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y
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20
Con
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Declartion
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Chapter
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1.
Denitos
1.2
Wh
1.3
A
as
a
.
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is
.
Stae
A
Strange
1.32
A
W
1.3
An
1.34
T
1.35
Bubling
.
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.
eird
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1.42
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1.43
Av
1.4
Finger
1.45
Riples
1.46
Sound
Ob
Pro
jectiv
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1
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3
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4
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5
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6
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7
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8
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Struces
.
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10
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10
.
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.
14
.
.
es
Gran
ular
Flo
Dunes
.
ducing
and
Extincos
ws
.
Sand
ter-paicl
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
15
.
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17
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18
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19
F
vi
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ortan
.
.
.
In
.
.
Earthquk
es:
.
.
Sand
and
.
.
Langue
in
.
.
.
hes,
.
.
e
alnc
.
Imp
Jams
Dispatv
.
.
and
atern
.
.
Fluid
ws
.
.
.
Flo
P
.
Materils
Sand
1.4
.
Mater
Gas
raÆc
1
.
Solid
and
and
.
ular
of
Un
aterns
Aims
.
System
Gran
1.3
P
.
Complex
Studying
Unique
1.4
1.5
Sand
orces
Chapter
2
2.1
Buildng
Ov
on
erviw:
Staic
2.1
The
2.1
Dynamic
2.13
Cohesiv
2.14
Metho
2.
Exp
Helmhotz
Chapter
3
3.1
P
Staic
Exp
3.
Result
3.4
Conclusi
erimn
Chapter
4
4.1
Ov
.
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20
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2
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23
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26
Bridges
e
F
orces
.
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27
.
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DEMO PDF produced by an unlicensed PStill, licensing will remove this mark
See http://www.pstill.com or for the MacOS X version http://www.stone.com
.
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shap
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102
Segration
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Discuon
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.
Drums
tal
and
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orce
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Progams
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125
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Progam
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for
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for
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126
Published
P
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xi
137
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List
1.
Prop
4.1
The
ertis
of
30
min
A.1
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See http://www.pstill.com or for the MacOS X version http://www.stone.com
.
y
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.
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2.17
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2.18
Sev
w
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dynamic
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other
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the
particles
enrgy
densit
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oth
198
of
h
sand
w
oured
aginst
suc
smo
al.,
p
or
in
and
teracion
of
es
on
materils
h
v
b
et
in
us,
w
fricton
erimn
ular
with
y
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es
mater
exampl
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ular
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v
.
eithr
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ws
gran
).
er.
ws
Th
t
proagte
hop
hop
y
ws,
ular
to
the
densit
en
end
190
hanics.
gran
ed
up
w
mec
observ
of
ular
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end
sho
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indep
When
throug
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ear
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heig
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can
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h
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3
This
exp
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erimn
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t
is
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simlar
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19
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4
This
nec
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sand,
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a
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than
t
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liqud,
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ving
a
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In
the
:
equalis
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materils,
del
h
slo
ahed
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parking.
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left
wil
someti
196
is
space
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top
depth
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b
one
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gran
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Nishdate,
A
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gran
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6
a
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ts
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gran
stae.
hing
elop
198
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aproc
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al.,
the
to
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ular
densit
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y
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,
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A
Unique
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Group
A
Mater
7
Size:
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10
m
exhibts
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oth
buling
and
buling
no
uidsaton
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Group
B
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50
m
bules
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C
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o
wders
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and
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m
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e
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1.35
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gran
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a
to
The
viour
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wder
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dep
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wil
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19
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whole,
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of
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sytem
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aterns
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1.3:
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alnc
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rice
Struces
8
exhibts
Self
Organised
Critcal
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ret
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(2
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P
aterns
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1.4:
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The
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h
9
to
banho
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es
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A
When
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driven
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P
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1.6:
The
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ut
ect
materils
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ban-
1.4
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Struces
12
a)
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1.7:
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ect
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tainer
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6
top,
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1.43
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of
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ap
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and
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Staic
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Beha
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self-con
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Figure
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particles
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Staic
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erag,
p
o
et
p
o
as
size,
than
tha
comp
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201
).
b
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ular
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v
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and
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h
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vil,
192
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osely
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teracion
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other
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der
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ular
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um
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In
h
a
2.1
Ov
erviw:
Staic
Figure
closey
2.4:
pac
sen
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ting
ed
in
The
they
b
in
etr
for
grains
t
togehr.
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tha
of
alo
but
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Figure
2
curv
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the
ature
This
is
with
ear
surface
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led
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capilry
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liqud
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the
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surface
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ular
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ater,
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are
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forming
to
retain
solid
their
bridges
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whic
h
2.1
Ov
erviw:
Staic
Beha
viour
in
Gran
ular
Materils
26
6
derw
ater.
In
2.14
b
oth
Metho
T
o
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examin
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v
One
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an
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to
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forces
note
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b
iron
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withn
1975
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7
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more
detail
in
e
al.
ort
of
rep
diÆcult
to
a
ose.
relat
force.
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6
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since
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ork
maner.
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of
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W
)
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coarse
step-wi
furthe
w
most
a
198
),
tensio
mon-sized
liquds
anlysi
the
of
u,
197
force.
king
Y
al.,
surface
with
also
and
et
ter-paicl
Ading
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erhaps
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teracion,
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in
on
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liqud
sev
(Horn
of
in
of
size
),
increas
trolabe
in
197
liquds
ter-paicl
con
ter-paicl
al.,
ade
are
in
particle
et
the
Ther
the
P
e
ect
198).
increas
in
v
e
the
Y
ert
observ
examing
decrasing
c
hapter
3.
).
than
Unlik
compresin.
e
con
v
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tional
struce,
w
as
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erimn
tal
examind.
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force
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et
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exp
induce
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als
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If
27
magneticly
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F
wil
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F
B
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198
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193
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is
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to
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force
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from
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for
same
et
used.
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b
as
p
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end
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w
and
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eld
d
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to
force
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magnetic
times
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er
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axis
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o
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from
al
o
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an
y
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p
but
than
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er
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of
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k
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midw
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eral
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to.
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iner
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les
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glued
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the
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adher
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jac
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ater
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eld
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16
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temp
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les
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erimn
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an
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erd
temp
e
76
with
o
the
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wil
for
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erimn
Figure
tal
2.6:
The
30
v
ariton
in
Figure
lab
T
oraty
o
obtain
eigh
p
the
t
new
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of
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square
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furthe
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magnetic
gure
the
ratio
eld
hand
of
at
axis
of
in
ter-
gure
2.8
Ramping
the
eld
do
wn
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slo
wly
serv
es
t
w
o
pur
ose.
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it
alo
w
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curen
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to
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to
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the
w
w
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set
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erimn
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31
Graph
eld
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Discuon
wn
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ting,
w
using
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v
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to
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images.
condute
to
measur
the
angle
of
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10
v
alues
of
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in
ter-paicl
force
Result
The
and
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cleary
in
sen
the
image,
Discuon
dynamic
in
angle
Figure
and
.
of
2.1
the
angles
The
w
rep
ose
er
angle
with
of
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rep
detrmin
ose
in
using
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a
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rst
can
segmn
b
This
ting
aproc
h
10
The
(F
orsyth
result
of
et
al.,
the
authors
20)
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exp
erimn
ts
ha
v
e
b
en
published
in
(F
orsyth
et
al.,
e
201a
)
and
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Win
tz,
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of
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creas
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et
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ular
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o
rep
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angle
er
of
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measur
a
19)
ecoms
plastic
to
w
exp
liqud
more
for
of
the
angle
force.
regim,
t
v
the
197)
seri
thes
only
b
case,
angles
ter-paicl
d
ular
increas,
eac
al.,
metho
al.,
of
w
oth
dynamic
elswhr
et
gran
es
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ears
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olv
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surface
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hniques
demonstra
a
et
o
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en
er
in
v
lev
of
ose
maner.
in
w
fal
of
linear
in
b
den
egzs
surface
grains
angle
e
b
ts
viour
(T
lo
t
r
v
eha
al.
at
e
measurn
ha
b
amoun
elat
atc
tec
and
in
197)
ose
and
the
al.,
of
et.
itself
al.
rep
In
bak
et
al.
homgenus
manifest
v
(Horn
linear
egzs
2.13
ha
existnc
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ting
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increasg
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ert
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and
19),
et.
ostulae
gime
rep
of
egzs
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r
al.,
angle
o
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the
with
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dynamic
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curv
measur
2.1
of
crate
The
other
to
lineary
egzs
draing
ts
Figures
angle
(T
the
to
erimn
ximately
staic
197),
prefd
exp
wn
apro
for
is
).
result
p
32
noise
1987
The
Discuon
case
rep
ose
actuly
decras.
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is
Ob
unclear
whetr
viously
plastic
the
angle
of
or
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ose
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con
tin
wil
ue
to
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up
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higer
with
elds.
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o
eld,
as
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the
angle
b
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iron
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spher
diÆcult
e
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aproc
egan
canot
excd
hed
to
b
ose
to
measur
closey
.
due
clump,
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90
blo
to
c
king
the
A
t
and
one
hig
cohesiv
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angle
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rep
studie
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ose
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Result
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on
gle
of
Discuon
stabil
3
y
stabil
y
critea
(Alb
should
ert
increas
et
al.,
apro
197)
demonstra
ximately
tha
lineary
with
the
maxi
um
increasg
in
ter-paicl
o
force
from
of
in
ab
out
o
23
ter-paicl
an-
,
at
force
zero
to
in
w
eigh
ter-paicl
t
force,
of
1.
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t
up
ratios
ab
o
to
v
e
a
lite
one
o
the
v
er
80
graph
,
tails
at
a
o
ratio
to
w
ards
o
the
maxi
um
consider
angle
of
liqud
based
on
p
um
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rep
tilng
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b
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in
ork
of
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ter-paicl
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(Alb
cohesiv
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et
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al.,
197)
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particles,
theory
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angle
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e
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based
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cit
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used
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ws
angles
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gain
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ed
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tal
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comes
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force
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at
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192)
aligned
with
tha
tha
the
in
(at
teracion
least
the
for
eld
is
separtion
giv
enrgy
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en
her.
for
large
It
particles
can
b
aligned
compared
in
to
the
e
demonstra
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directon
dimenso
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of
the
eld
the
is
dip
vil,
t
ole)
wice
2.3
Result
and
Discuon
34
Figure
2.9:
Figure
Magnetic
tha
of
line
t
w
o
dip
joing
rep
eld
el
than
tres
of
the
The
line
a
F
.
Picture
parle
cen
when
lines.
2.10:
aligned
the
and
les
ole
v
\sand
to
our
eac
force
Henc,
h
the
b
ratio
of
at
of
the
in
the
same
with
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y
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aligned
cen
felt
the
other
is
the
erag
in
particles
joing
castle"
separtion.
the
the
eld
our
particles
is
particles
wil
ter-paicl
When
o
force
v
p
dip
erp
oles
atrc,
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eral
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to
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e
to
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particle
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eigh
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is
alw
from
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the
slop
a
ys
as
e,
in
in
liqud
atrciv
result
e
the
the
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magnetic
a
net
bridge
and
force
horizn
acts
along
tal
case.
is
a
force
One
also
w
to
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w
line
anisotrpc.
ards
joing
the
therfo
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exp
e,
cen
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liqud
of
tha
than
t
the
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angle
w
w
a
o
y
2.3
Result
of
and
rep
of
ose
in
b
Discuon
for
w
rect
w
maner
in
to
to
197)
plots
and
ose
of
)
(Alb
v
et
ert
in
ose
the
a
197)
b
erag
the
la
er
for
p
erhaps
y
using
stage
no
liqud
et
done
robust
bridges
al
with-
(Horn
bak
er
metho
er
thic
knes.
liqud
tha
this
draing-cte
increasg
demonstra
ts
to
bak
liqud
with
at
due
Horn
y
ratio
so
erimn
is
force
of
the
and
exp
ther
ter-paicl
v
those
as
obtained
of
197).
to
ork
functio
case,
al.,
dat
w
a
magnetic
et
our
lineary
al.,
(Alb
as
the
force
rep
ximately
ert
al
in
ter-paicl
ersu
rapidly
than
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angle
apro
et
parmets.
1970
rise
t
the
ted
hards,
in
calute
staic
Ric
eigh
compare
the
h
more
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ely
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whic
resoting
Alb
tiav
to
increas
w
of
quan
bridges
ould
particle
theory
to
liqud
al.
wders
to
the
diÆcult
out
o
force
is
p
p
ter-paicl
etr
It
et
35
la
sligh
tly
er
thic
wn
angle
of
knes.
rough
al.,
d(Bro
The
y
et
Alb
particles,
re-
ert
the
et.
liqud
1
3
bridge
force
F
l
liqud
bridge
in
Qualitv
ely
of
rep
ose
V
wher
V
ter-paicl
,
this
giv
es
is
the
the
v
y
b
with
critea
pro
same
lineary
stabil
is
force
increas
Basic
,
olume
of
the
liqud
bridge.
Henc,
the
iq
(Alb
ortinal
eha
to
viour
sen
increasg
ert
al.,
197)
thic
knes
using
in
et
the
the
magnetic
liqud
la
forces,
ter-paicl
w
of
tha
of
apro
ximately
diernc
force.
ould
predict
an
angle
of
rep
ose
at
It
has
b
(Dury
p
en
sho
et
al.,
.
osibly
b
wn
tha
198
Our
e
angle
of
atribued
w
).
to
al
Rep
rep
ects
our
is
the
can
eating
ose
naro
tly
w
ad
exp
signca
sev
b
eral
erimn
men
and
8
ts
w
m
ga
er
ascertin
p
v
e
angles
of
erfomd
on
whetr
iron
w
as
ose
of
spher
residual
magnetiso
rep
ts
x
used
at
(
for
the
to
zero
31
).
exp
the
eld
erimn
angle
with
b
ts.
of
o
The
xes
of
rep
ose
width
6
0
30
and
tha
28
had
magnetiso
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0
m
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23
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er.
angle
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exp
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ect
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due
to
residual
found.
o
The
dynamic
angle
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rep
ose
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eld
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)
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considerably
higer
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staic
o
angle
of
rep
caries
the
ose
staic
the
the
(31
the
dynamic
more
of
eld
up
thoug
inerta
zero
particles
case,
force,
at
w
angle
slo
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particles.
