A Note on Parallel Preconditioning for the All-at-Once Solution of Riesz Fractional Diffusion Equations

The $p$-step backward difference formula (BDF) for solving systems of ODEs can be formulated as all-at-once linear systems that are solved by parallel-in-time preconditioned Krylov subspace solvers (see McDonald et al. [36] and Lin and Ng [32]). However, when the BDF$p$ (2 ≤ $p$ ≤ 6) method is used to solve time-dependent PDEs, the generalization of these studies is not straightforward as $p$-step BDF is not selfstarting for $p$ ≥ 2. In this note, we focus on the 2-step BDF which is often superior to the trapezoidal rule for solving the Riesz fractional diffusion equations, and show that it results into an all-at-once discretized system that is a low-rank perturbation of a block triangular Toeplitz system. We first give an estimation of the condition number of the all-at-once systems and then, capitalizing on previous work, we propose two block circulant (BC) preconditioners. Both the invertibility of these two BC preconditioners and the eigenvalue distributions of preconditioned matrices are discussed in details. An efficient implementation of these BC preconditioners is also presented, including the fast computation of dense structured Jacobi matrices. Finally, numerical experiments involving both the one- and two-dimensional Riesz fractional diffusion equations are reported to support our theoretical findings.     

A molecular dynamics simulation of nanoscale convective heat transfer with the effect of axial heat conduction

Effective heat dissipation from nano-fluidic devices is sometimes necessary to ensure their performance and lifespan. In the molecular dynamics simulation of nanoscale convective heat transfer, thermostats cannot be directly applied to the fluid because of the non-uniform temperature distribution. Periodic boundary is typically utilised, but unrealistic axial heat conduction exists when there is a temperature difference between the outlet and images of inlet atoms. In this paper, the effect of axial conduction caused by periodic boundary is investigated through the Péclet number (Pe). Taking viscous dissipation into consideration, the magnitude of outlet thermal diffusion is observed to decrease with increasing Pe. The local average temperature of fluid changes in an exponential form except in the region close to the outlet. Results show that the contribution of outlet axial conduction to the local average temperature is less than 2.0% when Pe > 10. The main reason is that the magnitude of fluid velocity and viscous heat dissipation in nanochannels is much larger than that in macro-channels at the same Péclet number.     

A bubble detection technique based on light intensity and Mie scattering theory for spinning solution

A novel bubble detection technique based on light intensity and Mie scattering theory for spinning solution is presented theoretically and experimentally. With the light intensity in every direction, the particle or bubble size distribution can be calculated with the Mie scattering theory. The light intensity distribution in every direction, corresponding to the light intensity received by every assumed annulus of the detector has been calculated theoretically. According to the light intensity distribution, the size distribution of bubbles can be deduced. A series of standardized polystyrene micro-sphere (with 7 μm diameter) solution has been used not only as sample for experiments and calibration, but also as the bubbles in the glycerin. Theoretical and experimental results show that the technique can be used for bubble detection, in order to improve the traditional bubble detection scheme, and to lower production costs.     

Performance characteristics of single photon pulse ranging system using Monte Carlo simulation

Single photon pulse ranging system with extremely high sensitivity has been widely used in distance measurement and 3D imaging. To analyze the factors that affect the measurement precision and accuracy will help to improve system performance. According to system structure and principle, we mainly discussed the following factors: laser intensity, pulse width, detection efficiency and time jitter. A simulation model based on Monte Carlo stochastic method was constructed in this paper, and we get the specific influence of factors on measurement precision and accuracy by simulation. Finally, we set up laboratory experiment system and took effective experiments on ranging precision and accuracy.     

Soft X‐ray absorption spectroscopy and resonant inelastic X‐ray scattering spectroscopy below 100 eV: probing first‐row transition‐metal M‐edges in chemical complexes

X‐ray absorption and scattering spectroscopies involving the 3d transition‐metal K‐ and L‐edges have a long history in studying inorganic and bioinorganic molecules. However, there have been very few studies using the M‐edges, which are below 100 eV. Synchrotron‐based X‐ray sources can have higher energy resolution at M‐edges. M‐edge X‐ray absorption spectroscopy (XAS) and resonant inelastic X‐ray scattering (RIXS) could therefore provide complementary information to K‐ and L‐edge spectroscopies. In this study, M_2,3‐edge XAS on several Co, Ni and Cu complexes are measured and their spectral information, such as chemical shifts and covalency effects, are analyzed and discussed. In addition, M_2,3‐edge RIXS on NiO, NiF₂ and two other covalent complexes have been performed and different d–d transition patterns have been observed. Although still preliminary, this work on 3d metal complexes demonstrates the potential to use M‐edge XAS and RIXS on more complicated 3d metal complexes in the future. The potential for using high‐sensitivity and high‐resolution superconducting tunnel junction X‐ray detectors below 100 eV is also illustrated and discussed.     

