Statistical Analysis of Interconnect-Limited Systems II

这个项目正在开发一个基于重整化群(RG)理论的数学框架，它能够预测非常密集和优化的网络的几何结构，而不需要求助于经验拟合参数。RG技术的强大之处在于，它不是一种描述性理论，而是一种构建理论的通用方法。因此，它能够分析从导线放置到串扰的广泛的互连分析问题。它通过连续地重新正规化导线排列而成功，将强耦合的多长度尺度问题简化为大量简单得多的单长度尺度问题。根据这项资助开展的研究活动包括：(A)确定处理芯片设计参数中的所谓临界点，这表明从容易扩展的设计到不可扩展的设计的转变；(B)开发算法，将这些临界点移动到使以前不可扩展的设计可扩展的位置；(C)将优化互连几何结构的理论与包括磁铁、沸水和渗流在内的临界点系统的更一般和普遍的物理联系起来。

This project is developing a mathematical framework based on Renormalization Group (RG) theory that is capable of predicting the geometrical structure of very densely wired and optimized networks without recourse to empirical fitting parameters. The power of the RG technique is that it is not a descriptive theory but rather a general method for constructing theories. It is therefore capable of analyzing a wide range of interconnect analysis problems ranging from wire placement to cross-talk. It succeeds by successively renormalizing wire arrangements, reducing a strongly coupled, multiple-length scale problem to a large number of much simpler single-length scale problems. The research activities being carried out under this grant include: (a) the identification of so-called critical points in the design parameters of processing chips which indicate a transition from easily scaleable designs to unscaleable designs, (b) the development of algorithms to move these critical points to positions which make previously unscaleable designs scaleable, (c) to relate the theory of optimized interconnect geometries to the more general and universal physics of critical point systems which include magnets, boiling water, and percolation.