Generalization of the Kelvin equation for arbitrarily curved surfaces

Capillary condensation, which takes place in confined geometries, is the first-order vapor-to-liquid phase transition and is explained by the Kelvin equation, but the equation's applicability for arbitrarily curved surface has been long debated and is severe problem. Recently, we have proposed generic dynamic equations for moving surfaces. Application of the equations to the vapor/fluid interfaces in chemical equilibrium conditions nearly trivially solves the generalization problem for the Kelvin equation. The equations are universally true for any surfaces: atomic, molecular, micro or macro scale, real or virtual, Riemannian or pseudo-Riemannian, active or passive.     

Synthesis and characterization of silica-coated Fe3O4 nanoparticle@silylpropyl triethylammonium polyoxometalate as an organic–inorganic hybrid heterogeneous catalyst for the one-pot synthesis of tetrahydrobenzimidazo[2,1-b]quinazolin-1(2H)-ones

In this study, silica-coated Fe₃O₄ nanoparticle@silylpropyl triethylammonium polyoxometalate catalyst was fabricated and characterized using atomic absorption, inductively coupled plasma optical emission spectrometry, elemental analysis, thermogravimetric analysis, Fourier-transform infrared, scanning electron microscopy, energy-dispersive X-ray spectroscopy, and vibrating sample magnetometry analyses. The activity of this catalyst was examined in the synthesis of tetrahydrobenzimidazo[2,1-b]quinazolin-1(2H)-ones. The bonding of the polyoxometalate to the surface of the nanoparticles exhibited excellent catalytic activity in this synthesis. Besides, the catalyst showed good reusability and recovery from the reaction mixture. Tetrahydrobenzimidazo[2,1-b]quinazolin-1(2H)-ones were synthesized in high yields in the presence of inexpensive supported solid acid catalysts under classical heating conditions.     

Co-hydrolysis and Seed-Induced Synthesis of Basic Mesoporous ZSM-5 Zeolites with Enhanced Catalytic Performance

For zeolite catalysts, the regulation of active site and pore structure plays an important role in the enhancement of their catalytic performance. In this work, a one-pot and organic template-free co-regulation route is proposed to straightforwardly synthesize basic mesoporous ZSM-5 zeolites with adjustable alkaline-earth metal species. The synthesis pathway combines two decisive strategies: 1) the seed-induced interface assembly growth method and 2) the acidic co-hydrolysis/condensation of aluminosilicate species and alkaline-earth metal (e.g., Mg, Ca, Sr, or Ba) sources. It is interesting that the mesoporous structure was self-evolved through particle-attached seed-interfacial crystallization without the assistance of any template. Meanwhile, the incorporation of alkaline-earth metals species is homogeneous and highly dispersed in the solid products during the whole crystallization process, and finally generate the superior basicity. Catalysis tests of the as-synthesized samples displayed their novel performance in the typical base reaction of Knoevenagel condensation, even for bulky substrates owing to the enhanced diffusion arising from the meso/microporous network. This finding opens new possibilities for facile, cost-effective, and environmentally friendly synthesis of mesoporous high-silica zeolites with tunable acid/base properties, and deepens our understanding of the particle-attached crystallization.     

Synthesis,crystal structure and conformational analysis of an unexpected [1,5]dithiocine product of aminopyridine and thiovanillin

The condensation reaction of 2‐mercapto‐3‐methoxybenzaldehyde with 3‐aminopyridine afforded an unexpected N‐alkylated [1,5]dithiocine instead of the N‐salicylideneaniline. The proposed mechanism for this condensation involves a strong intramolecular hydrogen bond between the thiol and the amine groups, leading to a second condensation. The corresponding product, i.e. 4,10‐dimethoxy‐13‐(pyridin‐3‐yl)‐6H,12H‐6,12‐epiminodibenzo[b,f][1,5]dithiocine methanol 0.463‐solvate, C₂₁H₁₈N₂O₂S₂·0.463CH₃OH, was characterized by single‐crystal X‐ray diffraction analysis. The supramolecular structure shows π–π stacking and S…S interactions in the crystal packing. Within the asymmetric unit, two geometries of the N atom are observed. Although a planar geometry should be expected, a pyramidal one is observed due to the crystal packing. The presence of the two geometries was further supported by density functional theory (DFT) calculations that show an electronic energy difference of less than 2 kJ mol^?1 between the two conformers.     

Preparation of highly ordered mesoporous AlSBA-15-SO3H hybrid material for the catalytic synthesis of chalcone under solvent-free condition

Single-step preparation of SBA-15 materials functionalized with both propylsulfonic acid groups and aluminum species (AlSBA-15-SO₃H) was carried out by hydrothermal treatment of a mixture of aluminum isopropoxide, 3-mercaptopropyltriethoxysilane, tetraethoxysilane, and triblock copolymer surfactant. At Si/Al molar ratio of 11-96, the materials exhibited well-ordered hexagonally arranged mesopores with pore diameter of ca. 9 nm, BET surface area of 546.9-666.0 m² g⁻¹, and pore volume of 0.82-1.03 cm³ g⁻¹. As-prepared AlSBA-15-SO₃H was successfully used in the Claisen-Schmidt condensation reaction of benzaldehyde with acetophenone to produce chalcone under solvent-free condition, and the influence of the reaction parameters including temperatures, molar ratios of BZD to APN, and aluminum loadings were considered during the chalcone synthesis procedure. It showed that AlSBA-15-SO₃H exhibited significantly high catalytic activity and selectivity, outperforming the reference catalysts such as sulfuric acid, ZSM-5, and acidic MCM-49. In addition, the catalytic stability and regeneration of AlSBA-15-SO₃H was studied.     

Collective Strategy Condensation: When Envy Splits Societies

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait—the propensity to compare one’s own success with that of others—expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.     

On non-measurability of in its second dual

We show that with the weak topology is not an intersection of Borel sets in its Cech-Stone extension (and hence in any compactification). Assuming (CH), this implies that has no continuous injection onto a Borel set in a compact space, or onto a Lindelöf space. Under (CH), this answers a question of Arhangel'ski.

     

二维六角晶体材料中的Dirac 电子

本文综述由碳、硅、硼氮和二硫化钼等单元素或双元素构成的二维六角晶体材料中Dirac 电 子的研究成果与最新进展。文章从引言开始,接着介绍这些二维六角晶体材料的空间结构和基本 电子性质;然后探讨外场调控下这些材料在能谱和光吸收、量子输运、激子凝聚和热Josephson 效 应,以及拓扑量子相变等方面所表现出来的新奇的物理现象、简要的理论处理和可能的应用前景; 最后给出二维六角晶体材料相关研究的总结和展望。谨以本文献给南京大学建立物理学科100 周 年。     

谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似方法研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC)．导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响．以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合．     

An effective method of accelerating Bose gases using magnetic coils

Based on the experimental device which is a non-uniform magnetic field to trap an atom, we show how to obtain a certain velocity of a Bose gas by controlling the magnetic coils. By comparing the relationship of the different current supply and delay time versus the ultimate velocity of the atom, we theoretically predict the method of accelerating the gases to an expected velocity. This method is of great convenience and significance for the applications in cold atom physics and precision measurements.