Spatial Structure and Dynamics of Non-Equilibrium Systems

9311444克罗斯这项建议涉及对远离热力学平衡的图案形成系统的理论理解。这位PI以他在这里的工作而闻名，他刚刚完成了一篇关于这个主题的长篇《现代物理学评论》的合著。PI使用的技术是多方面的--从空间均质态的线性和非线性稳定性分析--到包括缺陷和边界对图案演化的影响--到模型系统的数值研究。具体地说，PI建议考虑流体和化学系统中的不稳定性和模式--例如条状相、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表征较少的图案领域--例如应变晶体中的变形带和位错图案。许多流体体系在远离平衡的条件下都会表现出花样。例如，热(底)板和冷(顶)板之间的流体呈现对流模式。同样，固体材料在外加应力(如剪切)下会产生变形带。这种非平衡状态在日常生活中无时无刻不在发生(如云的形成)，并且在材料加工(如研磨、轧制、烧结等)中形成了大多数情况。他们的研究对于理解物质和液体的行为很重要。这一建议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，这项工作处于已知和理解的前沿。***

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. ***