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83
W
Con
Skutella
tin
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uum
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deling,
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analysis
and
rer.
sim
orsitzender:
ulation
Prof.
of
ter:
the
ter:
selfassem
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T
of
11.10.2010
thin
haften
genehmigte
lms
uss:
Dr.
v
h
orgelegt
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v
on
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DiplomMathematik
er
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w
Dominik
ter:
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Rybk
der
geb
Aussprac
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2010
in
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d?
nat.
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Dissertation
olen)
h
V
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on
Prof.
der
Martin
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akult?t
ter:
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Dr.
I
olk

Mehrmann
Mathematik
h
und
PD
Barbara
haften
agner
der
h
T
PD
ec
Andreas
h
hen
eiterer
Univ
h
ersit?t
Prof.
Berlin
Piotr
zur
a
Erlangung
ag
des
wissensc
ak
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he:
hen
Berlin
Grades
D
Doktor
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selfassem
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ation
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arra
thin
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lms
rip
on
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driving
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strates
parameter
yields
metho
CahnHilliard
een
t
[102
yp
sim
e
y
equations
y
of
pseudosp
fourth
ed
or
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to
order.
ed
T
ening
o
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e
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understand
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solutions
the
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phase
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or
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elopmen
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orated
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undreds
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energy
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tial
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w
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linear
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[62
PDE
the
that
ump
describ
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es
to
the
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ert
of
function
a
analytical
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are
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fareld
in
in
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limit
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small
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force
it
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is
liv
sho
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v
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dimensional
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space
eak
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tin
exist.
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ectiv
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e
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e
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umerical
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brings
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of
b
solutions
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[24
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y
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ux
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is
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ux
yp
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extension
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of
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rip
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d
Keyw
of
Selfassem
matc
of
hed
tum
asymptotics
where
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exp
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onen
slop
tially
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ectral
terms
d,
are
surface
retained.
,
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onen
using
matc
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generalization
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of
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the
ald
ansatz
ening,
b
stabilit
y
analysis
Lange.
Con
2
ten
.
ts
.
In
.
tro
.
.
1
.
0.1
Spaces
A
.
quan
.
tum
.
of
gro
selfassem
HCCH
bled
2.2
solids
2.3
.
and
.
of
.
.
.
.
.
.
.
.
.
.
.
.
of
.
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.
.
.
42
.
.
.
and
.
.
.
.
.
solutions
.
.
.
d
.
.
.
onen
1
.
0.2
w
Pro
.
.
pro
.
.
and
Deriv
applications
The
of
.
quan
.
tum
.
dots
.
.
.
.
.
.
.
.
.
.
systems
.
.
.
.
.
.
.
functional
.
.
.
.
.
fractions,
.
.
.
.
5
time,
0.3
.
Gro
HCCH
wth
.
t
.
yp
Stationary
es
equation
and
equation
.
prop
.
erties
A
.
.
.
.
.
.
.
.
.
asymptotics
.
.
.
.
.
3.1.3
.
data
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.
.
.
.
.
.
.
.
.
.
.
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.
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.
.
HCCH
.
and
.
34
.
of
.
surface
.
.
.
.
.
.
8
.
0.4
.
Ge/Si(001)
.
quan
2.1.1
tum
.
dots
.
.
.
.
.
.
.
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.
.
.
.
.
.
phase
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.
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Concepts
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.
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.
.
.
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.
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.
Op
.
v
.
.
.
.
.
.
.
43
.
v
.
spaces,
.
useful
.
2.4
.
to
11
.
0.5
.
Con
.
ten
.
t,
.
results
53
and
and
the
of
3.1
this
the
w
.
ork
.
.
.
.
.
.
.
.
61
.
space
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3.1.2
.
matc
.
.
.
.
.
.
.
.
.
.
.
.
.
b
13
n
1
analytical
Surface
.
diusion
.
based
iii
.
tin
.
uum
.
mo
.
deling
.
17
.
1.1
.
A
.
.
ux
.
.
.
.
.
.
31
.
The
.
equation:
.
ation
.
existence
.
solutions
.
2.1
.
.
a
.
wing
.
.
.
.
.
.
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.
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.
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.
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.
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.
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.
.
35
.
The
.
equation
.
.
.
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.
.
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.
.
.
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.
.
19
.
1.2
.
T
.
yp
36
es
Related
of
separation
surface
.
energies
.
.
.
.
.
.
.
.
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.
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.
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.
.
.
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.
.
40
.
Preliminaries:
.
from
.
analysis
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2.3.1
.
erators,
.
eigen
.
alues
.
.
.
.
.
20
.
1.2.1
.
F
.
.
deriv
2.3.2
ativ
in
es
olving
of
dual
surface
inequalities
energy
other
form
results
ulas
46
.
Existence
.
solutions
.
the
.
equation
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
23
3
1.2.2
solutions
kink
surface
to
energy
HCCH
of
60
regular
Stationary
surfaces
to
.