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for
al,
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leading
of
than
the
predict
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ose
to
m
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As
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197)
drum
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the
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Result
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Figure
2.1:
Discuon
T
ypical
Ying-
hig
Figure
ang
rotainl
2.1:
of
A
exp
in
Unlik
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b
als
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o
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complety
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ha
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t
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repsn
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Sand
elo
angle
gures
2.13:
2.31
shap
v
Dynamicl
the
Figure
36
When
this
2.3
Result
and
Figure
2.14:
Graph
Figure
2.15:
Graph
Discuon
37
of
staic
of
w
eigh
t
squared.
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dynamic
angle
angle
of
rep
of
ose
rep
vs
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the
vs
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38
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t
problem
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w
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40
F ractal D imension v ersu s Coil Voltage
F ractal D imension
1 .1 2
1 .0 8
1 6 0 0 mm m
8 0 0 mmm
3 5 0 mm m
1 .0 4
1 .0 0
0
5
10
15
20
Coil Voltage (V)
Figure
2.17:
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Graph
of
fractl
dimenso
vs
coil
v
oltage.
2.5
Conclusi
41
sytem
wher
particle
in
force
o
w
m
and
Exp
w
force
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ter-paicl
b
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b
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b
y
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b
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A
no
of
v
p
of
in
o
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the
presn
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rep
piles.
question
w
of
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rice.
v
di
196),
grained
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angle
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they
of
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then
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tha
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viour.
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hes.
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the
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190)
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alnc
surface
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of
v
b
moen
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hes
ev
Simlar
al.,
t
w
of
metho
tha
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This
al.
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ter-
termin
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in
dynamics.
of
simple.
hes.
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in
isue
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alnc
they
w
measur
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patern
ving
elo
et.
far
v
v
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agin.
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to
tha
192)
crital
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mo
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wn
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ular
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for
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the
2.5
Conclusi
Figure
42
a
b
c
d
2.18:
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ariton
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b
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P
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study
of
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T
w
imp
particule
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pro
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3.1
Staic
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b
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ter-
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y
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3.1)
struce
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v
Figure
is
the
eÆcien
h
(se
than
of
top
arc
complex
formatin
on
spher
t
more
ha
the
taly
43
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task
grains.
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20
30
40
50
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Interp article F orce
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in
1 .0 E + 0 7
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sytem.
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ratio
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0 .7
M od e l 2 (K ru p p )
M od e l 3 (H a m a k e r)
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0 .5
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50
100
150
200
250
300
350
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u,
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198),
fraction
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for
orsyth
dry
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19
1
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3
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3
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givn
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p
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eing
der
tribue
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erstimad.
b
for
ter-paicl
than
v
fraction
sho
Molerus
Rho
oid
198).
asp
large
is
v
u,
tha
and
fraction
fraction
Y
the
from
diametrs
the
and
only
er
the
is
eng
consider
w
w
predicton
to
del
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Y
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del
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m
ho
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estima
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than
w
and
mo
t
no
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and
henc
erimn
can
eng
Krup's
orsyth
exp
F
er
and
parmets
of
of
Hamk
wn.
e
diametr.
dat
of
sho
w
particle
force
predictons
dat,
with
dels
ter-paicl
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ary
tal
mo
are
in
this
erimn
the
force
Using
v
exp
using
als
to
.
should
with
curv
ely
o
m.
due
F
or
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viously
a
this
ip
apro
ximaton
m
ust
break
do
wn
at
hig
v
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of
F
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ip
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.
By
denito,
the
v
d
oid
3.4
Conclusi
51
fraction
can
this
v
nev
alue.
F
er
or
excd
a
unit
20
m
y
,
and
in
particle,
F
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v
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is
oid
apro
fractions
nev
ximately
er
137,
ev
whic
en
h
aproc
is
h
far
b
ey
ond
ip
the
maxi
it
is
um
not
the
of
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osing
more
b
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magnetic
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w
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t
more
et
w
sytem
breaks
to
and
relationshp
y
mo
force
rise
a
the
ter-paicl
3.2
ho
b
tha
Figure
c
examind
surping
ratio
in
ratio
slo
en
v
is
wn
for
do
to
as
"
v
wn
wly
oidage,
(apro
,
54).
smal
fact,
A
one
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tha
t
25
se
force
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particles.
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in
and
ery
70.
the
ximately
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m,
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ip
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e
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,
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oid
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theorical
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of
til
the
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the
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form
F
ip
"
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"
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"
"
0
)
max
Exp
k
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0
mg
wher
"
is
the
maxi
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atinble
v
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b
e
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t
the
exp
erimn
tal
max
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more
3.4
closey
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linear
mo
del
in
equation
(3.1)
Conclusi
The
result
dep
of
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our
only
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on
tha
in
p
thoug
no
t
role
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the
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next
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ter-paicl
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with
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w
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gran
o
ular
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tha
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v
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the
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particle
result
c
wil
ratio
to
of
ts
oured
force
often
erimn
the
the
ter-paicl
In
exp
examind.
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ect
of
in
ter-paicl
force
on
buling
in
uidse
gran
ular
Chapter
4
Bubles
njectig
ne
uidse.
jets
I
Thes
v
fuels
uidse
ine
w
the
is
eigh
b
t
eha
v
in
4.1
erviw:
Fluidse
(Geldart
ular
and
Ob
W
jects
are
lo
er
or
densr
ular
y
exp
ts
b
ed
is
ter-paicl
from
exam-
to
buo
b
of
viour
to
buling
ts
the
in-
eha
used
force
measurn
of
erimn
no-bulig
viour
eha
y
an
t
viour
presu
drop
Mater
no-uidse
gran
ular
mater
in
sev
eral
w
a
ys
exampl:
than
densit
hapter,
cesing
the
than
the
uidse
materil
uidse
wil
materil
wil
sink
while
oat
on
ob
the
jects
tha
surface
of
the
ed.
A
b
a
ed
tha
at
or
The
When
ed
intaly
has
horizn
surface
b
w
phar-
re-po
b
in
eha
hemical,
the
uidse
of
to
aried.
F
are
c
materil
etro-c
in
and
ratio
and
as
this
tal
the
p
el
viour
erimn
the
the
w
In
eha
b
from
1984).
tha
of
b
v
in
).
anlysi
diers
ong,
19
exp
as
Gran
mater
,
no-bulig
Fluidse
gran
el
shot
video
is
y
v
cause
as
b
no
to
force
materil
used
buling
iron
ed
ular
routinely
orth
A
hig-sp
gran
industre
en
transio
ter-paicl
Ov
w
uidse
A
using
et
discue.
of
aried.
ed
the
are
viour
is
observ
as
eds,
of
duction
amo
b
eds
are
Sathiy
transio
b
eds
pro
and
the
in
b
enrgy
(Gupta
estigan
thoug
b
and
uclear
air
uidse
maceutil
n
of
is
lev
tal
an
unev
surface
el
of
en
when
surface
t
w
o
in
the
un-idse
stae
wil
gran
ular
conetd
regions
mater
wil
of
o
52
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v
uidse.
the
b
ed
wil
equalis
when
uidse.
uidse,
ha
w
lik
e
a
liqud
throug
an
outle.
the
e
4.1
Ov
erviw:
Fluidse
Gran
GELDART
ular
Mater
53
’S POWDER CLA
SSIFICA
TION
10,000
5,000
3
B
2,000
r p - r g Kg/m
A : Aeratable
B : Bubbles
C : Cohesive
D : Spoutable
D
1,000
A
500
C
300
200
10
20
50
100
200
500
1,000
2,000
d p mm
Figure
In
4.1:
some
Phase
uidse
diagrm
for
materils,
forming.
Thes
Fluidse
an
bules
gran
ha
ular
v
media
uidse
p
increas
e
in
some
can
the
o
e
F
rom
(Geldart,
uidsaton
v
simlarte
b
wders.
with
clasied
in
to
elo
cit
bules
sev
1973).
y
in
eral
result
in
bules
diern
liquds.
t
phase
tha
dep
end
1
up
b
on
their
y
pro
Geldart
ertis
am
t
and
Group
A
4.2c
Group
C
Group
D
fort
eds
great
wders
o
of
y
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are
as
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es
p
o
hem
w
wders,
as
p
fol
as
in
tro
duce
uidse
dives
are
o
b
wders
in
to
y
air
groups
ws:
uidsaton
bule
pro
h
y
ould
duce
resac
not
b
made
men
dry
hem
no-bulig
e
can
e
to
molecuar
w
sc
groups
tras
w
of
et
regim
imedatly
in
in
great
up
ards
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to
this
one.
not,
sp
the
in
b
(Figure
on
4.2a),
uidsaton
Lev
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(Ho
b
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omans
et
).
A
al.,
eds,
a
unifyg
theory
of
19).
to
193
uidse.
4.2e)
uid
ortance
(Clift,
sen,
(Figure
ensp
imp
dels
stric
eds
of
and
goal
the
outed
nature
practil
mo
c
do
(Kuni
dynamics
tioned
and
dep
exist
1
As
This
thes
cohesiv
wders
of
do
using
sc
of
4.1)
a
b
deal
w
b
wders
o
p
theory
has
o
p
viour
a
clasiton
uidsaton
Figure
exhibt
A
4.2d)
h
b
p
and
a
Suc
wders
.
buling.
B
eha
o
bule
the
ertis
undergo
Group
Despit
pro
p
wil
b
(se
The
to
for
condits
D).
but
y
1973)
bien
(A,BC
ed
abilt
(Geldart,
under
b
and
industry
and
temps
196
to
so
)
are
limted
mo
del
m
uc
h
uidse
b
y
their
ef-
4.1
Ov
erviw:
Fluidse
Gran
4.2:
Bubling
in
slugin,
hig
p
ear
ely
to
en
used
to
to
mo
putaionly
exp
latice
gas
not
e,
alo
celuar
w
v
elo
(v
d
autom
large
some
eds
metho
cit
y
ed
W
tro
ts.
wn
197
hes
also
a
ha
far
v
e
en
t
les
also
com-
bules
y
exist
ap-
v
exampl,
w
eds
cirum
This,
or
articl
aproc
increas
b
to
).
F
an
to
autom
limtaons.
in
hanelig.
ue
orde
celuar
duce
Other
tin
In
al.,
(b)
c
uidse
come.
et
expansio,
(e)
scale
hem
ed
con
industral
to
ac
o
b
and
eds
resticon,
its
in
gradien
stable
buling
sp
time
an
has
are
(a)
t
of
sp
b
right
turblen
ulations
for
uidse
ensiv
to
or
sim
computainl
del
left
cesing
(MD)
due
om
haotic
computer-
impractl
limtaons
b
While
remain
fr
c
e
d
eds
(d)
Dynamics
lik
the
b
buling
cost.
Molecuar
54
c
uidse
(c)
computainl
direct
Mater
b
a
Figure
ular
and
the
in
(Ding
mo
and
dels
do
Gidasp
o
w,
2
190
)
(Seib
4.1
ert
and
Burns,
196
),
but
al
thes
aproc
hes
ha
v
e
limtaons
.
Bubles
If
the
o
the
in
w
rate
of
tersic
b
gas
frictonal
et
w
presu
lift.
The
U
The
a
en
the
drop
o
.
throug
w
v
alue
at
of
ed
great
h
for
is
If
is
whic
U
mf
b
particles.
tha
rate
uid
o
w
the
then
o
than
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a
lo
w
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curs
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w
kno
uid
the
rate
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t
as
ed
wil
is
wn
b
air
large
of
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to
ed,
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ermat
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the
wil
p
t
end
up
obtain
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the
b
ed
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wil
on
rate
a
wide
range
of
mf
factors.
The
w
t
ak
e
terio
of
ypical
shap
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e
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extrio
the
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a
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uidse
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to
is
b
b
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is
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spherical
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el
b
with
oundary
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b
The
et
amoun
w
a
t
the
of
en
materil
2
se
(Clift,
193)
for
o
v
erviw
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of
the
strengh
and
limtaons
of
the
v
arious
aproc
smal
hes
in-
4.1
Ov
erviw:
Fluidse
Gran
ular
Figure
Figure
4.:
Ho
around
(1)
Mater
4.3:
5
Struce
of
a
bule
1a
1b
1c
1d
2a
2b
2c
2d
w
bules
the
split.
side
Figure
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(2)
of
the
\Kniv
es"
of
materil
ap
4.5:
bule.
Ho
w
bules
merg
ear
and
are
transp
orted
4.2
Exp
in
erimn
the
tal
inde
ted
56
base
is
kno
wn
as
the
\w
ak
e
fraction",
f
,
and
is
genraly
observ
ed
w
to
v
ary
sligh
surface
tly
of
bules
o
the
elo
b
oin
bule
rise
bules
in
the
do
not
materil
kno
ak
bule
throug
the
burst
lik
from
the
ro
o
wing
get
in
w
pro
e
e
b
ed.
bules
of
Up
in
of
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on
reac
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hing
the
Instead,
bule
fals
in
the
to
the
ca
vit
y
eld
y
a
the
).
for
bules
w
up
tha
ard
4.2)
end
rapidly
wn
Figure
and
so
do
(se
bule
w
This
side
faster
b
mo
disolvng
they
cause
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y
t
side,
ving
ypical
hap
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bule
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er
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mo
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ving
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the
bule
underath
4.5)
signca
t
other
ob
w
ak
h
e
distorn
if
jects.
