... field vectors are (left) perpendicular to the plane of incidence and (right) parallel
to the plane of incidence (Zohdi [218]).
9.2.4 Reflection and absorption of energy
Now we consider a plane harmonic ... very dilute gases and, in the limit, in a vacuum. For general
overviews pertaining to scattering, see Bohren and Huffman [33] and van de Hulst [195].
Remark. An applica...
... Szabo and Babúska [185], and Zienkiewicz and Taylor [2 07] .
For work specifically focusing on the continuum mechanics of particles, see Zohdi and
Wriggers [216]. For a detailed numerical analysis of ... in Zohdi [212] and [2 17] .
11
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16 Chapter 2. Modeling of particulate flows
where v
cm
(t) is the mean velocity of the group of...
... motion.
Top to bottom and left to right, for e
o
= 0.5, µ
s
= 0.2, µ
d
= 0.1: (1) no near-field
interaction, (2)
α
1
= 0.1 and α
2
= 0.05, (3) α
1
= 0.25 and α
2
= 0.125, and (4) α
1
= 0.5
and
α
2
= ... developed, based
on simultaneous particle flow and growth, by Torquato and coworkers (see, for example,
Kansaal et al. [119] and Donev et al. [55]–[59]). This class of meth...
... models
X
Y
Z
X
Y
Z
X
Y
Z
X
Y
Z
Figure 7. 13. Top to bottom and leftto right, a charged cloud against animmovable
obstacle.
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70 Chapter 7. Advanced particulate flow models
XY
Z
XY
Z
XY
Z
XY
Z
Figure ... where
z
rK
def
=
rK
TOL
r
and z
θK
def
=
θK
TOL
θ
,
(7. 37)
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... fluid.
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80 Chapter 7. Advanced particulate flow models
X Y
Z
X Y
Z
X Y
Z
X Y
Z
Figure 7. 17. Top to bottom and left to right, fast impact of charged clouds. ... 0 .7 0.8 0.9 1
TOTAL FORCE (N)
TIME
TOTAL X NORMAL FORCE
TOTAL Y NORMAL FORCE
TOTAL Z NORMAL FORCE
TOTAL X TANGENTIAL FORCE
TOTAL Y TANGENTIAL FORCE
TOTAL Z TANGENTIAL FORCE
Fig...
... see
Fuster [72 ], Shah [ 174 ], van der Wal and Becker [1 97] , Chyu and Shah [46], and Libby
[134], [135], Libby et al. [136], Libby and Aikawa [1 37] , Richardson et al. [169], Loree
et al. [141], and Davies ... Kahn and Hackett [1 17] , [118], and Zohdi and Szeri [222].
Clearly, the number of applications in the biological sciences is enormous and growing.
More general...
... coupling.
Journal of Fluid Mechanics, Vol. 429, 23–61.
[61] Duran, J. 19 97. Sands, Powders and Grains. An Introduction to the Physics of Gran-
ular Matter. Springer-Verlag.
[62] Eber, S. and Lux, S. ... L., and Makse, H. 2005. Fluctuations and the
effective moduli of an isotropic, random aggregate of identical, frictionless spheres.
The Journal of Mechanics and Ph...