Continuum modeling, analysis and simulation of the self-assembly of thin crystalline films [Elektronische Ressource] / vorgelegt von Maciej Dominik Korzec

Sujets

• Mathematics

Informations

• Publié par: technische_universitat_berlin
• Publié le: 01 janvier 2010
• Nombre de lectures: 22
• Langue: English
• Poids de l'ouvrage: 5 Mo

Extrait

83

W
Con
Skutella
tin
Dr.
uum

mo
er
deling,
M?nc
analysis

and
rer.
sim
orsitzender:
ulation
Prof.
of
ter:
the
ter:
self-assem

bly
T
of
11.10.2010
thin
haften

genehmigte
lms
uss:

Dr.
v
h
orgelegt
V
v

on
Dr.
Diplom-Mathematik

er
Dr.

w
Dominik
ter:
K
Rybk

der
geb
Aussprac
oren
2010
in

??
Dr.
d?
nat.
(P
Dissertation
olen)
h
V
V
on
Prof.
der
Martin
F

akult?t
ter:
I
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
hen

he:
hen
Berlin
Grades
D
Doktor
derolution

self-assem
Deriv
the
ation
sho
of


trac

and
tin
ork
uum
ones,
mo
spacing
dels
a
for
used
epitaxial
b
gro

wth
observ
of
arra
thin
bigger
solid
quan
lms
rip
on
W

driving
sub-

strates
parameter
yields
metho
Cahn-Hilliard
een
t
[102
yp
sim
e
y
equations
y
of
pseudosp
fourth
ed
or

sixth
to
order.
ed
T
ening
o
small
describ
hed
e
℄
and
the
understand
expressions
solutions
the
and
solutions
solution
phase
spaces
hnique
to

these
solutions
semi-
for
or
mo
quasilinear
tum
partial
extends
dieren
align
tial
an
equations

(PDEs),
Stranski-Krastano
the
out.
dev
fourth
elopmen
eect
t

of
ulations
elab
While
orated

theory

is
undreds

so
.

Existence
Higher
of
smaller
solutions
or
has
Ost
to
ords:
b
tin
e
pseudosp
sho
exp
wn
solutions,
in
y
un
h
t
related
ypical
b
high
and
order
found
Sob
parameter
olev
of
spaces,
strength.
the
e
n
e
umerics
and
has
uation
to
ws
b
them
e
in

The
to
b
deal
initial
with
n
high
A
order
for
deriv
of
ativ
has
es
ed.
for
w
the
T
time-dep
Sp
enden
b
t
surface
problems
atomic
and
that
with
of
high
gro
order
e
phase
linear
spaces
to
for
quasilinear
the
the
stationary
the

whic
and
b
metho
in
ds
on
of
metho
matc
the
hed
the
asymptotics
b
require
w
matc
h
hing

at

man
sim
y
the
orders.
the
In
e
this
erimen
w
rates
ork
densities
new
are
theory
fa
is
the
presen
in
ted
ald
for


bly
mo
dots,
dels
mo
of
e
high
metho
order.
energy
F
tial
or
existence
a
w
sixth
linear
order
[62
PDE
the
that
ump
describ
is
es
to
the
Lam

ert
of
function
a
analytical
gro
are
wing
for
surface
far-eld
in
in
2D
limit
[89
small
℄
force
it
These
is
liv
sho
in
wn
v
that
dimensional
w
space
eak
a
solutions
tin
exist.

While
allo
for
to
a
k
related
on

hes
v
a
ectiv
plane.
e
asymptotic
Cahn-Hilliard

equation
e
pro
as
ving
input
the
the
existence
umerical
of
d.
absorbing
new
balls
del

the
brings
bly
along
quan
existence
dots
of
b
solutions
deriv
[24
It
℄
a
estimates
ork
for
y
the
ek
sixth
and
order

mo
℄
del
y
are

more
energy
dicult
an
to
ux
obtain
h
since

the
ulations

a
surface
v
energy
wth
leads
b
to

undesired
A
terms.
stabilit
The
analysis
problem
the
is
order
solv
PDE
ed
ws
b
destabilizing
y
of
application
anisotrop
of
,
fractional
h
op
also
erators
e
to
ed
deriv
sim
e
based
lo
a
w
ectral
er
d.
order
in
b
w
ounds
for
from

a
single
transformed
ell-shap
equation,
dots
whic
ere
h
here
are
uge
then
ys
used
h
to
of
obtain
nanoislands
higher
are
order
ulated,
b
that
ounds
ev
from
of
the

original
b
equation.

Next,
exp
new
ts.
t
ux
yp
yield
es
island
of
and
stationary
dots
solutions
absorb
are
in
found
v
b
of
y
bigger
an
resulting
extension
an
of
w
a
rip
metho
pro
d
Keyw
of
Self-assem
matc
of
hed
tum
asymptotics

where
uum
exp
deling,
onen
slop
tially

small
ectral
terms
d,
are
surface
retained.
,
By
onen
using
matc
this
asymptotics,
generalization
of
of
Ost
the
ald
ansatz
ening,
b
stabilit
y
analysis
Lange.
Con
2
ten
.
ts
.
In
.
tro
.

.
1
.
0.1
Spaces
A
.
quan
.
tum
.
of
gro
self-assem
HCCH
bled
2.2
solids
2.3
.
and
.
of
.

.
.
.
.
.
.
.
.
.
.
.
of
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
HCCH
.
and
.
34
.
of
.
surface
.
.
.
.
.
.
8
.
0.4
.
Ge/Si(001)
.
quan
2.1.1
tum
.
dots
.
.
.
.
.
.
.
.
.
.
.
.
.
.
phase
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Concepts
.
.
.
.
.
.
.
.
.
.
.
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
.