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materil
e
wil
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so
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ough
t
wil
in
close
also
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genral
tha
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e
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ha
the
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ter
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b
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the
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the
v
signca
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a
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v
ary
bules.
o
for
wder
particle
to
(Clift,
193).
observ
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buo
exp
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t
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w
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uidse
197
quite
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es
bules
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oups
eha
buling
al.,
top
kniv
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is
4.1)
undergo
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It
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tal
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er
uidse.
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w
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w
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ts
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4.2
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thin
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v
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o
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tal
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ular
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The
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tal
58
Side Elevation
Outer T
Helmholtz coils
ube
O-ring seal
Air inlet
windbox
Plan
Distributor
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4.6:
Fluidb
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design
4.2
Exp
erimn
tal
59
Side Elevation
Outer T
ube
Inner T ube
Spacer
Light Source
placed here
Helmholtz coils
O-ring seal
Air inlet
windbox
Plan
Distributor
nylon bolts
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here
Light Source placed
in centre
Figure
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4.7:
Mo
die
Fluidb
ed
design
4.2
Exp
erimn
tal
60
Maximum
P ressure
Drop
P ressure Drop
P ack ed
Bed
Magnetically
Stabilised
Fluidised
Bed
Minimum
Fluidisation
V elocity V m
Minimum
Bubbling
V elocity V
f
Fluidisation V
Figure
4.8:
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v
line
in
detrming
aditon
to
ed
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link
b
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ed
to
v
in
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Me
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0
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hed
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4.3
Result
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61
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o
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for
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c
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w
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b
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length
particles
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b
to
can
of
surface
b
of
e
4.3
Result
and
Discuon
62
B ed Pressu re D rop v ersu s G as Velocity (0 V)
B ed Pressu re D rop (Pa)
3500
3000
2500
2000
Inc re a sing v e loc ity
D e c re a sing v e loc ity
1500
1000
500
0
0 .0
0 .1
0 .2
0 .3
0 .4
G as Velocity (m/s)
Figure
4.10:
The
b
ed
presu
drop
v
ersu
the
gas
v
elo
cit
y
(coil
v
oltage
=
0
V)
B ed Pressu re D rop v ersu s G as Velocity (1 .9 V)
B ed Pressu re D rop (Pa)
3500
3000
2500
2000
Inc re a sing v e loc ity
D e c re a sing v e loc ity
1500
1000
500
0
0 .0
0 .1
0 .2
0 .3
0 .4
G as Velocity (m/s)
Figure
4.1:
4.32
The
Hyster
the
alues
of
ect
the
ap
v
elo
cit
presu
of
result
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ears
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U
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hig-sp
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Result
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Discuon
63
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B ed Pressu re D rop (Pa)
3500
3000
2500
2000
Inc re a sing v e loc ity
D e c re a sing v e loc ity
1500
1000
500
0
0 .0
0 .1
0 .2
0 .3
0 .4
G as Velocity(m/s)
Figure
4.12:
The
b
ed
presu
drop
v
ersu
the
gas
v
elo
cit
y
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v
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3500
B ed Pressu re D rop
3000
2500
2000
Inc re a sing v e loc ity
D e c re a sing v e loc ity
1500
1000
500
0
0 .0
0 .1
0 .2
0 .3
0 .4
G as Velocity (m/s)
Figure
4.13:
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presu
drop
v
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the
gas
v
elo
cit
y
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v
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Result
and
Discuon
64
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B ed Pressu re D rop (Pa)
3500
3000
2500
2000
Inc re a sing v e loc ity
D e c re a sing v e loc ity
1500
1000
500
0
0 .0
0 .1
0 .2
0 .3
0 .4
G as Velocity (m/s)
Figure
4.1:
The
b
ed
presu
drop
v
ersu
the
gas
v
elo
cit
y
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v
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5.7
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B ed Pressu re D rop (Pa)
3500
3000
2500
2000
Inc re a sing v e loc ity
D e c re a sing v e loc ity
1500
1000
500
0
0 .0
0 .1
0 .2
0 .3
0 .4
G as Velocity (m/s)
Figure
4.15:
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b
ed
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presu
drop
v
ersu
the
gas
v
elo
cit
y
(coil
v
oltage
=
4.3
Result
and
Discuon
65
Increase in hysterisis with field
Hysterisis (Pa s/m)
200
180
160
140
120
100
80
60
40
20
0
0
2
4
6
8
Coil Voltage (V)
Figure
H
(A/m)
4.16:
U
=U
The
(30
mb
increas
in
m)
U
1.05
1.05
1.8
2784
T
able
The
min
of
30
w
as
m,
m
1
1
1
1
1.05
1
1.09
1
80
found
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160
tha
m
v
m
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U
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cit
y
as
a
elo
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eld.
F
v
from
o
B
curs
160
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1.3
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of
aplied
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for
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m
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er
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mf
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160
mf
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1.27
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268
265
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1
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1.4
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mb
190
246
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2069
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1
1034
157
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mb
10
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mf
0
h
the
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stabiled
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eld
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alues
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in
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m,
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ely
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4.
Conclusi
6
Acording
to
for
a
sp
Molerus
eci
(Molerus,
v
alue
of
1982)
K
wher
the
K
is
B/A
transio
curs
for
ne
p
o
wders
den
F
F
ip
K
o
ip
=
=
(4.1)
3
F
dr
wher
F
,
dr
densit
y
exp
d
is
the
particle
d
(
ag
)
p
diametr,
g
=
6
g
is
ag
the
particle
densit
y
,
is
p
and
g
erimn
is
ts
the
for
uidsaton
gra
30
vitaonl
acelrtion.
m
transio
particles
Using
for
K
is
particles
equal
of
the
gas
g
to
2
the
:
63.
diametrs
F
80
result
rom
obtained
visual
m
in
observ
and
thes
ation
160
of
m,
the
v
the
alues
4
for
K
are
Thes
2
v
:
34
and
alues
2
are
dimensoal
29
resp
consite
ectiv
t
uid
4.
:
b
eds
ely
with
(Rho
.
recn
des
t
and
discret
W
elmn
ang,
t
20
metho
d
sim
ulations
of
t
w
o-
).
Conclusi
A
no
v
fect
of
el
uid
b
in
ed
has
b
ter-paicl
tha
In
y
increasg
v
construed
forces
demonstra
b
en
uid
b
transio
the
estigaon
on
whic
in
of
b
et
ter-paicl
w
ed
h
b
eha
en
enabls
visual
viour.
examinto
Group
Using
A
of
this
and
B
b
uid
eha
b
viour
ed,
it
the
can
ef-
b
has
e
b
induce
forces.
this
transio
region
ha
v
e
found
tha
transio
o
curs
for
F
=F
ip
of
2.5
for
creasd,
the
the
uidsaton
v
In
the
next
particle
um
elo
cit
c
namely
thre
min
size
y
buling
in
v
remaind
hapter
elo
cit
the
a
patern
diern
in
y
estigad.
As
w
as
found
in
to
ter-paicl
force
increas
while
thin
asp
ect
of
uidse
vibrated
gran
gran
ular
la
ular
the
y
media
ers.
is
v
alues
of
F
w
er
ip
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obtained
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tal
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w
min
same.
t
formatin
v
4
The
en
in
v
estigad,
as
ag
um
in-
Chapter
5
P
W
e
forga
gro
v
o
v
es
dogs
e
Bagnold
and
ev
the
erything
w
hand
in
the
sand
That
inqurg
for
corugated
mouth.'
aterns
to
as
ws
y
he
ble
real
ja
a
resm
the
the
w
wrote
the
hol
Bagnold,
of
a
ab
a
out
w
man
dunes.
of
The
the
who
ro
w
ould
19
P
in
)
in
tha
namics.
therfo
e
pro
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of
reaction
One
197).
v
this
in
v
in
ter-paicl
estigad.
v
es
c
ts
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and
of
sytem
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t
resac
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1984
)
suc
the
include
other
dwin,
ph
194
h
as
pat-
denritc
and
o
can
of
h
(Go
Langer,
dy-
thes
sytem.
coats
Figure
(Golub
formatin
one
recn
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o
)
ysical
curs
and
the
in
the
BZ
5.1)
excln
t
of
patern
mediu
studying
formatin
in
banho
for
vibrated
w
whic
gran
ar,
196b)
patern
ular
h
in
la
y
has
forma-
only
ers
ter-paicl
(Um
recn
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banho
forces
w
ha
v
e
b
ar,
en
paterns.
patern
formatin
Using
the
force
of
English
patern
other
Stengrs,
(se
(Um
simlar
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of
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cus
in
dels
an
his
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h
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also
alter
b
is
gro
is
to
In
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mould
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e
and
w
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found
v
h
particuly
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a
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same
ha
paterns
materils
tion.
en
uring
slime
ular
div
the
(whic
spiral
and
to
h
19a)
formatin
b
in
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ces),
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ts
sytem
wth
y
eys
patern
insgh
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gro
man
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tern
nature
a
dog.
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formatin
of
put
Mic
atern
of
on
metho
in
the
paterns
d
thin
outlined
vibrated
is
in
examind.
67
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previous
c
la
hapters
y
ers
of
the
gran
ects
ular
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atern
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A
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atern
thin
F
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the
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y
2
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the
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haotic
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v
patern
b
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eha
of
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thes
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the
ho
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f
v
sho
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b
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paterns
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b
sho
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w
5.2)
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a
or
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5.3
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p
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and
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complex
strip
are
196b).
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of
hexagons,
ha
ar,
amplitude
frequncy
paterns
w
and
is
paterns
thes
banho
viour
and
include
of
),
y
(5.2)
and
(some
estigaon
195
vit
paterns
kins
in
gra
=g
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Thes
and
erimn
(Melo
um
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spiral
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maxi
to
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el
as
Extensiv
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Um
e
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phase
w
ar
diagrm
vibraton
of
frequncy
,
f,
and
.
5.1
Mo
Ther
dels
ha
v
mation
e
b
in
banho
w
grains
en
sev
vibrated
ar,
196b)
erio
step
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F
with
atern
at
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ery
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and
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lo
w
v
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patern
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Um
theorical
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amplitudes
tainer.
es
o
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w
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place.
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mo
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con
tak
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y
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la
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ular
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ulated
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lar
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mo
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sigh
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ho
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ulations
b
pbu/
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Chris
Bizon
on
P
aul
Um
banho
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P
atern
F
5.1:
Some
ormatin
in
patern
wings
uring
Gran
forming
(b
T
Vibrated
otm
paterns
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ular
sytem
left)
in
spiral
in
animl
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w
coats
a
v
69
nature.
es
(top)
in
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Bal
BZ
bacteri
reaction
19a).
and
(cen
(b
ter)
otm
butery
righ
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5.1
P
atern
F
Figure
5.2:
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in
Some
of
from
patern
teracions.
In
hemical
other
el
o
simple
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mater
suc
h
gran
b
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en
and
elop
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the
mo
the
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ro
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kwise
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featurs
mec
patern
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pro
sytem.
canot
h
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formatin
for
w
and
suc
formatin
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mater
of
particle
formatin
the
ular
the
patern
ws,
of
gran
patern
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are
formatin
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brot,
en
fo
a
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its
simplct
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instead
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of
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h
gran
osciln,
ned
t
vibrated
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in
70
196b).
no-liear,
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end
Media
hexagons,
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banho
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dynamics,
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formatin
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strip
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ular
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left,
F
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paterns
top
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the
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k
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del
h
able
ular
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motin
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to
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is
gran
del
tal
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mo
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the
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197).
cuse
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t
grains.
This
Grains
acoun
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most
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colide
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of
the
P
atern
F
ormatin
in
Vibrated
Gran
ular
Media
71
8
5.1
7
Disordered
6
5
Flat with kinks
3
4
Squares(f/4)
Stripes(f/4)
Hexagons (f/2)
Squares(f/2)
Stripes(f/2)
1
2
G( Amplitude )
Hexagons (f/4)
Flat
0
70
50
30
110 120
90
Frequency (Hz)
Figure
Figure
5.3:
5.4:
Some
Phase
of
diagrm
the
materils
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paterns
of
observ
patern
ed
b
the
eha
authors
viour(fm
exp
(Um
erimn
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w
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ar,
196b)
gran
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5.1
P
atern
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Figure
5.:
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in
Phase
diagrm
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paterns
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mo
namics
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ts.
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comp
of
exp
del
aproc
of
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197)
found
Shin
Vibrated
-
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the
form
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b
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paterns
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predicts
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paterns
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um
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erimn
of
t
thoug
new
(Um
banho
t
paterns
to
tha
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ar,
197).
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parmet
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P
atern
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Figure
5.6:
ormatin
in
Oscilon
ha
shevki
5.12
Oscil
v
et
Vibrated
e
Gran
al.,
recn
tly
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ular
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Media
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73
ed
in
cla
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lons
Another
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del
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gran
ular
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b
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2
made
up
exp
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erimn
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cla
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ts
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particles
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in
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cla
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e
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of
196a)
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ar,
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5.6
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es.
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cm
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and
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can
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in
the
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Figure
5.8:
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the
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act
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of
hig
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0.5,
0.7
thes
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m
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magnetic
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82
for
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5
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b
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2
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of
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Figure
83
5.1:
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the
b
eha
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196b).
+
kinks
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4
6
8
Coil V oltage (V)
10 12 14 16
G = 3.3
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flat
20
30
25
Frequency (Hz)
Figure
5.16:
Phase
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of
the
ect
on
paterns
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5.4
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84
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w
t
form
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cla
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197).
patern
formatin
in
gran
ular
materils
is
Chapter
6
Segration
Ho
w
do
w
faling
e
and
kno
w
grains
tha
of
the
Straicon
creations
of
w
orlds
are
not
detrmin
b
y
sand?
Victor
Hugo
L
ne
featur
of
O
of
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in
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observ
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due
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details.
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Figure
6.4:
Figure
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pro
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Figure
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6.1:
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High
sp
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93
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Celuar
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increasg
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6.5
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o
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hapter
3
listng
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phase
as
)
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ect
In
197b
exampl
the
forces
mixtures.
