...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Applied Mathematical Modelling >Mixed quadratic-cubic autocatalytic reaction-diffusion equations: Semi-analytical solutions
【24h】

Mixed quadratic-cubic autocatalytic reaction-diffusion equations: Semi-analytical solutions

机译：混合二次立方自催化反应扩散方程：半解析解

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Semi-analytical solutions for autocatalytic reactions with mixed quadratic and cubic terms are considered. The kinetic model is combined with diffusion and considered in a one-dimensional reactor. The spatial structure of the reactant and autocatalyst concentrations are approximated by trial functions and averaging is used to obtain a lower-order ordinary differential equation model, as an approximation to the governing partial differential equations. This allows semi-analytical results to be obtained for the reaction-diffusion cell, using theoretical methods developed for ordinary differential equations. Singularity theory is used to investigate the static multiplicity of the system and obtain a parameter map, in which the different types of steady-state bifurcation diagrams occur. Hopf bifurcations are also found by a local stability analysis of the semi-analytical model. The transitions in the number and types of bifurcation diagrams and the changes to the parameter regions, in which Hopf bifurcations occur, as the relative importance of the cubic and quadratic terms vary, is explored in great detail. A key outcome of the study is that the static and dynamic stability of the mixed system exhibits more complexity than either the cubic or quadratic autocatalytic systems alone. In addition it is found that varying the diffusivity ratio, of the reactant and autocatalyst, causes dramatic changes to the dynamic stability. The semi-analytical results are show to be highly accurate, in comparison to numerical solutions of the governing partial differential equations.
机译：考虑混合二次和三次项的自动催化反应的半解析解。动力学模型与扩散相结合，并在一维反应堆中考虑。通过试验函数来近似反应物和自催化剂浓度的空间结构，并取平均值来获得低阶常微分方程模型，作为对控制的偏微分方程的近似。这允许使用针对常微分方程开发的理论方法获得反应扩散池的半分析结果。奇异性理论用于研究系统的静态多重性并获得一个参数图，其中会出现不同类型的稳态分叉图。通过半分析模型的局部稳定性分析也可以找到Hopf分支。随着三次和二次项的相对重要性的变化，分叉图的数量和类型的过渡以及发生霍普夫分叉的参数区域的变化都得到了非常详细的探讨。该研究的关键成果是混合系统的静态和动态稳定性比单独的立方或二次自催化系统具有更高的复杂性。另外发现，改变反应物和自催化剂的扩散率会引起动态稳定性的显着变化。与控制偏微分方程的数值解相比，半解析结果显示出很高的准确性。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号