A Theoretical study on the charge and discharge states of Na-ion battery cathode material,Na1+xFePO4F

Na₂FePO₄F is a promising cathode material for a Na-ion battery because of its high electronic capacity and good cycle performance. In this work, first principle calculations combined with cluster expansion and the Monte Carlo method have been applied to analyze the charge and discharge processes of Na₂FePO₄F by examining the voltage curve and the phase diagram. As a result of the density functional theory calculation and experimental verification with structural analysis, we found that the most stable structure of Na_1.5FePO₄F has the P2₁/b11 space group, which has not been reported to date. The estimated voltage curve has two clear plateaus caused by the two-phase structure composed of P2₁/b11 Na_1.5FePO₄F and Pbcn Na₂FePO₄F or Na₁FePO₄F and separated along the c-axis direction. The phase diagram shows the stability of the phase-separated structure. Considering that Na₂FePO₄F has diffusion paths in the a- and c-axis directions, Na₂FePO₄F has both innerphase and interphase diffusion paths. We suggest that the stable two-phase structure and the diffusion paths to both the innerphase and interphases are a key for the very clear plateau. We challenge to simulate a nonequilibrium state at high rate discharge with high temperature by introducing a coordinate-dependent chemical potential. The simulation shows agreement with the experimental discharge curve on the disappearance of the two plateaus. © 2018 Wiley Periodicals, Inc.     

QEPAS系统中石英音叉模态仿真计算与研究

对石英音叉增强型光声光谱(QEPAS)系统中常用的石英音叉进行了有限元模态计算，获得石英音叉前6阶振型与模态频率，认知了第4阶对称摆动振型为有效振动，利用单因素法分析了石英音叉的音臂长度l₁、音臂宽度w₁、音臂厚度t、音臂切角θ、音臂圆孔直径d及音臂圆孔高度h对低阶有效共振频率(Fre)的影响，敏感度依次为： l₁> w₁>d>θ>t>h，考虑实际设计情形，筛选出了l₁，w₁，d与h四个石英音叉设计变量，采用Box-Behnken实验设计方案与RSM(response surface methodology)方法，以Fre为函数目标，建立l₁，w₁，d与h的二次回归响应面模型，得到了参数之间的交互作用，利用Design-Expert软件对响应面模型进行设计参数反求，结果表明，在15 000 Hz≤Fre≤25 000 Hz计算区域内误差较小，基本满足QEPAS系统的计算需求，所提出的研究与设计方法具有一定通用性，可为QEPAS系统中石英音叉结构参数设计提供参考。     

Binary functions,degeneracy, and alternating dimaps

This paper continues the study of combinatorial properties of binary functions — that is, functions $f:2^E\to ?$ such that $f(0?)=1$, where $E$ is a finite set. Binary functions have previously been shown to admit families of transforms that generalise duality, including a trinity transform, and families of associated minor operations that generalise deletion and contraction, with both these families parameterised by the complex numbers. Binary function representations exist for graphs (via the indicator functions of their cutset spaces) and indeed arbitrary matroids (as shown by the author previously). In this paper, we characterise degenerate elements – analogues of loops and coloops – in binary functions, with respect to any set of minor operations from our complex-parameterised family. We then apply this to study the relationship between binary functions and Tutte’s alternating dimaps, which also support a trinity transform and three associated minor operations. It is shown that only the simplest alternating dimaps have binary representations of the form we consider, which seems to be the most direct type of representation. The question of whether there exist other, more sophisticated types of binary function representations for alternating dimaps is left open.     

Periodic Solutions of the Duffing Differential Equation Revisited via the Averaging Theory

We use three different results of the averaging theory of first order for studying the existence of new periodic solutions in the two Duffing differential equations $\ddot y+ a \sin y= b \sin t$ and $\ddot y+a y-c y^3=b\sin t$, where $a$, $b$ and $c$ are real parameters.     

