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20 Jan 2009: MATHEMATICAL TRIPOS PART IB. ELECTROMAGNETISM. Examples 2. 1. A potential difference V is maintained between two coaxial cylinders of radiir = a, b, b > a and the gap a < r < b is ... Repeat the calculation in spherical geometry, i.e. for concentric

9 Jan 2009: E B) = (B)E (E)B E(B) B(E). Position vector: let r or ri denote the position vector, and r = |r|. ... φ) dl = φ(b) φ(a). 1. Curl in curvilinear coordinates (ξ1, ξ2, ξ3):.

9 Apr 2009: Φ =. S. B dS, (3). then we get Faraday’s Law of induction. ... B2dτ. (9). It can easily be seen, using the expression for L above and (7) for B = |B|, that the twoexpressions for the magnetic energy W give the same result in

29 Jan 2009: the direction of the normal b, |b| = 1 to the plane,is arbitrary. ... We get. (B+ B).tl = µ0s.bl. (B+ B).n b = µ0s.b.

23 Jul 2009: find that it is not necessary to know the tensors A , B and C in full detail, because the final answer only depends on the combination. ... w - [G+&A-l.B : B T A - l G ]. p(4.rcvt)$ vt. Finally we recall t h a t the angular-velocity autocorrelation

21 Jul 2009: J. HINCH’ A N D B. S. BHATT? Department of Applied Mathematics and Theoretical Physics, University of Cambridge,. ... Hinch and B. S. Bhatt. 1.6 I 1 1.4. 1.2. I.

23 Jul 2009: B : b = [3/4(2n l ) ( n l)In/2n, c = 0. ... A similar conclusion applies to c, with b = 0 and m replacing n.

31 Jul 2009: 1, 367. LUMLEY, J. L. MAIJGREN, B. Molecular aspects of the drag-reduction phenomenon. ... MANDELBROT, B. B. 1974 Intermittent turbulence in self-similar cascades : divergence of.

31 Jul 2009: Thus. B = (B,),-dd.B-B.dddd(d.B.d). The equation governing the development of the full tensor B is then found to be. ... 2(d’d’. E. B B. E. d’d’) o(cY2). ( 1 4 b ) These results are not dependent in any essential way on the detailed nature of the

21 Jul 2009: Let b,, = b:, E and b,, = b,, e2, then. ... py/e K u Ge(b,,, b:,) K E V , , -py/e, 24, v, = 0,.

23 Jul 2009: with the three shape constants. a = $ ( B 2 - B 1 ) , /3 = # ( B , B l ) and y = 4B3. ... At O ( B ) , the variation in q5 a t O( 1) drives harmonic oscilla- tions, i.e.

13 Jul 2009: where b, = b,/b. ... a tridiagonal matrix for the tensions. T,&,. b, -2T,b, b, T,_,&_, 6,.

27 Jul 2009: Plansangkate. where x j, j = 1, 2, 3, are local coordinates on B. ... s = b(y)eu3α and n = αx. for some b = b(y) = 0.

10 Nov 2009: FIG. 1. Concentration profile vs normalized height z / H for particles of batches A a, B b, D c in the cell having a cross section 10 10 cm2, and C ... FIG. 2. Time evolution of the velocity fluctuations w open symbols and the concentration gradient ad /

10 Jul 2009: away from the (collapsed) numerical results. and secularity is averted at order O(β1) if T0 B 0, whence B = B(T1) and. ... B(T ) ={. 1 T. 24β. }1/2. (5.2). Thus, for T 1,.

10 Jul 2009: a) Gravity acts on the fundamental mode to create the firstharmonic in (b). ... b) Capillary pressure gradients act to create the phase-shifted first harmonicin (c).

3 Sep 2009: Bernard, B. Hambrecht, P. Lugan, D. Clement,L. Sanchez-Palencia, P. Bouyer, A. ... Rev. Lett. 101 (2008)080401. [65] Th. Anker, M. Albiez, B. Eiermann, M.

14 Jul 2009: 2 = y e x - i B y , y = e y - - B x , 1. ... 0.05 1 b B 0.05. 0 0.02 0.04 0.06 0.08. (b) 0.04.

24 Aug 2009: 3A(sin4 8, sin 24,) - 2(A - B)(sin28, sin 24,)}, of, = of. = ... A , B, F, 211, would not be related to the particle aspect ratio in 6he manner described for spheroids.

13 Jul 2009: As a model problem we take. %(x) = U_[l - exp( -x/b)], (1). ... As indicated above, to make the calculation tractable we shall, however, assume that b B a so that the flow is almost unidirectional almost everywhere and lubrication methods can be employed.

10 Jul 2009: Combination Particles Fluid Tube ξ(0.1)1 A a 1 2.302 A b 1 2.153 D a 1 3.354 B a 2 1.805 B b 2 ... 30 2.84 0.02 0.615 0.590 0.5455 B b 2 16 17.4 0.40 3.65 0.10 0.600 0.565 0.5206 C a

8 Jul 2009: B′ cos KX instead of A and B, with solution. N (0) ce(. ... Q(1)t= cuN (1)Θ. t. =cec. 2uΘ. 2a. 22(A A′ 1. 4(B B′).

21 Jul 2009: which - owing to transverse isotropy - are encapsulated in the single case b’ = ex. ... b ) ] d2r. [ k V 2 n 3 - qcos(tcp)V3(n.b)] d2r.