将随机游走法和层次法相结合,采用层次化随机游走法对静态P/G网(Power and Ground Networks)进行分析.针对大规模的电路,在通过多层的参数提取和建模得到静态P/G网模型后,运用层次法将P/G网分割,在子网内采用随机游走法,并且在此基础上...将随机游走法和层次法相结合,采用层次化随机游走法对静态P/G网(Power and Ground Networks)进行分析.针对大规模的电路,在通过多层的参数提取和建模得到静态P/G网模型后,运用层次法将P/G网分割,在子网内采用随机游走法,并且在此基础上比较5种加速算法.实验数据表明,改进的双共轭梯度(BCG)随机游走法的计算速度是普通随机游走法的6倍以及是层次法的14倍.新方法有效地节省了计算时间,有益于对P/G网的研究.展开更多
Power integrity (PI) has become a limiting factor for the chip's overall performance, and how to place in-package decoupling capacitors to improve a chip's PI performance has become a hot issue. In this paper,...Power integrity (PI) has become a limiting factor for the chip's overall performance, and how to place in-package decoupling capacitors to improve a chip's PI performance has become a hot issue. In this paper, we propose an improved trans- mission matrix method (TMM) for fast decoupling capacitance allocation. An irregular grid partition mechanism is proposed, which helps speed up the impedance computation and complies better with the irregular power/ground (P/G) plane or planes with many vias and decoupling capacitors. Furthermore, we also ameliorate the computation procedure of the impedance matrix whenever decoupling capacitors are inserted or removed at specific ports. With the fast computation of impedance change, in-package decoupling capacitor allocation is done with an efficient change based method in the frequency domain. Experimental results show that our approach can gain about 5× speedup compared with a general TMM, and is efficient in restraining the noise on the P/G plane.展开更多
As known, the spontaneous symmetry breaking (SSB) and the Brout-Englert-Higgs Mechanism (BEH-M) solved the Yang-Mills Mass Gap Problem. However, various mathematicians, even prestigious ones, consider the basic assump...As known, the spontaneous symmetry breaking (SSB) and the Brout-Englert-Higgs Mechanism (BEH-M) solved the Yang-Mills Mass Gap Problem. However, various mathematicians, even prestigious ones, consider the basic assumptions of the gauge theories to be wrong, as well as in conflict with the experimental evidence and in clear disagreement with the facts, distorting the physical reality itself. Likewise, these theories are mathematically inconsistent, adopting a mathematical structure somewhat complicated and arbitrary, which does not satisfy the strong demands for coherence. The weakest point of the gauge theories, in our opinion, consists in imposing that all the particles must be free of an intrinsic mass. On the contrary, even for the particle considered universally massless, i.e. the photon, our calculations show a dynamic-mass, a push-momentum (p) of 1.325 × 10<sup>-22</sup> [g⋅cm/s]. With this work we try to provide a possible solution to the Yang-Mills Mass Gap Problem, but without taking into account the SSB, nor using the BEH-M. We try to provide a mathematical explanation for this phenomenon, considering that in the spectrum of the Yang-Mills theory, there is a mass gap, that is, the difference between the energy of the vacuum state and the first excited state is different from zero. In other words, the lightest of the particles predicted by the theory must have a strictly positive mass to explain the short range of strong nuclear forces. It is clear, indeed, that if we replaced this value with the null value of the photon inserted in the equations of the Perturbation Theory, the Quantum Fields Theory and the Yang-Mills theories, all divergences, that is all zeroes and infinities, would suddenly disappear. Consequently, the limits imposed by the SSB disappear so that there is no longer any need to deny the mass to the Nuclear Forces bosons, including the Yang-Mills b quantum.展开更多
文摘将随机游走法和层次法相结合,采用层次化随机游走法对静态P/G网(Power and Ground Networks)进行分析.针对大规模的电路,在通过多层的参数提取和建模得到静态P/G网模型后,运用层次法将P/G网分割,在子网内采用随机游走法,并且在此基础上比较5种加速算法.实验数据表明,改进的双共轭梯度(BCG)随机游走法的计算速度是普通随机游走法的6倍以及是层次法的14倍.新方法有效地节省了计算时间,有益于对P/G网的研究.
基金the Ph.D Programs Foundation of Ministry of Education of China (No. 20060335065)the Natural Science Foundation of Zhejiang Province, China (No. Y106513)
文摘Power integrity (PI) has become a limiting factor for the chip's overall performance, and how to place in-package decoupling capacitors to improve a chip's PI performance has become a hot issue. In this paper, we propose an improved trans- mission matrix method (TMM) for fast decoupling capacitance allocation. An irregular grid partition mechanism is proposed, which helps speed up the impedance computation and complies better with the irregular power/ground (P/G) plane or planes with many vias and decoupling capacitors. Furthermore, we also ameliorate the computation procedure of the impedance matrix whenever decoupling capacitors are inserted or removed at specific ports. With the fast computation of impedance change, in-package decoupling capacitor allocation is done with an efficient change based method in the frequency domain. Experimental results show that our approach can gain about 5× speedup compared with a general TMM, and is efficient in restraining the noise on the P/G plane.
文摘As known, the spontaneous symmetry breaking (SSB) and the Brout-Englert-Higgs Mechanism (BEH-M) solved the Yang-Mills Mass Gap Problem. However, various mathematicians, even prestigious ones, consider the basic assumptions of the gauge theories to be wrong, as well as in conflict with the experimental evidence and in clear disagreement with the facts, distorting the physical reality itself. Likewise, these theories are mathematically inconsistent, adopting a mathematical structure somewhat complicated and arbitrary, which does not satisfy the strong demands for coherence. The weakest point of the gauge theories, in our opinion, consists in imposing that all the particles must be free of an intrinsic mass. On the contrary, even for the particle considered universally massless, i.e. the photon, our calculations show a dynamic-mass, a push-momentum (p) of 1.325 × 10<sup>-22</sup> [g⋅cm/s]. With this work we try to provide a possible solution to the Yang-Mills Mass Gap Problem, but without taking into account the SSB, nor using the BEH-M. We try to provide a mathematical explanation for this phenomenon, considering that in the spectrum of the Yang-Mills theory, there is a mass gap, that is, the difference between the energy of the vacuum state and the first excited state is different from zero. In other words, the lightest of the particles predicted by the theory must have a strictly positive mass to explain the short range of strong nuclear forces. It is clear, indeed, that if we replaced this value with the null value of the photon inserted in the equations of the Perturbation Theory, the Quantum Fields Theory and the Yang-Mills theories, all divergences, that is all zeroes and infinities, would suddenly disappear. Consequently, the limits imposed by the SSB disappear so that there is no longer any need to deny the mass to the Nuclear Forces bosons, including the Yang-Mills b quantum.
