By Adler R.J.
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Additional resources for An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes
The normal probability density function (PDF) for the boundary head Ho or HL is given by Eq. 34). 7 EXERCISES 39 Hi can take. Show that if both 0 - Ho 2 -0 and 0-2 _ O, the joint PDF of Ho and HL is PI-I,,I-IL(Ho, HL) = 8(Ho - (Ho))8(HL - (Ha)). 8. In this chapter, one-dimensional steady-state flow is mainly considered. In the absence of internal source/sink the divergence free condition reads as d q / d x = 0 in the onedimensional domain, which means that q must be a (random or deterministic) constant in space.
115) where bl (x) -- [2J1 (x) - 1](a). 5 UNSATURATED FLOW IN RANDOM MEDIA 33 subject to appropriate boundary conditions. 103) with Eq. 118), which are linear, are fully solvable. It is thus seen that different procedures may lead to different equations. 107) coupled with Eq. 113) should be equivalent to Eqs. 118) in terms of final results, the latter are more desirable because they are linear. Similarly, the second-order mean head correction term (1/r(2) (x)) is governed by a linear equation and can be solved with these covariances.
O 2 f / L = O . 5 (a) t'NI ,... 6. The cross- and autocovariances of head in one-dimensional domain of two constant head boundaries based on the white noise covariance and the exponential covariance of various ~f. 1 ....... 05 o- - o 2 f / L = 0 . 0 CXl ~.. 7. The second-order mean head corrections and head variances in a one-dimensional domain of t w o constant head boundaries based on the white noise covariance and the exponential covariance of various i f . on fluid continuity (see Dagan [ 1989, Fig.
An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes by Adler R.J.