Localized Structures in Spatially Extended Systems: Fronts and Defects

在许多连续介质系统中，诸如前沿、缺陷、斑点或脉冲的空间局部化结构是常见的，并且包括沿沿着神经纤维传播的脉冲、光学和化学系统中的耗散孤子、压缩下细长结构的局部屈曲以及振动颗粒介质中的耗散孤子。 流体的例子包括局部对流、涡流和液滴。 这些不同的系统有两个共同点：（i）它们是由空间均匀强迫驱动的耗散系统，以及（ii）有一个强迫范围，在这个范围内，不同的有限振幅扰动可以导致不同的局域态。 研究人员试图在新的方向上扩展现有的理论，重点关注材料科学中出现的问题，例如从过冷液体中成核和生长晶体，以及可能导致的有序和无序结构。 这些包括具有短程有序但没有长程有序的结构，称为准晶。 形成的结构类型反过来又决定了所得材料的强度和其他性能，这在很大程度上取决于结晶过程的速度。 该项目的目的是提供一个全面的了解背后的机制，发生在不同温度的液体在这个和相关的系统中的不同类型的增长。 本项目由两名博士后研究生参与，主要研究二维和三维空间局域结构的性质。 保守和非保守系统被认为是重点相场和动力学密度泛函理论模型的软物质结晶从过冷熔体。 取决于该过程的速度，所得到的材料可以是晶体、非晶或准晶体。 每种类型的局部化结构都可以作为晶体成核的临界核，因此特别令人感兴趣。 该项目的重点是这些结构的性质，以及将它们与熔体分离的前沿的性质。 稳定和传播的前线被认为是和过程，确定的传播速度进行了详细的研究。 这些包括钉扎的前面的微观结构背后，并与守恒质量模式的相互作用。 该项目还包括在非保守系统中并行研究行进脉冲，并详细研究不同类型的缺陷，其中钉扎到微观结构是重要的。 研究人员使用的技术包括分叉理论，再加上数值分支以下和直接数值模拟的现实系统。 该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Spatially localized structures such as fronts, defects, spots or pulses are common in many continuum systems, and include pulses propagating along nerve fibers, dissipative solitons in optical and chemical systems, localized buckling of slender structures under compression, and oscillons in vibrating granular media. Examples from fluids include localized convection, vortices and drops. These diverse systems have two things in common: (i) they are dissipative systems driven by spatially uniform forcing, and (ii) there is range of forcing within which the application of different finite amplitude perturbations can lead to distinct localized states. The investigator seeks to extend existing theory in new directions, focusing on problems arising in materials science such as the nucleation and growth of crystals from a supercooled liquid, and the ordered and disordered structures that may result. These include structures with short-range order but no long-range order called quasicrystals. The type of structure that forms in turn determines the strength and other properties of the resulting material and this depends strongly on the speed of the crystallization process. The aim of the project is to provide a comprehensive understanding of the mechanisms behind the different types of growth that take place at different temperatures of the liquid both in this and in related systems. Two postdoctoral students are engaged in the research of the project.In this project the investigator and his colleagues study the properties of spatially localized structures in two and three dimensions. Both conserved and nonconserved systems are considered with a focus on phase field and dynamical density functional theory models of soft matter crystallization from a supercooled melt. Depending on the speed of this process, the resulting material may be crystalline, amorphous, or a quasicrystal. Localized structures of each type may serve as critical nuclei for the nucleation of the crystal and are therefore of particular interest. The project focuses on the properties of these structures, and the properties of the fronts that separate them from the melt. Both steady and propagating fronts are considered and the processes that determine the propagation speed are studied in detail. These include pinning of fronts to the microstructure behind them and the interaction with the conserved mass mode. The project also includes a parallel study of traveling pulses in nonconserved systems and a detailed study of different types of defects where pinning to microstructure is important. The techniques used by the investigator include bifurcation theory, coupled with numerical branch-following and direct numerical simulations of realistic systems. Two postdoctoral students are engaged in the research of the project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.