(Makse,
materils
segration
the
ular
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w
ter-paicl
Segration
are
It
In
al.
ects
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oth
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estigaon
is
alnc
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thes
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Makse
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thesi
and
a
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Chapter
7
Bands
otaing
drums
are
exampl
R
of
stance
placed
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v
adv
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t
and
7.1
Ov
A
ular
in
ts
thes
et
al.,
ed
to
form.
familr
certain
taneous
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segration
in
when
ter-paicl
force
pla
Segration
A
mo
exp
del
for
axil
distnc
v
ys
in
erimn
ts
segration
is
split
p
eas
is
length
scale
but
ap
ears
time
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tendcy
rotaes.
throug
for
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of
and
the
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axis
width
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the
mixture
rotaed
along
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smaler,
a
The
bands
In
to
When
drum
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merg.
core
198).
ap
bands
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tha
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to
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half
eas
observ
to
observ
al.,
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also
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to
er
et
p
the
is
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a
as
ther
v
than
and
mix
,
les
rice
)
paterns
o
(Dury
of
193
in
are
in
homgenus
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materils
placed
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taneously
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to
am,
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tha
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to
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Oy
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193,
ts,
cemn
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A
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smal
197).
rice
the
do
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ted.
pro
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early
exp
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drum
w
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7.1
Ov
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Segration
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97
19a).
The
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ose
in
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192
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y
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tha
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In
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ma
axil
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197
rotain
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than
er
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rep
nev
al.,
core
surface
bulk
ersibl
197).
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Kaklois,
This
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al.,
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and
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orde
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bands
et
for
et
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agin.
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when
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rst
MRI)
thes
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195),
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is
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withn
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imples
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rotain
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axily
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7.1)
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Figure
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tha
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erimn
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dive.
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7.1
Ov
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Segration
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98
Top
Cross Section
Figure
7.1:
Cros
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imagn
exp
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Figure
7.2:
b
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al.,
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Discuon
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e
gation
2
In
thes
The
exp
eld
erimn
gation
w
ts,
as
then
observ
in
the
the
The
result
ametr
segrat
to
and
the
cen
tre.
wise
350
Ho
w
ev
er,
m
segration
and
result
are
c
the
ect
eld
ery
ts
the
segr-
the
a
of
iron
v
alnc
60
w
as
segration
result
of
the
authors
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exp
erimn
ts
ha
v
e
b
en
published
in
(Huton
al.,
201
m
found
w
et
he
di-
as
to
found
2
The
.
sumaried
mixtures
the
ed
radil
to
particles,
increasd
observ
are
simlar
or
as
on
erimn
F
iron
the
v
hapter.
diametr
as
w
exp
previous
radil
segration
Thes
the
til
maner
radil
7.5)
in
particles
un
step
the
discue
bronze
rotaed
a
of
(Figure
result
as
in
diagrm
segration
w
increasd
ed.
phase
drum
)
7.3
Result
and
Figure
7.6:
Discuon
The
10
gro
wth
of
diuson
to
disap
cen
then
tral
of
It
t
yp
e
leads
of
is
to
of
the
another
exp
traced.
drum
w
ha
or
v
ratio
e
a
m
uc
h
ask
cohesin
in
ect
c
is
a
e
mo
del
as
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v
on
in
h
alnc
a
to
w
the
to
particle
w
size.
eigh
segration
the
is
and
k
to
increasd,
Increasig
particles
ed
the
straicon,
is
are
from
exp
tha
t
size.
observ
en
stic
at-
the
cen
tre
mixed.
increasd
Giv
to
at
segration
eigh
iron
other
egin
furthe
segration
t
w
the
ander
el
mixng
the
the
particle
h
atrced.
and
to
whic
result
are
b
e
hanism
thes
particles
of
axil
consider
mec
at
result
ectiv
e
wth
oking
force
large
gro
particles
The
in
b
surface
iron
w
of
lo
hing
particles
result
mixng.
v
a
of
h
ter-paicl
and
on
e
a
y
bands
can
h
whic
increasgly
force
ha
the
iron
furthe
ect
ards
atrco
ecoms
e
w
the
core
a
duration.
uc
the
b
an
to
the
the
The
h
m
radil
Suc
increasd,
of
e
a
w
ts
of
ratio
increasd
ectiv
they
oin
tre
hangi
ersd.
of
Another
p
is
v
sytem
large
suc
o
cen
the
ter-paicl
has
what
of
rev
of
b
as
20).
and
stil
as
w
the
ha
increasd
w
t
at
they
the
as
segration
the
if
eld
and
eld
ving
as
ect
the
can
den
wth
7.6)
frequncy
as
the
As
as
ha
tha,
sharply
gro
Figure
force
suget
has
The
(se
ter-paicl
act
the
form
increasg
ts
eld
of
in
the
not
(Duran,
is
particles
the
e
with
erimn
the
tha
agretion
as
the
is
noted
\atrcos"
As
region
ces.
segration
en
sytem
thes
base.
one
b
lik
the
segratd
pro
radil
has
fractl
view
One
the
limted
a
radily
ers.
diuson
to
tral
agretion
rev
core
segration.
a
cen
limted
ear,
The
the
to
decras
erimn
as
ts
particles
suget
tha
act
altering
it
in
the
ter-paicl
as
if
they
sem
force
naturl
to
7.3
Result
and
Figure
Discuon
7.:
102
Chaotic
mixng
in
Figure
7.32
7.8:
rotaing
Rev
drums
ersal
of
(from
(Shin
segration
brot
at
et.
hig
al.,
19b).
eld.
Mixng
Consider
a
of
binary
particle
gran
B
(suc
h
ular
tha
mixture
comp
+
=
1).
osed
A
of
mixture
a
is
fraction
den
as
of
particle
A
and
homgenusly
mixed
3
if
on
scale
pro
d
if
ortins.
exp
ts
increasg
the
fre
p
this
er
v
alnc
y
y
er
of
after
comp
materil
in
con
z
b
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tin
=
o
al
b
del
the
end
to
ts
al.,
brot
y
)
pro
do
coret
v
19
e
)
sho
k
ces
is
wn.
The
ed
es
lo
w
er
tha
shearing
describ
undergo
and
wn
slip-tc
surface
crep
the
al.,
ha
increasg
fre
in
et
198
mixng
of
ues
ingred
(Shin
et
mo
er
w
et
(Nasuno
's
up
en
t
mixng
the
giv
the
brot
al
al.
materil
is
Shin
increas
et.
materil
of
y
et
brot
h
b
can
Shin
whic
osed
Nasuno
forces
la
hing
is
out
b
In
cyle
a
out
ter-paicl
The
slip
d
caried
surface.
ws.
olume
ulations
caried
in
fol
v
Sim
erimn
in
the
b
a
slip
as
oundary
once
f
y
of
(
x
+
A
(
t
)
f
(
x
)
(7.1)
7.3
Result
and
wher
f
is
a
Discuon
103
functio
giv
en
b
y
2
y
(the
b
and
oundary
a
b
is
sa
wto
et
w
oth
en
the
o
=
f
(
wing
x
)
=
and
ax
D
solid
b
o
(7.2)
dy
regions
is
therfo
parb
olic)
functio
8
<
1
A
(
t
)
=
(2
t=
)
if
0
<
t
j
j
A
o
:
(2
This
slip-tc
and
k
an
eha
al.
viour
ed
with
b
b
en
sho
w
en
in
One
linear
in
w
exp
mix.
in
Se
sho
of
gr
e
axil
is
from
this
slip
with
of
mixng.
This
m
w
iron
k.
w
er
in
increasd
k
o
w
b
e
oth
o
w
mo
del
segration
the
can
oth
smo
brots
radil
tha
b
surface
Shin
the
so
alues
the
in
ted.
out
v
ev
mixng
ed
pain
particles
eld
haotic
er
caried
magnetic
e
iron
Thes
er
w
cohesiv
using
w
blac
observ
stic
out
particles
ho
c
of
caried
ts
lo
earnc
er
increasd,
er
as
w
other
or
as
w
w
lineary
materil
sen
b
in
egan
Figure
7.8
gation
the
wn
ws
are
iregula
ap
erimn
the
force
resulting
the
F
w
o
for
segration
350
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exp
m
iron
particles
y
mixng
increas
rate
the
ts
exp
bled
k
ter-paicl
striaon
result
stic
to
60
mixng
eld
b
particles
h
tial
due
and
resm
slip
the
Axial
sequnc
mixng
e
of
white
the
particles
higly
one
7.)
the
whic
ecoms
erimn
eld.
As
the
when
The
7.3
The
and
b
exp
and
ed.
to
tainers
ted
glas
coarse
of
exp
Figure
haotic.
idea,
con
pain
c
j
decras
Large,
b
t
magnetic
Simlar
ts
o
e
of
rate
mixng
thoug
drum
observ
7.)
erimn
as
b
this
aplied
as
k
Figure
tes
Tw
rotaing
the
slip-tc
(se
to
a
to
mixng
is
the
an
j
(se
particles
and
<
paterns
on
the
the
mixng
.
striaon
is
o
of
er
brot
T
if
the
mixng,
ev
mixng
w
to
oth
e
1
dramticly
w
Shin
grains.
withou
ecam
y
)
ts
size
hange
smo
lik
haotic
particles
mixng
c
eld.
of
and
b
magnetic
loade
with
c
the
a
group
er
wn
erimn
the
ho
-
in
as
ely
fractl
(
Exp
tha
particles
of
et
particles
b
ne
earnc
forces
w
or
=
mixng.
can
of
ap
wn
particles
earnc
has
The
sho
)
striaon
of
relativ
F
mixng
e
fractl
rate
undergo
time.
ap
v
the
to
to
the
ha
of
observ
leads
in
et.
the
w
increas
Nasuno
b
o
t
erimn
and
ts
sho
60
are
wn
m
bronze
in
Figure
particles.
7.9
The
The
7.3
Result
and
Discuon
Figure
drum
w
eld
to
7.9:
as
w
then
un
migh
t
the
wn
b
e
a
axil
v
t
he
p
the
er
axil
w
w
er
osible
tha
is
w
e
en
the
simply
c
includg
eithr
y
hangi
white
shot
or
In
a
iron
lings
2,
w
er
sugar
h
(just
as
The
caried
out
t
and
er
to
mixtures
bronze.
w
of
hapter).
Diern
(whic
ersal
eld
c
It
rev
aplied
ts
wn
hapter
eld.
force.
bro
c
increasg
previous
ter-paicl
sugar,
based
materils
erimn
ed
segratd
mixture.
the
observ
segration
the
exp
er
the
axil
of
eral
in
o
the
in
magnetic
w
with
ersd
the
iron
for
increasg
rev
Sev
sand,
with
as
simple.
y
del
binato
b
6V.
The
hed
increas
com
and
utes.
switc
in
t
w
b
as
mo
ose
righ
min
4,
bands
w
rep
2,
of
materils
of
tha
mater
a
the
V=0,
segratd
osed
induce
quite
a
eld
pro
straicon
not
mixed
the
for
b
tried
er
et
for
The
angle
segration
materils
materils
ev
in
has
b
and
w
age
dynamic
segration
ho
ers
v
could
situaon,
of
the
drum
increasd.
angle
segration
alnc
rev
kinetc
tha
rotaing
When
Sa
thoug
wly
mergd.
retund.
sho
a
segratd
slo
they
in
as
particles
and
til
dierncs
w
in
the
aplied
rapidly
it
segration
and
broaden
on
The
rotaed
as
bands
104
Thes
roughe
and
Æ
had
a
higer
angle
of
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rep
ose
38
).
In
al
exp
erimn
ts,
the
result
w
er
the
7.4
An
Alternaiv
e
Mo
del
for
Axial
Segration
Figure
same.
Axial
segration
segration
7.4
An
e
ations
of
particles
are
smal
tes
wil
A
b
particles
more
rapidly
e
a
ed
ed,
ho
v
t
e
w
ev
er,
as
the
eld
increasd
the
rotaing
b
to
more
tra
v
smal
el
quic
w
do
wn
unstable.
tin
ue
wil
acros
slo
therfo
con
kly
particles.
wil
is
particles
more
large
but
therfo
large
since
than
stae
wil
with
grains
mixed
the
reasonbl
particles
The
particles
tha
sem
other
smal
particles.
able
y
acros
large
tha
This
tly
rapidly
region
are
suget
particles.
frequn
of
a
drum
smaler
large
wheras
Segration
the
more
excs
they
Axial
more
other
sligh
as
for
the
trap
with
with
large
del
in
mo
colide
region
segration.
observ
than
wil
they
Mo
mobile
particles
when
intaly
particles
more
particles
Large
as
Axial
eard.
Alternaiv
Observ
7.10:
w
disap
105
to
lose
acum
ulate
large
particles
it.
3
The
crital
featur
observ
ed
to
of
elastic
segrat
Al
result
in
Consider
the
a
wil
v
can
b
mo
v
e
v
er
trea
taly
the
and
a
Let
v
no
v
particle
w
h
v
consider
v
elo
y
the
cit
er
as
y
later
,
during
v
a
sink
do
t
the
time
of
writng,
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pa
er
wn
the
v
o
ular
gas
v
for
a
surface
e
b
en
w
t
ould
b
e
exp
of
mo
del
of
ectd
alnc
and
the
The
whic
slop
den
h
of
e
mo
but
they
a
elo
cit
particles
acros
mean
deling
wil
rol.
also
W
fre
is
in
preation
the
y
particles
ose
hing
er
v
mobile
pur
alnc
v
hing.
e
path,
can
l
.
diuson
describng
v
co-eÆcien
More
so
3
A
so
depth.
and
the
gran
and
a
with
e
ha
and
y
drum
wil
mo
materils
fricton
rapidly
in
la
ular
del.
the
decras
aritons
surface
erag
us
to
mo
in
wil
Gran
mobilt
this
whic
.
roughnes,
inuec
materil
particles
y
surface
ertis
particles
due
uidse
an
e,
wil
The
horizn
the
mobile
mobilt
to
materil
les
particle
shap
pro
of
ignored.
e
is
size,
thes
surface
hing
o
del
acording
alnc
rol
y
segration
the
of
mo
b
restiuon.
to
this
surface.
