Gaspard P., Klages R.
Center for Nonlinear Phenomena and Complex Systems and Service de Chimie Physique, Faculte des Sciences, Universite Libre de Bruxelles, Campus Plaine, Code Postal 231, B-1050 Brussels, Belgium.
Chaos. 1998 Jun;8(2):409-423. doi: 10.1063/1.166323.
We study the consequences of deterministic chaos for diffusion-controlled reaction. As an example, we analyze a diffusive-reactive deterministic multibaker and a parameter-dependent variation of it. We construct the diffusive and the reactive modes of the models as eigenstates of the Frobenius-Perron operator. The associated eigenvalues provide the dispersion relations of diffusion and reaction and, hence, they determine the reaction rate. For the simplest model we show explicitly that the reaction rate behaves as phenomenologically expected for one-dimensional diffusion-controlled reaction. Under parametric variation, we find that both the diffusion coefficient and the reaction rate have fractal-like dependences on the system parameter. (c) 1998 American Institute of Physics.
我们研究了确定性混沌对扩散控制反应的影响。作为一个例子，我们分析了一个扩散反应确定性多面包师模型及其参数依赖变体。我们将模型的扩散和反应模式构建为弗罗贝尼乌斯 - 佩龙算子的本征态。相关的本征值提供了扩散和反应的色散关系，因此，它们决定了反应速率。对于最简单的模型，我们明确表明反应速率的表现符合一维扩散控制反应的唯象预期。在参数变化下，我们发现扩散系数和反应速率对系统参数都有类似分形的依赖性。（c）1998年美国物理研究所。
