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An empirical relation for the phase distribution transition from wall peak to core peak was fitted by using the phase distribution pattern transition criterion and the present experimental data and verified by other researchers' experimental data.
A recently developed bottom-up model of fracture by Stormo et al. (2013) has shown to have similar diffuse to localized damage distribution transition.
The crowd distribution transition probability Pcd (m, n) can be obtained from Eq. 5 from the m dataset to the n dataset.
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It is a problem, though, for quasibrittle materials for which the type of strength distribution transitions from Gaussian to Weibullian as the structure size increases.
Around breakpoints the probability distribution transitions through a short region of uncertainty in which the strain probabilities are more equal.
First, data reconciliation is discussed, including log and core porosity comparisons, permeability porosity cross plots, core and pressure transient permeability comparison, evaluation of permeability distributions, transition zones, and assessing the fluid characterization based on production and pressure data.
Learning the model involves 1) building the structure (i.e. deciding on the direct transitions between prototypes); 2) training the model to estimate the numerical parameters of the HMM (i.e. Gaussian distributions, transition probabilities, and prototype prior probabilities).
This assumption was tested by examining the distribution of transition times where the number of observed transition was large enough to allow for it (>10).
For low input intensities (λ̅<λ̅c) transitions between network states are fluctuation-driven, and the distribution of transition times is very skewed right, close to an exponential or a gamma with very low shape parameter.
The posterior distribution for transition rate α (I to R) was symmetric, but for the transition rate β (S to I) and ν (R to I), the posterior distributions were asymmetric.
Monika Hartmann and Jurgen Wandel, Food Processing and Distribution in Transition Countries: Problems and Perspectives, IAMO 1999.
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