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8 Jan 2018: diameters) long with t = 0, 0.25, 0.5, 1, 2.5, 5, 10, 20 and Topt = 29.35 D/U (going downwards: flowis from left to right) where U is ... Red dots indicate thetimes (t = 0, 20, 60 and 100) where cross-sections of the total flow (left: 8 contours across [1

11 Jan 2018: rts (. I 12. rs rs. ) vs 1. 2(rss rs rs rss ) (rt v), (20). ... 0. 10. 20. 30. Bu=2. Bu=30. Bu=60. (a). (b. ( )(c).

19 Jan 2018: 2.2 Free field theory 14. 2.3 Perturbation theory 17. 2.3.1 Feynman diagrams 20. ... D eS[]/. (1.20). evaluates the map acting on |'0i 2 H and ending on |'1i 2 H.

22 Jan 2018: Q2 n1=2? L. 1=2x1=2G1=20 ð1 " q1=2Þhpl! 2þ G0. 2pl. " #2; (44). ... 20=ð2plÞ. 2 þ F2ah2=ðplÞ2. G20=ð2plÞ2 þ F2e h2=ðplÞ. 2! 1=2" 1; (47).

23 Jan 2018: In fact, the result. K0(q,q′;t) := ⟨q|exp(i p̂. 2. 2mt)|q′⟩ (1.20). ... 2.21). 19Green, George (1793-1841)20Fourier, Joseph (1768-1830). 20. So the equation that you then get is.

26 Jan 2018: T=. (S. E. )V,N. (1.20). where the subscript denotes that V,N are held fixed when we take the partial derivative. ... pi = 1 (1.67). Part 2 Statistical Physics January 26, 2018 20 H.S.

12 Feb 2018: CS1. Dx eS/ , (3.20). 29In flat space, the heat kernel (3.9) obeys KT (y, y) = KT (0, 0) so is independent of y.

27 Feb 2018: J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom. (Received 19 December 2017; published 20 February 2018). ... 0 10 20 30Time t. 0.0. 0.1. 0.2. 0.3. 0.4. 0.5.

3 Apr 2018: O(h4)︷ ︸︸ ︷iΛ [ψ]1,1(h) 2i. 〈2xµ2,1(h). 〉2, (2.20). whereψ(h,ζ,ξ) = ζ ξ h3. ... Magnus–Lanczos. In Figure 4.3 (right) and Figure 4.4 (right) we show the errorsin exponentiating the order six Magnus expansions (with and without

13 Apr 2018: As a sanity check forcotton, μ 0.3–0.4 [4,5], and thus, hΘi 20. ... 20] M. Abramowitz and I. A. Stegun, Handbook of MathematicalFunctions (Dover, New York, 1965).