Complex	B-Process
Langevin	I-Process
(	O
CL	B-Process
)	O
dynamics	O
[	O
1,2	O
]	O
provides	O
an	O
approach	O
to	O
circumvent	O
the	O
sign	B-Task
problem	I-Task
in	O
numerical	B-Process
simulations	I-Process
of	I-Process
lattice	I-Process
field	I-Process
theories	I-Process
with	O
a	O
complex	O
Boltzmann	O
weight	O
,	O
since	O
it	O
does	O
not	O
rely	O
on	O
importance	O
sampling	O
.	O
In	O
recent	O
years	O
a	O
number	O
of	O
stimulating	O
results	O
has	O
been	O
obtained	O
in	O
the	O
context	O
of	O
nonzero	B-Process
chemical	I-Process
potential	I-Process
,	O
in	O
both	O
lower	B-Process
and	I-Process
four-dimensional	I-Process
field	I-Process
theories	I-Process
with	O
a	O
severe	O
sign	B-Task
problem	I-Task
in	I-Task
the	I-Task
thermodynamic	I-Task
limit	I-Task
[	O
3	O
–	O
8	O
]	O
(	O
for	O
two	O
recent	O
reviews	O
,	O
see	O
e.g.	O
Refs.	O
[	O
9,10	O
])	O
.	O
However	O
,	O
as	O
has	O
been	O
known	O
since	O
shortly	O
after	O
its	O
inception	O
,	O
correct	O
results	O
are	O
not	O
guaranteed	O
[	O
11	O
–	O
16	O
]	O
.	O
This	O
calls	O
for	O
an	O
improved	B-Task
understanding	I-Task
,	I-Task
relying	I-Task
on	I-Task
the	I-Task
combination	I-Task
of	I-Task
analytical	I-Task
and	I-Task
numerical	I-Task
insight	I-Task
.	O
In	O
the	O
recent	O
past	O
,	O
the	O
important	O
role	O
played	O
by	O
the	O
properties	O
of	O
the	O
real	O
and	O
positive	O
probability	B-Process
distribution	I-Process
in	O
the	O
complexified	B-Process
configuration	I-Process
space	I-Process
,	O
which	O
is	O
effectively	O
sampled	O
during	O
the	O
Langevin	B-Process
process	I-Process
,	O
has	O
been	O
clarified	O
[	O
17,18	O
]	O
.	O
An	O
important	O
conclusion	O
was	O
that	O
this	O
distribution	B-Process
should	O
be	O
sufficiently	O
localised	O
in	O
order	O
for	O
CL	B-Process
to	O
yield	O
valid	O
results	O
.	O
Importantly	O
,	O
this	O
insight	O
has	O
recently	O
also	O
led	O
to	O
promising	O
results	O
in	O
nonabelian	B-Task
gauge	I-Task
theories	I-Task
,	O
with	O
the	O
implementation	O
of	O
SL	B-Material
(	I-Material
N,C	I-Material
)	I-Material
gauge	I-Material
cooling	I-Material
[	O
8,10	O
]	O
.	O

This	O
work	O
shows	O
how	O
our	O
approach	O
based	O
on	O
the	O
combination	O
of	O
Statistical	B-Process
Mechanics	I-Process
and	O
nonlinear	B-Process
PDEs	I-Process
theory	I-Process
provides	O
us	O
with	O
a	O
novel	O
and	O
powerful	O
tool	O
to	O
tackle	O
phase	B-Task
transitions	I-Task
.	O
This	O
method	O
leads	O
to	O
solution	O
of	O
perhaps	O
the	O
most	O
known	O
test-case	O
that	O
exhibits	O
a	O
first	B-Process
order	I-Process
phase	I-Process
transition	I-Process
(	O
semi-heuristically	O
described	O
)	O
such	O
as	O
the	O
van	B-Process
der	I-Process
Waals	I-Process
model	I-Process
.	O
In	O
particular	O
we	O
have	O
obtained	O
the	O
first	O
global	O
mean	O
field	B-Process
partition	I-Process
function	I-Process
(	O
Eq.	O
(	O
9	O
))	O
,	O
for	O
a	O
system	O
of	O
finite	O
number	O
of	O
particles	O
.	O
The	O
partition	O
function	O
is	O
a	O
solution	O
to	O
the	O
Klein	B-Task
–	I-Task
Gordon	I-Task
equation	I-Task
,	O
reproduces	O
the	O
van	B-Process
der	I-Process
Waals	I-Process
isotherms	I-Process
away	O
from	O
the	O
critical	O
region	O
and	O
,	O
in	O
the	O
thermodynamic	B-Process
limit	I-Process
N	I-Process
→∞	I-Process
automatically	O
encodes	O
the	O
Maxwell	B-Process
equal	I-Process
areas	I-Process
rule	I-Process
.	O
The	O
approach	O
hereby	O
presented	O
is	O
of	O
remarkable	O
simplicity	O
,	O
has	O
been	O
successfully	O
applied	O
to	O
spin	B-Process
[	O
17	O
–	O
19,14,16	O
]	O
and	O
macroscopic	B-Process
thermodynamic	I-Process
systems	I-Process
[	O
20,15	O
]	O
and	O
can	O
be	O
further	O
extended	O
to	O
include	O
the	O
larger	O
class	O
of	O
models	O
admitting	O
partition	B-Process
functions	I-Process
of	I-Process
the	I-Process
form	I-Process
(	O
4	O
)	O
to	O
be	O
used	O
to	O
extend	O
to	O
the	O
critical	O
region	O
