frequencies.     

Quantum state and process tomography via adaptive measurements

We investigate quantum state tomography(QST) for pure states and quantum process tomography(QPT) for unitary channels via adaptive measurements. For a quantum system with a d-dimensional Hilbert space, we first propose an adaptive protocol where only 2d. 1 measurement outcomes are used to accomplish the QST for all pure states. This idea is then extended to study QPT for unitary channels, where an adaptive unitary process tomography(AUPT) protocol of d2+d.1measurement outcomes is constructed for any unitary channel. We experimentally implement the AUPT protocol in a 2-qubit nuclear magnetic resonance system. We examine the performance of the AUPT protocol when applied to Hadamard gate, T gate(/8 phase gate), and controlled-NOT gate,respectively, as these gates form the universal gate set for quantum information processing purpose. As a comparison, standard QPT is also implemented for each gate. Our experimental results show that the AUPT protocol that reconstructing unitary channels via adaptive measurements significantly reduce the number of experiments required by standard QPT without considerable loss of fidelity.     

Precision measurement ofK-shell fluorescence yields in actinide elements

High-precision measurements ofK Auger electron andK x-ray intensities have been made for several transuranium elements and these have been used to determineK-shell fluorescence yields (ω _K ). The electron spectra were measured with a cooled Si(Li) spectrometer and the photon spectra were taken with Ge(Li) diodes. Very thin mass-separated samples of nuclides, which decay predominantly by electron capture, were used in the present experiments. From our present measurements the following values ofK- shell fluorescence yield have been obtained: Np, 97.2±0.3%; Pu, 97.2±0.4%; Cm, 97.1 ±0.6%; Bk, 97.1±0.4%; Cf, 97.3±0.4%; and Es, 97.2±0.5%. These numbers indicate that theK-fluorescence yield for elements in theZ=93 toZ=99 region remains constant within the experimental error. The weighted average of these numbers is 97.19% with external error of 0.03% and internal error of 0.17%. This value is in excellent agreement with known theoretical calculations.     

Mutual coupling of elements in finite microstrip antennas

The mutual coupling of the radiating elements in microstrip antennas is studied using a rigorous electrodynamic approach in which the field singularities at the radiator edges are taken into account with analytic accuracy. A spectral method is employed in combination with a method of semi-inversion by extraction of the Green-function singularity. The degree of interaction of the elements of microstrip structures at the fundamental and higher current harmonicsis determined, and the applicability of various approximations is assessed.Radio-Astronomy Institute, Academy of Sciences of Ukraine. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 8, pp. 688–701, August, 1992.