Structure dependent elastic properties of supergraphene

Complete replacement of aromatic carbon bonds in graphene by carbyne chains gives rise to supergraphene whose mechanical properties are expected to depend on its structure. However, this dependence is to date unclear. In this paper, explicit expressions for the in-plane stiffness and Poisson’s ratio of supergraphene are obtained using a mole-cular mechanics model. The theoretical results show that the in-plane stiffness of supergraphene is drastically (at least one order) smaller than that of graphene, whereas its Pois-son’s ratio is higher than 0.5. As the index number increases (i.e., the length of carbyne chains increases and the bond density decreases), the in-plane stiffness of supergraphene decreases while the Poisson’s ratio increases. By analyzing the relation among the layer modulus, in-plane stiffness and Poisson’s ratio, it is revealed that the mechanism of the faster decrease in the in-plane stiffness than the bond density is due to the increase of Poisson’s ratio. These findings are useful for future applications of supergraphene in nanomechanical systems.     

O,O-二丁基二硫代磷酸锌制备及光谱分析

采用二步法合成出O,O-二丁基二硫代磷酸锌(ZBPD),通过UV-Vis,FTIR,TG-DSC对其进行检测和表征,揭示出ZBPD的微观结构和内在规律性。UV-Vis检测出了ZBPD在212.0和227.0 nm有二个吸收峰,分别是n→σ*和π→π*电子跃迁产生的,吸收峰强度随ZBPD浓度呈规律性变化,为企业ZBPD产品质量检测,提供了基础数据。FTIR揭示了ZBPD分子内部的各元素之间的化学键键型。TG-DSC检测出ZBPD的质量变化与热效应两种信息,ZBPD的DSC曲线很复杂,84.3 ℃存在一个很宽的吸收峰,245.0,344.3,476.1,518.7 ℃存在四个放热峰,和ZBPD分子结构和少量杂质有关,ZBPD分解温度偏高,为采用硫化仪研究ZBPD的橡胶硫化性能提供参考。本研究为企业选定工作标准品,对ZBPD工业化生产进行跟踪检测,评判ZBPD的产品性能指标,填报立项ZBPD化工行业标准的申报,撰写标准草案提供基础实验数据。     

考虑专家偏好的创新型企业创新能力评价方法

为解决创新型企业创新能力评价过程中专家偏好差异和指标量纲不一致等问题,文章构建了一个科学的评价指标体系,运用考虑专家偏好的效用函数对创新能力评价指标进行效用估算,并计算灰色关联系数;最后运用TOPSIS方法对创新型企业的创新能力进行综合评价和排序。数值实例证明了该方法的科学性和实用性。     

多扇图的Pebbling数和Graham猜想

图G的pebbling数f(G)是最小的整数n,使得不论n个pebble如何放置在G的顶点上,总可以通过一系列的pebbling移动把1个pebble移到任意一个顶点上,其中一个pebbling移动是从一个顶点处移走两个pebble而把其中的一个移到与其相邻的一个顶点上。Graham猜想对于任意的连通图G和H有f(G×H)f(G)f(H)。多扇图F_n1,n2,…,nm是指阶为n₁+n₂+…+n_m+1的联图P₁∨(P_n1∪P_n2∪…∪P_nm)。本文首先给出了多扇图的pebbling数,然后证明了多扇图F_n1,n2,…,nm具有2-pebbling性质,最后论述了对于一个多扇图和一个具有2-pebbling性质的图的乘积来说,Graham猜想是成立的。作为一个推论,当G和H都是多扇图时,Graham猜想成立。     

Comments on ＂General solutions of plane problem for power function curved cracks＂

An error has been found in Ref.[1].In the case of n =2,authors of Ref.[1] suggested the following conformal mapping function:     

Non-homogeneous model for a side heated square cavity filled with a nanofluid

A side heated two dimensional square cavity filled with a nanofluid is here studied. The side heating condition is obtained by imposing two different uniform temperatures at the vertical boundary walls. The horizontal walls are assumed to be adiabatic and all boundaries are assumed to be impermeable to the base fluid and to the nanoparticles. In order to study the behavior of the nanofluid, a non-homogeneous model is taken into account. The thermophysical properties of the nanofluid are assumed to be functions of the average volume fraction of nanoparticles dispersed inside the cavity. The definitions of the nondimensional governing parameters (Rayleigh number, Prandtl number and Lewis number) are exactly the same as for the clear fluids. The distribution of the nanoparticles shows a particular sensitivity to the low Rayleigh numbers. The average Nusselt number at the vertical walls is sensitive to the average volume fraction of the nanoparticles dispersed inside the cavity and it is also sensitive to the definition of the thermophysical properties of the nanofluid. Highly viscous base fluids lead to a critical behavior of the model when the simulation is performed in pure conduction regime. The solution of the problem is obtained numerically by means of a Galerkin finite element method.     

On a difficulty in the formulation of initial and boundary conditions for eigenfunction expansion solutions for the start-up of fluid flow

Most mathematics and engineering textbooks describe the process of “subtracting off” the steady state of a linear parabolic partial differential equation as a technique for obtaining a boundary-value problem with homogeneous boundary conditions that can be solved by separation of variables (i.e., eigenfunction expansions). While this method produces the correct solution for the start-up of the flow of, e.g., a Newtonian fluid between parallel plates, it can lead to erroneous solutions to the corresponding problem for a class of non-Newtonian fluids. We show that the reason for this is the non-rigorous enforcement of the start-up condition in the textbook approach, which leads to a violation of the principle of causality. Nevertheless, these boundary-value problems can be solved correctly using eigenfunction expansions, and we present the formulation that makes this possible (in essence, an application of Duhamel's principle). The solutions obtained by this new approach are shown to agree identically with those obtained by using the Laplace transform in time only, a technique that enforces the proper start-up condition implicitly (hence, the same error cannot be committed).     

Combinatorial interpretations of Ramanujan’s tau function

We use a $q$-series identity by Ramanujan to give a combinatorial interpretation of Ramanujan’s tau function which involves $t$-cores and a new class of partitions which we call $(m,k)$-capsids. The same method can be applied in conjunction with other related identities yielding alternative combinatorial interpretations of the tau function.