general	B-Process
equations	I-Process
of	I-Process
state	I-Process
of	I-Process
the	I-Process
form	I-Process
(	O
7	O
)	O
including	O
a	O
class	B-Process
virial	I-Process
expansions	I-Process
.	O

We	O
use	O
open	O
and	O
close	O
aperture	B-Process
Z-scan	I-Process
experiments	I-Process
,	O
in	O
analogy	O
to	O
the	O
saturation	B-Task
absorption	I-Task
work	O
discussed	O
earlier	O
in	O
water	B-Material
[	O
8	O
]	O
,	O
to	O
respectively	O
measure	O
the	O
β	O
and	O
n2	O
for	O
a	O
series	O
of	O
primary	B-Material
alcohols	I-Material
with	O
the	O
help	O
of	O
1560nm	B-Material
femtosecond	I-Material
laser	I-Material
pulses	I-Material
,	O
however	O
,	O
with	O
the	O
important	O
inclusion	O
of	O
an	O
optical-chopper	B-Material
.	O
The	O
vibrational	B-Process
combination	I-Process
states	I-Process
of	O
the	O
alcohols	B-Material
are	O
coupled	O
by	O
the	O
femtosecond	B-Material
laser	I-Material
pulses	I-Material
at	I-Material
1560nm	I-Material
.	O
These	O
couplings	O
result	O
in	O
the	O
absorption	B-Process
of	O
1560nm	O
and	O
the	O
excited	O
molecules	B-Material
undergo	O
relaxation	O
through	O
non-radiative	B-Process
processes	I-Process
,	O
which	O
gives	O
rise	O
to	O
transient	B-Process
thermal	I-Process
effects	I-Process
.	O
These	O
transient	O
thermal	O
effects	O
are	O
related	O
to	O
the	O
pure	B-Process
optical	I-Process
nonlinearity	I-Process
of	O
the	O
samples	O
and	O
can	O
be	O
measured	O
as	O
a	O
change	O
in	O
their	O
n2	O
values	O
[	O
14	O
]	O
.	O
The	O
transient	B-Process
thermal	I-Process
effects	I-Process
of	O
individual	O
pulses	O
accumulate	O
in	O
case	O
of	O
high	B-Material
repetition-rate	I-Material
lasers	I-Material
to	O
produce	O
a	O
cumulative	B-Process
thermal	I-Process
effect	I-Process
at	O
longer	O
timescales	O
.	O
We	O
measure	B-Task
this	I-Task
cumulative	I-Task
thermal	I-Task
effect	I-Task
with	O
the	O
mode-mismatched	B-Process
two-color	I-Process
pump	I-Process
–	I-Process
probe	I-Process
experiment	I-Process
.	O

The	O
control	O
of	O
the	O
RP	B-Process
re-encounter	I-Process
probability	I-Process
finds	O
a	O
direct	O
application	O
to	O
improve	B-Task
the	I-Task
performance	I-Task
of	I-Task
chemical	I-Task
devices	I-Task
.	O
Here	O
,	O
we	O
show	O
how	O
a	O
simple-to-implement	O
control	B-Process
scheme	I-Process
highly	O
enhances	O
the	O
sensitivity	O
of	O
a	O
model	B-Material
chemical	I-Material
magnetometer	I-Material
by	O
up	O
to	O
two	O
orders	O
of	O
magnitude	O
.	O
The	O
basic	O
idea	O
behind	O
a	O
chemical	O
magnetometer	O
is	O
that	O
,	O
since	O
a	O
change	O
in	O
the	O
magnetic	B-Process
field	I-Process
modifies	O
the	O
amount	O
of	O
singlet	B-Material
products	I-Material
,	O
one	O
can	O
reverse	O
the	O
reasoning	O
and	O
measure	O
the	O
chemical	B-Material
yield	I-Material
to	O
estimate	O
B	B-Process
.	O
Intuitively	O
,	O
the	O
magnetic	B-Process
sensitivity	I-Process
is	O
high	O
when	O
a	O
small	O
change	O
in	O
the	O
magnetic	B-Process
field	I-Process
intensity	I-Process
produces	O
large	O
effects	O
on	O
the	O
singlet	B-Material
yield	I-Material
.	O
Formally	O
,	O
it	O
is	O
defined	O
as	O
:(	O
2	O
)	O
Λs	O
(	O
B	O
)≡∂	O
Φs	O
(	O
B	O
)∂	O
B	O
=∫	O
0	O
∞	O
pre	O
(	O
t	O
)	O
gs	O
(	O
B,t	O
)	O
dt,with	O
gs	O
(	O
B,t	O
)≡∂	O
fs	O
(	O
B,t	O
)∂	O
B	O
being	O
the	O
instantaneous	O
magnetic	O
sensitivity	O
.	O
The	O
functional	O
form	O
of	O
fs	O
(	O
B,t	O
)=	O
Sρel	O
(	O
t	O
)	O
S	O
strongly	O
depends	O
on	O
the	O
specific	O
realization	O
of	O
the	O
radical	O
pair	O
,	O
in	O
particular	O
on	O
the	O
number	O
of	O
the	O
surrounding	O
nuclear	O
spins	O
.	O
Here	O
,	O
we	O
consider	O
a	O
radical	O
pair	O
in	O
which	O
the	O
first	O
electron	O
spin	O
is	O
devoid	O
of	O
hyperfine	O
interactions	O
,	O
while	O
the	O
second	O
electron	O
spin	O
interacts	O
isotropically	O
with	O
one	O
spin-1	O
nucleus	O
,	O
e.g.	O
nitrogen	O
.	O
In	O
the	O
context	O
of	O
the	O
chemical	O
