Stability of equilibrium solutions of a double power reaction-diffusion equation with a Dirac interaction

In this paper, information about the instability of equilibrium solutions of a nonlinear family of localized reaction-diffusion equations in dimension one is provided. More precisely, explicit formulas to the equilibrium solutions are computed and, via analytic perturbation theory, the exact number of positive eigenvalues of the linear operator associated to the stability problem is analyzed. In addition, sufficient conditions for blow up of the solutions of the equation are also discussed.     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

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.     

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.     

30℃时MgCl2-MgSO4-CH3CH2OH-H2O四元体系液固相平衡的研究

采用等温法测定了30℃时Mg Cl2-Mg SO4-CH3CH2OH-H2O四元体系及边界三元体系Mg Cl2-CH3CH2OH-H2O和Mg SO4-CH3CH2OH-H2O的相平衡数据,绘制了相图并划分了相应的结晶区。实验结果表明,随着乙醇-水体积比不同,四元体系Mg Cl2-Mg SO4-CH3CH2OH-H2O出现了不同的结晶区,随着乙醇含量的增加,Mg Cl2和Mg SO4的溶解度越来越小,不饱和区越来越小,体系中平衡固相的结晶水含量越来越低,说明乙醇具有一定的盐析作用和脱水作用。当乙醇-水体积比为5∶5时,是获得镁盐的最佳比例。这为芒硝和白钠镁矾共生矿中镁盐的分离和提纯提供基础的理论数据。     

基于认识模型建构与应用的化学教学设计*——“水溶液中的离子反应与离子平衡”一轮复习课

分析了“水溶液中的离子反应与离子平衡”主题内容,通过学生前测发现学生对这一部分内容的认识存在着认识水平较低、认识不够深入等问题。针对这一问题,在实际教学中通过构建水溶液中的离子反应与离子平衡认识模型的方式,创设真实的问题情境,引导学生明确任务类型、丰富认识角度、形成认识思路,从而使学生对主题内容的认识走向深入和系统。通过后测,分析了教学效果,进行了教学反思,为在教学实践中开展认识模型建构教学提供参考。     

基础化学教学中从化学视角解释医学知识*——以“龋齿的形成与防护”为例

为解决医学院学生难以运用化学知识联系解释医学内容的问题,以医学案例“龋齿的形成与防护”作为切入点,通过医学现象去揭示其中所蕴含的化学原理,探索将基础化学教学与医学内容相结合。采用化学与医学融合教学模式能够激发起学生学习化学的兴趣,培养学生思考分析解决问题的能力,为培养新时代复合型医学人才奠定基础。     

深入理解化学平衡常数及其应用——对2019年全国理综(Ⅰ卷)化学第28题的分析

在已有的化学平衡常数教学的基础上,提出认知化学平衡常数的新角度--化学平衡常数的多种表达式。依据教材中用浓度表示的化学平衡常数并结合理想气体状态方程,推导用物质的量分数及分压表示的化学平衡常数表达式,分析3者之间的区别和联系,进而应用化学平衡常数的多种表达形式解决2019年全国(Ⅰ卷)化学第28题中的相关问题,使学生深入理解解答这道高考试题的关键所在。同时,拓展了学生对平衡常数的认识,提升了学生灵活应用平衡常数解决问题的能力。