稳定锂电化学沉积和溶解行为的LiC6异质微结构界面层

本文采用机械辊压方法在金属锂表面通过原位固相反应生成LiC₆异质微结构界面层,并研究了在碳酸酯有机电解液体系下该异质层对锂电化学沉积和溶解行为的影响。通过形貌表征与电化学测试发现,LiC₆异质层能够有效提升锂电化学沉积的可逆性与均匀性,从而抑制枝晶生长及维持沉积/溶解界面的稳定。使用异质层改性金属锂负极的扣式全电池也较纯金属锂负极体系表现出更为优异的循环稳定性。     

A cell edge‐based linearity‐preserving scheme for diffusion problems on two‐dimensional unstructured grids

We propose a new finite volume scheme for 2D anisotropic diffusion problems on general unstructured meshes. The main feature lies in the introduction of two auxiliary unknowns on each cell edge, and then the scheme has both cell‐centered primary unknowns and cell edge‐based auxiliary unknowns. The auxiliary unknowns are interpolated by the multipoint flux approximation technique, which reduces the scheme to a completely cell‐centered one. The derivation of the scheme satisfies the linearity‐preserving criterion that requires that a discretization scheme should be exact on linear solutions. The resulting new scheme is then called as a cell edge‐based linearity‐preserving scheme. The optimal convergence rates are numerically obtained on unstructured grids in case that the diffusion tensor is taken to be anisotropic and/or discontinuous. Copyright © 2017 John Wiley & Sons, Ltd.     

New interpolation error estimates and a posteriori error analysis for linear parabolic interface problems

We derive residual‐based a posteriori error estimates of finite element method for linear parabolic interface problems in a two‐dimensional convex polygonal domain. Both spatially discrete and fully discrete approximations are analyzed. While the space discretization uses finite element spaces that are allowed to change in time, the time discretization is based on the backward Euler approximation. The main ingredients used in deriving a posteriori estimates are new Clément type interpolation estimates and an appropriate adaptation of the elliptic reconstruction technique introduced by (Makridakis and Nochetto, SIAM J Numer Anal 4 (2003), 1585–1594). We use only an energy argument to establish a posteriori error estimates with optimal order convergence in the ‐norm and almost optimal order in the ‐norm. The interfaces are assumed to be of arbitrary shape but are smooth for our purpose. Numerical results are presented to validate our derived estimators. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 570–598, 2017     

基于再生核三次样条基底的构造及其应用

将三次样条理论与再生核理论相结合,利用再生核函数巧妙地构造了三次样条函数空间的一组基底.基于三次样条插值的高收敛特点,得到了微分方程边值问题近似解的一种新的求解方法.数值算例展现出算法简单、有效.     

Planar interpolation with a pair of rational spirals

Spirals are curves of one-signed, monotone increasing or decreasing curvature. Spiral segments have the advantage that the minimum and maximum curvatures are at their endpoints. Two situations where the planar, two-point G²$G^2$ Hermite interpolation problem can be solved with a pair of rational spiral segments are outlined here.     

On weighted Lebesgue function type sums

Let I be a finite or infinite interval and dμ a measure on I. Assume that the weight function w(x)>0, w^′(x) exists, and the function w^′(x)/w(x) is non-increasing on I. Denote by ℓ_k's the fundamental polynomials of Lagrange interpolation on a set of nodes x₁<x₂<<x_n in I. The weighted Lebesgue function type sum for 1≤i<j≤n and s≥1 is defined by

In this paper the exact lower bounds of S_n(x) on a “big set” of I and are obtained. Some applications are also given.     

Uniform stability theorems for delay differential equations with impulses

In the paper, we obtain sufficient conditions for the uniform stability of the zero solution of the delay differential equation with impulses

     

Strong and uniform mean stability of cosine and sine operator functions

It is first observed that a uniformly bounded cosine operator function C() and the associated sine function S() are totally non-stable. Then, using a zero-one law for the Abel limit of a closed linear operator, we prove some results concerning strong mean stability and uniform mean stability of C(). Among them are: (1) C() is strongly (C,1)-mean stable (or (C,2)-mean stable, or Abel-mean stable) if and only if 0ρ(A)σ_c(A); (2) C() is uniformly (C,2)-mean stable if and only if S() is uniformly (C,1)-mean stable, if and only if , if and only if , if and only if C() is uniformly Abel-mean stable, if and only if S() is uniformly Abel-mean stable, if and only if 0ρ(A).     

Hermite interpolation by Pythagorean Hodograph space curves

We solve the problem of Hermite interpolation by Pythagorean Hodograph (PH) space curves. More precisely, for any set of space boundary data (two points with associated first and second derivatives) we construct a four-dimensional family of PH interpolants of degree and introduce a geometrically invariant parameterization of this family. This parameterization is used to identify a particular solution, which has the following properties. First, it preserves planarity, i.e., the interpolant to planar data is a planar PH curve. Second, it has the best possible approximation order 6. Third, it is symmetric in the sense that the interpolant of the ``reversed' set of boundary data is simply the ``reversed' original interpolant. This particular PH interpolant is exploited for designing algorithms for converting (possibly piecewise) analytical curves into a piecewise PH curve of degree which is globally , and for simple rational approximation of pipe surfaces with a piecewise analytical spine curve. The algorithms are presented along with an analysis of their error and approximation order.

     

大型纵向加筋截断锥壳稳定性的半离散分析

如何计算大型纵向加筋截断锥壳的稳定问题，尚未见到有关报导。本文在沿纵向和环向分别采用Ｈｅｒｍｉｔｅ插值和三角级数插值的基础上，建立了几何非线性带筋环单元，进而导出了半离散分析法，并经过实例检验了它的正确与可靠。这样，本文为建立各类工程结构的半离散单元提出了一种新的途径。