compass	O
(	O
i.e.	O
when	O
the	O
task	O
is	O
determining	O
the	O
magnetic	O
field	O
direction	O
through	O
anisotropic	O
hyperfine	O
interactions	O
)	O
,	O
an	O
analogous	O
configuration	O
(	O
with	O
only	O
one	O
spin-1	O
/	O
2	O
nucleus	O
)	O
has	O
been	O
proposed	O
[	O
3	O
]	O
,	O
and	O
numerically	O
characterized	O
[	O
8	O
]	O
,	O
as	O
being	O
optimal	O
:	O
Additional	O
nuclear	O
spins	O
would	O
perturb	O
the	O
intuitive	O
‘	O
reference	O
and	O
probe’	O
picture	O
.	O
The	O
Hamiltonian	O
then	O
simplifies	O
to	O
H	O
=-	O
γeB	O
(	O
S1	O
(	O
z	O
)+	O
S2	O
(	O
z	O
))+|	O
γe	O
|	O
αS	O
→	O
2	O
·	O
I	O
→	O
,	O
where	O
α	O
is	O
the	O
isotropic	O
hyperfine	O
coupling	O
.	O

It	O
is	O
well-known	O
that	O
the	O
optical	B-Task
properties	I-Task
of	O
atoms	B-Material
and	O
molecules	B-Material
can	O
be	O
influenced	O
by	O
their	O
electronic	B-Process
environment	I-Process
.	O
Local	B-Process
field	I-Process
effects	I-Process
on	O
spontaneous	O
emission	O
rates	O
within	O
nanostructured	B-Material
photonic	I-Material
materials	I-Material
for	O
example	O
are	O
familiar	O
,	O
and	O
have	O
been	O
well	O
summarized	O
[	O
1	O
]	O
.	O
Optical	B-Process
processes	I-Process
,	O
including	O
resonance	B-Process
energy	I-Process
transfer	I-Process
are	O
similarly	O
dependent	O
on	O
the	O
local	B-Process
environment	I-Process
of	I-Process
molecular	I-Process
chromophores	I-Process
[	O
2	O
–	O
4	O
]	O
.	O
Many	O
biological	O
systems	O
are	O
known	O
to	O
contain	O
complex	O
organizations	O
of	O
molecules	O
with	O
absorption	B-Material
bands	I-Material
shifted	O
due	O
to	O
the	O
electronic	B-Process
influence	I-Process
of	O
other	O
,	O
nearby	O
optical	O
centres	O
.	O
For	O
instance	O
,	O
in	O
widely	O
studied	O
light-harvesting	B-Process
complexes	I-Process
,	O
there	O
are	O
two	O
identifiable	O
forms	O
of	O
the	O
photosynthetic	B-Material
antenna	I-Material
molecule	I-Material
bacteriochlorophyll	I-Material
,	O
with	O
absorption	B-Material
bands	I-Material
centred	O
on	O
800	O
and	O
850nm	O
;	O
it	O
has	O
been	O
shown	O
that	O
the	O
most	O
efficient	O
forms	O
of	O
energy	B-Process
transfer	I-Process
between	O
the	O
two	O
occurs	O
when	O
there	O
is	O
a	O
neighbouring	O
carotenoid	B-Material
species	I-Material
5	O
–	O
7	O
.	O
Until	O
now	O
,	O
research	O
on	O
the	O
broader	O
influence	B-Task
of	I-Task
a	I-Task
neighbouring	I-Task
,	I-Task
off-resonant	I-Task
,	I-Task
molecule	I-Task
on	I-Task
photon	I-Task
absorption	I-Task
has	O
mostly	O
centred	O
on	O
the	O
phenomenon	O
of	O
induced	B-Process
circular	I-Process
dichroism	I-Process
,	O
where	O
both	O
quantum	B-Process
electrodynamic	I-Process
(	O
QED	B-Process
)	O
calculations	O
[	O
8	O
–	O
10	O
]	O
and	O
experimental	B-Process
procedures	I-Process
[	O
11	O
–	O
13	O
]	O
predict	O
and	O
verify	O
that	O
a	O
chiral	B-Material
mediator	I-Material
confers	O
the	O
capacity	O
for	O
an	O
achiral	B-Material
acceptor	I-Material
to	O
exhibit	O
circular	B-Process
differential	I-Process
absorption	I-Process
.	O

Since	O
the	O
receptors	O
in	O
human	O
biology	O
mostly	O
consist	O
of	O
chiral	B-Material
molecules	I-Material
,	O
drug	O
action	O
mostly	O
involves	O
a	O
specified	O
enantiomeric	O
form	O
.	O
This	O
has	O
spurred	O
the	O
development	O
,	O
especially	O
in	O
the	O
pharmaceutical	O
industry	O
,	O
of	O
a	O
host	O
of	O
techniques	O
to	O
secure	O
enantiopure	O
products	O
.	O
Such	O
methods	O
,	O
mostly	O
multi-step	O
and	O
time-consuming	O
,	O
can	O
typically	O
be	O
cast	O
in	O
one	O
of	O
two	O
distinct	O
categories	O
:	O
synthetic	O
mechanisms	O
designed	O
to	O
produce	O
a	O
single	O
stereoisomer	O
,	O
or	O
separation	O
techniques	O
to	O
isolate	O
distinct	O
enantiomers	O
from	O
a	O
racemic	O
mixture	O
.	O
A	O
significant	O
drawback	O
,	O
for	O
either	O
approach	O
,	O
is	O
a	O
dependence	O
on	O
a	O
supply	O
of	O
enantiopure	O
reagents	O
or	O
substrates	O
