Errata

Boundary Integral and Singularity Methods for Linearized Viscous Flow

C. Pozrikidis
Cambridge University Press, 1992

1. Page  9
Line 11: Should be: " If the flows u and u' are regular "

2. Page 11
Line 19: Change to: " ... particle of radius a are given by "
Line 23 up: Replace "the sphere" with "the particle"

3. Page 16
8 up:  Change to; " ... it is often useful ..."
6 up:  Should be: "u(t=0-)=0, P(t=0-)=0"

4. Page 19
2 up:  At the end of this paragraph append the endnote superscript: "(1)"

5. Page 22
Equation (2.2.23):  The "I" on the right-hand side should be bold-faced: "I"

6. Page 28
4 up:  Change to read: " ... a fluid executing rigid body motion ... "

7. Page 30
5 up:  Replace "and character" with "or other special features"

8. Page 31
Line 2: Replace "Thus, we will reduce" with "In effect, we reduce"
Line 4:  Replace "several solid boundaries" with "solid boundaries with several shapes"

9. Page 32
Line 9up: Replace "the body SB" with "the body B"
Equation (2.3.27):  At the lower side of the integral sign replace "SB" with "B"

10. Page 33
Line 9: Replace "is a closed surface" with "is a closed surface D"
Line 8up: Cross out "the surface of"

11. Page 34
Line 3:  Replace "on A" with "on S"
Line 9:  Replace "potential," with "potential alone,"
Equation (2.3.33):  In the second line the "+" sign should be a "-" sign.

12. Page 38
Line 7:  Number this equation: (3)

13. Page 42
Line 7:  Insert a comma after "Bakr" to read "Bakr,"

14. Page 43:
Line 3:  Cross out the second minus sign on the right-hand side
Equation (2.4.18):  Insert the argument "(l)" in between "bneinf"  to read: "bn(l)einf"
Equation (2.4.21):  Row 2, Column 2: "I10"  should be "I11"
Row 3, Column 3:  "I31" should be "I11"

15. Page 44
Line 1: Insert  endnote mark to read "...by one (3), whereas"
Equation (2.4.23):    Row 2, Column 3 :  "-1" should be: "-I10"
Row 3, Column 1:  "(I32-I30)"  should be "(I30-I32)"
Row 3, Column 2:  "1" should be "I10"
Equation (2.4.24):  Change the argument in the parenthesis on the LHS to read: (l0, f0)
Equation (2.4.24):  Change the argument in the parenthesis on the RHS to read: (l0)
Equation (2.4.25): The right-hand side should be: 8pmuµn(l0)
Line3 up: At the end of this section add the sentence: "Kim & Karrila (1991) discuss similar reductions of generalized double-layer representations discussed in Chapter 4 of this book."

16. Page 48
Line9 up: Change in three places to read: "...when the domain of integration Sp is replaced by an arbitrary surface that encloses Sp; in addition, for a force-free particle, they are independent of the choice of xc (problem 2.5.1)."

17. Page 52
Line52: Change to read: "...the rotation of the particle ..."
Equation (2.5.34): Switch the two terms on the rhs to read:  ui(x) = wk a3 ½eklj((Iij)/(¶x0,1))(x, x0)

18. Page 57
Line 17:  Insert a comma to read "...to become a sphere, ..."
9 up:  Replace "deduce" with "show"

19. Page 59
5 up:  Enhance the end of this sentence to read "...sense discussed in section 2.3."

20. Page 60
Line 10:  Replace "the delta function" with "the two-dimensional delta function"

21. Page 61
Equation (2.6.21):  The "2" before the left parenthesis should be "4".
Equation (2.6.22):  Hats should be placed on top of x and y.

22. Page 63
7 up:  To the end of the paragraph add: "The origin is set at the centre of the circle."
6 up:  Change "... flow D ..." to "... flow A ..."
5 up:  Modify to read: "...to obtain for any function c"
2 up:  Change "... into D." to "...into A."

23. Page 64
Line 16up: Change "potential dipoles" to "vortex dipoles"

24. Page 71
Line 9: Change "on the surface Sp" to "on the surface B"
Line 11:  At the lower limit of the integral change "Sp" to "B"

25. Page 72
Equation (2.8.1):  Change to: uz(x0) = òD [ - GL(x, x0)Ñuz(x) + uz(x) ÑGL(x, x0)] . n dS(x)
Line 10:  Insert a minus sign to read:  Ñ2GL=-5 up:   Add an endnote mark to read: "(problem 4.1.3) (4)."

26. Page 94
Equation (3.5.6): Please inert the superscript ``ST'' at the first two T on the right-hand side (thanks to Mark Blyth.)

27. Page 107
Line 6 up: Please change ``section 1.2'' to ``section 1.5''.

28. Page 108
15 up:   Add an endnote mark to read: "for the density q.(5)"

29. Page 111
Line 12:  Replace "which depend" with "that depend"

30. Page 115
Equations (4.5.4), (4.5.5):  Replace after the "=" sign replace "qj" with "qi"

31. Page 125
Line 4:  Should be: u(k)=(I-a A") . u(k)
4 up:  Replace "behavior" with "behaviour"

32. Page 126
Line 5:  Replace "requiring" with "stipulating"
11 up:  Replace "unit normal vectors" with "unit vectors"

33. Page 128
Equation (4.7.2):  The argument of the left-hand side should be bold-faced.  Change "Vi(x0)" to "Vi(x0)"

34. Page 129
Equations (4.7.9), ( 4.7.10):  Remove the argument "(x0)" from the left-hand side.
Line 3:  Replace "two-dimensional" with "three-dimensional"
Equation (4.7.11):  Right after this equation add: "where X0=x0-xc."

