An efficient statistical timing analysis algorithm that can handle arbitrary (spatial and structural) causes of delay correlation is described. The algorithm derives the entire cumulative distribution function of the circuit delay using a new mathematical formulation. Spatial as well as structural correlations between gate and wire delays can be taken into account. The algorithm can handle node delays described by non-Gaussian distributions. Because the analytical computation of an exact cumulative distribution function for a probabilistic graph with arbitrary distributions is infeasible, we find tight upper and lower bounds on the true cumulative distribution. An efficient algorithm to compute the bounds is based on a PERT-like single traversal of the sub-graph containing the set of N deterministically longest paths. The efficiency and accuracy of the algorithm is demonstrated on a set of ISCAS'85 benchmarks. Across all the benchmarks, the average rms error between the exact distribution and lower bound is 0.7%, and the average maximum error at 95 th percentile is 0.6%. The computation of bounds for the largest benchmark takes 39 seconds.
Moisture has a profound effect on the physical properties of paper and thus determines the
performance characteristics of paper products including the so-called mechanosorptive effect
where the creep behavior of paper is accentuated by cyclic humidity variations. Moisture
transport in a paper sheet exposed to ramp changes in the external humidity has been studied.
Our transport model considers a paper sheet as a composite medium of fibers and void spaces
with moisture transported by diffusion through each one. Diffusion in the fibers is approximated
by a lumped linear relaxation process. The important dimensionless parameters consist of the
Biot, fiber, and void diffusion numbers. A comparison of the model predictions with experimental
transient moisture uptake of a bleached kraft paper board sample showed that a single value of
the fiber relaxation parameter, k
i, was sufficient to give good estimates of transient moisture
sorption data.
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