–	O
synthesis	O
routes	O
generally	O
utilise	O
chiral	O
building	O
blocks	O
or	O
enantioselective	O
catalysts	O
[	O
7,8	O
]	O
,	O
while	O
enantiomer	O
separation	O
techniques	O
typically	O
incorporate	O
chiral	O
selector	O
molecules	O
to	O
form	O
chemically	O
distinct	O
and	O
distinguishable	O
diastereomeric	O
complexes	O
[	O
8,9	O
]	O
.	O
A	O
key	O
requirement	O
in	O
aiming	O
to	O
achieve	O
enantiopure	O
products	O
,	O
irrespective	O
of	O
the	O
synthetic	O
method	O
,	O
is	O
therefore	O
a	O
means	O
to	O
measure	O
,	O
and	O
duly	O
quantitate	O
the	O
enantiomeric	O
excess	O
–	O
signifying	O
the	O
degree	O
of	O
chirality	O
within	O
molecular	O
products	O
.	O
Chiral	O
discrimination	O
through	O
optical	O
means	O
is	O
well-known	O
to	O
offer	O
direct	O
,	O
non-contact	O
ways	O
to	O
distinguish	O
between	O
molecules	O
of	O
different	O
handedness	O
,	O
based	O
on	O
observations	O
such	O
as	O
the	O
subtle	O
differences	O
in	O
absorption	O
of	O
left	O
-	O
and	O
right-handed	O
circularly	O
polarised	O
light	O
,	O
or	O
indeed	O
the	O
twisting	O
of	O
polarisation	O
in	O
optical	O
rotation	O
.	O
Other	O
optical	O
methods	O
,	O
under	O
more	O
recent	O
development	O
,	O
also	O
show	O
some	O
promise	O
to	O
achieve	O
enantiomer	O
separation	O
,	O
as	O
will	O
be	O
introduced	O
later	O
.	O

For	O
any	O
quantum	B-Process
dynamical	I-Process
method	I-Process
,	O
existing	O
or	O
emerging	O
,	O
reliable	O
benchmarks	B-Task
are	O
required	O
to	O
assess	O
their	O
accuracy	O
.	O
A	B-Process
model	I-Process
Hamiltonian	I-Process
exhibiting	O
tunnelling	B-Process
dynamics	I-Process
through	O
a	O
multidimensional	B-Process
asymmetric	I-Process
double	I-Process
well	I-Process
potential	I-Process
has	O
been	O
used	O
as	O
a	O
test	O
by	O
the	O
MP	B-Process
/	I-Process
SOFT	I-Process
[	O
18	O
]	O
and	O
CCS	B-Process
methods	I-Process
[	O
19	O
]	O
mentioned	O
above	O
,	O
and	O
also	O
more	O
recently	O
by	O
a	O
configuration	B-Process
interaction	I-Process
(	I-Process
CI	I-Process
)	I-Process
expansion	I-Process
method	I-Process
[	O
20	O
]	O
and	O
two-layer	B-Process
version	I-Process
of	I-Process
CCS	I-Process
(	O
2L-CCS	B-Process
)	O
.	O
[	O
21	O
]	O
The	B-Process
Hamiltonian	I-Process
consists	O
of	O
a	O
1-dimensional	B-Process
tunnelling	I-Process
mode	I-Process
coupled	O
to	O
an	O
(	B-Process
M	I-Process
−	I-Process
1	I-Process
)-	I-Process
dimensional	I-Process
harmonic	I-Process
bath	I-Process
,	O
hence	O
it	O
is	O
a	O
system-bath	B-Task
problem	I-Task
which	O
bears	O
some	O
similarity	O
to	O
the	O
Caldeira-Leggett	B-Process
model	I-Process
of	I-Process
tunnelling	I-Process
in	O
a	O
dissipative	O
system	O
[	O
22,23	O
]	O
.	O
This	O
Hamiltonian	B-Process
is	O
non-dissipative	O
,	O
however	O
and	O
the	O
harmonic	B-Process
modes	I-Process
all	O
have	O
the	O
same	O
frequency	O
.	O
System-bath	B-Process
models	I-Process
play	O
an	O
important	O
role	O
in	O
physics	B-Task
,	O
being	O
used	O
to	O
describe	O
superconductivity	B-Process
at	I-Process
a	I-Process
Josephson	I-Process
junction	I-Process
in	O
a	O
superconducting	B-Process
quantum	I-Process
interface	I-Process
device	I-Process
(	O
SQUID	B-Process
)	O
[	O
24	O
]	O
,	O
for	O
which	O
the	O
Caldeira-Leggett	B-Process
model	I-Process
provides	O
a	O
theoretical	O
basis	O
,	O
and	O
magnetic	B-Process
and	I-Process
conductance	I-Process
phenomena	I-Process
in	O
the	O
spin-bath	B-Task
regime	I-Task
[	O
25	O
]	O
.	O

Based	O
on	O
the	O
theoretical	B-Task
analysis	I-Task
,	O
the	O
value	B-Process
of	I-Process
the	I-Process
measuring	I-Process
resistor	I-Process
,	O
Rm	B-Process
,	O
has	O
no	O
effect	O
on	O
the	O
corrosion	B-Process
process	I-Process
and	O
on	O
the	O
estimated	O
value	B-Process
of	I-Process
noise	I-Process
resistance	I-Process
.	O
In	O
order	O
to	O
validate	B-Task
this	I-Task
conclusion	I-Task
,	O
the	O
experiment	O
of	O
Fig.	O
9	O
