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31 Dec 2018: V. A. B. Path I. Path II. Figure 24:. underline the meaning of the new symbol d. ... energy gives us,. @S. @V. T. =@p. @T. V. (4.24). The Gibbs free energy gives us.

31 Dec 2018: 23. 1. z. 4p2+. (3.24). The next part’s a little fiddly. ... 1. 1. 2p2. 3N. V+. which we then substitute into (3.24) to get.

31 Dec 2018: f(r) = eU(r) 1 (2.24). This is a nicer expansion parameter.

28 Dec 2018: checked in a 24-hour period, finding that thetemperature was 21.5 0.5 C and humidity was 38 2%. ... Tbase O(h20/D. ) O (103 ) minutes. (24)for h0 = 0.01 m and D = 1 109 m2/s.

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: g = (A’ B’)m. where. A’ = a2 -@g. 8’ = -2r [l -! Jtt, $1,! (<, 59 = f(E) f(d. l = @1- 22 - 23 td)/SL, 7 = (21 - 22 2s - 24)/2L, and

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

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: 2.1. Formal solution and splitting series. The method of solution is analogous to that applied to the electromagneticproblem in 2-d or 3-d [23, 24]. ... 24] M. Spivack, J. Ogilvy, C. Sillence, Electromagnetic scattering by large com-plex scatterers in 3d,

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)