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A reciprocal theorem for boundary-driven channel flows
www.damtp.cam.ac.uk/user/lauga/papers/111.pdf31 Dec 2015: 2p 1)" 2p1. L. x. 2+. 2q1Ly. 2# ez, (24). while the sensitivity on the vertical walls Hvert(y) at x = 0 and x = Lx can be obtained by symmetry.The ... Rev. Lett. 99, 048102 (2007).24 R. Golestanian, T. B. Liverpool, and A. -
Propulsion of Bubble-Based Acoustic Microswimmers Nicolas Bertin,1,*…
www.damtp.cam.ac.uk/user/lauga/papers/113.pdf31 Dec 2015: 24]), forexample, at an air-water interface such as the surface of abubble [25,26]. ... Rev. 73, 68 (1948). [24] W. L. Nyborg, Acoustic streaming near a boundary,J. -
Why geometric numerical integration? A. Iserles & G.R.W. Quispel…
www.damtp.cam.ac.uk/user/na/NA_papers/NA2015_05.pdf17 Dec 2015: 2. ) f(x′). ], (2.24). preserving all quartic Hamiltonians.We note that (2.22) has second order accuracy. -
10 Green’s functions for PDEs In this final chapter ...
www.damtp.cam.ac.uk/user/dbs26/1BMethods/GreensPDE.pdf30 Nov 2015: φ|Rn{0} = 0 , tφ|Rn{0} = 0 and lim|x|. φ = 0 , (10.24). -
Mathematical Methods University of Cambridge Part IB Mathematical…
www.damtp.cam.ac.uk/user/dbs26/1BMethods/All.pdf30 Nov 2015: 2.3 Self-adjoint differential operators 22. 2.4 Eigenfunctions and weight functions 24. ... 1)k1. ikeikθ (1.24). do in fact converge on the sawtooth function everywhere except at the discontinuity. -
8 Fourier Transforms Given a (sufficiently well behaved) function ...
www.damtp.cam.ac.uk/user/dbs26/1BMethods/FourierT.pdf18 Nov 2015: f, f) =1. 2π(f̃, f̃) (8.24). so that the L2-norm of a Fourier transform agrees with the L2-norm the original function,. -
Banded, stable, skew-symmetricdifferentiation matrices of high order…
www.damtp.cam.ac.uk/user/na/NA_papers/NA2015_03.pdf9 Nov 2015: We have (P 1)K = 24 equa-tions for K(K 1)/2 = 28 unknowns. ... Dj,k = 0 for |k j| 6. There remain 25 unknowns for the 24 equations. -
7 Green’s Functions for Ordinary Differential Equations One of ...
www.damtp.cam.ac.uk/user/dbs26/1BMethods/GreensODE.pdf9 Nov 2015: shape. y(x) =µg. 2Tx(x L). (7.24). that obeys y(0) = y(L) = 0. – -
SM.dvi
www.damtp.cam.ac.uk/user/ho/SM.pdf8 Nov 2015: By following a similar argument as forthe bosonic field and using eq.(1.24) we see that. ... P̂ψ(x)P̂1 = ηPγ0ψ(xP). (1.54). The u spinor has the property (1.24) which leads to eq.(1.25). -
On the Solvability Complexity Index, the n-Pseudospectrumand…
www.damtp.cam.ac.uk/research/afha/anders/JAMS_Final_Preprint2.pdf8 Nov 2015: RTkz RTz‖2 ‖R(Tkz) R(Tz)‖2 p(Tk z,T z)2. 8δ̂(Tk z,T z)2. 24(1 |z|2)2δ̂(Tk,T)2. ... ζ(z)2 ζ̃2k(z)| C. 24(1 |z|2)δ̂(Tk,T). (5.4). If z σ(T) then at least one of ‖R(Tz)‖ and ‖R(Tz)‖ is equal
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