was	O
performed	O
.	O
Specifically	O
,	O
a	O
pair	B-Material
of	I-Material
nominally	I-Material
identical	I-Material
specimens	I-Material
was	O
initially	O
coupled	O
by	O
a	O
4.7kΩ	B-Material
resistor	I-Material
and	O
their	O
potential	O
with	O
respect	O
to	O
a	O
saturated	B-Material
calomel	I-Material
electrode	I-Material
was	O
recorded	O
by	O
using	O
a	O
NI-USB	B-Material
6009	I-Material
analog-to-digital	I-Material
converter	I-Material
.	O
The	O
electrochemical	B-Process
noise	I-Process
signal	I-Process
was	O
recorded	O
using	O
in-house	B-Material
developed	I-Material
software	I-Material
,	O
acquiring	O
at	O
1023Hz	O
segments	O
of	O
1000	O
points	O
at	O
each	O
iteration	O
.	O
Between	O
iterations	O
,	O
the	O
1000	O
values	O
acquired	O
were	O
averaged	O
to	O
obtain	B-Task
a	I-Task
single	I-Task
value	I-Task
of	I-Task
potential	I-Task
,	O
subsequently	O
saved	O
to	O
the	O
file	O
used	O
for	O
later	O
processing	O
.	O
The	O
final	O
dataset	B-Material
comprised	O
potential	O
values	O
spaced	O
1	O
±	O
0.05s	O
in	O
time	O
.	O
Under	O
the	O
assumption	O
that	O
the	O
noise	O
present	O
above	O
1023Hz	O
is	O
negligible	O
compared	O
with	O
the	O
noise	O
present	O
below	O
0.5Hz	O
,	O
this	O
procedure	O
enables	O
an	O
accurate	B-Task
recording	I-Task
of	I-Task
the	I-Task
potential	I-Task
noise	I-Task
in	I-Task
the	I-Task
frequencies	I-Task
of	I-Task
interest	I-Task
,	O
avoiding	O
aliasing	O
of	O
frequencies	O
between	O
0.5	O
and	O
1023Hz	O
and	O
minimizing	O
the	O
50Hz	O
interference	O
from	O
the	O
mains	O
supply	O
.	O

A	O
surfactant	B-Material
is	O
a	O
surface	B-Material
active	I-Material
agent	I-Material
.	O
In	O
this	O
work	O
a	O
surfactant	B-Material
term	O
will	O
be	O
used	O
for	O
compounds	B-Material
which	I-Material
improve	I-Material
the	I-Material
dispersability	I-Material
of	O
the	O
CI	B-Material
in	O
the	O
acid	B-Material
(	O
as	O
emulsifiers	B-Material
providing	O
dispersed	B-Material
emulsion	I-Material
–	O
not	O
separated	O
)	O
while	O
wetting	O
the	O
surface	O
of	O
the	O
metallic	B-Material
material	I-Material
[	O
14,20,24	O
]	O
.	O
However	O
,	O
surfactants	O
can	O
offer	O
corrosion	B-Task
protection	I-Task
themselves	O
.	O
Some	O
examples	O
when	O
the	O
same	O
compound	O
was	O
used	O
as	O
a	O
surfactant	B-Material
or	I-Material
active	I-Material
corrosion	I-Material
inhibitor	I-Material
ingredient	O
are	O
given	O
below	O
.	O
Typical	O
surfactants	B-Material
in	O
the	O
oilfield	O
services	O
industry	O
are	O
alkylphenol	B-Material
ethoxylates	I-Material
,	O
e.g.	O
nonylphenol	B-Material
ethoxylate	I-Material
(	O
NPE	B-Material
)	O
[	O
14,15,30,106,107	O
]	O
.	O
However	O
,	O
NPEs	B-Material
have	O
been	O
banned	O
from	O
use	O
in	O
the	O
North	O
Sea	O
because	O
of	O
their	O
toxicity	O
.	O
On	O
the	O
other	O
hand	O
,	O
ethoxylated	B-Material
linear	I-Material
alcohols	I-Material
are	O
more	O
acceptable	O
[	O
20	O
]	O
.	O
The	O
quaternary	B-Material
ammonium	I-Material
salts	I-Material
and	O
amines	B-Material
(	I-Material
when	I-Material
protonated	I-Material
)	I-Material
are	O
the	O
most	O
used	O
compounds	O
of	O
the	O
cationic	B-Material
surfactants	I-Material
class	I-Material
,	O
where	O
the	O
cation	B-Material
is	O
the	O
surface	B-Material
active	I-Material
specie	I-Material
.	O
As	O
the	O
amines	B-Material
only	O
function	O
as	O
a	O
surfactant	B-Material
in	O
the	O
protonated	B-Process
state	I-Process
,	O
they	O
cannot	O
be	O
used	O
at	O
high	O
pH	O
.	O
On	O
the	O
other	O
hand	O
,	O
quaternary	B-Material
ammonium	I-Material
compounds	I-Material
,	O
frequently	O
abbreviated	O
as	O
“	O
quats	B-Material
”	O
,	O
are	O
not	O
pH	O
sensitive	O
.	O
Long-chain	B-Material
quaternary	I-Material
ammonium	I-Material
bromides	I-Material
were	O
also	O
reported	O
to	O
work	O
as	O
efficient	O
CIs	B-Material
for	O
steel	B-Material
materials	I-Material
[	O
106	O
]	O
.	O
A	O
frequently	O