The
,
7.4
An
Alternaiv
e
Mo
del
for
Axial
Segration
106
Axial
segregation
{
R adial
segregation
{
mixed band
{
pure band
“More mobile” particles
move rapidly across
sur face until they reach
mixed band (where they
are slowed down)
mixed band
“Less mobile” particles are
rapidly buried
“Less mobile” particles
are trapped in bands
“More mobile”particles
find their way to low points
Figure
7.1:
Segration
at
in
whic
h
the
more
ends
of
mobile
the
drum.
particles
The
aro
ws
repsn
t
the
directon
rol
l
Collision
x-l/2
x+l/2
Figure
diuson
equation
can
b
7.12:
e
Diuson
writen
in
with
terms
of
colisn
the
mean
fre
path
and
a
v
erag
v
elo
as
cit
1
n
A
(
v
t
)
1
v
=
n
v
(7.3)
v
6
A
t
6
(
The
ux
of
particles
to
the
*
left
and
righ
t
are
J
J
*
(
1
dn
1
dn
v
=
(
n
v
l
)
v
;
=
J
(
n
+
l
)
v
(7.4)
J
v
v
6
dx
6
dx
Therfo
*
(
1
dn
dn
v
J
=
=
J
l
v
v
=
D
(7.5)
J
3
dx
dx
1
D
=
v
3
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l
(7.6)
y
7.4
An
The
Alternaiv
e
mean
fre
Mo
path
del
can
for
Axial
Segration
writen
107
as
v
l
t
=
(7.)
2
n
(2
r
)
v
r
and
so
D
b
t
el
ecoms
2
1
D
v
=
v
t
v
=
(7.8)
2
3
n
(2
r
2
)
v
r
The
v
face
elo
cit
y
under
wil
b
gra
write
v
vit
e
y
inuecd
b
and
the
y
the
enrgy
t
n
(2
r
)
v
r
enrgy
lost
3
el
gained
b
throug
y
a
inelastc
v
el
alnc
hing
acros
colisn.
W
the
e
can
sur-
therfo
as
p
v
=
2
g
h
2(
K
:E
:
)
=m
(7.9)
2
subting
for
v
w
e
get
1
D
2
g
h
1
=
2
K
:E
:
+
=
D
+
D
(7.10)
1
2
3
n
(2
r
)
v
3
r
D
can
therfo
b
e
sen
as
2
2
the
mn
(2
r
)
v
el
r
sum
of
t
w
o
comp
el
eting
pro
ces
D
and
D
.
1
diuson
driv
ing
en
cone
b
y
dierncs
in
traion.
D
is
surface
due
heig
to
t
dispatv
e
and
acts
in
colisn
the
directon
and
of
acts
D
is
2
in
the
1
decras-
directon
of
2
increasg
cone
giv
es
rise
traion.
the
\solid
axil
phase",
fre
bands.
h
elo
surface
y
of
can
p
v
er
la
elo
ers
e
e
F
shet
les
mobile
w
the
con
tin
v
this
p
oin
rst,
fol
t
undergo
form
of
w
more
b
y
la
o
v
erlaid
axil
The
t
fre
v
la
a
v
alnc
hing
at
et
ers
w
en
t
suce-
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of
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mobile
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the
e
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siv
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y
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the
more
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es
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v
is
undergo
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Figure
7.1)
7.5
Conclusi
108
7.41
Thr
Exp
e
erimn
of
Particle
ts
size
b
e
0
:
otm,
Exp
w
25
er
m
caried
,
0
:
mediu
with
fo
the
o
dy
e.
surface.
to
the
wn
b
ed
e
end
t
up
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face
c
as
colisn
mo
higer
the
del.
b
e
sen
7.5
rep
in
con
ose
Figures
the
7.13
and
tin
uos
so
as
as
the
colured
w
o
the
tha
smal.
on
o
but
curs
at
sytem
the
b
mediu
Radil
also
elo
w
cit
y
di
e-
sized
segration
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result
it
elop
w
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ed.
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not
noticed
not
ap
is
size
with
t
tha
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rotainl
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than
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as
ha
ear
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to
e
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e
tainer.
carefuly
thre
Glas
Balotin
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es.
drum
con
themslv
the
yp
the
orde,
cur.
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to
tha
particul
and
segration
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The
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t
with
ers
so
align
o
t
top).
sequnc.
of
bands
particle
y
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rotae
to
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angles
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e
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loade
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and
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also
0
strip
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using
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m
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out
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erimnts
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7.14)
Conclusi
Thes
exp
tha
in
erimn
of
as
eha
viour
found
tha
2).
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thes
w
result,
a
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alnc
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In
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as
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tha
magnetic
from
rep
rev
strai-
this
and
found
to
of
the
in
mixng
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ose
outlined
increasg
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demonstra
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result
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hapter,
segration
ts
segration
b
in
the
erimn
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the
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e
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ha
he
ed
of
predictons
alnc
observ
del
surface
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previous
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w
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segration
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migh
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parles
force
c
cause
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this
ular
radil
Axial
the
gran
This
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in
can
of
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in
forces
b
w
outlined
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cation
it
ts
exist
b
ts.
y
b
exp
It
grain
enath
erimn
should
t.
b
e
7.5
Figure
Conclusi
109
7.13:
Axial
segration
gle
for
to
diers
the
with
ends.
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the
t
bands.
w
o
particle
exp
The
more
erimn
ts
mobile
sho
particles
wing
ho
(grey)
w
the
kinetc
wil
an-
segrat
7.5
Conclusi
10
Figure
7.14:
End
on
view
of
thre
particle
segration
exp
erimn
ts
a
b
Figure
7.15:
Thre
particle
drum
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exp
erimn
ts
sho
wing
the
curving
to
w
ard
the
ends
of
the
7.5
Figure
Conclusi
1
7.16:
time
w
A
er
tak
seri
for
en
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at
half-our
thre
particle
in
axil
terv
als.
segration
exp
erimn
ts.
The
images
Chapter
8
Conclusi
uring
thes
ular
D
in
en
in
tro
the
v
ho
exp
ulate
e
b
of
en
arious
observ
in
the
in
b
erimn
force
ts
materils
giv
e
wher
new
in
and
eha
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viour
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ter-paicl
to
A
b
in
oth
the
p
pla
o
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means
t
has
of
p
osible
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to
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mixtures
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of
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ular
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and
eld,
b
no
magnetic
magnetic
forces
in
anlysed.
the
ts
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inuecs
insgh
of
ter-paicl
in
ter-paicl
ects
ed
materils
w
asp
altering
considerg
no-magetic
estiga
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v
ect
By
and
in
v
ha
duce.
magnetic
estigaon,
materils,
studying
b
v
other
role
in
partic-
the
materils
dynamics.
8.1
What
The
Has
metho
rials
in
d
tro
in
w
in
in
to
erimn
geomtry
to
ts
increas
on
the
dynamic
in
the
ter-paicl
of
of
the
in
metho
rep
in
force
ect
This
p
used
angle
ed
of
rep
ose
b
w
a
er
also
condute
to
in
12
v
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estiga
ho
w
the
v
oid
es-
of
rep
ose
acompnied
b
of
as
al
eal
v
ects
(Bak
linear
et
al.,
fraction
ho
1987)
increas
with
is
aectd
y
the
to
force.
w
in
dimenso
et.
rev
e
the
question
Bak
also
as
fractl
raise
y
study
b
angle
This
This
describ
to
staic
The
eld.
mate-
to
oured
prole.
aplied
stae
as
force.
ular
particule
force
w
The
ter-paicl
on
ter-paicl
d
ose.
gran
with
ter-paicl
ts
ws
angle
of
crital
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alo
with
self-organid
in
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the
lineary
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of
factors.
on
found
the
increasg
h
other
increas
as
ects
resac
force
w
Exp
this
from
of
robust
the
isolatn
found
prole
Learnd
estigan
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alterion
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v
ter-paicl
as
an
of
duce
tigaed
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Ben
w
8.1
What
b
y
in
Has
Ben
ter-paicl
13
forces.
particle
force
w
Learnd
eigh
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It
and
F
tha
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it
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as
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found
tha
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oid
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in
with
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in
force
ersal
to
ter-
particle
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ip
plies
to
other
Hydro
no-magetic
sytem.
dynamic
of
mo
uidse
gran
result
of
forces
They
A
Exp
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y
ts
ers.
The
mation
v
er
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particle
force
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w
as
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found
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mixng.
certain
In
b
y
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in
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aplied
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terials
diusv
w
e
as
b
presn
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ted
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o
b
ular
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mater.
wder
group
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b
e
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reduc
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insgh
out
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forces
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lik
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has
ely
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dispatv
b
en
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particles,
drums
w
ev
gained
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tha,
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as
alter-h
tly
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comp
for-
supre
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tha
als
patern
of
segration
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segration
olv
tha
ular
amplitude.
also
ts
the
to
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suget
gran
on
found
found
straicon
axil
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as
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of
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w
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in
erticaly
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and
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v
del
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viour
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uidse
ter-paicl
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ed
straicon
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The
is
Geldart
on
force
ter-paicl
and
w
to
segration
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this
of
force
ho
describ
in
hanges
viour
b
unscefl.
y
from
in
ter-paicl
ts
tha
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the
mostly
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transio
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demonstra
Hz
ter-paicl
erimn
b
F
force
exp
en
explain
buling
ter-paicl
ect
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the
frequncis.
30
ter-paicl
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the
altering
of
simlar
in
b
formatin
and
and
tha
e
wh
patern
In
Hz
a
of
a
v
to
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on
range
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ect
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23
ha
atemp
ed.
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wide
dels
4
lo
out
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a
mo
to
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o
as
ard
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er
ect
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h
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w
w
forw
hapter
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c
when
in
eha
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group
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in
for
e
b
ts
onsible
b
e
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erimn
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v
mater.
exp
canot
By
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ular
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are
la
dels
canot
ha
v
e
of
a
e
gran
colisn
b
signca
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ular
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ma-
and
8.2
Directons
for
8.2
F
Directons
Lik
e
eha
F
prelimnay
ab
b
W
for
most
tions
utre
the
viour
range
of
ther
1.
man
y
rep
eat
rep
ose
Av
alnc
observ
ed?
ary
Ho
w
is
in
the
2
our
ould
e
v
in
stae
e
to
y
on
the
and
in
in
tersing
metho
ds
tersing
the
This
w
of
e.
at
ho
w
organised
a
v
alnc
h-
crital
altering
in
er-
elimnat
slop
ok
p
angle
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the
lo
for
to
measur
self-
b
e
t
b
to
aectd
b
of
Can
e
erd
ould
creation
force.
crital
w
ould
tersing
v
exampl:
ts.
the
ery
ter-paicl
w
erimn
in
b
ha
diern
d
exp
or
using
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ects
w
F
It
hapter
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unasw
ose.
it
in
inertal
with
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particul
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erd
forces
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crate
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v
c
unasw
ter-paicl
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in
y
remain
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In
man
question
futre
draing
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staic
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metho
staic
t
angle
the
ciated
he
ing
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left
in
ortan
ose.
has
tha
imp
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rep
the
aso
2.
of
than
problems
en
ts
ts
rathe
y
v
h
ects
and
erimn
angle
resac
the
ds
exp
erimn
of
Man
metho
the
exp
t
a
the
measuring
form
this
promisng
t
ork
estigaon,
mater.
Measurmn
to
v
extn
ular
remain
W
and
gran
14
utre
in
out
ork
y
ter-paicl
b
e
force?
1
Thes
are
question
isolated
suc
plate
Figure
on
8.1)
to
h
exp
whic
The
erimn
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ts
grains
grains
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of
are
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Consider
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drop
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ed
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b
vibratonly
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y
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means
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(se
a
\lot"
2
mac
hine
and
lated
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a
size
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to
the
P
a
exp
v
lev
a
of
atern
er
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v
hes
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means
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Some
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in
atc
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h
The
of
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fractl
ter-paicl
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formatin
calu-
giv
of
gran
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ular
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piles
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impro
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This
m
imagn
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staic.
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a
hanges
crital
alnc
one
y
from
self-organid
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with
alnc
alnc
erimn
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b
could
the
of
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a
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nature
3.
the
to
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alnc
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to
to
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Thes
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tics
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suÆcien
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design
exp
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coun
actuly
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ned
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er
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of
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er
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mon
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y
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ears
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A
Matro
time
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2
This
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iron
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esn
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w
a
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the
hole
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o
in
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8.2
Directons
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arm
atc
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utre
hed
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to
vibratons.
the
This
able
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to
b
exp
w
ould
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y
15
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b
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aces
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to
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y
Shin
e
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brot
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amplitude
This
(Shin
tersing
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to
ma
197),
study
,
the
y
en-
but
in
a
not
sytemaic
3
w
4.
a
y
,
the
ect
Axial
of
in
ter-paicl
forces
segration
the
mo
Sev
del
imen
for
ts
The
wher
of
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fect
on
the
drum.
rates
if
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hig-sp
v
ed
Flo
w
tec
et
198)
y
is
alue
of
netic
a
w
a
v
only
b
et
w
It
v
ould
in
o
in
could
b
particles
in
to
rough
in
ef-
diern
t
tersing
to
(eithr
b
y
using
Baxter
er,
y
w
a
v
using
v
for
e
sug-
a
crital
aplied
surface
al.
suget
es
an
the
ha
They
densit
ulate
et
hop
grains.
estigad
sim
e
bands
a
and
v
the
throug
w
e
b
to
the
at
out
of
o
se
rotaed
caried
ws
oth
e
terfomy).
ws
o
8.2)
to
also
in
ts
es
smo
This
w
e
er-
relativ
out
b
exp
Figure
rotae
caried
to
tes
out
(se
can
e
furthe
cary
alterd
er
in
cur
en
magnetisbl
w
erimn
a
o
roughnes.
and
w
er
b
Dopler
y
es
transio
surface
eld
laser
densit
to
particles
Exp
on
densit
ther
v
or
to
tersing
then
hing
erfomd
they
drum
alnc
.
p
tha
itself.
dynamics
al.,
tha
v
e
w
could
drum
a
in
drums
the
the
the
e
so
of
hniques
fractue
(Baxter
gestd
of
b
design
ends
cites
video
and
tha
the
b
ould
ts
to
elo
e
could
the
erimn
directons)
measur
5.
b
Exp
segration
w
of
could
osciln
ts
condits
drum
indvual
erimn
It
end
the
of
exp
segration.
the
ends
the
axil
eral
on
mag-
fricton.
