Thermal States in Conformal QFT. I

We analyze the set of locally normal KMS states w.r.t. the translation group for a local conformal net A{{\mathcal A}} of von Neumann algebras on \mathbb R{\mathbb R} . In this first part, we focus on the completely rational net A{{\mathcal A}} . Our main result here states that, if A{{\mathcal{A}}} is completely rational, there exists exactly one locally normal KMS state j{\varphi} . Moreover, j{\varphi} is canonically constructed by a geometric procedure. A crucial r?le is played by the analysis of the “thermal completion net” associated with a locally normal KMS state. A similar uniqueness result holds for KMS states of two-dimensional local conformal nets w.r.t. the time-translation one-parameter group.     

扁平多分支管内两相流流量分配的数值模拟

利用FLUENT软件,对一水平矩形扁平多分支管内,氮气和水为工质的气液两相流流量分配问题进行了数值模拟,并与实验数据进行了对比.数值模拟计算分析了相间曳力作用模型、气液进口条件、壁面粗糙度、离散相直径、结构参数对两相流流量分配的影响,指出为了提高模拟计算准确度,需要改进和完善现有模型.     

Cationic β-Scission of C−H and C−C Bonds for Selective Dimerization and Subsequent Sulfur-Free RAFT Polymerization of α-Methylstyrene and Isobutylene

A series of exo-olefin compounds ((CH₃)₂C(PhY)−CH₂C(=CH₂)PhY) were prepared by selective cationic dimerization of α-methylstyrene (αMS) derivatives (CH₂=C(CH₃)PhY) with p-toluenesulfonic acid (TsOH) via β-C−H scission. They were subsequently used as reversible chain transfer agents for sulfur-free cationic RAFT polymerization of αMS via β-C−C scission in the presence of Lewis acid catalysts such as SnCl₄. In particular, exo-olefin compounds with electron-donating substituents, such as a 4-MeO group (Y) on the aromatic ring, worked as efficient cationic RAFT agents for αMS to produce poly(αMS) with controlled molecular weights and exo-olefin terminals. Other exo-olefin compounds (R−CH₂C(=CH₂)(4-MeOPh)) with various R groups were prepared by different methods to examine the effects of R groups on the cationic RAFT polymerization. A sulfur-free cationic RAFT polymerization also proceeded for isobutylene (IB) with the exo-olefin αMS dimer ((CH₃)₂C(Ph)−CH₂C(=CH₂)Ph). Furthermore, telechelic poly(IB) with exo-olefins at both terminals was obtained with a bifunctional RAFT agent containing two exo-olefins. Finally, block copolymers of αMS and methyl methacrylate (MMA) were prepared via mechanistic transformation from cationic to radical RAFT polymerization using exo-olefin terminals containing 4-MeOPh groups as common sulfur-free RAFT groups for both cationic and radical polymerizations.