employed	O
surfactant	B-Material
was	O
N-dodecylpyridinium	B-Material
bromide	I-Material
(	O
DDPB	B-Material
)	O
[	O
9,60,61,108,109	O
]	O
.	O
Anionic	B-Material
sulphates	I-Material
,	O
anionic	B-Material
sulphonates	I-Material
,	O
alkoxylated	B-Material
alkylphenol	I-Material
resins	I-Material
,	O
and	O
polyoxyethylene	B-Material
sorbitan	I-Material
oleates	I-Material
are	O
also	O
useful	O
surfactants	B-Material
.	O
Ali	O
reported	O
that	O
a	O
particularly	O
useful	O
surfactant	B-Material
is	O
a	O
blend	B-Material
of	I-Material
polyethylene	I-Material
glycol	I-Material
esters	I-Material
of	I-Material
fatty	I-Material
acids	I-Material
and	I-Material
ethoxylated	I-Material
alkylphenols	I-Material
[	O
15	O
]	O
.	O
Several	O
examples	O
of	O
the	O
surfactants	B-Material
used	O
are	O
given	O
below	O
in	O
Section	O
5.6	O
.	O

The	O
related	O
Volta	B-Process
potential	I-Process
(	O
Ψ	B-Process
)	O
is	O
the	O
potential	B-Process
difference	I-Process
between	O
a	O
position	O
infinitely	O
far	O
away	O
from	O
the	O
surface	O
and	O
a	O
position	O
just	O
outside	O
the	O
surface	O
,	O
and	O
is	O
the	O
measureable	B-Process
quantity	I-Process
characterising	O
electrochemical	B-Process
behaviour	I-Process
of	I-Process
a	I-Process
metal	I-Process
[	O
12,17	O
]	O
.	O
The	O
scanning	B-Process
Kelvin	I-Process
probe	I-Process
force	I-Process
microscopy	I-Process
(	O
SKPFM	B-Process
)	O
technique	O
allows	O
detection	B-Task
of	I-Task
local	I-Task
EWF	I-Task
(	O
if	O
the	O
EWF	O
of	O
the	O
tip	O
is	O
known	O
)	O
,	O
or	O
Volta	B-Task
potential	I-Task
differences	I-Task
(	O
ΔΨ	B-Task
)	O
between	O
an	O
atomic	B-Material
force	I-Material
microscopy	I-Material
tip	I-Material
(	O
usually	O
Pt	B-Material
coated	I-Material
)	O
and	O
the	O
metal	B-Material
surface	I-Material
[	O
14,15,19	O
]	O
.	O
The	O
lateral	O
resolution	O
of	O
SKPFM	B-Process
can	O
be	O
as	O
high	O
as	O
10	O
’s	O
of	O
nm	O
in	O
ambient	B-Material
air	I-Material
,	O
with	O
a	O
sensitivity	O
up	O
to	O
10	O
–	O
20meV	O
[	O
19	O
]	O
.	O
Volta	B-Process
potential	I-Process
is	O
a	O
characteristic	O
property	B-Process
of	I-Process
a	I-Process
metal	I-Process
surface	I-Process
and	O
can	O
be	O
used	O
to	O
understand	B-Task
electrochemical	I-Task
processes	I-Task
[	O
16	O
]	O
.	O
It	O
is	O
sensitive	O
to	O
any	O
kind	O
of	O
surface	O
defects	O
,	O
chemical	O
variations	O
,	O
and	O
residual	O
stress	O
[	O
13,17	O
]	O
.	O
Volta	B-Process
potential	I-Process
differences	I-Process
in	I-Process
microstructure	I-Process
have	O
been	O
used	O
to	O
predict	B-Task
corrosion	I-Task
behaviour	I-Task
[	O
10,15,18,20	O
–	O
22	O
]	O
.	O
Regions	O
with	O
larger	B-Process
(	I-Process
ΔΨ	I-Process
)	I-Process
indicate	I-Process
increased	I-Process
surface	I-Process
reactivity	I-Process
[	O
11,15,18	O
]	O
,	O
and	O
even	O
a	O
correlation	O
between	O
Volta	B-Process
potential	I-Process
differences	I-Process
measured	O
in	O
nominally	O
dry	B-Material
air	I-Material
and	O
their	O
free	B-Process
corrosion	I-Process
potential	I-Process
(	O
Ecorr	B-Process
)	O
pre-determined	O
under	O
immersed	O
conditions	O
has	O
been	O
reported	O
[	O
18	O
]	O
.	O

The	O
homologous	B-Material
series	I-Material
of	I-Material
n-alkanes	I-Material
are	O
represented	O
here	O
as	O
homonuclear	B-Material
chains	I-Material
of	I-Material
tangent	I-Material
Mie	I-Material
spherical	I-Material
CG	I-Material
segments	I-Material
.	O
The	O
development	B-Task
of	I-Task
CG	I-Task
models	I-Task
for	I-Task
long	I-Task
n-alkanes	I-Task
such	O
as	O
n-decane	B-Material
(	O
n-C10H22	B-Material
)	O
and	O
n-eicosane	B-Material
(	O
n-C20H42	B-Material
)	O
has	O
already	O
been	O
successfully	O
demonstrated	O
using	O
the	O
SAFT-γ	B-Process
Mie	I-Process
formalism	I-Process
[	O
118	O
]	O
.	O
The	O
n-decane	B-Material
molecule	I-Material
was	O
represented	O
by	O
chains	O
of	O
three	O
and	O
