Statistical Analysis of Interconnect-Limited Systems II

该项目正在开发一个基于重整化群（RG）理论的数学框架，该框架能够预测非常密集的有线和优化网络的几何结构，而无需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一般方法。因此，它能够分析范围广泛的互连分析问题，从电线放置到串扰。它的成功之处是通过不断地重新规范化导线排列，将一个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。在这项资助下进行的研究活动包括：(a)在处理芯片的设计参数中识别所谓的临界点，这表明从易于扩展的设计到不可扩展的设计的过渡，(b)算法的发展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)将优化互连几何理论与临界点系统的更一般和通用的物理联系起来，包括磁铁，沸水和渗透。

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.