Spatial Structure and Dynamics of Non-Equilibrium Systems

9311444 Cross这一提议涉及对远离热力学平衡的图案形成系统的理论理解。PI以他在这里的工作而闻名，并且刚刚完成了一篇关于这个主题的长篇“现代物理学评论”。PI所使用的技术是多重的-从空间均匀状态的线性和非线性稳定性分析-包括缺陷和边界对图案演变的影响-到模型系统的数值研究。 具体而言，PI建议考虑流体和化学系统中的不稳定性和异常-例如条纹相，对流相和稳定的周期性化学模式。此外，PI建议研究材料系统中的图案特征不太好的领域-例如应变晶体中的变形带和位错图案。 许多流体系统在远离平衡的条件下会显示出模式。例如，热（底部）和冷（顶部）板之间的流体表现出对流模式。 同样，固体材料在外加应力（如剪切）下也会产生变形带。这种非平衡状态在日常生活中经常发生（例如云的形成）-并且在材料加工（研磨，轧制，烧结等）中形成了大多数情况。它们的研究对于理解物质和液体的行为具有重要意义。本提案对这些现象进行了理论研究。PI是这一领域的领军人物之一，其工作处于所知和所理解的最前沿。 ***

9311444 Cross This proposal is concerned with the theoretical understanding of pattern forming systems far from thermodynamic equilibrium. The PI is well known for his work here and has just finished coauthoring a long "Reviews of Modern Physics" article on the subject. The techniques used by the PI are multifold - varying from linear and non-linear stability analyses of spatially homogeneous states - to including the effects of defects and boundaries on the pattern evolution - to the numerical investigation of model systems. Specifically, the PI proposes to consider instabilities and paterns in fluid and chemical systems - such as stripe phases, convective phases and stationary periodic chemical patterns. Further, the PI proposes to study the less well-characterized field of patterns in materials systems - such as deformation bands and dislocation patterns in strained crystals. %%% Many fluid systems exhibit patterns when they are kept under conditions away from equilibrium. For example, a fluid between hot (bottom) and cold (top) plates exhibits convective patterns. Similarly, solid materials under applied stress (eg shearing) can develop deformation bands. Such non-equilibrium conditions occur all the time in everyday life (eg the formation of clouds) - and form by far the majority of cases in the processing of materials (milling, rolling, sintering etc). Their study is important in the understanding of material and liquid behavior. This proposal undertakes a theoretical study of these phenomena. The PI is one of the leading lights in this field and the work is at the cutting- edge of what is known and understood. ***