Spectral Analysis of Powers of the Operator (Vf)(x)=q(x)∫0 xw(t)f(t),dt

Mathematical Notes -     

几乎各向同性的高维空间分数阶扩散方程的分块快速正则Hermite分裂预处理方法

一类空间分数阶扩散方程经过有限差分离散后所得到的离散线性方程组的系数矩阵是两个对角矩阵与Toeplitz型矩阵的乘积之和.在本文中,对于几乎各向同性的二维或三维空间分数阶扩散方程的离散线性方程组,采用预处理Krylov子空间迭代方法,我们利用其系数矩阵的特殊结构和具体性质构造了一类分块快速正则Hermite分裂预处理子.通过理论分析,我们证明了所对应的预处理矩阵的特征值大部分都聚集于1的附近.数值实验也表明,这类分块快速正则Hermite分裂预处理子可以明显地加快广义极小残量(GMRES)方法和稳定化的双共轭梯度(BiCGSTAB)方法等Krylov子空间迭代方法的收敛速度.     

Dense Sphene-type Solid Electrolyte Through Rapid Sintering for Solid-state Lithium Metal Battery

The sphene-type solid electrolyte with high ionic conductivity has been designed for solid-state lithium metal battery. However, the practical applications of solid electrolytes are still suffered by the low relative density and long sintering time of tens of hours with large energy consumption. Here, we introduced the spark plasma sintering technology for fabricating the sphene-type Li_1.125Ta_0.875Zr_0.125SiO₅ solid electrolyte. The dense electrolyte pellet with high relative density of ca. 97.4% and ionic conductivity of ca. 1.44×10^-5 S/cm at 30℃ can be obtained by spark plasma sintering process within the extremely short time of only ca. 0.1 h. Also the solid electrolyte provides stable electrochemical window of ca. 6.0 V(vs. Li⁺/Li) and high electrochemical interface stability toward Li metal anode. With the enhanced interfacial contacts between electrodes and electrolyte pellet by the in-situ formed polymer electrolyte, the solid-state lithium metal battery with LiFePO₄ cathode can deliver the initial discharge capacity of ca. 154 mA·h/g at 0.1 C and the reversible capacity of ca. 132 mA·h/g after 70 cycles with high Coulombic efficiency of 99.5% at 55℃. Therefore, this study demonstrates a rapid and energy efficient sintering strategy for fabricating the solid electrolyte with dense structure and high ionic conductivity that can be practically applied in solid-state lithium metal batteries with high energy densities and safeties.     

Convergence rates of a global optimization algorithm

Second order conditions for the (pseudo-) convexity of a function restricted to an affine subspace are obtained by extending those already known for functions on ⁿ . These results are then used to analyse the (pseudo-) convexity of potential functions of the type introduced by Karmarkar.This research was completed while the first author was on sabbatical leave at the Département d'Informatiques et de Recherche Opérationelle, Université de Montréal, and supported by NSERC (grant Q015807). This research was also supported by NSERC (grants A8312 and A5408) and la Coopération franco-québécoise (project 20-02-13).     

单A直和子空间

引入单直和子空间的概念,证明了线性空间可唯一分解为单直和子空间的直和,并且给出了计算方法.     

计及气动和隐身约束结构综合优化的并行子空间优化方法

通过分析基于响应面的并行子空间优化算法的特点指出并行子空间优化算法学科级优化的作用在于向系统级优化响应面提供性能优良的设计点.在此基础上,建立了不要求学科级优化的改进的并行子空间优化算法,进一步降低了设计优化的计算量,解决了分析模块与优化模块间的接口困难.依据该算法建立了结构、气动和隐身一体化设计优化框架,实现了某无人机机翼计及气动和隐身约束的结构综合优化.     

关于量子体系的高效相干能量转移的最优初始化的研究

For an energy transfer network, the irreversible depletion of excited electron energy occurs through either an efficient flow into an outer energy sink or an inefficient decay. With a small decay rate, the energy transfer efficiency is quantitatively reflected by the average life time of excitation energy before being trapped in the sink where the decay process is omitted. In the weak dissipation regime, the trapping time is analyzed within the exciton population subspace based on the secular Redfield equation. The requirement of the noise-enhanced energy transfer is obtained, where the trapping time follows an exact or approximate 1/Γ-scaling of the dissipation strength Γ. On the opposite side, optimal initial system states are conceptually constructed to suppress the 1/Γ-scaling of the trapping time and maximize the coherent transfer efficiency. Our theory is numerically testified in four models, including a biased two-site system, a symmetric three-site branching system, a homogeneous onedimensional chain, and an 8-chromophore FMO protein complex.