集中生长系统中亚微米图灵斑图的标度
Scaling of submicrometric Turing patterns in concentrated growing systems
摘要：
图灵型的周期性空间结构的波长是所考虑的反应扩散动力学的一个内在属性，我们解决了在微观尺度上给定的动力学参数的控制问题。直接模拟蒙特卡罗方法，最初介绍了模拟粒子动力学在稀薄气体，适用于模拟浓溶液。我们在适当的边界条件下对亚微米图灵图案进行了模拟，并表明考虑到溶剂在化学机制中的作用使我们能够控制结构的波长。通常，溶液浓度加倍导致波长减小2。研究结果可用于化工中亚微米性能可控材料的设计。这也可以被认为是胚胎在形态发生中比例保持的一种可能解释。
英文摘要：
The wavelength of a periodic spatial structure of Turing type is an intrinsic property of the considered reaction-diffusion dynamics and we address the question of its control at the microscopic scale for given dynamical parameters. The direct simulation Monte Carlo method, initially introduced to simulate particle dynamics in rarefied gases, is adapted to the simulation of concentrated solutions. We perform simulations of a submicrometric Turing pattern with appropriate boundary conditions and show that taking into account the role of the solvent in the chemical mechanism allows us to control the wavelength of the structure. Typically, doubling the concentration of the solution leads to decreasing the wavelength by two. The results could be used to design materials with controled submicrometric properties in chemical engineering. They could also be considered as a possible interpretation of proportion preservation of embryos in morphogenesis.
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