Formation of intermediate coupling optical polarons and bipolarons in two-dimensional systems

The formation of the optical polaron and bipolaron in two-dimensional (2D) systems is studied in the intermediate electron–phonon coupling regime. The total energies of the 2D polaron and bipolaron are calculated by using the Buimistrov–Pekar method of canonical transformations. The obtained results are compared with other existing results obtained by using the Feynman path integral method and the modified Lee–Low–Pines unitary transformation method. It is shown that the electron–phonon correlation significantly reduces the total energy of the 2D polaron in comparison with the energy of the strong coupling (adiabatic) polaron. It is found that the polaron formation in 2D systems is possible when the electron–phonon coupling constant α is greater than the critical value ${\alpha }_c?2.94$, which is much lower than a critical value of the electron–phonon coupling constant α in three-dimensional (3D) systems. The critical values of the Fröhlich coupling constant α and the ratio $\eta ={\epsilon }_{\infty }/{\epsilon }_0$ (where ${\epsilon }_{\infty }$ and ${\epsilon }_0$ are the high frequency and static dielectric constants, respectively), which determine the bipolaron stability region in 2D systems, are calculated numerically. It is interesting for application to the layered cuprate superconductors that the (bi)polarons are formed more easily in quasi-2D regions than in the bulk. It is argued that the high-$T_c$ cuprate superconductivity can exist above the bulk superconducting transition temperature $T_c$ as the persisting superfluidity of polaronic (bosonic) Cooper pairs and large bipolarons at quasi-2D grain boundaries or in the CuO₂ layers above $T_c$.     

Explicit estimates of sums related to the Nyman–Beurling criterion for the Riemann Hypothesis

We give an estimate for sums appearing in the Nyman–Beurling criterion for the Riemann Hypothesis. These sums contain the Möbius function and are related to the imaginary part of the Estermann zeta function. The estimate is remarkably sharp in comparison to other sums containing the Möbius function. The bound is smaller than the trivial bound – essentially the number of terms – by a fixed power of that number. The exponent is made explicit. The methods intensively use tools from the theory of continued fractions and from the theory of Fourier series.     

New findings for two new type sine hyperbolic potentials

We propose two new type sine hyperbolic potentials $V(x)=a^2{\sinh }^2?(x)?k{\tanh }^2?(x)$ and $V(x)=c^2{\sinh }^4?(x)?k{\tanh }^2?(x)$. They may become single- or double-well potentials depending on the potential parameters $a,c$ and k. We find that its exact solutions can be written as the confluent Heun functions $H_c(\alpha ,\beta ,\gamma ,\delta ,\eta ;z)$, in which the energy level E is involved inside the parameter η. The properties of the wave functions, which is strongly relevant for the potential parameters $a,c$ and k, are illustrated.     

A new endocytic model based on the co-rotational grid method

Endocytosis plays important roles in many cellular physiological processes, such as metabolism and immune. Many theoretical models have been proposed to study the endocytic process, but little has considered the tensile deformation of the membrane and the actin forces. In this paper, a new endocytic model is proposed based on the co-rotational grid method. Our model gives a direct estimation of the in-plane strain of the plasma membrane and provides a basis for the calculation of further scission process of the vesicle. The results fit well with experimental data in the literature. Moreover, it is suggested that the active forces of actin at the endocytic site is the main mechanism driving the invagination of the plasma membrane.     

棒状LiZnPO4的低温合成与表征

LiZnPO₄的性能与其形貌密切相关,其合成常用的固相法和水热法均无控制其微观形貌的优势。 本文采用改进的沉淀法成功合成了具有棒状结构的LiZnPO₄。 利用热重-差热分析仪(TG-DSC)、X射线衍射仪(XRD)、傅里叶变换红外光谱(FTIR)以及场发射扫描电子显微镜(FE-SEM)等技术研究了LiZnPO₄形成过程、晶相组成、微观结构和形貌。 同时探究了合成方法、煅烧温度、煅烧时间、酸的种类对LiZnPO₄形貌的影响。 结果表明,相比较于固相法,以醋酸为原料的改进沉淀法不仅可以有效降低LiZnPO₄的合成温度至500 ℃,而且很容易控制棒状LiZnPO₄的形成。 在600 ℃下煅烧2 h后可以获得分散性良好、横截面为矩形、直径约为2 μm的规则棒状LiZnPO₄。 此外,对比颗粒状LiZnPO₄和棒状LiZnPO₄的光响应能力,发现棒状LiZnPO₄的光响应能力明显增强。