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14 Dec 2018: T R I N I T Y A N N UA L R EC OR D 2018 24.

14 Dec 2018: T R I N I T Y A N N UA L R EC OR D 2018 24.

13 Dec 2018: T-•=Tg'(1--To •AT Tg:A •. ) (24) so that. E = (2 - 4At 8A•. ... 2. It is easy and computationally inexpensive to take further terms in the se- ries (24).

13 Dec 2018: h(Xn) = z |Sn(xn Xn)3/2. αφ(Xn)δ|. (24). 2. Medium with Linear Profile. ... Reconstruct the surface h(Xn) by eq. (24) for uniformmedium or (26) for linear profile using Φ obtained aboveend for.

13 Dec 2018: 0 Zl ( (•(x,zi))=--• Do(X)-- likzi cos 0 --• COS 2 0 eikXx+ h(x)• ,. (24). where • is the variance of the surface height. Here we have neglected an O(a ... 29) Collecting terms, and using (25), (26), and (29), Eq. (24) can now be written. ( {•

13 Dec 2018: F′n1, An,n =τ. 2ξF′n. (24). This is easily and rapidly inverted by back-substitution.

13 Dec 2018: and7!:. cr! 5 ESFG r;r8! ]c]z r8!2 ]G]z r;r8!cr8!Gdx8,. 24! where againr85[x8,S(x8)], and S is the union of the sur-facesh1

13 Dec 2018: By (24),〈h(X). I(r). r. 〉=. 〈h(X). d. dr. r0. ikh(r′) cos θeikSr. ′. ... 24] P. Tran, Calculation of the scattering of electromagnetic waves from a two-dimensional per-fectly conducting surface using the method of ordered multiple interaction,

13 Dec 2018: elements. (Bn)mj = Anmnj. (24). We thus require. bn = B1n cn (25). ... from rough surfaces, Waves in Random Media, 6, 151-167 (1996). [24] A.A.

13 Dec 2018: As an illustration of the method, Figure 1 shows comparisons between the firstand second iterations of the operator series with ’exact’ computations from (24 ),restricted to the rough portion of the ... αr r′. = f(r,r′) (24). the expression (23)