Also
4
fractue
mec
A
con
b
tainer
of
The
could
pac
otm
6.
hanics
k
the
n
what
and
and
Mixng
it
w
ould
als
could
e
in
b
the
to
the
y
ut
ter-paicl
could
force.
b
w
ects
e
ed
imaged
to
as
could
fal.
b
phenom.
e
examind
The
grains,
the
ob
to
ect
jects
b
the
eing
of
fric-
segratd
studie.
tec
condut
the
in
alo
n
in
the
e
of
materil
Hex
en
al
Using
tersing
w
functio
eld
and
pla
et
a
magnetic
and
b
stirng
b
ed
forces
w
a
Brazil
forces
and
in
v
ter-paicl
tainer
as
remo
The
ter-paicl
con
examind
shot
is
ect
in
in
the
7.
ut
e
iron
tainer
ect
tion
with
con
Brazil
se
ed
b
hniques
outlined
mixng
exp
in
erimn
ts
c
in
v
hapters
olving
5
and
mixng
6
in
3
Unfortuaely
osciln
the
dynamics
in
aprtus
used
detail.
in
4
Se
Duran
(Duran,
20)
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c
hapter
4.
the
authors
exp
erimn
ts
w
as
not
stable
enough
to
study
8.3
Conclusi
16
con
tainers
with
the
diern
ects
of
of
t
stirng
geomtris.
It
on
mixng
w
and
ould
ho
also
w
in
b
e
in
tersing
to
ter-paicl
forces
detrmin
ect
the
rate
8.
mixng.
Stres
exp
erimn
ts
The
ect
on
stre
paterns
withn
gran
ular
materi-
5
als
on
the
in
rimed
ter-paicl
forces
with
out
iron
using
iron
nately
on
er
w
struce.
eithr
It
dens
is
p
materils
9.
w
to
Bubling
exp
particle
fain
t
a
ts
pla
y
in
to
e
mak
e
out
to
more
uidse
b
eds.
h
Exp
Unfortu-
is
ould
an
yield
b
in
ts
car-
y
and/or
ned
erimn
the
detrmin
particles
w
caried
er.
to
disk
er
on
large
resac
pa
uniform
materil
h
w
impreson
o
using
magnetisbl
on
the
or
ts
ts
carb
as
t
erimn
using
erimn
Muc
bi-refng
Exp
conlusiv
exp
in
erimn
forces
not
tha
coated
using
measurd
er
o
osible
examind
materil.
stre
ts
e
magnetic
the
erimn
er
b
other
and
exp
pa
some
shot
thes
b
or
could
could
to
b
les
etr
result.
the
e
role
in
caried
ter-
out
on
6
the
other
x-ra
transio
ys
to
or
10.
se
.
some
other
what
ma
out
on
forces
8.3
e
in
usefl
fraction
to
ts
It
w
ould
b
forces.
relaxtion
to
and
e
in
Exp
particles
time
3D
buling
using
could
then
b
e
tak
en
are.
ter-paicl
of
image
measurn
force
and
the
e
b
factors
coletins
alters
ak
ould
ter-paicl
ces
vibrated
w
inuecg
in
pro
it
W
jor
and
relaxtion
,
means.
the
Relaxtion
Idealy
nal
to
erimn
se
pac
tersing
ho
ts
w
ok
could
in
densit
at
b
increasg
king
lo
of
e
the
caried
ter-paicl
the
particles.
Conclusi
Our
exp
erimn
featurs
ts
p
of
earnc
a
ha
v
a
w
h
earnc
gran
ap
rep
ose
ersal
materils
(c
b
as
(c
an
eha
mater
exhibts
t
hapter
of
drums
univ
ular
emrgn
earnc
rotaing
of
ular
of
the
in
ap
Viewng
as
gran
include
angle
segration
the
Thes
el-dn
suc
and
tha
sytem.
Self-organist
axil
demonstra
complex
of
and
e
2)
(c
of
viour
hapter
suc
y
h
(c
atern
a
v
alnc
of
as
buling
in
P
viours
eha
and
straicon
hapter7).
exampl
b
man
the
the
ap-
hapter
hes
formatin
4).
(c
hapter
6)
(c
hapter
5)
3).
complex
sytem
suget
new
a
v
en
ues
5
F
or
simlar
exp
erimn
ts
(not
in
v
olving
in
ter-paicl
forces)
se
(da
Silv
a
and
Ra
jc
hen
bac
20).
6
Suc
Univ
h
ersit
exp
y
erimn
ts
are
alredy
.
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under
w
a
y
in
the
Chemical
Engier
departmn
t
at
Monash
h,
8.3
Conclusi
17
Camera
Figure
8.1:
Av
alnc
of
he
the
a
exp
v
erimn
alnc
t:
hes
can
By
b
measuring
e
8.2:
The
ends
of
barel
of
in
v
of
estigaon
b
exampl,
her
1.
gran
few
drum
ular
in
featurs
the
gran
ular
prole
the
size
c
could
b
e
made
to
rotae
indep
end
tly
of
the
drum.
for
a
in
b
rotaing
the
oth
are
What
the
hanges
detrmin.
a
Figure
c
of
a
materils
tersing
and
for
question
gran
ular
complex
to
sytem
are
sytem
in
genral.
F
consider.
or
indep
end
t
of
the
history
of
the
sytem?
2.
Ho
w
do
the
microsp
macrospi
3.
ph
featurs
Under
what
of
gran
ular
dynamics
\emrg"
from
ysic
condits
are
gran
ular
dynamics
dep
end
t
on
the
history
of
sytem?
4.
What
are
the
the
atrco
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stae
and
on
what
v
aribles
do
they
dep
end?
the
8.3
Conclusi
5.
18
Is
it
to
the
the
random
nature
patern
the
the
o
dep
formatin
w
of
end
T
o
7.
the
is
in
it
materils
the
vibrated
gran
ular
homgenus
la
nature
acros
depth.
This
t
observ
can
o
ation
ers
of
to
self-organi
metaphor.
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is
gran
tra
v
thes
the
mo
to
ular
w
in
a
c
other
sytem
surface
or
the
y
of
es
and
e
hapter
rev
ers
whic
the
h
leads
spreading
of
a
lik
slop
e
viscot
is
end
to
y
ersibl
strongly
in
liquds.
viscou
axil
uids?
segration
b
7?
question
for
wn
of
b
v
do
denito
materils
eling
del
and
a
simlar
wing
of
terms
answ
complex
a
on
in
Ultimaey
ular
extn
explaind
as
impacts
or
gran
t
what
can
other
the
particles?
6.
of
of
whic
ma
h
gran
ular
y
giv
materils
e
a
b
etr
ha
understaig
v
e
b
en
used
e
Apendix
A
Equipmen
t
Materil
and
Materils
Sizes
Bras
Shot
Iron
Suplier
m
60-71
m
350-42
m
80-9
m
Shot
50-6
1.6-8
Iron
Filng
Sin
tec
Australi
Spherical
Sin
y
Ltd
Pt
y
Ltd
bronze
tec
Australi
m
0.5
-0.71
m
\T
ec
hnical"
brand
batc
h
apren
t
1507/2
densit
y
mesh
White
Pt
Sugar
710
m
CSR
g/cm
Sugar
Ground
18
4.9
5-12
Flo
Litle
or
Crib
Stre
Milton
QLD
406
Australi
PO
Bo
Milton
x
2059
QLD
406
Australi
Bro
wn
Sugar
Sand
850
m
360
m
CSR
Sugar(se
F
ab
rom
squeaky
Wilson
Promity
(So
able
A.1:
Materils
19
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and
b
squeak)
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eac
Victora
named
it
T
b
o
ecaus
v
h
e)
120
Equipmen
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Signal
Suplier
genrato
W
a
v
etk
20
MHz
pulse/fnctio
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San
P
o
(for
w
er
suply
P
Helmhotz
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w
del
19
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CA
suply
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toal
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amplier
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P
o
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Jan
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photgras
recognit
progesiv
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del
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x
milon
CD
no.
camer
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image
anlysi
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anlysi
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video
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Pt
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able
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A.2:
Equipmen
t
Used
C-108
p
con
Supliers
tin
40(H)m
1.5
bly
ounds
ats
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X
p
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eigh
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ot
w
w
T
fo
er:18
Size
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Motr
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um
er
force:
p
scale
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materil:
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y
materil:
Actuaor
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F
AL
lev
Lond
Subsonic
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frames/cond
ful
256
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mo
High
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pixel
and
1987
Electronis
Olympus
Image
Amplier
kgs
uos
er
w
RMS
at
Apendix
B
Matro
B.1
Matro
x
x
Progams
-
-
THIS
PROGAM
AND
TAKES
LOKS
IS
USED
IN
GRANUL
AT
TO
Progams
TWO
THE
-
-
IMAGES,
-
THRESOLD
DIFERNCS
THE
-
-
THEM
BETWN
DETRMIN
-
THEM.
SCALE
OF
IT
AVLNCHES
MATERILS
-
FIRST
WE
CLEAR
THE
FRAME
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
BUFERS
-
clear
4
0
clear
5
0
-
GRAB
AND
THRESOLD
IMAGE
1
-
AND
opmde
2
STORE
-
-
-
-
-
-
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-
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4
outpah
0
inmode
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0
0
1
chan
0
sync
1
video
0
1
snap
1
0
pause
-
12
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B.1
Matro
GRAB
x
AND
Progams
12
THRESOLD
IMAGE
2
AND
-
snap
STORE
-
-
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-
-
-
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-
1
outpah
1
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0
0
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MOD
SUBTRAC
IMAGE2
FROM
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1
intermag
0
absolute
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1
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1
2
pause
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STORE
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histample
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dat.ou
25
2
FILE
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-
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-
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-
-
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1
2
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UNTIL
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10
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Apendix
C
Mathemic
The
progams
tha
C.1
ap
Christma
Str
This
atic
as
as
del
b
acoun
y
t
mo
del
mo
del
b
b
e
in
the
ed
b
v
y
b
ear
on
author
the
to
increasg
acompn
et
al.,
ying
of
disk.
egin
can
tak
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of
b
e
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en
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at
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and
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alue
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e
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ery
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a
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se
Makse
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(Makse
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for
details
123
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;
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in
or
3.
to
this
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Straicon
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of
e
in
increasd.
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ects
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force.
alue
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2;
1;
C.2
P
er
Bak's
Av
alnc
he
Mo
del
of
Self
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125
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E
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E
J.
the
J.,
,
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Horn
angle
eviw
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of
ev.
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um
al
calution
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Alb
Maxim
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al.,
the
R.,
(197).
media.
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of
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stabil
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.,
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vi,
of
bak
J.
rep
P
ose
.,
and
Herman,
from
H.
the
J.
microsp
(198).
Mo
grain
pro
del
ertis.
58(1):672.
196]
Anderso,
R.
S.
(196).
The
atrcion
of
sand
dunes.
Natur
e
,
379:24.
[Bak,
197]
Bak,
Critc
ality
[Bak
.
and
D
P
et
Univ
Natur
ersit
198]
al.,
y
Bak,
1987]
crital
P
Bak,
y:
et
An
al.,
.
e
Pres,
Works:
The
Scien
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of
Self
Or
ganise
d
Lond.
and
y
[Bal,
P
Chen,
P
Physic
19a]
al
Bal,
Natur
e
.
R
P
Oxford
.
.,
K.
C.,
T
(198).
P
The
ph
ang,
ysic
of
,
K.
Physic
C.,
al
and
fractls.
Physic
a
R
(1987).
eviw
L
Wiesnfld,
K.
etrs
,
Self
organised
Self
organised
59(4).
(198).
38(1).
The
y
Wiesnfld,
noise.
(19a).
.
and
1/f
A
ersit
Bal,
suplimen
ang,
eviw
Univ
19b]
T
of
Bak,
.
.,
explantio
198]
crital
[Bal,
How
38:5{12.
[Bak
[Bak
(197).
Oxford
Chen,
,
.
Self
Pres,
Made
T
ap
estry:
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F
ormatin
in
(19b).
Oxford.
T
ransito
stil
to
b
e
made.
Natur
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,
402:c73{6.
t.
[Baxter
and
Behring,
autom
190]
[Baxter
mo
(198).
et
P
al.,
dels
atern
198]
of
gran
Baxter,
formatin
Baxter,
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o
G.
w.
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W.
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Behring,
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R.
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R.
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Celuar
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R
P
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L
and
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,
Johns,
62(4).
A.
Refrncs
128
[Boutrex
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F
r
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[Bro
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e
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,
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wn,
Clift,
Particle
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o
c
and
P
and
Degns,
P
princles
wn,
and
.
G.
minal
(197).
mo
Surface
del.
J.
Phys,
I
,
(197).
A
An
o
193]
The
and
Ric
hards,
J.
C.
(1970).
Princples
patern
emrgs.
camist
NewScints
reviw
of
,
uidze
b
ed
page
mo
34.
deling.
Fluid
89(26):1{7.
Higheld,
Complexity:
L.
Oxford.
(193).
es
R.
ergamon,
M.
R.
Pr
Y
genral
Bro
.
Cho
193]
v
1970]
chanis
197]
[Clift,
T.
I.
hards,
Me
wn,
[Co
mixtures:
Ric
Powder
[Cho
Boutrex,
6(10):295{34.
and
of
197]
Se
ar
Co
ch
for
v
Or
eny
,
der
P
in
.
and
a
Higheld,
R.
