Pentapnictogen heterocyclic monoanions: Structure,stability, and aromaticity

Inorganic planar ring-shape molecules with 4n + 2 π electrons are always the focus of experimental synthesis and theoretical research due to their potential aromaticity and stability. In this work, the whole series of five-membered heterocycle monoanions X _nY_5-n⁻ (X, Y = group 15 elements; n = 1-4) were thoroughly investigated by means of density functional theory calculations. They all have large formation energies and HOMO-LUMO gap energies, suggesting the potential thermodynamic and kinetic stability. Their aromaticities are comparable to that of typical aromatic hydrocarbons. Their thermal stabilities were firmly established by the ab initio molecular dynamics simulations. As most of them are predicted for the first time, their various spectra were simulated for experimental characterization. Furthermore, we demonstrate that these five-membered cyclic anions can be employed as η⁵-ligand to construct novel all-inorganic metallocenes, which may serve as the building blocks of low-dimensional nanomaterials.     

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 $T_c$.     

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。     

一类改进最大熵方法的可调参数分析

在结构可靠性分析中,引入含可调参数的转换函数能对传统的最大熵方法进行改进,获得更高的失效概率预测精度。但是,此可调参数的最佳取值很难确定。针对这一问题,引入概率守恒方程,从功能函数转换前后所得概率密度函数出发,建立其最大熵值的变化关系,给出转换前后最大熵值之差的理论形式。通过对三种典型单调非线性转换函数开展算例研究,发现功能函数转换前后的最大熵值之差与转换函数的最佳可调参数值有关。改变可调参数值驱使最大熵值之差变化的同时,改进最大熵方法能遍历到更好的失效概率估计值。     

椭球粒子声辐射力计算及分析

针对水下椭球粒子,以声散射理论为基础,采用分波序列的方法,建立了椭球粒子声辐射力的理论计算模型。进而根据声辐射力计算公式,以刚性椭球粒子和液体椭球粒子为例,计算并分析不同Bessel波束作用下椭球粒子的轴向声辐射力函数特征。数值仿真计算结果表明,对于刚性椭球粒子,扁平椭球粒子相对于细长椭球粒子更有助于激发负声辐射力；对于液体椭球粒子,细长椭球粒子相对于扁平椭球粒子更加容易产生负声辐射力；对于不同介质的椭球粒子,不同的入射波束激发的负声辐射力的效果也存在明显的差异。该结果为复杂的尺寸和介质粒子声操控技术提供了理论的可行性。     

Positive ground state solutions for Schrödinger–Poisson system with critical nonlocal term in ℝ3

This paper is dedicated to studying the following Schrödinger–Poisson system $$\left\{\begin{array}{ll}-\mathrm{\Delta }u+V(x)u-K(x)\varphi |u{|}^{3}u=a(x)f(u),& x\in {ℝ}^3,\\ -\mathrm{\Delta }\varphi =K(x)|u{|}^5,& x\in {ℝ}^3.\end{array}\right.$$ Under some different assumptions on functions V(x), K(x), a(x) and f(u), by using the variational approach, we establish the existence of positive ground state solutions.