Two-photon-excited photoluminescence and heating of gold nanorods through absorption of supercontinuum light

Most of lasers used for imaging and heating gold nanorods are single-wavelength lasers and their efficiency to interact with different gold nanorods is limited. In this study, we demonstrated that supercontinuum light could be a fast, effective and energy efficient excitation source for heating of gold nanorods. The photothermal effect and the heating speed of gold nanorods illuminated by a supercontinuum light and femtosecond pulses through two-photon excitation are experimentally studied through using transmission electron microscopy images and photoluminescence images of gold nanorods. It is found that the supercontinuum light improves the heating speed by 39 %, and melts 30 % more of gold nanorods compared with the femtosecond pulse excitation approach. The heating speed of gold nanorods by supercontinuum light depends not only on its polarization states, but also on the pulse width and numerical aperture of its focused beam. It has been found that the supercontinuum is more efficient in heating of gold nanorods, making it potentially valuable for clinical applications.     

Synthesis and Characterization of Pressure and Temperature Dual‐Responsive Polystyrene Microbeads

A facile approach to the synthesis of pressure and temperature dual‐responsive polystyrene (PS) microbeads with controlled sizes via dispersion polymerization is described. Three different luminophors are selected and directly introduced into the reaction system and thus incorporated into the resultant PS microbeads during polymerization. By manipulating the reaction conditions, including concentrations of the initiator and monomer, polarity of the reaction medium, and injection rate for the monomer, uniform PS microbeads with sizes ranging from 1 to 5 μm are obtained. When a light source centered at 365 nm is used to excite all the luminophors in the PS beads, three distinct and resolvable emission peaks corresponding well with the luminophors are observed. By taking advantage of their sensitive responses to both pressure and temperature, the PS beads can be utilized for quantitative measurements of these two stimulations simultaneously. The PS beads loaded with multiple luminophors have the ability to serve as building blocks for the fabrication of novel sensing and imaging devices and therefore provide a promising strategy for the study of aerodynamics.     

大气湍流三维波前探测模式层析算法分析

大气湍流三维波前探测是实现多层共轭自适应光学技术的关键和前提. 对湍流三维波前探测中最常用的模式法层析技术进行理论研究与分析, 提出该算法存在原理性限制, 并基于此对模式法层析技术产生误差的原因展开分析, 最后针对不同类型的模式层析重构误差给出数值仿真实验结果.分析表明, 模式层析重构中使用了Zernike分解基的一部分作为新的分解基进行波面拟合, 从而引入模式混淆和模式耦合两个方面的误差; 部分Zernike分解基不相关是避免模式混淆误差的必要条件, 模式耦合误差则无法避免. 最后结合仿真结果提出大视场探测、小区域重构的方法, 很好地抑制了模式耦合误差. 关键词： 三维波前探测 大气层析 模式法 误差分析     

初态对光波导阵列中连续量子行走影响的研究

本文使用近邻耦合模型得到的解析解,分析了周期性波导中输入态对量子行走的粒子数的概率分布函数 和二阶相干性的影响.结果表明:输入态的对称性质对量子行走过程的二阶相干度有影响, 而对粒子数的概率分布函数影响不大. 关键词： 周期性光波导阵列 量子行走 二阶相干度 纠缠态     

一种直接用示波器观测单变量非线性系统状态的新方法

为解决用示波器观测单变量非线性系统难的问题, 本文提出了一种45°线法, 该方法能将随时间变化的连续信号以特殊的方式转换成直角坐标上45°线上的点图, 并可用通用双踪示波器 (模拟或数字均可)直接显示出来, 从而达到直接方便地观测和分析单变量被测系统运行时的各种状态, 如周期稳定态, 局部和全局不稳定态. 文中详细阐述了该方法的机理. 同时, 研究和解决了设计实现该方法物理电路的关键问题, 即从连续变化的信号中提取出能反映系统状态的有用信号. 由于蔡氏电路是典型的非线性系统, 且能随参数的变化产生各种丰富的状态, 本文选用该电路作为被测系统进行了大量的物理实验, 实验结果证实了该方法的有效性和实用性. 关键词： 45°线法 单变量系统 系统状态 双踪示波器