HCCH
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3.1.1
.
phase
.
metho
26
.
1.3
.
The
.
strain
.
energy
.
densit
.
y
.
for
.
Ge/Si
.
lik
.
e
.
systems
.
.
.
.
.
.
64
.
Exp
.
tial
.
hed
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
67
28
Comparison
1.3.1
et
The
een
base
umerical
state
and
.
results
.
.
.
.
.
.
.
.
.
78
.
..
3.2
.
Coarsening
.
for
ds
the
.
HCCH
.
equation
.
.
.
.
(FDMs)
.
ds
.
ectral
.
.
.
discussion
.
.
.
osition
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
149
79
.
4
.
The
4.5
QDM
.
equation:
.
Deriv
.
ation,
.
analysis
108
and
equations
sim
Finite
ulation
.
results
.
86
.
4.1
5.2
Deriv
.
ation
.
of
.
the
.
QDM
equation
.
.
.
.
PSMs
.
.
.
.
.
.
.
131
.
.
.
.
.
.
.
.
.
.
.
.
.
of
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
ev
.
p
.
114
87
metho
4.2
.
Linear
.
stabilit
.
y
.
analysis
.
.
.
.
.
.
ectral
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
5.2.1
.
tiation
.
.
.
.
.
.
.
.
.
.
.
124
.
3D
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Summary
.
A
.
mo
.
Mathematical
.
152
.
155
94
.
4.3
.
P
.
erio
.
.
stationary
.
solutions
.
.
.
.
104
.
Eect
.
dep
.
.
.
.
.
.
.
.
.
.
.
.
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.
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.
.
.
.
.
5
.
metho
.
for
.
olution
.
on
.
erio
.
domains
97
5.1
4.4
dierence
Ev
ds
olution
.
on
.
big
.
domains
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
116
.
Pseudosp
.
metho
.
(PSMs)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
124
.
Sp
.
dieren
.
and
.
.
101
.
4.4.1
.
Coarsening
.
of
.
t
.
w
.
odimensional
.
arra
.
ys
.
.
.
.
5.2.2
.
for
.
problems
.
.
.
.
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.
6
.
and
102
137
4.4.2
Mathematical
Threedimensional
Surface
selfassem
deling
bly
B
.
.
systems
.
C
.
y
.
iv
.{105}1−x x
an
F
treatmen
or
During
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e
In
ach
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emplo
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When
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Then
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e
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ely
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Ernest
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b
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resulting
y
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(1899
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STM
1961)
Si
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tum
ermission
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ery
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Sometimes,
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orld
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Who
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ould
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do
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e
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ed
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drinking
orld
essel.
thirt
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y
y
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ears
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1
selfassem
/Si(001)
tum
ago
quan
when
dot.
programming
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quan
of
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ted.
mean
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ted
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p
holes
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to
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pap
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er?
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oration
b
nanostructures
eliev
v
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elds
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ying
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200
v
y
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ears
and
ago?
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These
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ere
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out
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e
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for
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ery
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t
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t
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p
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and
of
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the
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orld
of
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impro
orld,
e
of
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this
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asp
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wth
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er,
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fo
eople
Anisotrop
migh
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is
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ortan
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ots
h
where
scales.
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is
pla
to
ys
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a
dels
role.
describ
Quietly
the
and
bly
unin
thin
trusiv1−x x
ensiv
resulting
w
partial
surfaces.
dieren
though
tial
already
equations
the
(PDEs)
ears,
are
are
of
of
high
situations
order
b
and
role
new
the
theory
mark
is
visionary
dev
giv
elop
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ed
man
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ect
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in
them
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on
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sev
sizes
eral
oltaic
asp
ears.
ects,
explo
QDs
h
as
e
equilibrium
sizes
states,
prop
linear
er
stabilit
selfassem
y
w
or
kno
general
existence
of
of
Gen
solutions.
on
The
m
results
on
are
small
supp
When
orted
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y
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sim
nor
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their
that
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are
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tin
out
next
with
and
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pseudosp
is
ectral
of
metho
it
ds.
eral
One
of
of
for
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small
but
that
mak
has
p
raised
kind
great
e
atten
tion
eryda
in
ysical
ed
t
In
y
opular
ears
54
and
ears
whic
sites,
h
or
pla
sand,
ys
sky
a
b
big
formation),
role
or
in
small
this
with
w
osited
ork
manner,
is
ed.
the
this
socalled
the
quantum
Since
dot
ordering
,
the
or
photo
also
or
nano
will
dot
tly
,
few
nanoisland
are
or
state
articial
for
atom
.
during
Quan
e
tum
displa
dots
based
(QDs)
b
are
for
v
[88
ery
quan
small
on
whose
enden
t
t
ypical
implemen
sizes
remained
range
for
b
[66].
et
shap
w
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