传输线方程的高精度龙格−库塔数值求解方法

提出了一种求解传输线方程的高精度龙格-库塔(RK)方法。此方法在空间上采取高阶泰勒展开,提高了对空间微分的近似精度,减少了数值色散所带来的误差。与传统的时域有限差分法(FDTD)方法相比,在每波长采样数相同时,RK方法的计算精度更高。同时,根据Taylor模型,对外界平面波激励源进行离散,成功利用RK方法对外部场激励传输线进行求解,扩大了龙格-库塔方法在求解传输线方程时的应用范围。通过编程对平面波辐照下无限大地平面上的单导体与双导体的算例分别应用FDTD方法与RK方法进行了计算,验证了RK方法的正确性。结果表明同等计算条件下RK方法的计算精度更高。     

A control volume finite element method for three-dimensional three-phase flows

A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three-dimensional three-phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P₁DG-P₂ elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second-order finite element methods. A force-balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three-dimensional three-phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.     

Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

Concurrence and Quantum Discord in the Eigenstates of Chaotic and Integrable Spin Chains

There has been some substantial research about the connections between quantum chaos and quantum correlations in many-body systems. This paper discusses a specific aspect of correlations in chaotic spin models, through concurrence (CC) and quantum discord (QD). Numerical results obtained in the quantum chaos regime and in the integrable regime of spin-1/2 chains are compared. The CC and QD between nearest-neighbor pairs of spins are calculated for all energy eigenstates. The results show that, depending on whether the system is in a chaotic or integrable regime, the distribution of CC and QD are markedly different. On the other hand, in the integrable regime, states with the largest CC and QD are found in the middle of the spectrum, in the chaotic regime, the states with the strongest correlations are found at low and high energies at the edges of spectrum. Finite-size effects are analyzed, and some of the results are discussed in the light of the eigenstate thermalization hypothesis.     

The connected partition lattice of a graph and the reconstruction conjecture

Previously we showed that many invariants of a graph can be computed from its abstract induced subgraph poset, which is the isomorphism class of the induced subgraph poset, suitably weighted by subgraph counting numbers. In this paper, we study the abstract bond lattice of a graph, which is the isomorphism class of the lattice of distinct unlabelled connected partitions of a graph, suitably weighted by subgraph counting numbers. We show that these two abstract posets can be constructed from each other except in a few trivial cases. The constructions rely on certain generalisations of a lemma of Kocay in graph reconstruction theory to abstract induced subgraph posets. As a corollary, trees are reconstructible from their abstract bond lattice. We show that the chromatic symmetric function and the symmetric Tutte polynomial of a graph can be computed from its abstract induced subgraph poset. Stanley has asked if every tree is determined up to isomorphism by its chromatic symmetric function. We prove a counting lemma, and indicate future directions for a study of Stanley's question.     

含酰胺结构超低膨胀聚酰亚胺薄膜的热膨胀行为

采用联苯二酐与3种含酰胺结构二胺制备了具有不同取代基团的聚酰胺-酰亚胺薄膜, 考察了酰胺结构对薄膜力学、 耐热及尺寸稳定性的影响, 研究了聚集态结构与薄膜热膨胀行为的关系和规律. 该系列薄膜具有超高强度和优异的耐热性能, 拉伸强度高达280.5 MPa, 玻璃化转变温度在389~409 ℃, 并在30~300 ℃温度范围内表现出超低负膨胀, 热膨胀系数(CTE, ppm/℃, 即10 ⁶ cm·cm ^-1·℃ ^-1)在-3.05~-1.74 ppm/℃之间. 聚集态分析结果表明, 酰胺结构使分子链间形成了强氢键相互作用, 分子链在薄膜面内方向高度有序取向, 并在膜厚方向堆积更为紧密, 使薄膜表现出热收缩现象. 通过不同体积大小的取代基团进一步调控分子链间相互作用及排列堆积, 可实现薄膜在高温下近乎零尺寸形变, 为设计制备超低膨胀聚合物基板材料提供了新思路.     

Expanded Analogs of Three-Dimensional Lead-Halide Hybrid Perovskites

Replacing the Pb−X octahedral building unit of A^IPbX₃ perovskites (X=halide) with a pair of edge-sharing Pb−X octahedra affords the expanded perovskite analogs: A^IIPb₂X₆. We report seven members of this new family of materials. In 3D hybrid perovskites, orbitals from the organic molecules do not participate in the band edges. In contrast, the more spacious inorganic sublattice of the expanded analogs accommodates larger pyrazinium-based cations with low-lying π* orbitals that form the conduction band, substantially decreasing the band gap of the expanded lattice. The molecular nature of the conduction band allows us to electronically dope the materials by reducing the organic molecules. By synthesizing derivatives with A^II=pyridinium and ammonium, we can isolate the contributions of the pyrazinium-based orbitals in the band gap transition of A^IIPb₂X₆. The organic-molecule-based conduction band and the inorganic-ion-based valence band provide an unusual electronic platform with localized states for electrons and more disperse bands for holes upon optical or thermal excitation.     

Spatially restricted Double Z-Simplified Box Orbital basis sets: Optimization and comparison with some standard basis sets

As part of previous studies, we introduced a new type of basis function named Simplified Box Orbitals (SBOs) that belong to a class of spatially restricted functions which allow the zero differential overlap (ZDO) approximation to be applied with complete accuracy. The original SBOs and their Gaussian expansions SBO-3G form a minimal basis set, which was compared to the standard Slater-type orbital basis set (STO-3G). In the present paper, we have developed the SBO basis functions at double-zeta (DZ) level, and we have assessed the option of expanding the SBO-DZ as a combination of Gaussian functions. Finally, we have determined the quality of the new basis set by comparing the molecular properties calculated with SBO-nG with those achieved with some standard basis sets.