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19 Oct 2013: #"$ %'&)(,.-0/$1#(23547684:9 ;8< = >?9A@B9DCFE7;8<G9IH 4KJ L59NM. OPRQST U U U U V W XY XY X X X XZ XY XY X. X XU XU. [#[T U U U U]_)]_)a.bc)_edXU XZ X X XZ X X XU XZ X f b)ghd. XZ X XZ X X Xi. [)jT U U U Uk]_l]DmBnoDdXi Xi XZ XU XZ X XU XZ XZ XZ X

26 Jul 2013: with similar viscosities (, ) and densities (, ),(b) dimensionless membrane-viscous number, Me U=KA, for two fluids separated by an elastic membrane(thickness t, area modulus KA, density m, bending stiff-ness ... f 2= is an intrinsic viscocapillary

19 Oct 2013: Another importantwave activity measure is given by the pseudomomentum vector,. p = kA =h′ u′. ... Because of the ray-invariance of absolute frequency we have that |kA| = |kB | asympto-tically.

4 Oct 2013: if ψ = 0at r = a then Rnk(a) = Jn(ka) = 0 so for each n, ka = kni with i = 1, 2,.

26 Jul 2013: FIG. 4. (Color online) Instantaneous velocity and pressure fields (left) and z component of the vorticity (right) for the in-plane beating oftwo flagella, with ka = kb = 0.05, R = 1, ... Bottom: Variation of the ratio of the minimum to themaximum of the

4 Oct 2013: Its FT is easy to calculate:. f̃(k) =. aaeikx dx =. aa. cos(kx) dx =2 sin(ka). k. (41). so by the Fourier inversion theorem we get. ... 1. π. eikxsin ka. kdk =. {1 |x| < a,0 |x| > a.

19 Oct 2013: J<6{4)01# "9#mI =9? : : "9#r=:; DJzG=x? 0- I?6,z#1 Kj BKj'Kä :6#(8º Jz0 G= 8G? ... 6'? ] BKj0G=>=# Kj Km'Kä :#I =º? :;81#G5#6: º#=>c0- "GG "(8º J= G= 0G=º# Km Kj'EKà :#c X8Ñ?

19 Oct 2013: iσζ̂ kA sinh kh = 0. and from the second (pressure) (). gζ̂ iσA cosh kh = 0. Regarding these as a system of two linear algebraic equations for the two unknown constants ζ̂

3 Feb 2013: Phys Rev Lett 105(16):168101. 17. Guasto JS, Johnson KA, Gollub JP (2010) Oscillatory flows induced by microorganismsswimming in two dimensions.

26 Jul 2013: ¤ and compute a matrix F with components fij = cij =( i ¤j ).The minimal-energy stabilizing feedback controller is then given by u = KÀ , whereK = B ¤ F ¡1.