Mathematical Analysis of helical waves arising in some-reaction diffusion systems

部分反应扩散系统中产生的螺旋波的数学分析

基本信息

批准号：
12440032
负责人：
IKEDA Tsutomu
金额：
$ 7.23万
依托单位：
Ryukoku University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-12440032/
关键词：
self-propagating high-temperature syntheses planar traveling wave planar pulsating wave regular helical wave irregular helical wave wave patterns apparent activation energy bifurcation theory

项目摘要

A helical wave is observed in self-propagating high-temperature syntheses (SHS), for instance. One can create a high-quality uniform product by the SHS when a combustion wave keeps its profile and propagates at a constant velocity. When experimental conditions are changed, however, the planar traveling wave may lose its stability and give place some non-uniform ones. Actually, a planar pulsating wave appears through the Hopf bifurcation of planar traveling wave. Moreover, we observe a wave that propagates in the form of spiral encircling the cylindrical sample with several reaction spots. This wave is called a helical wave since it has been shown by our 3D numerical simulation that the isothermal surface of the wave has some wings and it helically rotates down as time passes on. Similar helical waves are observed also in propagation fronts of polymerizations in laboratory and they are obtained also by numerical simulation of some autocatalytic reactions as well as the SHS.We have been studied the existing condition of helical wave and the transition process of wave patterns from traveling mode to pulsating mode and/or helical mode, and we have obtained the following results:1. A stable helical wave can bifurcate directly from a planar traveling wave.2. Even if a traveling wave is stable in R, the corresponding planar traveling wave can be unstable in the band domain as well as in the cylindrical domain, and a helical wave takes the place of planar traveling wave.3. There are no stable helical wave when the band width L is small or the radius R of cylindrical domain is small.4. Helical waves with different numbers of reaction spots can coexist stably.

例如，在自我传播的高温合成（SHS）中观察到螺旋波。当燃烧波保持其轮廓并以恒定的速度传播时，可以通过SHS创建高质量的统一产品。但是，当更改实验条件时，平面行驶波可能会失去其稳定性，并给一些不均匀的稳定性。实际上，平面脉动波通过平面行驶波的HOPF分叉出现。此外，我们观察到一个波浪以螺旋形形式传播的波，用几个反应斑环绕圆柱样品。该波被称为螺旋波，因为我们的3D数值模拟已显示出波浪的等温表面具有一些翅膀，并且随着时间的流逝，它螺旋向下旋转。在实验室聚合的繁殖方面也观察到了类似的螺旋波，也通过数值模拟某些自催化反应以及SHS.S.我们进行了数值模拟，并且已经研究了螺旋波的现有条件以及从行进模式到脉动模式和/或螺旋模式的波动模式的过渡过程，我们已经获得了以下结果：1：1。稳定的螺旋波可以直接从平面行动波分叉2。即使行动波稳定在R中，相应的平面行驶波在带状域以及圆柱域中也可能不稳定，并且螺旋波代替了平面行动波。3。当带宽度L小或圆柱域的半径为小时时，没有稳定的螺旋波。4。具有不同反应斑点的螺旋波可以稳定共存。