Laboratory of Nonlinear Chemical Dynamics, Institute of Chemistry, Eötvös Loránd University, PO Box 32, H-1518 Budapest 112, Hungary.
Interface Focus. 2012 Aug 6;2(4):417-32. doi: 10.1098/rsfs.2012.0010. Epub 2012 Mar 28.
In his seminal 1952 paper, Alan Turing predicted that diffusion could spontaneously drive an initially uniform solution of reacting chemicals to develop stable spatially periodic concentration patterns. It took nearly 40 years before the first two unquestionable experimental demonstrations of such reaction-diffusion patterns could be made in isothermal single phase reaction systems. The number of these examples stagnated for nearly 20 years. We recently proposed a design method that made their number increase to six in less than 3 years. In this report, we formally justify our original semi-empirical method and support the approach with numerical simulations based on a simple but realistic kinetic model. To retain a number of basic properties of real spatial reactors but keep calculations to a minimal complexity, we introduce a new way to collapse the confined spatial direction of these reactors. Contrary to similar reduced descriptions, we take into account the effect of the geometric size in the confinement direction and the influence of the differences in the diffusion coefficient on exchange rates of species with their feed environment. We experimentally support the method by the observation of stationary patterns in red-ox reactions not based on oxihalogen chemistry. Emphasis is also brought on how one of these new systems can process different initial conditions and memorize them in the form of localized patterns of different geometries.
在他 1952 年的开创性论文中，艾伦·图灵预测扩散可以自发地驱动最初均匀的化学反应溶液形成稳定的空间周期性浓度模式。直到近 40 年后，才能在等温单相反应系统中首次无可置疑地证明这种反应-扩散模式的存在。在接下来的近 20 年中，这类例子的数量几乎没有增加。我们最近提出了一种设计方法，使得在不到 3 年内此类例子的数量增加到了 6 个。在本报告中，我们正式证明了我们原始的半经验方法，并通过基于简单但现实的动力学模型的数值模拟支持该方法。为了保留真实空间反应器的一些基本特性，同时将计算复杂度保持在最低水平，我们引入了一种新的方法来简化这些反应器的受限空间方向。与类似的简化描述不同，我们考虑了在受限方向上的几何尺寸的影响，以及扩散系数的差异对物种与其进料环境之间交换速率的影响。我们通过观察基于氧化卤化学的氧化还原反应中的稳定模式来实验支持该方法。还强调了这些新系统中的一个如何处理不同的初始条件，并以不同几何形状的局部模式形式将它们记忆下来。
