Pattern and wavenumber selection in the wake of fronts

在各种化学、生物和制造过程中，模式出现在界面之后。这个建议是特别动机Liesegang模式在经常性降水，细菌菌落图案，和自组织的纳米波纹形成离子轰击下的表面。在所有这些背景下，在实验和直接模拟中，都观察到了大量的规则和复杂的模式，因为它们是在移动的锋面之后形成的。从数学的角度来看，图案形成的前线一直知之甚少，但他们提供了一个主要途径，以系统地了解图案相分离过程中，表面演变，和生物生长。一个系统的，独立于模型的理解模式在前面，结合定量预测的计算工具，有可能既解释经典的100年历史的化学实验，并阐明生物聚集机制。锋后的相干模式允许对模式进行清晰的定性和定量预测。在这方面，拟议的研究将提供新的工具，定量的，确定性的模型验证。对图案化表面不稳定性的预测在制造过程中具有潜在的高影响。教育方面的拟议研究涉及本科生在两个夏季雷乌斯和四个研究生。

Pattern and wavenumber selection in the wake of frontsIn a variety of chemical, biological, and manufacturing processes, patterns emerge in the wake of interfaces. This proposal is particularly motivated by Liesegang patterns in recurrent precipitation, bacterial colony patterning, and self-organized nano-ripple formation under ion-bombardment of surfaces. In all those contexts, a plethora of regular and complex patterns has been observed as they form in the wake of moving fronts, both experimentally and in direct simulations. Pattern-forming fronts have been poorly understood from a mathematical view point, yet they provide a prime avenue to a systematic understanding of patterning in phase separation processes, surface evolution, and biological growth. A systematic, model-independent understanding of patterning in the wake of fronts, combined with computational tools for quantitative predictions, has the potential to both explain classic 100-year old chemical experiments and shed new lights on biological aggregation mechanisms. Coherent patterns in the wake of fronts allow for clean qualitative and quantitative predictions of patterns. In this respect, the proposed research will give new tools for quantitative, deterministic model validation. Predictions on patterned surface instabilities have potentially high impact in manufacturing processes. The educational aspect of the proposed research involves undergraduate students during two summer REUs and four graduate students.