N-body Aspects in the Kinetic Theory of Plasmas and Gravitating Systems

建议：0204939 PI：Michel JabbourInstitution：University of Bucky标题：多组分薄膜生长过程中的相分离现象是多组分薄膜生长过程中普遍存在的现象，在薄膜表面会形成二次相岛，从而影响薄膜的性能。 这种影响可能是有害的，也可能是有益的。 例如，富钡的YBCO薄膜可能会失去它们的超导特性，但另一方面，YBCO薄膜上的岛可能会充当磁场的钉扎中心。 相分离和第二相岛的形成的进一步应用被发现在半导体中的量子点和线中。 因此，了解相分离的机制和第二相岛的稳定性对于薄膜的设计和可控性至关重要。 本研究项目的一个目标是提供，在多物种薄膜的沉积的背景下，一个数学上严格的和approxically一致的推导方程的演变，远离平衡，沿沿着的膜，蒸汽和第二相相交的界面三重结。 这样一个连续体模型本身的稳定性分析，并因此可能揭示的条件下，可以预期的表面沉淀物的形成和生长。 当薄膜表面是邻位时，生长可以通过台阶流发生-也就是说，原子高台阶的横向运动将几个单元格宽的台阶分开。 在多组分薄膜中，气相原子的沉积可以是竞争性的-也就是说，不同种类的吸附在单独的平台上可以发生在相同的位置上。 这个建议的第二个目标是开发一个多组分薄膜的微观力学模型，该模型考虑了平台和凸缘微观结构，吸附原子扩散和竞争吸附-脱附动力学的综合影响。 本项目的第三个目标是通过将上述薄膜生长的微观力学模型均匀化获得的平均信息以本构关系的形式纳入宏观模型，将纳米尺度与微观尺度联系起来。 例子包括微电子和光电器件应用中的半导体、工业切割工具中的金刚石、各种防腐蚀和耐磨涂层、微机电系统（MEMS）中作为致动器的形状记忆合金以及无线通信设备中的超导体。 在大多数工业应用中，多组分薄膜比单组分薄膜应用更广泛。 这些膜的性质和它们在非常严格的条件下的性能取决于它们的化学组成和膜表面的形态细节。 为了在生长过程中更好地控制薄膜的化学和微观结构，必须对基本的物理和化学机制进行严格的数学理解，特别是当材料的原子-原子制造不再是遥远的梦想时。 应用数学家可以（并且已经）通过开发物理上合理的预测模型来为这样的全球努力做出重大贡献，这些模型可以进行严格的分析并用于数值模拟。 现代连续介质物理学的概念，当与现代数学的工具（例如，均匀化和非线性偏微分方程理论）相结合时，构成了一种有效的方法，可以解决与多组分薄膜生长相关的许多具有挑战性的问题。

Proposal: 0204939PI: Michel JabbourInstitution: University of KentuckyTitle: Some studies on phase segregation and the influence of microstructure on multispecies thin film growthABSTRACTThe phenomenon of phase segregation is commonly observed in many multispecies thin films, where secondary-phase islands may nucleate and grow on the surface of a film and thus influence the properties of the film. The influence may be detrimental or beneficial. For example, barium-rich YBCO films may loose their superconducting properties but, on the other hand, islands on YBCO films may act as pinning centers for the magnetic field. Further applications of phase segregation and the formation of secondary-phase islands are found in quantum dots and wires in semiconductors. Understanding the mechanisms underlying phase segregation and the stability of secondary-phase islands is therefore crucial for the design and controllability of thin films. One objective of the present research project is to provide, in the context of deposition of multispecies thin films, a mathematically rigorous and thermodynamically consistent derivation of the equations governing the evolution, away from equilibrium, of interfacial triple junctions along which the film, vapor, and secondary phases intersect. Such a continuum model lends itself to a stability analysis and may thus shed light on the conditions under which surface precipitates can be expected to form and grow. When the film surface is a vicinal one, growth can occur via step flow---that is, lateral motion of atomic-high steps which separate several-unit-cell-wide terraces. In multicomponent films, the deposition of gas-phase atoms can be competitive---that is, adsorption of distinct species on individual terraces can occur on the same site. The second objective of this proposal is to develop a micromechanical model for multicomponent films that accounts for the combined effects of the terrace-and-ledge microstructure, adatom diffusion, and competitive adsorption-desorption kinetics. A third objective of this project is to link the nanoscale to the microscopic scale by incorporating averaged information obtained by homogenization of the micromechanical model of film growth discussed above into macroscopic models in the form of constitutive relations.Thin films constitute a fundamental component of numerous novel technologies. Examples include semiconductors in micro- and opto-electronic device applications, diamonds in industrial cutting tools, various anticorrosion and antiwear coats, shape-memory alloys as actuators in microelectromechanical systems (MEMS), and superconductors in wireless communication devices. In most industrial applications, multispecies films are more widely used than their single-component counterparts. The properties of these films and their performance under very stringent conditions depend on their chemical composition and the morphological details of the film surface. To better control the chemistry and microstructure of thin films during the growth process, a mathematically rigorous understanding of the fundamental physical and chemical mechanisms at play is necessary, especially as the atom-by-atom fabrication of materials is no longer a remote dream. Applied mathematicians can (and already do) make a significant contribution to such a global effort by developing physically sound predictive models which can be analyzed rigorously and implemented for numerical simulations. The concepts of modern continuum physics, when combined with the tools of modern mathematics (for example, homogenization and the theory of nonlinear partial differential equations), constitute a potent methodology with which to address many of the challenging issues related to the growth of multicomponent thin films.