Relaxation oscillations in a slow–fast modified Leslie–Gower model

In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.     

氢键准则在DMSO水溶液中应用的评价

利用分子动力学模拟方法, 分别采用几何准则和能量准则分析了不同浓度下的二甲基亚砜(DMSO)水溶液的氢键统计和动力学等特性. 结果显示, 两种氢键准则可以很好地反映出溶液的氢键性质随浓度的变化趋势. 通过分析比较发现, 由于几何准则不能有效地排除具有弱对势能的分子对, 因此其统计的氢键数量要大于能量准则的结果.此外, 能量准则对于分子间相对取向的区分存在不足, 进而引起氢键寿命的计算结果偏大.因此,为使氢键分析更加准确, 本文建议使用几何-能量混合型氢键准则.     

Geometric and operational optimization of 20-kHz probe-type sonoreactor for enhancing sonochemical activity

The use of a 20-kHz probe-type sonicator irradiating downward in a 500 mL vessel was optimized for the enhancement of the sonochemical activity in terms of the geometric and operational factors. These factors included the probe immersion depth (the vertical position of the probe), input power, height of the liquid from the bottom, horizontal position of the probe, and thickness of bottom plate The sonochemical oxidation reactions were investigated both quantitatively and qualitatively using calorimetry, KI dosimetry, and luminol (Sonochemiluminescence, SCL) techniques. The sonochemical activity was very positively affected by the vertical boundaries. The highest sonochemical activity was obtained when the probe was placed close to the bottom of the vessel (immersion depth of 60 mm), with a high input power (input power of 75%), and optimal liquid height condition (liquid height of 70 mm). The SCL image analysis showed that the cavitational activity zone gradually expanded around the probe body and changed into a circular shape as the experimental conditions were optimized, and consequently the sonochemical activity increased. The formation of a large bright circular-shaped activity zone could be attributed to the strong reflections of the ultrasound firstly, at the vessel bottom and secondly, at the liquid surface. On the other hand, the cavitational activity zone and the sonochemical activity were negatively affected by the horizontal boundaries when the probe was placed close to the side wall of the vessel. In addition, it was found that the sonochemical activity was also significantly affected by the thickness of the support plate owing to the reflection and transmission of the ultrasound at the boundary between the liquid and the solid media.     

电解水金属单原子催化剂的研究进展

氢能因其能量密度高、清洁无污染等特点,作为替代化石燃料的能源载体得到了广泛的研究.如何清洁高效地制备氢气受到了大量研究者的关注.当前,以化石能源的热反应所得副产氢气是主要来源.然而,采用该类方法不仅不能摆脱化石能源的使用以及温室气体的排放,还会造成生产氢气的纯度不高,碳氧化物杂质浓度过高的问题,严重影响氢气的后续使用.采用可再生能源(太阳能、风能等)所产富余电,进行电解水制氢,产生的氢气不含碳氧化合物杂质,纯度很高,可以真正实现碳的零排放,被认为是未来氢气来源的重要方式.目前,电解水制氢在制氢市场的所占份额较小,而造成这样局面的主要因素是该过程中的高能耗问题.为了降低能耗,开发高效催化剂加速两个电极上的电解反应的动力学尤为重要.近年,金属单原子催化剂(SACs)因其独特的结构,在很多研究中被用作电解水催化剂,进而开发出大量高性能的金属单原子电解水催化剂.本文综述了近年SACs在电解水催化方面的应用.首先,针对电解水反应本身,总结了阴阳极两侧的电极反应机制以及影响电极催化性能的关键吸附中间物种;然后,根据载体的不同,即合金、碳以及其它化合物将SACs分为三类,总结了相关电解水催化研究现状,并且针对不同类型SACs目前的发展情况,提出了它们各自存在的问题.其次,进一步总结了影响SACs电解水催化活性的因素,提出了四种决定SACs催化性能的影响因子,分别为金属原子的固有元素性质、配位环境、几何结构和负载量;同时讨论了这四类影响因素对SACs催化活性的影响机制,总结了调控各类影响因素的方法,为SACs的设计提出了一些建议.最后,展望了SACs在电解水催化中的应用,探讨了SACs在催化剂设计及催化机制研究方面的问题,提出了SACs在电解水催化中的未来发展方向.     

悬索大挠度风振响应的有限体积法分析

基于Lagrange原理,建立了一套新的悬索大挠度动力特性和动力响应分析的有限体积法列式,推导了结点力向量、质量矩阵和单元刚度矩阵的显式表达式。该列式的一个显著特点是直接利用工程应变定义结构变形,其物理意义明确,列式简单,适用于各种垂度和荷载情况的悬索大挠度动力分析。实例动力特性和随机风振响应分析表明,该有限体积列式不仅计算效率高,而且具有良好的计算精度。     

误差非线性回归模型基于几何方法的若干二阶渐近性质

该文用微分几何方法对AR(q)误差非线性回归模型若干二 阶渐近性质进行了研究. 作者基于Fisher信息阵在欧氏空间定义了内积，并在期望参数空间建立了几何结构. 基于上述几何结构，给出了AR(q)误差非线性回归模型若干二阶渐近性质的曲率表示. 将前人的一些结果推广到AR(q)误差非线性回归模型.      

Nodal Solutions of a p-Laplacian Equation

We prove that the p-Laplacian problem –_p u = f(x, u),with u on a bounded domain R^N, with p > 1 arbitrary, has a nodal solution providedthat f : x R R is subcritical, and f(x, t) / |t|^p –² is superlinear. Infinitely many nodal solutions are obtainedif, in addition, f(x, –t) = –f(x, t). 2000 MathematicsSubject Classification 35J20, 35J65, 58E05.     

A probabilistic analysis of a discrete-time evolution in recombination

We study the discrete-time evolution of a recombination transformation in population genetics. The transformation acts on a product probability space, and its evolution can be described by a Markov chain on a set of partitions that converges to the finest partition. We describe the geometric decay rate to this limit and the quasi-stationary behavior of the Markov chain when conditioned on the event that the chain does not hit the limit.     

Variational Analysis of Toda Systems

The author surveys some recent progress on the Toda system on a two-dimensional surface Σ,arising in models from self-dual non-abelian Chern-Simons vortices,as well as in differential geometry.In particular,its variational structure is analysed,and the role of the topological join of the barycentric sets of Σ is shown.