Stabilization to a positive equilibrium for some reaction–diffusion systems

The aim of this paper is to study the asymptotic behavior of solutions for some reaction–diffusion systems in biology. First, we establish a Liouville type theorem for entire solutions of these reaction–diffusion systems. Based on this theorem, we derive the stabilization of the solutions of the reaction–diffusion system to the unique positive constant state, under the condition that this positive constant state is globally stable in the corresponding kinetic systems. Two specific examples about spreading phenomena from ecology and epidemiology are given to illustrate the application of this theory.     

1,3-丁二烯选择性加氢催化剂的设计策略以及构效关系

催化裂化是石油化工的核心单元之一.从催化裂化尾气中分离出来的碳四馏分富含许多的不饱和烯烃,如1-丁烯、顺、反式-2-丁烯以及少量的1,3-丁二烯,这些不饱和烯烃可以通过后续聚合反应,生成合成橡胶和工程塑料的重要原料,具有重要的应用价值.上述工艺过程对原料中1,3-丁二烯的含量(<100~200 ppm)有严苛的要求.采用选择性加氢技术对碳四馏分中的1,3-丁二烯进行选择性加氢,将其转化为更高附加值的单烯烃是一个理想的解决方案.然而,1,3-丁二烯加氢反应得到的单烯烃可能发生深度加氢得到副产物丁烷.因此,开发高效选择性加氢催化剂对碳四资源的利用具有重要的现实意义.另一方面,1,3-丁二烯加氢反应可以作为模型反应,用来考察选择性加氢催化剂的性能.基于此,该反应无论在工业界还是学术界均受到广泛关注.尽管如此,有关1,3-丁二烯加氢催化剂研究进展方面的综述极少.仅有关于1,3-丁二烯加氢作为模型反应的综述报道.本文对过去半个世纪以来1,3-丁二烯加氢反应中不同催化剂的发展历程进行系统综述,特别是包括Pd,Pt和Au等的单一贵金属催化剂.重点介绍以下内容:(1)固体催化剂构效关系,包括活性金属尺寸效应、晶面和形貌效应以及载体效应(晶相、孔道和酸碱性);(2)高性能催化剂的设计新策略,如单原子催化剂、核壳结构催化剂、金属-离子液复合催化体系以及载体的形貌调控;(3)催化剂的反应机理和失活机理.提出了1,3-丁二烯选择性加氢高性能催化剂开发面临的挑战,并对潜在的发展方向进行了展望.本文认为随着纳米技术和金属纳米材料合成方法的快速发展,对贵金属活性组分进行原子层面上的调控(包括形貌、尺寸以及单原子配位环境等)已成为可能.这将有助于研制出一类新型高性能选择性加氢催化材料,从而实现高转化率条件下高附加值单烯烃的定向转化.此外,载体的酸碱性和孔道结构的调控有助于进一步调节催化剂的抗积炭性能,也是未来发展的一个重要方向.     

Classical solution for a nonlinear hybrid system modeling combustion in a multilayer porous medium

Combustion processes in porous media have been used by the petroleum engineering industry to extract heavy oil from reservoirs. This study focuses on a one-dimensional nonlinear hybrid system consisting of $n$ reaction–diffusion–convection equations coupled with $n$ ordinary differential equations, which models a combustion front moving through a porous medium with $n$ parallel layers. The state variables are the temperature and fuel concentration in each layer. Coupling occurs in both the reaction function and differential operator coefficients. We prove the existence of a classical solution, first locally and then globally over time, to an initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. The local solution is obtained by defining an operator in a set of Hölder continuous functions and using Schauder’s fixed-point theorem to find a fixed point as the desired solution. Using Zorn’s lemma, we extend the local solution to a global solution, proving that the first-order spatial derivative of the temperature in each layer is a bounded function.     

Theoretical study on the catalytic properties of single-atom catalyst stabilised on silicon-doped graphene sheets

ABSTRACT

The stable configurations, electronic structures and catalytic activities of single-atom metal catalyst anchored silicon-doped graphene sheets (3Si-graphene-M, M?=?Ni and Pd) are investigated by using density functional theory calculations. Firstly, the adsorption stability and electronic property of different gas reactants (O₂, CO, 2CO, CO/O₂) on 3Si-graphene-M substrates are comparably analysed. It is found that the coadsorption of O₂/CO or 2CO molecules is more stable than that of the isolated O₂ or CO molecule. Meanwhile, the adsorbed species on 3Si-graphene-Ni sheet are more stable than those on the 3Si-graphene-Pd sheet. Secondly, the possible CO oxidation reactions on the 3Si-graphene-M are investigated through Eley–Rideal (ER), Langmuir–Hinshelwood (LH) and new termolecular Eley–Rideal (TER) mechanisms. Compared with the LH and TER mechanisms, the interaction between 2CO and O₂ molecules (O₂?+?CO → CO₃, CO₃?+?CO → 2CO₂) through ER reactions (< 0.2?eV) are an energetically more favourable. These results provide important reference for understanding the catalytic mechanism for CO oxidation on graphene-based catalyst.     

Functional sample path properties of subsequence's C-R increments for a Wiener process in Hlder norm

In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by H¨older norm, we discuss the functional sample path properties of subsequence's C-R increments for a Wiener process in H¨older normThe obtained results,generalize the corresponding results of Chen and the classic Strassen's law of iterated logarithm for a Wiener process.     

Predicting polycyclic aromatic hydrocarbon formation with an automatically generated mechanism for acetylene pyrolysis

Using Reaction Mechanism Generator (RMG), we have automatically constructed a detailed mechanism for acetylene pyrolysis, which predicts formation of polycyclic aromatic hydrocarbons (PAHs) up to pyrene. To improve the data available for formation pathways from naphthalene to pyrene, new high‐pressure limit reaction rate coefficients and species thermochemistry were calculated using a combination of electronic structure data from the literature and new quantum calculations. Pressure‐dependent kinetics for the CH potential energy surface calculated by Zádor et al. were incorporated to ensure accurate pathways for acetylene initiation reactions. After adding these new data into the RMG database, a pressure‐dependent mechanism was generated in a single RMG simulation which captures chemistry from C to C. In general, the RMG‐generated model accurately predicts major species profiles in comparison to plug‐flow reactor data from the literature. The primary shortcoming of the model is that formation of anthracene, phenanthrene, and pyrene are underpredicted, and PAHs beyond pyrene are not captured. Reaction path analysis was performed for the RMG model to identify key pathways. Notable conclusions include the importance of accounting for the acetone impurity in acetylene in accurately predicting formation of odd‐carbon species, the remarkably low contribution of acetylene dimerization to vinylacetylene or diacetylene, and the dominance of the hydrogen abstraction CH addition (HACA) mechanism in the formation pathways to all PAH species in the model. This work demonstrates the improved ability of RMG to model PAH formation, while highlighting the need for more kinetics data for elementary reaction pathways to larger PAHs.