n-eicosane	B-Material
chains	O
of	O
six	O
fully	O
flexible	O
tangentially	O
bonded	O
Mie	B-Material
segments	I-Material
.	O
A	O
certain	O
degree	O
of	O
parameter	O
degeneracy	O
in	O
terms	O
of	O
overall	O
performance	O
is	O
expected	O
as	O
a	O
consequence	O
of	O
the	O
conformal	O
nature	O
of	O
the	O
EOS	O
description	O
[	O
132	O
]	O
.	O
In	O
our	O
current	O
work	O
,	O
we	O
use	O
an	O
alternative	B-Process
CG	I-Process
mapping	I-Process
for	O
n-alkanes	B-Material
developed	O
in	O
reference	O
[	O
122	O
]	O
,	O
where	O
each	O
segment	O
was	O
taken	O
to	O
represent	O
three	O
alkyl	B-Material
carbon	I-Material
backbone	I-Material
atoms	I-Material
and	O
their	O
corresponding	O
hydrogen	B-Material
atoms	I-Material
.	O
By	O
applying	O
this	O
mapping	O
,	O
n-alkanes	B-Material
chains	I-Material
containing	O
multiples	O
of	O
three	O
carbon	B-Material
units	I-Material
can	O
be	O
represented	O
directly	O
:	O
n-C6H14	B-Material
,	O
n-C9H20	B-Material
,	O
n-C12H26	B-Material
,	O
n-C15H32	B-Material
,	O
n-C18H38	B-Material
,	O
etc	O
.	O
A	O
good	O
description	B-Task
of	I-Task
the	I-Task
thermodynamic	I-Task
properties	I-Task
of	O
these	O
alkanes	B-Material
is	O
found	O
to	O
be	O
provided	O
with	O
CG	B-Material
alkyl	I-Material
beads	I-Material
characterised	O
by	O
the	O
Mie	B-Process
(	I-Process
15	I-Process
–	I-Process
6	I-Process
)	I-Process
potential	I-Process
.	O
For	O
convenience	O
,	O
the	O
exponent	O
pair	O
(	O
15	O
–	O
6	O
)	O
is	O
also	O
used	O
to	O
represent	O
the	O
interactions	O
between	O
the	O
CG	B-Material
beads	I-Material
of	O
the	O
intervening	O
alkanes	B-Material
considered	O
here	O
;	O
the	O
number	O
of	O
segments	O
m	O
is	O
taken	O
to	O
be	O
the	O
nearest	O
integer	O
of	O
the	O
division	O
of	O
the	O
carbon	B-Material
number	O
C	O
by	O
three	O
.	O
The	O
size	O
σ	O
and	O
energy	O
∊	O
parameters	O
are	O
then	O
estimated	O
from	O
the	O
experimental	O
saturated-liquid	B-Process
density	I-Process
and	O
vapour	B-Process
pressure	I-Process
of	O
the	O
individual	O
alkanes	B-Material
following	O
the	O
usual	O
SAFT-γ	B-Process
Mie	I-Process
procedure	I-Process
.	O
The	O
chosen	O
mapping	O
is	O
by	O
no	O
means	O
unique	O
,	O
as	O
one	O
can	O
postulate	O
parameter	O
sets	O
that	O
fulfil	O
other	O
requisites	O
,	O
such	O
as	O
being	O
“	O
universal	O
”	O
across	O
the	O
entire	O
homologous	O
series	O
[	O
119	O
]	O
or	O
correlated	O
to	O
the	O
critical	O
properties	O
[	O
125	O
]	O
.	O

This	O
study	O
proposes	O
a	O
new	B-Task
framework	I-Task
of	I-Task
a	I-Task
numerical	I-Task
modelling	I-Task
of	O
the	O
gas	B-Process
exchange	I-Process
between	O
air	B-Material
and	O
water	B-Material
across	O
their	O
interface	O
,	O
and	O
subsequent	O
chemical	B-Process
reaction	I-Process
in	I-Process
water	I-Process
based	O
on	O
an	O
extended	O
two-compartment	B-Process
model	I-Process
.	O
The	O
major	O
purpose	O
of	O
this	O
study	O
is	O
to	O
provide	O
a	O
fundamental	B-Process
concept	I-Process
for	O
modelling	B-Task
physicochemical	I-Task
processes	I-Task
of	O
the	O
gas	B-Material
exchange	O
,	O
followed	O
by	O
the	O
chemical	B-Process
reaction	I-Process
in	I-Process
water	I-Process
.	O
Demonstrating	O
fundamental	O
data	O
and	O
knowledge	O
on	O
the	O
important	O
environmental	O
transport	O
phenomena	O
,	O
especially	O
the	O
effects	B-Process
of	I-Process
the	I-Process
Schmidt	I-Process
number	I-Process
and	O
the	O
chemical	B-Process
reaction	I-Process
rate	I-Process
on	O
the	O
gas	B-Process
exchange	I-Process
mechanisms	I-Process
across	I-Process
the	I-Process
interface	I-Process
have	O
also	O
been	O
attempted	O
.	O
The	O
gas	B-Process
exchange	I-Process
processes	I-Process
are	O
separated	O
into	O
two	O
physicochemical	O
substeps	O
,	O
the	O
first	O
is	O
the	O
gas	B-Process
–	I-Process
liquid	I-Process
equilibrium	I-Process
between	O
the	O
two	O
phases	O
,	O
and	O
the	O
second	O
is	O
the	O
chemical	B-Process
