The predictive accuracy for estimating infinite dilution activity coefficients by γ∞-based UNIFAC

The predictive accuracy for estimating infinite dilution activity coefficients by a modification of the UNIFAC method wherein the group interaction parameters were based on only data (referred to as -based UNIFAC) has been studied. Estimates and measured values were compared for six prototypical solutes in a series of homologous n-alkanes, l-alcohols and alkanenitrile solvents. Despite the fact that the interaction parameters were derived using only data, this approach still gave serious errors due to several inherent problems in the original UNIFAC model. Its performance is sometimes even poorer than that of the original UNIFAC method. For example for nitromethane in alcohols and p-dioxane in nitriles values predicted by the -based UNIFAC are essentially zero. The large errors for these systems are most likely due to inaccurate interaction parameters in the -based UNIFAC method.     

A greedy algorithm for finding maximum spanning trees in infinite graphs

In finite graphs, greedy algorithms are used to find minimum spanning trees (MinST) and maximum spanning trees (MaxST). In infinite graphs, we illustrate a general class of problems where a greedy approach discovers a MaxST while a MinST may be unreachable. Our algorithm is a natural extension of Prim's to infinite graphs with summable and strictly positive edge weights, producing a sequence of finite trees that converge to a MaxST.     

Time correlation functions of a one-dimensional infinite system

We investigate the time evolution of a simple one-dimensional system with an infinite number of particles. We calculate some time correlation functions and show that they behave asymptotically as 1/t.     

超临界CO2中甲醇和乙醇无限稀释扩散系数的分子动力学模拟与实验测定

采用分子动力学模拟(MD)方法对甲醇和乙醇在超临界二氧化碳中的无限稀释扩散系数进行了模拟计算, 并应用泰勒分散理论, 采用超临界色谱仪对模拟结果进行了实验验证. 模拟计算值与实验值较吻合, 且变化规律基本一致, 表明采用这种新方法可以准确有效地预测超临界体系的扩散性质, 能够方便地应用于工程设计.     

A new formulation of regularized meshless method applied to interior and exterior anisotropic potential problems

This paper proposes a new formulation of regularized meshless method (RMM), which differs from the traditional RMM in that the traditional formulation generates the diagonal elements of influence matrix via null-field integral equations, while our new one directly employs the boundary integral equations at the domain point to evaluate the diagonal elements. We test the present RMM formulation to two-dimensional anisotropic potential problems in finite and infinite domains in comparison with the traditional RMM. Numerical results show that the present RMM sharply outperforms the traditional RMM in the solution of interior problems, while the latter is clearly superior for exterior problems. A rigorous theoretical analysis of circular domain case also corroborates such numerical experiment observations and is provided in the appendix of this paper.     

Infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm system

We consider the infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm (mDGH2) system. The infinite propagation speed is derived for the corresponding solution with compactly supported initial data that does not have compact support any longer in its lifespan.     

Dynamic response of a growing inclusion in a discrete system

The propagation of a semi-infinite line defect, contained in an infinite square-cell lattice is considered. The defect is composed of particles lighter than those in the ambient lattice and it is assumed this defect propagates with constant speed. Dispersion properties of the lattice are related to waves generated by the propagating defect. In order to determine these properties, the Wiener–Hopf technique is applied. Additional features, related to localisation along the defect are also identified. Analysis of the dispersion relations for this lattice, from the kernel function inside the Wiener–Hopf equation, is carried out. The solution of the Wiener–Hopf equation is presented for the case when an external load is applied corresponding to an energy flux at infinity.     

Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice

The Allen-Cahn equation ? Δu = u ? u ³ in ?² has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem ?u″ =u ? u ³. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the infinite Toda lattice. We show that for each one-soliton solution to the infinite Toda lattice we can find a singly periodic solution to the Allen-Cahn equation, such that its level set is close to the scaled one-soliton. The solutions we construct are analogues of the family of Riemann minimal surfaces in ?³.     

A New Tricarboxylate‐Terbium(III) Compound: Synthesis,Structure, and Luminescent Property

The Tb^III compound [Tb(tci)(H₂O)]_n · n(DMF) ( 1 ) [H₃tci = tri(2‐carboxythyl)isocyanurate, DMF = N,N′‐dimethylformamide] was synthesized by the reaction of terbium oxide, H₃tci, and two drops of concentrated nitric acid in the presence of DMF and H₂O. Single crystal X‐ray analysis reveals that it features a three‐dimensional (3D) framework based on infinite –Tb–COO–Tb– chains. The tci ligand in 1 links six different Tb^III ions with its two carboxylate groups in μ₂‐κ¹O;κ²O,O′ mode and the third in μ₂‐κ¹O;κ¹O′ mode. Thermal analysis reveals that it remains high thermal stability until 390 °C. Luminescence investigation shows that it emits characteristic green light of Tb^III ions.