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，该理论能够预测非常密集的有线和优化网络的几何结构，而无需依赖经验拟合参数。RG技术的力量在于它不是一个描述性的理论，而是一种构建理论的一般方法。因此，它能够分析广泛的互连分析问题，从布线到串扰。它成功地通过连续重新规范化线的安排，减少了强耦合，多长度尺度的问题，大量的简单得多的单长度尺度问题。在该补助金下开展的研究活动包括：（a）识别处理芯片的设计参数中的所谓临界点，其指示从容易可缩放设计到不可缩放设计的转变，（B）开发算法以将这些临界点移动到使先前不可缩放设计可缩放的位置，（c）将优化互连几何形状的理论与临界点系统的更一般和普遍的物理学（包括磁体、沸水和渗透）相关联。

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.