By Barry Max Brandenberger
ISBN-10: 0028655613
ISBN-13: 9780028655611
ISBN-10: 0028655621
ISBN-13: 9780028655628
ISBN-10: 0028655648
ISBN-13: 9780028655642
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18) for an initial condition that represents an incoherent finite source [7]. Finally we point out that Eq. 18) may be generalized to include the effect of a slowly varying mean sound speed. That is we may replace Eq. 29) where v(x) is a deterministic function of position. Details are given in McCoy and Beran [12]. 6 Scattering in a one-dimensional random medium In this section we consider scattering in a one-dimensional random medium in which hack-scattering plays a very prominent role. The formulation we use is appropriate for both the acoustic problem and the elastic problem but again in the interests of simplicity we shall consider only acoustic propagation.
23) may be solved in a number of ways. Here we note that S. Frankenthal and I have solved the hierarchy numerically by using a cut-off procedure. We assumed that at any stage of the hierarchy we may use the approximation wN+l = [W 1]N+l. For N not too large the results are poor in the sense that the result of making the approximation at N = m differs from that at N = rn + 1. However, for N ยป 1 the results converge, albeit slowly. For W 1 the numerical results are the same as that given in Papanicalaou and Keller [16].
This is the true for any stationary random set with zero measure. 1 Poisson point process The non homogeneous Poisson point process in If' with a regionalized intensity O(x) (x E R"-; () ~ 0) is a point process with the following properties: the numbers N(Ki) are independent random variables for any family of disjoint compact sets Ki . ' (volume in R3 ), the process is stationary, and P11 (K) = Pn(I
Encyclopedia of Mathematics Da-Lo by Barry Max Brandenberger
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