Chaotic
World
(193).
.
F
Balen
tine
r
ontiers
of
Bo
oks,
New
ork.
[Cum
b
erland
and
Packing
of
Cra
[da
Silv
a
wford,
1987]
Particles
and
.
Ra
jc
transmio
hen
Cum
Elsevir
b
erland,
Scien,
bac
h,
throug
da
mo
J.
and
Cra
wford,
R.
J.
(1987).
Amsterda.
20]
a
R.
Silv
del
a,
M.
sytem
and
of
Ra
jc
hen
bac
cohesinl
h,
J.
elastic
(20).
Stres
grains.
Natur
e
406(1):78.
,
[Daer
and
b
eha
Douady
vior
[Ding
,
in
and
gran
mo
o
[Duran,
del
Y
[Dury
190]
al.,
198]
(198).
theory
S.
(19).
Gidasp
o
gran
ular
Sands,
o
w,
D.
w.
o
.
P
and
artily
(190).
t
yp
A
AIChE
Powders
Materils
Tw
es
of
a
v
alnc
he
39.
and
of
(20).
anulr
Dury
,
Boundary
,
J.
,
,
,
Gr
buling
36(4).
ains:
Orde
uidza-
A
System.
n
Intr
o
duction
to
Springe-V
erlag,
ork.
et
E
Douady
e
Ding,
J.
Gr
and
Natur
kinetc
of
New
w,
Duran,
Physic
A.
media.
using
20]
the
Daer,
ular
Gidasp
tion
19]
C.
M.,
ects
on
Risto
w,
angle
of
G.
rep
H.,
ose
in
Mos,
J.
rotaing
L.,
and
cylinders.
Nak
ag
Physic
w
al
R
a,
M.
eviw
57(4):91.
[Egers,
19]
Egers,
J.
(19).
Sand
as
maxw
el's
demon.
Phys.
R
ev.
L
et.
83(25):.
,
[Enis
neglct
et
al.,
in
194]
the
U.S
Enis,
B.,
Chem.
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Eng.
Gren,
Pr
J.,
o
g.
,
and
90(4):32{.
Da
vies,
R.
(194).
The
legacy
of
Refrncs
129
[F
alcon
et
J.
K.
al.,
19]
(19).
y
on
r
F
and
the
Y
b
pac
u,
e
[Finey
,
,
[F
ose
eculiar
clas
and
p
of
o
Bhatc
harje,
wder
under
v
,
u,
acoustil
ertical
gures:
elastic
ond
A.
surface.
B.
(198).
Philospc
Eect
T
rom
And
al
52:9.
Powder
F
e
of
chnol
liqud
gy
cinderla's
aditon
,
on
9:2{8.
dilema
to
Physic
orsyth,
F
al
and
R
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the
macrospi
o
c
the
e
e
ro
c
struce
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k
slide.
of
of
the
R
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force
20]
,
F
ect
of
spherical
on
the
E
Rho
des,
king
,
of
erth.
orne
dynamic
angles
63().
M.,
of
angles
C.FOsb
and
eviw
P
and
staic
R
pac
the
and
C.FOsb
spherical
gran
orne
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mate-
87(24).
orsyth,
A.
and
Rho
deformatin
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solid
M.,
orne
and
.
the
S.,
y
des,
al
C.FOsb
CHEMIA
Rho
Physic
and
densit
at
on
Huton,
M.,
king
d
force
materil.
etrs
pac
S.,
ter-paicl
A.,
des,
esnt
Huton,
ular
L
Rho
on
pr
ter-paicl
des,
S.,
A.,
orsyth,
eviw
Rho
and
Pr
force
in
in
kings
king.
materil.
gran
of
pac
ter-paicl
aplied
201b]
pac
Huton,
ular
spherical
Eect
Random
A.,
F
al.,
(201b).
incorp
S.,
of
vibratng
close
in
of
of
orsyth
p
spher.
random
gran
Eect
et
[F
Y
(1970).
aplied
201a]
(201a).
rial.
and
orsyth,
mon-sized
al.,
orsyth
M.
A.
F
of
et
[F
L
(197).
L.
Ser
20]
in
rep
L.
of
Eect
of
J.
319:47.
al.,
orsyth
of
coarse
geomtry
,
(20).
[F
a
on
ciety
J.
K.
59():716{20.
particles
So
j,
formatin
On
C.
,
the
ond
ose
oyal
eng,
Finey
et
rep
R
ja
hexagon
(183).
mon-sized
1970]
orsyth
M.
Fineburg,
I
L
,
Ba
386.
liquds:
of
K.,
,
of
F
197]
Natur
E
groups
the
of
[Fineburg,
y
198]
king
eviw
y
of
eng
R
ard
forms
ansctio
Kumar,
and
al
183]
certain
T
[F
,
E.,
corugatin
Physic
ard
alcon,
Heap
vibratons.
[F
F
particles.
des,
M.
ertis
in
Journal
of
(20).
to
A
the
Col
v
loid
ander
and
w
simple
mo
als
del
interfac
force
e
for
Scien
e
23:1{8.
[F
orsyth
Rho
et
materils.
des,
al.,
M.
201c]
F
orsyth,
Powder
(201c).
A.,
T
Eects
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chnol
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.
h
umidt
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F.
on
W.,
the
P
o
ark
w
er,
c
I.
harcteis
H.,
Huton,
of
S.,
gran
ular
and
,
Refrncs
130
[F
ret
et
al.,
196]
Josang,
F
T.,
and
ret,
V.,
Meakin,
Christen,
P
.
K.,
(196).
Av
Malthe-Sorns,
alnc
he
A.,
dynamics
in
a
pile
F
of
edr,
J.,
rice.
Natur
e
,
379.
[F
uler,
1975]
F
Thinkg
.
[Galieo,
uler,
[Ga
est
B.
Macmiln
Galieo,
Univ
Syner
y
and
(1968).
Pres.
b
Ga
autom
[Geldart,
1973]
D.
y
yp
ometry
Scien
de
es
K.
(196).
gas
.
North-
Mo
Springe-V
of
of
Silvo.
matheic.
es
Ge
New
Nishdate,
with
T
Two
Alfons
and
the
ork.
and
ulations
in
ernig
Henry
R.
(1973).
ations
Y
Conc
ylord,
sim
Geldart,
New
gues
ranslted
196]
Explor
Inc,
Dialo
T
Nishdate,
nature:Cl
getics:
Co.
G.
ersit
ylord
(1975).
Publishng
1968]
w
R.
deling
erlag
uidzaton.
Powder
T
.
e
chnol
gy
,
7:285{9.
[Geldart
and
p
o
W
wders
ong,
sho
Scien
e
[Geldart
,
wing
o
wders
Engie
Physic
,
Langer,
[Go
o
Win
esing
.
dwin,
W
o
d
gran
esly
e
.
eviws
B.
A.
C.
Y.
erimn
al
(1985).
ts
mater:
and
Engie
ering
Fluidzaton
on
a
Langer,
of
,
dwin,
ular
Mo
J.
dern
rates
ten
of
of
taiv
e
(19).
MA,
P
,
and
Win
2nd
How
S.
Physic
C.
Reading
(194).
de-artion.
view.
R
eviws
tz,
atern
formatin
71(2).
P
.
(1987).
Digtal
Image
editon.
the
chnol
Graseli,
heaps.
amo
T
P
R.
197]
Sathiy
Be
of
L
e
op
ar
d
Change
d
its
Sp
ots
.
W
ei-
Lond.
dry
and
Fluid
Fluidzaton
Chemic
ong,
ular
Gonzale,
Herman,
of
[Gupta
(1984).
.
J.
R
Nicolsn,
and
angles
Y.
40:653.
tenary
ysic.
W
Gran
Cen
Adison
and
[Graseli
C.
expansio.
exp
(19).
1987]
Go
,
Golub,
tz,
194]
denfl
G.
19]
and
c
.
71(2).
ph
[Gonzale
o
A.
ed
ens-i
e
P
and
cohesiv
Scien
noequilbrm
Pr
ong,
b
D.
of
Gens,
and
in
W
ens-i
Geldart,
ering
dern
[Golub
and
cohesiv
degrs
19]
Mo
1985]
wing
al
of
of
ong,
sho
[Gens,
D.
degrs
W
Chemic
Geldart,
39:148.
and
p
1984]
orth
gy
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Physic
y
in
Y.
Materils
,
19]
a
A
and
,
Gupta,
o
c
esing
H.
P
.
(197).
On
the
246:301{.
C.
Pr
Herman,
K.
.
and
CR
C
Sathiy
Pres,
amo
Florida.
orth
y
,
D.
(19).
Refrncs
13
[H.
Kalmn
and
(193).
Ben-Dor,
The
Hand
ect
ling
[Hamk
,
er,
b
et
w
et
Civl
[Hil
Engie
R
and
eviw
L
regation
and
in
aij,
al.,
W.
a
2D
Hil,
P
gas
.
Imp
rep
G.
ose.
Bulk
Solids
,
erial
atrcion
W.
crital
J.,
mas
Horn,
P
.
uctaions
M.,
in
an
65(9).
on
Coleg
Staics:
A
n
Esay
in
the
Pres.
and
Kak
alios,
b
and
M.
y
J.
(197).
magnetic
alios,
Bulk
seg-
resonac
gran
ular
imagn.
.
Rev
eviw
E
,
Rev
Physic
B.,
Kuip
sim
spher
al
ers,
J.
h.
seg-
axil
eviw
E
M.,
of
axil
ersibl
R
A.
ulation
aproc
ersibl
52(4).
(194).
materil.
P
(195).
J.
particle
hard
R
Kaklois,
B.
A
J.
al
and
omans,
ed:
Kak
Physic
Discret
b
Wals
Hag,
Memoir
M.
K.
(196).
uidse
T.,
of
measurd
of
M.
study
etrs
media.
Hil,
Ho
D.
A.,
ular
196]
L
K.
mixtures
et
Sw
of
Ben-Dor,
78(1):50.
gran
binary
omans
and
der
Kean,
tal
materil
,
194]
S.,
Caprihn,
ular
rotaing
Kaklois,
gation
angle
Lond-Va
Coulmbs
M.,
195]
of
[Hil
R.
4:1058.
H.
eviw
.
etrs
alios,
D.
(198).
K.
gran
Kak
R
ering
rotaed
al
I,
,
erimn
al
Hil,
in
Physic
M.
the
The
a
Exp
J.
197]
gation
der,
on
(1937).
I
(190).
Heyman,
al.,
Go
fricton
C.
A.,
Physic
of
in
G.
G.
History
D.
Physic
sandpile.
[Hil
H.
Held,
198]
[Ho
er,
190]
olving
Kalmn,
surface
particles.
al.,
[Heyman,
particle
Hamk
Grinste,
ev
H.
13():2.
spherical
et
and
of
1937]
en
[Held
193]
Briels,
,
and
Chemic
al
49(5).
W.
bule
segr-
J.,
and
slug
Engie
v
an
formatin
ering
Scien
e
31():9{8.
[Horn
bak
P
.
er
et
al.,
(197).
197]
What
[Huton
et
k
al.,
[Huton
d
et
role
at
in
Thailnd.
Rep
seion
er
084,
S-I(2)5.
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See http://www.pstill.com or for the MacOS X version http://www.stone.com
ert,
I.,
F
Me
orsyth,
L
particule
F
Rho
in
orsyth,
os
Asian
A
M.,
Rho
T
materils.
M.,
pa
er
and
Symp
12g.
C.FOsb
force
hnolgy
hier,
orne
particule
ter-paicl
ec
Sc
C.FOsb
.
des,
and
and
Californ
In
article
des,
ngels,
I.,
387:65.
of
A.,
P
,
segration
materils:
First
A.
e
A.,
eting,
S.,
Barbsi,
Natur
force
Huton,
pa
Alb
standig?
nual
of
ort
J.,
ter-paicl
A
Segration
nical
D.
S.,
of
20b]
(20b).
er,
sandctle
AIChE
al.,
bak
Huton,
The
esnt
eps
20a]
(20a).
pr
Horn
osium,
ects.
orne
Bangk
T
ec
ok,
h-
,
Refrncs
132
[Huton
et
al.,
Eects
201]
W
of
orld
in
Huton,
S.,
ter-paicl
force
Engier
[Israelc
h
vil,
192]
and
ular
al.,
ysic
gran
el,
ciety
of
[Jones
M.,
a
and
C.FOsb
rotaing
orne
drum.
T
ec
(201).
hnical
rep
ort,
et
A
S.
al.,
198]
(198).
and
,
M.,
el,
and
Surfac
e
F
or
c
es
.
S.
R.
(192).
Ph
ysic
of
the
Nagel,
Nagel,
S.
T
letin
T.
R.
(197).
Dynamics
of
gran-
day
and
,
Behring,
page
(196).
The
32.
Lindsa
y
ducing
R.
dune
,
Da
vid
and
R.
b
eac
Crisw
h
el,
T.
sand.
Ge
L.
ol
C.
gic
al
87(463-).
B.,
Miler,
relaxtion
R.,
F.
pro
,
o
John
Sound
Bul
S.
85:40.
1976]
(1976).
Jones,
Charge
cular
Nagel,
Physic
Crisw
a
and
M.
Scients
H.
and
meric
Intermol
M.
H.
materils.
B.
(192).
25:13.
an
ular
y
Crisw
So
,
Jaegr,
Lindsa
and
meric
N.
H.
Jaegr,
196]
of
F.
des,
editon.
197]
A
et
[John
e
Nagel,
materil.
ph
Rho
in
J.
Jaegr,
Scien
and
[Jaegr
A.,
segration
vil,
2nd
192]
stae.
ular
h
Diego,
Nagel,
[Jaegr
on
Israelc
San
gran
orsyth,
Congres.
Academi,
[Jaegr
F
in
R.
D.,
partily
Robins,
K.
led
v
esl.
