Upper Bounds on Liouville First-Passage Percolation and Watabiki's Prediction

Given a planar continuum Gaussian free field h^𝒰 in a domain 𝒰 with Dirichlet boundary condition and any δ > 0, we let be a real-valued smooth Gaussian process where is the average of h^𝒰 along a circle of radius δ with center v. For γ > 0, we study the Liouville first-passage percolation (in scale δ), i.e., the shortest path distance in 𝒰 where the weight of each path P is given by . We show that the distance between two typical points is for all sufficiently small but fixed γ > 0 and some constant c^* > 0. In addition, we obtain similar upper bounds on the Liouville first-passage percolation for discrete Gaussian free fields, as well as the Liouville graph distance, which roughly speaking is the minimal number of euclidean balls with comparable Liouville quantum gravity measure whose union contains a continuous path between two endpoints. Our results contradict some reasonable interpretations of Watabiki's prediction (1993) on the random distance of Liouville quantum gravity at high temperatures.© 2019 Wiley Periodicals, Inc.     

工业催化:选择性提升策略

工业催化直接或间接贡献了世界GDP的20%-30%,推动了产业变革和社会进步.对于工业催化,开发高活性、高选择性和高稳定性的多相催化剂至关重要,而选择性是最主要的挑战.因为实现催化选择性的精确控制是绿色化学的重要概念之一,更是工业催化可持续发展的重要驱动力;而且,选择性不仅决定了催化过程的原子经济性,也影响到后续分离过程的能耗.针对多数工业催化反应存在'活性越高、选择性越低'的相互制约与矛盾问题,本文以若干能源化工催化反应为例,试图总结催化选择性提升的一般策略,以期为有关工业应用的催化新过程提供科学参考.多相催化一般经历与反应物有关的步骤(反应物的外扩散、内扩散和化学吸附)、与反应有关的步骤(活化和表面反应)、以及与产物相关的步骤(产物脱附、内扩散和外扩散).本文依此归纳并举例说明提高选择性的一般策略.在汽油催化吸附脱硫中,主要利用了催化剂中零价镍-氧化锌耦合活性中心的选择吸附策略,使零价镍优先吸附含硫化合物,从而实现选择性脱硫而不饱和烯烃.在甲苯和甲醇侧链烷基化反应中,主要利用了特定空间分布的酸碱吸附位,实现吸附甲苯和稳定甲醛中间体的协同匹配.在乙苯脱乙基型二甲苯异构化反应中,主要利用了双床层对催化剂功能的分离策略,在不同的择形催化剂床层中分别进行乙苯脱乙基反应和二甲苯异构化反应,从而提高对二甲苯的产量.在苯选择加氢制环己烯反应中,主要利用强化产品脱附的策略,促进环己烯产品从亲水改性的催化剂表面脱附,实现环己烯选择性的提升.这些炼油与化工研究案例中同时存在多个连串-平行反应,主要是利用吸附中心、反应中心在时间或空间上的耦合、解耦或限域策略,调控不同途径的扩散能垒、反应能垒,实现了催化剂选择性的提升.多相催化多是复杂过程,基于提高选择性的初步认识,还要结合具体复杂催化过程,系统研究单策略以及多策略组合作用下的选择催化过程,实现在合理时间尺度、空间尺度上设计高选择性的催化剂,而这本质上是一种介尺度催化.     

Solvent‐free ring‐opening polymerization of lactones with hydrogen‐bonding bisurea catalyst

Development of effective organocatalysts for the living ring‐opening polymerization (ROP) of lactones is highly desired for the preparation of biocompatible and biodegradable polyesters with controlled microstructures and physical properties. Herein, a new class of hydrogen‐bond donating bisurea catalysts is reported for the ROP of lactones under solvent‐free conditions. ROP of lactones mediated by the bisurea/7‐methyl‐1,5,7‐triazabicyclo[4.4.0]dec‐5‐ene (MTBD) catalyst exhibits a living/controlled manner, affording the polymers and copolymers with the well‐defined structure, predictable molecular weight, narrow molecular weight distribution, and high selectivity for monomer at low catalyst loadings at ambient temperature. The possible mechanism of bisurea/MTBD‐catalyzed ROP of lactones is proposed, in which the bisurea activates the carbonyl group of lactones while MTBD facilitates the nucleophilic attack of the initiating/propagating alcohol by hydrogen bonding. Moreover, the poly(ε‐caprolactone‐co‐δ‐valerolactone) [P(CL‐co‐VL)] random copolymers with various compositions were synthesized using the bisurea/MTBD catalyst. The measurements of thermal properties and crystalline structure demonstrate that the CL and VL units are cocrystallized in the crystalline phase of P(CL‐co‐VL) copolymers. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 90–100     

The spatial-temporal evolution of coherent structures in log law region of turbulent boundary layer

The spatial-temporal evolution of coherent structures(CS) is significant for turbulence control and drag reduction. Among the CS, low and high speed streak structures show typical burst phenomena. The analysis was based on a time series of three-dimensional and three-component(3D-3C) velocity fields of the flat plate turbulent boundary layer(TBL) measured by a Tomographic and Time-resolved PIV(Tomo TRPIV) system. Using multi-resolution wavelet transform and conditional sampling method, we extracted the intrinsic topologies and found that the streak structures appear in bar-like patterns. Furthermore, we seized locations and velocity information of transient CS, and then calculated the propagation velocity of CS based on spatial-temporal cross-correlation scanning. This laid a foundation for further studies on relevant dynamics properties.     

Binding of caffeic acid to human serum albumin by the retention data and frontal analysis

A new mathematical model and frontal analysis were used to characterize the binding behavior of caffeic acid to human serum albumin (HSA) based on high‐performance affinity chromatography. The experiments were carried out by injecting various mole amounts of the drug onto an immobilized HSA column. They indicated that caffeic acid has only one type of binding site to HSA on which the association constant was 2.75 × 10⁴/m . The number of the binding site involving the interaction between caffeic acid and HSA was 69 nm . The data obtained by the frontal analysis appeared to present the same results for both the association constant and the number of binding sites. This new model based on the relationship between the mole amounts of injection and capacity factors assists understanding of drug–protein interaction. The proposed model also has the advantages of ligand saving and rapid operation. Copyright © 2014 John Wiley & Sons, Ltd.     

Cobalt Imidazolate Metal–Organic Frameworks Photosplit CO2 under Mild Reaction Conditions

Metal–organic frameworks (MOFs) have shown great promise for CO₂ capture and storage. However, the operation of chemical redox functions of framework substances and organic CO₂‐trapping entities which are spatially linked together to catalyze CO₂ conversion has had much less attention. Reported herein is a cobalt‐containing zeolitic imidazolate framework (Co‐ZIF‐9) which serves as a robust MOF cocatalyst to reduce CO₂ by cooperating with a ruthenium‐based photosensitizer. The catalytic turnover number of Co‐ZIF‐9 was about 450 within 2.5 hours under mild reaction conditions, while still keeping its original reactivity during prolonged operation.