In 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.
