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

等离子体和引力系统动力学理论中的 N 体方面

• 批准号: 0207339
• 负责人: Carlo Lancellotti
• 金额: $ 7.25万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-01 至 2003-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0207339&HistoricalAwards=false
• 关键词: body; Aspects; Kinetic; Theory; Plasmas

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.

提案：0204939PI：米歇尔·贾布尔机构：肯塔基大学标题：关于相分离和微观结构对多物种薄膜生长影响的一些研究摘要相分离现象在许多多物种薄膜中常见，其中二次相岛可能在薄膜上成核和生长。薄膜的表面，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，富含钡的 YBCO 薄膜可能会失去其超导特性，但另一方面，YBCO 薄膜上的岛可能充当磁场的钉扎中心。 在半导体中的量子点和线中发现了相分离和二次相岛的形成的进一步应用。 因此，了解相分离的机制和二次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在多物种薄膜沉积的背景下，提供一种数学上严格且热力学一致的方程推导，该方程控制着界面三联结远离平衡的演化，薄膜、蒸汽、和次相相交。 这种连续体模型适用于稳定性分析，因此可以揭示表面沉淀物形成和生长的条件。 当薄膜表面为邻近表面时，生长可以通过阶梯流发生，即原子高度阶梯的横向运动，该阶梯将几个晶胞宽的平台分开。 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，各个平台上不同物种的吸附可以发生在同一位置。 该提案的第二个目标是开发多组分薄膜的微机械模型，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-解吸动力学的综合效应。 该项目的第三个目标是通过将上述薄膜生长微观力学模型均质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。薄膜构成了许多新型薄膜的基本组成部分。技术。 例如，微电子和光电设备应用中的半导体、工业切削工具中的金刚石、各种防腐和耐磨涂层、微机电系统 (MEMS) 中作为执行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，多品种薄膜比单组分薄膜应用更广泛。 这些薄膜的特性及其在非常严格的条件下的性能取决于它们的化学成分和薄膜表面的形态细节。 为了在生长过程中更好地控制薄膜的化学和微观结构，有必要对基本物理和化学机制进行严格的数学理解，特别是当逐个原子制造材料不再是一个遥远的梦想时。 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（可以对这些模型进行严格分析并用于数值模拟）为这样的全球努力做出重大贡献。 现代连续介质物理的概念与现代数学工具（例如均质化和非线性偏微分方程理论）相结合，构成了一种有效的方法论，可以用来解决与多组分薄层生长相关的许多具有挑战性的问题。电影。