S.,
and
F
Journal
o
of
wlk
es,
Ele
W.
ctr
Y.
ostaic
,
2(31).
[Kadno,
19]
spired
b
Kadno,
y
[Kadno
gran
et
(198).
L.
ular
al.,
o
198]
and
[Kaumn,
193]
Sel
L
aws
[Keplr,
Evolutin
Oxford
[Kno
Univ
wlton
et
W.
C.
Pr
ersit
o
g.
,
(194).
al.,
y
The
ersit
Kno
imp
90(4):{5.
DEMO PDF produced by an unlicensed PStill, licensing will remove this mark
See http://www.pstill.com or for the MacOS X version http://www.stone.com
ortance
c
of
T.
b
storage,
M.,
Pres,
in
e
Carson,
and
min
eviw
Or
A
der:
,
Zhao,
S.
Self
19(2).
Or
ganisto
d
Univers:
Y
The
Se
ar
ch
ork.
snowake
(de
Niv
sexangul)
.
Hardie.
J.,
transfe,
R
the
New
C.
in-
Oxford.
Pres,
y
L.,
al
Home
orne
edit
wlton,
t
y
6
u,
of
y
A
The
W
Origns
ideas
71().
Physic
ersit
Univ
Theortical
R.,
hes.
(195).
Oxford.
194]
alnc
The
A.
sand:
,
S.
Univ
(1976).
Pres,
Nagel,
v
on
Physic
(193).
Oxford
J.
up
dern
.,
a
Oxford
S.
.
in
A.
.
Keplr,
Mo
P
y
S.
Complexity
1976]
of
ersalit
Kaumn,
of
Built
L.
univ
in
195]
for
(19).
eviws
Kaumn,
ction
[Kaumn,
R
.
Kadno,
Scaling
and
ws.
P
and
Klinzg,
coletin.
G.
E.,
Chem.
and
Y
Eng.
ang,
Refrncs
13
[Ko
ep
a
e
v
et
alnc
al.,
197]
he
[Kuni
e,
ering
J.,
of
Lev
ensp
.
[Lewin,
ep
straicon
and
gine
Ko
eil,
gran
M.,
ular
19]
Buterw
Enz,
Kak
media.
Kuni,
and
R.
(193).
(197).
al
Lev
ensp
Sydne
Lewin,
alios
Physic
D.
orth-Heinma,
193]
and
,
R
eviw
eil,
2
Phase
E
O.
diagrm
,
for
4(58):R10.
(19).
Fluidzaton
En-
editon.
Complexity:Lf
on
the
Edge
of
Chaos
.
Pho
enix,
Lond.
[Lioubashevk
et
and
Fineb
al.,
erg,
vibrated
19]
J.
(19).
and
an
sup
Nagel,
[Luding
and
e
gro
in
[Makse,
19]
frely
co
197a]
al
R
eviw
E
197b]
al
R
E
Eur
[Makse
et
al.,
e
et
(197).
an
on
of
V.,
rice.
[Maslo
in
v
et
v
es
in
hes,
a
v
Z.,
erticaly
83(16):90{.
is
H.
,
not
just
co
ol
J.
(19).
Cluster
9(3):67{81.
instabl
y
Straicon
in
gran
ular
al
Physic
o
ws.
Phys-
y
in
gran
ular
o
ws.
Bal,
R.
A.,
Ha
Bak-TngWiesfld
83(12):49{5.
DEMO PDF produced by an unlicensed PStill, licensing will remove this mark
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Stanley
19]
al
vlin,
in
,
R
S.,
gran
King,
ular
v,
mo
S.,
aeloin
sand
P
W
S.
(198).
58:37.
.
R.,
and
Stanley
Natur
F
ar,
edr,
e
J.,
uctaions
and
,
,
H.
E.
386:79.
Christen,
K.,
corelatins
in
a
pile
83(4).
T
dels
in
and
,
mixtures.
Surface
,
E.,
E
A.,
(19).
etrs
hanism
H.
eviw
Malthe-Sorns,
L
Maslo
C.,
Physic
T.
eviw
mec
.
A.,
H.
al.,
R
instabl
segration
straicon.
Josang,
19]
a
Jaming
Chaos
straicon
and
al.,
,
Herman,
Grain
H.
taneous
Physic
etrs
(198).
and
media.
of
et
ret,
S.
(20).
Makse,
[Malthe-Sorns
F
A.
ular
197]
Sp
L
w
Rec
56:708{1.
Journal
gran
al.,
eviw
S.
(197b).
Makse,
of
[Makse
,
198]
Dynamics
R
Straicon
A.
H.
op
A.,
solitary
Nagel,
ular
H.
Makse,
riples.
Agno,
56().
eviw
20]
and
(197a).
Makse,
Physic
[Makse,
gran
H.
,
al
Luding,
oling
Makse,
[Makse,
J.
Y.,
396:21.
Herman,
wth
ic
,
A.
Hamiel,
proagtin
Physic
Liu,
Natur
and
ensio.
198]
ymore.
O.,
Oscilon
colida
[Liu
Lioubashevk,
ang,
on
C.,
naro
and
w
Zhang,
strip
es.
Y.-C
Physic
(19).
al
1
R
eviw
=f
L
noise
etrs
,
Refrncs
134
[McLaughlin
and
dicton
of
Rho
T
e
gy
et
b
,
al.,
,
b
y
et
Time
Um
the
banho
w
in
O.
taking
in
al.,
to
198]
resolv
R
and
Rho
presnc
des,
of
ar,
P
.
B.,
oscilated
(1982).
M.
J.
liqud
and
gran
In
acoun
t
E
am,
R
Nasuno,
ed
eviw
[Oy
in
(201).
Pre-
bridges.
Powder
Swiney
ular
terpaion
,
la
of
ter-paicl
,
es
ar
el1,
y
ers.
H.
L.
(195).
Physic
al
R
eviw
Geldart
t
cohesin
forces.
yp
e
A,
B,
Powder
C
T
e
and
D
chnol
gy
,
I
,
am,
et
el1,
N.
197]
gran
o
V
plexity
the
19]
et
in
al
Dialo
la
y
P
.
ers.
(198).
Physic
al
185]
con
with
ts.
.
W.
r
al
Chemistry
Gr
anulr
Solids
,
v
Sa
v
age,
S.
B.
(197).
Fin-
.
alnce,
F
J.
to
reman
Be
and
and
c
and
Compan
y
I.
Colins
and
Segration
oming:Te
Stengrs,
Wilam
S.,
(19).
9(3):621{0.
Being
I.
e
V
J.
New
Or
and
J.
Y
(1984).
Sons
Moreau,
,
ork.
der
Co.,
(19).
Com-
Out
Glasgo
of
Con
w.
tac
forces
(185).
exp
On
erimn
the
tal
dilatency
of
ilustraon.
media
comp
osed
Philospc
al
of
Magzine
rigd
,
20():469{81.
[Rho
C.
des
F.
et
(20).
al.,
20]
Rho
Inuec
DEMO PDF produced by an unlicensed PStill, licensing will remove this mark
See http://www.pstill.com or for the MacOS X version http://www.stone.com
des,
M.
of
in
ol-
9(3):54{0.
O.
with
and
,
om
H.
Roux,
,
and
and
Chaos
F
Natur
Chaos
tac:
O.
Prigone,
Reynolds,
in
Physic
386:1{7.
(1980).
F.,
king.
of
Powders
J.,
ouliqen,
es
Radji,
pac
particles
ular
Instiue
of
Delour,
fron
Scien
gue
19]
,
ular
1984]
's
ular
[Reynolds,
gran
Stengrs,
al.,
gran
P
I.
Physic
Man
[Radji
J.
Engier.
e
Prigone,
and
Chaos:
Golub,
gran
the
Flow
G.,
of
in
[Prigone
and
sheard
of
Chemical
Natur
alnce,
1980]
litn
The
ouliqen,
ws.
instable
[Prigone,
A.,
in
Bul
(1958).
P
ular
and
induce
fricton
Britsh
al.,
in
ouliqen
k-slip
Bak,
Japnes.
69{702.
ouliqen
A.,
(193).
In
pages
gerin
stic
Y.
18(5):60.
Pilp
I,
Kudoli,
58(2):16{7.
1958]
ume
of
Oy
ch
S.,
studie
193]
[Pilp
[P
in
J.
81{7.
[Nasuno
[P
viour
disore
Molerus,
wders
3:p
eha
F.,
and
1982]
o
b
L.
75:38{41.
[Molerus,
p
ed
Melo,
kins,
etrs
McLaughlin,
14:23{.
195]
Hexagons,
L
201]
uidze
chnol
[Melo
des,
ter-paicl
J.,
Huton,
forces
S.
on
R.,
the
F
orsyth,
pac
A.
king
fraction
J.,
and
of
Osb
spher.
orne,
Refrncs
135
AIChE
A
ings
nual
but
[Rho
Me
not
des
and
des
et
eting,
R
presn
W
ted
ang,
eno,
Nevad
due
to
20]
,
tra
Rho
v
des,
el
(pa
er
20e).
pa
er
ap
eard
in
pro
ced-
resticon.
M.
J.
and
W
ang,
X.
S.
(20).
Priv
ate
comin-
cation.
[Rho
al.,
Phadt
201]
Rho
japhn,
group
S.
B
[Sa
v
age,
to
A
M.
(201).
192]
J.,
Use
transio.
of
Sa
v
age,
S.
hro
fr
edr,
190]
om
[Seib
an
Sc
B.
b
T
[Shin
e
eds
and
et
(19).
[Shin
brot
Shin
e
,
and
paterns
in
et
ular
brot,
Muzio,
20]
Shin
brot,
et
[Sv
aro
mixng
197a]
Sholtz,
an
suremn
and
page
p25.
New
Y
aws:
Minutes
ork.
(196).
Sim
mec
ulation
of
hanics.
Par-
Journal.
b
et
w
en
randomizg
impacts
Natur
e
Meakhr,
,
M.,
389:574.
and
Muzio,
F.
J.
9(3):61{20.
and
Muzio,
F.
v
alnc
P
Sholtz,
hes.
.,
P
Contemp
1987]
Sv
vsky
,
and
Muzio,
(201).
J.
Physic
Bretz,
M.,
meric
an
.,
or
aro
T.
segration.
A
197b]
,
Y
,
,
L
,
A.
formatin.
T.
and
Scient
al.,
vsky
New
hE
etion
Chaos
dia
staicl
A.,
mixng.
Shin
ular
al.,
a
M.
Alexandr,
201]
sand.
sand
T.,
Geldhart
Power
y
using
patern
Muzio,
gran
squeaking
[Sholtz
ular
studying
and
Noise
to
orde.
410(6825):{.
brot
[Sholtz
gran
S.,
56:1{8.
Compan
Aic
K.
Hanse.
Burns,
Comp
,
and
and
and
in
Me
Chaos
42(3):60.
(197).
brot,
gran
and
Natur
[Shin
T.
19]
A
actls,
Gan,
anulr
and
r
D.
,
brot,
Chaotic
Bideau
Gr
J.,
ed
e
and
redman
K.
A.
Scien
sytem
in
al.,
F
Fluidzaton
colisn
brot
y
uid-partcle
and
Shin
inelastc
[Shin
other
gy
H.
orsyth,
b
der
F
ert,
F
ering
b
W.
Seib
and
197]
Engie
(190).
.
S.,
uidse
Disor
M.
196]
chnol
brot,
edr,
X.
magnetic
(192).
adise
Burns,
uidze
ticle
hro
Par
and
a
edit
Inite
ert
ang,
al
Amsterda.
[Sc
W
Chemic
North-Hland,
[T
des,
Bretz,
ary
,
M.,
and
day
F.
Nori,
,
(1987).
Nori,
o
Nonequilbrm
.
(197a).
Bo
oming
and
84.
Physic
L.
T
and
page
(20).
F.
(197b).
Sound
pro
ducing
38(5):29{4.
Powder
T
esting
Guide
.
Elsevir
Scien,
ork.
Jones,
ts
193]
on
T
feromagntic
DEMO PDF produced by an unlicensed PStill, licensing will remove this mark
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an,
C.
stel
and
bals.
Jones,
J.
T.
Apl.
B.
(193).
Phys.
In
,
73:59{8.
terpaicl
force
mea-
Refrncs
136
[T
egzs
et
P
.
al.,
(19).
No
v
[Um
em
b
egzs,
P
.,
Alb
L
ert,
R.,
P
transio
in
askv
an,
gran
M.,
ular
Vicsek,
T.,
media.
and
Physic
al
Sc
R
hier,
eviw
E
,
er(5):823{6.
w
ular
[v
T
Liqud-nce
banho
T
19]
ar,
196]
ayers
Um
.
PhD
banho
w
thesi,
ar,
P
Cen
.
ter
B.
(196).
for
Wave
Paterns
Nonliear
in
Dynamics:
Vibr
ate
The
d
Univ
Gr
an-
ersit
y
of
exas.
an
W
ac
hem
et
Hemls,
al.,
M.
with
197]
latice
W.,
and
gas
Article#
v
an
de
W
ac
celuar
Leu
hem,
B.
w,
S.
autom.
W.
G.
M.,
Bak
(197).
er,
Sim
Journal
of
A.
F.,
Sc
ulations
houten,
of
Computainl
J.
uidze
C.,
b
Physic
,
eds
135:{7.
CP9751.
[W
ern,
195]
atrco
W
[W
in
c
u
et
al.,
ern,
T.
terpaion.
197]
W
of
and
(195).
Ge
harcteis
magnetic
B.
u,
a
W.
Y.,
ol
Na
gy
v
magneticly
no-magetic
DEMO PDF produced by an unlicensed PStill, licensing will remove this mark
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Eolian
,
dunes:
sim
ulations
and
ad,
23:1057.
A.,
and
stabiled
particles.
Computer
Saxen,
Powder
air
S.
C.
T
uidse
(197).
e
b
Hydro
chnol
gy
,
ed
90:3{46.
of
an
admixture
dynamic
of
Apendix
Published
D
137
P
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