Center Manifold Theory for the Motions of Camphor Boats with Delta Function
Center Manifold Theory for the Motions of Camphor Boats with Delta Function
复制标题
具有Delta函数的樟脑船运动的中心流形理论
DOI：
10.1007/s10884-020-09824-9
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发表时间：
2020
影响因子：
1.3
通讯作者：
Ei Shin-Ichiro
中科院分区：
文献类型：
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作者：
Ikeda Kota;Ei Shin-Ichiro
研究了樟船的各种集体运动。樟船是通过樟脑分子改变水面表面张力而相互作用的自驱动颗粒。因此，即使在一维电路中，也可以观察到拥塞状态或阻塞(Suematsu等人。见Phys Revv E 81：056210,2010年)。在这种现象中，每个粒子的单向运动被认为是行波，樟脑分子的浓度形成了脉冲形状。因此，每一对粒子就像脉冲-脉冲相互作用一样相互作用。因此，我们认为EI(J dyn不同于EQU 14：85-137,2002)和EI等人提出的中心流形理论是正确的。(Physica D 165：176-198 2002)适用于分析樟脑船的集体运动。然而，我们模型中的空间不连续性，特别是线性化算子中Dirac Delta函数的存在，不能满足约化过程中的要求，因为作者在Ei(2002)和Ei等人的框架内发展了他们的关于光滑非线性的理论。(2002)。在本文中，我们推广了Ei(2002)和Ei等人的结果。(2002)，并在框架内建立了新的中心流形方法。最后，我们成功地严格简化了一个数学模型(Nagayama等人)。在Physica D：非线性现象194：151-165,2004)中)与牛顿方程和包括增量函数的反应扩散方程耦合到表示樟脑船运动的常微分系统。
Various collective motions of camphor boats have been studied. Camphor boats are self-driven particles that interact with each other through the change of surface tension on water surface by camphor molecules. Consequently, even in a one-dimensional circuit, a congested state or jamming can be observed (Suematsu et al. in Phys Rev E 81:056210, 2010). In this phenomenon, the unidirectional motion of each particle is considered a traveling wave, and the concentration of camphor molecules forms a pulse shape. Hence, each pair of particles interacts with each other like a pulse–pulse interaction. Thus, we expect that the center manifold theories proposed in Ei (J Dyn Differ Equ 14:85–137, 2002) and Ei et al. (Physica D 165:176–198 2002) are applicable for the analysis of the collective motion of camphor boats. However, spatial discontinuity in our model, in particular the existence of Dirac delta functions in a linearized operator, does not fulfill the requirement in the reduction process because the authors developed their theories in-framework and for smooth nonlinearity in Ei (2002) and Ei et al. (2002). In this article, we extend the results obtained in Ei (2002) and Ei et al. (2002) and establish a new center manifold approach in-framework. Finally, we succeed to rigorously reduce a mathematical model (Nagayama et al. in Physica D: Nonlinear Phenom 194:151–165, 2004) coupled with a Newtonian equation and a reaction–diffusion equation including delta functions to an ordinary differential system that represents the motions of camphor boats.