The intermolecular potential function of Smith–Thakkar type for C60

The intermolecular potential function of Smith–Thakkar type for C₆₀ has been proposed, and its expression is as follows

The unit of u(r) is J/mol, r is the distance between two C₆₀ molecules center and the unit is nm. Some properties of C₆₀ in the gas and crystal have been studied using the interaction potential of Smith–Thakkar type, such as stability of C₆₀ crystals, virial coefficient and lattice dynamics.     

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two-dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plane Poiseuille flow and the plane Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time , and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation. Using the analytical solution, it is shown that in Poiseuille flow the bounce-back boundary condition introduces an error of first order in the lattice spacing. The boundary condition used by Kadanoffet al. in lattice gas automata to simulate Poiseuille flow is also considered for the triangular lattice Boltzmann BGK model. An analytical solution is obtained and used to show that the boundary condition introduces an error of second order in the lattice spacing.     

Oxidation products of the niobium tungsten oxide Nb4W13O47: A high-resolution scanning transmission electron microscopy study

Nb₄W₁₃O₄₇, a member of the solid solution series Nb_8−nW_9+nO₄₇ (0?n?5), crystallizes in a threefold superstructure of the tetragonal tungsten bronze structure. While the oxidation of this reduced phase at T_OX=1200 °C leads to a separation into the thermodynamically stable phases, lower oxidation temperatures result in products that comprise new structural elements and ordering variants. The characterization of the oxidation products obtained at T_OX=1000 °C was performed by scanning transmission electron microscopy applying a high-angle annular dark field detector. At the selected imaging conditions (Z contrast), not only the metal positions are revealed by this technique but valuable additional information about the elemental distribution can be obtained simultaneously.     

Unexpected solids from enantiopure cationic palladium complexes and racemic anions: A structural study of chiral non-discrimination

Enantiomerically pure cationic complexes were obtained via cyclopalladation of primary amines and subsequent addition of a chelating ethylendiamine ligand. No diastereomeric resolution was observed upon combining these cations with racemic mandelate or hydratropate anions, but four less popular products, namely three double salts and a solid solution, were obtained and structurally characterized. For one of the double salts, the alternative ionic compounds based on different stereoisomers of the same residues were synthesized independently: The conventional racemic solid and both diastereomeric salts formed by enantiopure cations and anions were studied by single crystal X-ray diffraction. Lattice energy calculations confirm that the diastereomeric salts differ significantly; formation of the partially racemic double salt, however, is energetically favourable and precludes resolution.     

Repleteness and regular lattice measures

Let X be an abstract set and L a lattice of subsets of X. To each lattice regular measure µ, we associate two induced measures and on suitable lattices of the Wallman space IR(L) and another measure µ on the spaceIR(L). We will investigate the reflection of smoothness properties of p onto , and µ; and try to set some new criterion for repleteness and measure repleteness.     

偏序集上的滤子极大理想

在偏序集上引入并考察了滤子极大理想的概念,证明了相应的存在性定理。引入并考察了伪极大元和伪既约元的概念,利用图表的形式对连续格中各种类型的既约元和素元之间的关系进行了归纳总结,完善了文献《Continuous Lattices and Domains》(作者:G.Gierz,et al)中的一个图表的相关内容,填补了在分配的连续格情形该图表的一个未知内容,部分地回答了该文献中的一个问题。     

分配格的分式扩张

首先借助整数扩充为有理数的办法构作一个分配格对它的滤子的分式扩张,然后用泛映射性质来刻画由任意分配格所构作的分式扩张,最后讨论了这种扩张的理想结构。     

Permeability of microscale fibrous porous media using the lattice Boltzmann method

The permeabilities of microscale fibrous porous media were calculated using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Two models of the microscale fibrous porous media were constructed based on overlapping fibers (simple cubic, body-centered cubic). Arranging the fibers in skew positions yielded two additional models comprising non-overlapping fibers (skewed simple cubic, skewed body-centered cubic). As the fiber diameter increased, the fibers acted as granular inclusions. The effects of the overlapping fibers on the media permeability were investigated. The overlapping fibers yielded permeability values that were a factor of 2.5 larger than those obtained from non-overlapping fibers, but the effects of the fiber arrangement were negligible. Two correlations were obtained for the overlapping and non-overlapping fiber models, respectively. The effects of the rarefaction and slip flow are also discussed. As the Knudsen number increased, the dimensionless permeability increased; however, the increase differed depending on the fiber arrangement. In the slip flow regime, the fiber arrangement inside the porous media became an important factor.     

A new approach in modeling of constant temperature boundary condition in thermal lattice‐Boltzmann method

The lattice‐Boltzmann method is being applied to a diversity of fluid flow and heat transfer problems nowadays. Because of its microscale nature, strict attention should be paid when introducing macroscopic inputs to the model. One of the challenging issues dealing with macroscale and microscale treatment is the implementation of boundary conditions. In this regard constant‐temperature boundaries are frequently used in energy transfer problems. Such boundaries are simply modeled in Navier–Stokes based solvers, but they are not so harnessed in lattice‐Boltzmann models. One of the problems is that the calculated tangential heat flux is not zero along such boundaries in most of the previous models. In the present paper, a model has been developed, which has the capability of controlling tangential heat flux along the constant‐temperature boundaries. It aims to set the heat flux nearly zero along the boundary in midplane grid schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

Characterization of Oil-Wax Gel with Higher Velocity Gradient

The properties of solid surface on oil-wax gel are one of the most important factors which decide the quality of products such as cosmetics. The thixotropic property of solid surface depends on the velocity gradient and it is increased with higher velocity gradient as controlling the morphology on solid surface of oil-wax gel. The morphological change of oil-wax gel in compliance with surface properties of wax matrix can cause different rheological behaviors. Rheological behavior of oil-wax gel regarding the surface transition range in accordance with shear strain was observed to characterize surface properties. In an earlier article, the morphological mechanism of causing surface transition range and the factors of influencing surface transition range were examined by studying the rheological behaviors of a solid-state emulsion. Here, we investigated, in the lattice structure terms, the morphological change of oil-wax gel by measuring surface transition range depending on velocity gradient, which could influence the hardness and sweating phenomenon. We confirmed that the morphological change of oil-wax gel was accompanied by crystal size, crystal conformation, the degree of crystallinity. Surface transition range depending on velocity gradient was shown in large and regular lattice structure of oil-wax gel better than small and irregular one.