35. Page 132
Equation (4.8.11):  Remove the superscript "-" from D at the lower side of the last integral.

36. Page 142
5 up:  Modify to read: "(5.2.3), (5.2.8), and (5.2.9)..."

37. Page 147
Equation (5.5.1):  Insert a pair of parentheses to read: Df = Dr (g .x) n + D { -P I + m[Ñu + (Ñu)T]}.n

38. Page 148
Equation (5.5.2):  Enclose "g . x" with a pair of parentheses: "(g . x)"

39. Page 149

40. Page 150
Line 11:  Add some words to read: "...two curvilinear axes x and h that lie in the interface and measure arc length, and ..."

41. Page  151
Line 15:  Modify to read: "... and x with the azimuthal arc length sf, ..."

42. Page 155
Equation (5.5.37) and at the next line:  Change to bold to read: "es"

43. Page 157
Line 3:  Strike out the word "ordinary"

44. Page 166
Line 17:  Modify to read "...the first few derivatives of d|f|/db must be ..."

45. Page 174
Line 2:  Change the denominators in the first two equations for f1 and f2 from a-1 to 1-a and from b-1 to 1-b.

46. Page 175
Line 3:  Modify to read "... whose trace in the xy meridional ..."

47. Page 178
Line 4:  Modify to read "where g=fhn (see(6.2.12)).  The coördinates of the base points and the corresponding weights wn are indicated in Figure 6.4.1."

48. Page 180
Equation (6.4.10):  The arguments of the integrand on the left-hand side should be (h, x, h0, x0,)

49. Page 194
Equation (7.2.16):  The subscript "ijkl" at left-hand side should be "ijlk"

50. Page 203
12 up:  Hat should be placed on top of x
2 up:  Hat should be placed on top of x

51. Page 204
Line 3:  The first sentence should be: "At this point we stipulate that Trace(q)=0."

52. Page 205
Line 14:  Hat should be placed on top of x
7 up:  Should be: (7.3.22) and (7.3.27)

53. Page 207
Line 18:  Should read: (7.3.37) and (7.3.38)
Line 21:  Should read: (7.3.35), (7.3.36), and (7.3.39)

54. Page 211
4 up:  Should read: "and Kim & Karilla (1911, Chapter 13) present.."

55. Page 215
7 up:  Change to read: " whereas when the fluid is stationary T=V/V."

56. Page 218
15 up:  Delete " =0"

57. Page 224
Line 6:  Change to read "condition u = W x (x-xc)"

58. Page 225
Line 15:  Change to read "... to a surface integral ..."

59. Page 228
4 up:  Replace "where d is " with "and d is "

60. Page 229
Equation (11):  Replace the whole equation with:
E=(i/4) H0(1) (-l2)½(r)=(i/4)H0(1) (eip/4|l|r)=(1/2p)[ker0(|l|r) - i kei0(|l|r)]

61. Page 230
Equation (12)  Strike out the first 9 lines up to the end of this problem and replace with:

All of these functions may be computed accurately using polynomial approximations (Abramowitz & Stegun 1972, p.384).  Substituting (11) into (2) we find

H= - 1/(2pl2) [ ln r + ker0(|l|r) - (i kei0(|l|r)]                                        (12)

Substituting further (12) into (2.2.4), and carrying out the differentations we find the Green's function

Gij(x, x0) = dij A(R) +  (^xi^xj)/r2   B (R) - i 2/|l|2   (dij/r2   -   2 (^xi^xj)/r4)

where R=|l|r, and the functions A and B are defined as follows
A(x) = 2 [ ker0 (x) - kei'0(x) / x] - 2 i [ kei 0(x) - ker'0(x) / x]                                                                 (15)
B(x) = 2 [ - ker0 (x) + 2 kei'0 (x) / x] + 2 i [ kei0(x) + 2 ker'0 (x) / x]                                                     (16)

The pressure vector is given by (2.6.19).

62. Page 236
Problem 4.2.2:  Replace "SB" with "B" at two places in the text and in the equation.

63. Page 237
Problem 3:  Change to read "...at a rate that is slower..."
1 up:  Change in one place to read: [v . (A-l2*I)2] . u = (l1-l2*) [v . (A-l2*I)] . u = (l1-l2*)2 v . u = 0

64. Page 244
Problem 6.4.2:
First equation:  Change the subscript "i-1" to "i" in two places
Second equation:  Change the subscript "i-1" to "i" in four places
Right after the first equation add: "where the point x0 lies on the straight segment subtended by the points Pi and Pi+1."

65. Page 245
Line 11 up: Modify to read: "Using (7.2.2) and assuming the pressure vanishes at infinity, we find that ..."

66. Page 246
Equation 6: Add "a2" inside [] to read: [1 +  l /(2*(5l+2))  a2 Ñ2]0
Line 4up: Should be:  q = (1/6) a5 (l/(1+l)) E

67. Page 254
Second line of reference to Mikhlin