三维多孔颗粒中一级扩散和反应过程的蒙特卡罗模拟

The Monte Carlo method was employed to simulate diffusion and reaction processes within three-dimensional porous catalyst pellets. The porous pellets used were represented by a Menger sponge and a uniform-pore structure respectively. Results obtained from the fractal pellet showed an intermediate low-slope asymptote in the logarithmic plot of reaction rate and reaction probability. However, the low-slope one did not appear when the reaction occurred within the uniform pellet. Moreover, it was certified that the fractal structure not only generated a new asymptote, but also reduced diffusion resistance of reactants and products.     

受平衡约束的平行反应体系的催化剂粒内反应-扩散过程模拟

以甲烷化体系为例,研究了受平衡约束的平行反应的催化剂粒内状态。采用正交配置法求解催化剂的一维、二维反应－扩散非等温模型。模拟结果表明,由于甲烷化反应与变换反应交互作用,导致变换反应在催化剂粒内正、逆反应均存在。内扩散效率因子不能准确描述催化剂内表面利用率,应考虑粒内参数分布。     

多时滞反应扩散Cohen-Grossberg神经网络的稳定性

研究了一类具有反应扩散项的时滞Cohen—Grossberg神经网络模型利用拓扑度理论和Lyapunov函数方法，研究了此类系统平衡点的存在性及全局指数稳定性，给出了判定定理．     

基于REDIM方法构建的亚网格燃烧模型及其应用

将近年发展的详细反应机理简化方法:反应-扩散流形(REDIM)方法与假定滤波密度函数相结合,构造了新的亚网格燃烧模型。由于REDIM方法既能描述快速反应状态又能描述扩散过程起主导作用的慢速反应状态,因此新构造的燃烧模型理论上可用于计算扩散和化学反应均起重要作用的湍流部分预混燃烧及分层燃烧模式。为了验证其性能,利用新模型对基准的Darmstadt湍流分层火焰燃烧器进行了大涡模拟(LES)计算:首先分别采用粗、细两种网格对无反应湍流状态进行了计算,以检验网格精度;随后对一个有分层效应的湍流燃烧状态进行了计算。LES计算得到的速度、温度、组分等统计信息与实验结果吻合良好,验证了新亚网格燃烧模型在预测湍流分层火焰方面的能力。     

一类具有时滞的食饵-捕食者模型的时空斑图

研究了一类具有时滞和反应扩散的食饵-捕食者模型的动力学行为.通过数学分析,发现了两种不同类型的不稳定性,并且详细给出了图灵不稳定的条件.在由反应扩散引起的不稳定的条件下,通过一系列的数值模拟,得到了参数空间中丰富的图灵结构,分别有点状斑图、条状斑图以及点状和条状共存的斑图结构.在由时滞引起的不稳定的条件下,通过数值模拟,得到了"黑眼斑图".这些结果表明,受时滞和扩散影响的模型具有丰富的动力学,揭示了该模型在实际生活中是非常有用的.     

一类基于反应扩散方程的连续源水污染模型

考虑具有初边值条件情况的水污染连续源模型,以反应扩散方程的形式建立模型进行模拟,并根据偏微分方程的常用解法求出解析解.     

一类多维反应扩散方程组初边值问题整体强解的存在唯一性

研究从生物物理学中提出的一类反应扩散方程组的初边值问题,通过对非线性项作出增长性、有界性和连续性的假设,利用近似解的积分估计和Galerkin方法证明了整体强解的存在性,并证明了解的唯一性.其结果说明了解的存在时间为0～∞,并为数值求解提供了可能性和理论基础.     

Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control

Finite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov–Krasovskii's functional and utilisation of Jensen’s inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.     

Mean square exponential stability of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays

In this paper, we establish a method to study the mean square exponential stability of the zero solution of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays. By using the properties of M-cone and inequality technique, we obtain some sufficient conditions ensuring mean square exponential stability of the zero solution of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays. The sufficient conditions are easily checked in practice by simple algebra methods and have a wider adaptive range. Two examples are also discussed to illustrate the efficiency of the obtained results.