Linearized tensor renormalization group algorithm for the calculation of thermodynamic properties of quantum lattice models

A linearized tensor renormalization group algorithm is developed to calculate the thermodynamic properties of low-dimensional quantum lattice models. This new approach employs the infinite time-evolving block decimation technique, and allows for treating directly the transfer-matrix tensor network that makes it more scalable. To illustrate the performance, the thermodynamic quantities of the quantum XY spin chain as well as the Heisenberg antiferromagnet on a honeycomb lattice are calculated by the linearized tensor renormalization group method, showing the pronounced precision and high efficiency.     

Visible photoluminescence of nanometer-sized SiGe/Si heterostructure fabricated by ion implantation

An innovative fabrication technique for the nanometer-sized SiGe/Si heterostructure was developed in this study. Ge was induced in Si substrate by two-step ion implantation. The spherical SiGe nanoclusters are self-assembled in the Si substrate by subsequent rapid thermal annealing at 1,100 °C. The diameter of the spherical SiGe nanoclusters is 5–7 nm. Visible photoluminescence from this nanometer-sized SiGe/Si heterostructure at room temperature was investigated. We found three peak energies of visible luminescence spectra at 1.97, 2.13, and 2.16 eV, respectively. The luminescence intensity depends on the number of the nanoclusters and will be decreased because of the micro-defects around the heterostructure, which is discussed in detail.     

Hidden conformal symmetry of self-dual warped AdS<Subscript>3</Subscript> black holes in topological massive gravity

We extend the recently proposal of hidden conformal symmetry to the self-dual warped AdS₃ black holes in topological massive gravity. It is shown that the wave equation of massive scalar field with sufficient small angular momentum can be reproduced by the SL(2, R) Casimir quadratic operator. Due to the periodic identification in the φ direction, it is found that only the left section of hidden conformal symmetry is broken to U(1), while the right section is unbroken, which only gives the left temperature of dual CFT. As a check of the dual CFT conjecture of self-warped AdS₃ black hole, we further compute the Bekenstein–Hawking entropy and absorption cross section and quasinormal modes of scalar field perturbation and show these are just of the forms predicted by the dual CFT.     

一种检测低浓度化学需氧量的双波长光谱方法

提出了一种基于双波长光谱法快速测定低污染水样的化学需氧量(COD)的方法.结果表明:对低COD样品采用440和560 nm双波长的测定方法可有效地提高可靠性和检测灵敏性.该法的灵敏度(即定量检测下限)为8.6 mg·L-1;在低COD范围标样(≤100mg·L-1)的准确性对比测定相对标准误差在2%～15%的范围内.另外,该方法不需要用标准样品进行校正,可以通过光谱法检测消解液中重铬酸根的消耗直接计算出样品的COD值,使实验步骤得到了进一步的简化.     

Maskless laser tailoring of conical pillar arrays for antireflective biomimetic surfaces

Herein, we report a facile approach for rapid and maskless production of subwavelength structured antireflective surfaces with high and broadband transmittance-direct laser interference ablation. The interfered laser beams were introduced into the surface of a bare optical substrate, where structured surfaces consisting of a micropillar array were produced by two-step laser irradiation in the time frame of seconds. A multiple exposure of the two-beam interference approach was proposed instead of multiple-beam interference to simply realize planar patterns of a high aspect ratio. Tall sinusoidal pillars were created and shaped by pulse shot number control. As an example of the application, zinc sulfide substrates were processed with the technology, from which high transmission at an infrared wavelength, over 92%, at normal incidence was experimentally achieved.     

线圈炮电枢电磁-热耦合仿真分析

 从麦克斯韦方程组和导热微分方程出发,导出了3维多级感应线圈炮电磁场、温度场分布的基本方程,并以电磁场和温度场有限元分析为基础,建立了3维有限元分析模型,忽略级间的相互影响,多级线圈炮中电枢温升可以等效为多个单级电枢的温升,运用通用有限元分析软件ANSYS的耦合计算流程,对单级感应线圈炮中电枢电磁场和温度场进行仿真。计算中考虑了材料物理参数随温度变化对温度场的影响。仿真结果表明：电枢内的温升主要分布在电枢的外表面和尾部;电枢的温度随着电容器组电压和电容增加而升高,这是因为总能量增大,电枢中涡流也增大,从而电枢的温度升高;电枢的触发位置和速度匹配关系,也会对电枢温升造成很大的影响;电枢的温度随着级数的增加逐渐升高,说明电枢在一定级数后达到了材料的熔点而被破坏。     

A multi-objective evolutionary algorithm for facility dispersion under conditions of spatial uncertainty

Avoiding concentration or saturation of activities is fundamental in many environmental and urban planning contexts. Examples include dispersing retail and restaurant outlets, sensitivity to impacts in forest utilization, spatial equity of waste disposal, ensuring public safety associated with noxious facilities, and strategic placement of military resources, among others. Dispersion models have been widely applied to ensure spatial separation between activities or facilities. However, existing approaches rely on deterministic approaches that ignore issues of spatial data uncertainty, which could lead to poor decision making. To address data uncertainty issues in dispersion modelling, a multi-objective approach that explicitly accounts for spatial uncertainty is proposed, enabling the impacts of uncertainty to be evaluated with statistical confidence. Owing to the integration of spatial uncertainty, this dispersion model is more complex and computationally challenging to solve. In this paper we develop a multi-objective evolutionary algorithm to address the computational challenges posed. The proposed heuristic incorporates problem-specific spatial knowledge to significantly enhance the capability of the evolutionary algorithm for solving this problem. Empirical results demonstrate the performance superiority of the developed approach in supporting facility and service planning.     

On the guaranteed convergence of new two-point root-finding methods for polynomial zeros

We presented new two-point methods for the simultaneous approximation of all n simple (real or complex) zeros of a polynomial of degree n. We proved that the R-order of convergence of the total-step version is three. Moreover, computationally verifiable initial conditions that guarantee the convergence of one of the proposed methods are stated. These conditions are stated in the spirit of Smale’s point estimation theory; they depend only on available data, the polynomial coefficients, polynomial degree n and initial approximations \(x_{1}^{(0)},\ldots ,x_{n}^{(0)}\) , which is of practical importance. Using the Gauss-Seidel approach we state the corresponding single-step version and consequently its prove that the lower bound of its R-order of convergence is at least 2 + y _n > 3, where y _n ∈ (1, 2) is the unique positive root of the equation y ⁿ ? y ? 2 = 0. Two numerical examples are given to demonstrate the convergence behavior of the considered methods, including global convergence.     

On approximated ILU and UGS preconditioning methods for linearized discretized steady incompressible Navier-Stokes equations

When the artificial compressibility method in conjunction with high-order upwind compact finite difference schemes is employed to discretize the steady-state incompressible Navier-Stokes equations, in each pseudo-time step we need to solve a structured system of linear equations approximately by, for example, a Krylov subspace method such as the preconditioned GMRES. In this paper, based on the special structure and concrete property of the linear system we construct a structured preconditioner for its coefficient matrix and estimate eigenvalue bounds of the correspondingly preconditioned matrix. Numerical examples are given to illustrate the effectiveness of the proposed preconditioning methods.