催化剂孔道结构设计及孔内反应-扩散耦合模拟

采用硬球-拟颗粒(HS-PPM)耦合方法并结合简化的集总反应模型,模拟了碳四(C4)烯烃催化裂解过程中反应物和产物在孔道内的反应-扩散耦合过程,提出了一种多级孔道结构可控设计方法,实现了对孔隙率、孔径和孔体积占比等参数的独立量化调控,建立了包含三种不同孔径分布的催化剂孔道模型并定义了量化参数对反应-扩散耦合进行表征.结...     

具有反应扩散的Hopfield神经网络的稳定性

本文利用平均Lyapunov函数,研究了具有反应扩散的Hopfield神经网络平衡位置的全局渐近稳定性及局部渐近稳定性.其结果包含了国际上一些最新结果为特例.     

A noniterative solution approach for parallel pseudospectral domain decomposition

A simple superposition technique is proposed for the solution of spectral collocation equations in multi-nonoverlapping subdomains. It is based on a property of linear differential equations that allows the interface conditions to be fully decoupled; thus yielding a strategy with a very high level of concurrency suitable for parallel computations. Numerical experiments indicate, for a fixed total number of collocation points, a significant degradation of spectral accuracy as the number of subdomains increases. While the technique generally yields reasonably good solution, a compromise between accuracy and geometric flexibility must be realized.     

具有密度制约的两种群食物链模型解的整体性态

讨论了一个具有密度制约的两种群食物链模型解的整体性态。首先,讨论该模型解的整体存在性和一致有界性,然后应用线性化方法和Lyapunov函数方法讨论了该模型非负平衡点的局部渐近稳定性和全局渐近稳定性。     

具反应扩散项的脉冲时滞Cohen-Grossberg神经网络的稳定性

讨论了一类具反应扩散项的脉冲变时滞 Cohen GrossberG神经网络在neu mann边界条件下的稳定性.通过构造分片连续的Lyapunov函数,结合neumann特征值问题,并利用GronwaLL beLLman脉冲积分不等式,得到了新的与反应扩散项和时滞有关的保证平衡点全局指数稳定性的代数判据     

Numerical solutions of a nonlinear reaction-diffusion system

This paper is concerned with finite difference solutions of a coupled system of nonlinear reaction-diffusion equations. The investigation is devoted to the finite difference system for both the time-dependent problem and its corresponding steady-state problem. The existence and uniqueness of a non-negative finite difference solution and three monotone iterative algorithms for the computation of the solutions are given. It is shown that the time-dependent problem has a unique non-negative solution, whereas the steady-state problem may have multiple non-negative solutions depending on the parameters in the problem. The different non-negative steady-state solutions can be computed from the monotone iterative algorithms by choosing different initial iterations. Also discussed is the asymptotic behaviour of the time-dependent solution in relation to the steady-state solutions. The asymptotic behaviour result gives some conditions ensuring the convergence of the time-dependent solution to a positive or semitrivial non-negative steady-state solution. Numerical results are given to demonstrate the theoretical analysis results.     

非线性反应扩散方程的广义条件对称

非线性反应扩散方程是一类在物理、生物、种群上有较多应用的方程,考虑其在幂函数扩散下所允许的一类二阶广义条件对称,通过广义条件对称。借助数学软件Maple,求得相应方程及其满足的对称群,通过对称群进一步得到精确解。     

Travelling waves in a differential flow reactor with simple autocatalytic kinetics

A simple prototype model for a differential flow reactor in which the possible initiation and propagation of a reaction-diffusion-convection travelling-wave solution (TWS) in the simple isothermal autocatalytic system A+mB (m+1)B, rate kab^m (m 1) is studied with special attention being paid to the most realistic cases (m=1,2). The physical problem considered is such that the reactant A (present initially at uniform concentration) is immobilised within the reactor. A reaction is then initiated by allowing the autocatalyst species to enter and to flow through the reaction region with a constant velocity. The structure of the permanent-form travelling waves supported by the system is considered and a solution obtained valid when the flow rate (of the autocatalyst) is very large. General properties of the corresponding initial-value problem (IVP) are derived and it is shown that the TWS are the only long-time solutions supported by the system. Finally, these results are complemented with numerical solutions of the IVP which confirm the analytical results and allow the influence of the parameters of the problem not accessible to the theoretical analysis to be determined.     

半开放平方衰减的立方自催化反应扩散系统中化学波的研究

建立半开放带平方衰减反应,立方自催化反应扩散系统的数学模型,分析系统的初边值问题和化学波的局部行为,得化学波的类型及产生的条件.研究行波解所具有的性质,编制有限差分法的计算程序,通过计算以验证理论分析的结果.     

一类分布参数动态系统的周期性分析

通过构造适当的Lyapunov泛函、利用M矩阵性质和不等式技巧, 在不要求神经网络激励函数的有界性、单调性和可微性弱保守条件下, 探讨了一类具有分布参数和分布时滞的Cohen-Grossberg动态神经网络周期解的存在性和指数稳定性问题, 提出了一系列充分性判据来确保这类同时具有分布参数和分布时滞神经网络周期解的存在性和指数稳定性, 并通过几个注解以及与其他文献结果进行比较说明了该方法的优越性. 最后, 给出了数值例子和计算机仿真来验证这一理论的有效性.