reaction	I-Process
in	I-Process
the	I-Process
water	I-Process
phase	I-Process
.	O
A	O
first-order	O
,	O
irreversible	B-Process
chemical	I-Process
reaction	I-Process
of	O
the	O
gaseous	B-Material
material	I-Material
after	O
its	O
uptake	O
into	O
the	O
water	B-Material
phase	I-Material
is	O
assumed	O
here	O
to	O
simplify	O
interactions	O
of	O
the	O
chemical	B-Process
reactions	I-Process
and	O
turbulent	B-Process
transport	I-Process
phenomena	I-Process
in	I-Process
water	I-Process
.	O
While	O
a	O
traditional	O
two-compartment	B-Process
model	I-Process
assumes	O
uniform	O
concentration	O
of	O
a	O
material	O
in	O
each	O
compartment	O
,	O
the	O
present	O
two-compartment	O
model	O
uses	O
a	O
computational	B-Process
fluid	I-Process
dynamics	I-Process
(	O
CFD	B-Process
)	O
technique	O
in	O
the	O
water	B-Material
compartment	O
to	O
evaluate	B-Task
temporal	I-Task
development	I-Task
of	I-Task
three-dimensional	I-Task
profiles	I-Task
of	I-Task
the	I-Task
velocity	I-Task
and	I-Task
concentration	I-Task
fields	I-Task
.	O
A	O
direct	B-Process
numerical	I-Process
simulation	I-Process
(	O
DNS	B-Process
)	O
approach	O
is	O
used	O
to	O
evaluate	B-Task
profiles	I-Task
of	I-Task
fluid	I-Task
velocities	I-Task
and	I-Task
concentrations	I-Task
in	I-Task
water	I-Task
,	O
and	O
several	O
important	O
turbulence	O
statistics	O
have	O
been	O
evaluated	O
without	O
using	O
turbulent	O
closures	O
,	O
and	O
subgrid-scale	B-Process
models	I-Process
.	O
We	O
assume	O
that	O
a	O
fluid	B-Process
flow	I-Process
in	I-Process
the	I-Process
water	I-Process
phase	I-Process
is	O
a	O
well-developed	O
turbulent	O
water	O
layer	O
of	O
a	O
low	O
Reynolds	O
number	O
,	O
and	O
the	O
Schmidt	O
number	O
is	O
varied	O
from	O
1	O
to	O
8	O
to	O
observe	B-Task
the	I-Task
effects	I-Task
of	I-Task
the	I-Task
molecular	I-Task
diffusion	I-Task
of	O
the	O
gas	B-Material
in	O
sub-interface	O
water	B-Material
on	O
the	O
gas	B-Material
exchange	O
rate	O
at	O
the	O
interface	O
.	O
Six	O
degrees	O
of	O
the	O
nondimensional	B-Process
chemical	I-Process
reaction	I-Process
rate	I-Process
are	O
used	O
to	O
find	O
the	O
effect	B-Task
of	I-Task
the	I-Task
chemical	I-Task
reaction	I-Task
rate	I-Task
on	I-Task
the	I-Task
gas	I-Task
exchange	I-Task
mechanisms	I-Task
.	O
Extrapolations	O
of	O
the	O
gas	B-Process
exchange	I-Process
rates	I-Process
and	O
the	O
related	O
transport	B-Process
phenomena	I-Process
toward	O
larger	O
Schmidt	O
number	O
and	O
the	O
faster	O
chemical	B-Process
reaction	I-Process
rate	O
will	O
also	O
be	O
examined	O
to	O
predict	B-Task
the	I-Task
gas	I-Task
exchange	I-Task
processes	I-Task
of	O
the	O
actual	O
gases	B-Material
of	O
Sc	B-Material
∼	I-Material
O	I-Material
(	I-Material
102	I-Material
)	I-Material
based	O
on	O
results	O
from	O
the	O
present	O
numerical	B-Task
experiments	I-Task
.	O

Although	O
the	O
free	B-Task
Kelvin	I-Task
wave	I-Task
problem	I-Task
is	O
of	O
considerable	O
theoretical	O
importance	O
,	O
problems	B-Task
with	I-Task
forcing	I-Task
and	I-Task
damping	I-Task
have	O
greater	O
practical	O
importance	O
.	O
In	O
nature	O
,	O
the	O
forcing	O
could	O
be	O
due	O
to	O
a	O
wind	B-Material
stress	O
at	O
the	O
free	O
surface	O
or	O
an	O
astronomical	B-Process
tidal	I-Process
potential	I-Process
,	O
and	O
the	O
damping	B-Process
could	O
be	O
due	O
to	O
the	O
turbulent	B-Process
stress	I-Process
of	I-Process
a	I-Process
bottom	I-Process
boundary	I-Process
layer	I-Process
.	O
Regardless	O
of	O
the	O
details	O
,	O
the	O
forced	B-Process
response	I-Process
is	O
composed	O
of	O
shallow-water	B-Material
waves	I-Material
,	O
possibly	O
including	O
Kelvin	B-Material
waves	I-Material
,	O
with	O
the	O
largest	O
amplitudes	O
in	O
waves	O
with	O
a	O
natural	B-Process
frequency	I-Process
ωf	B-Process
close	O
to	O
that	O
of	O
the	O
forcing	B-Process
frequency	I-Process
ω	B-Process
;	O
various	O
examples	O
of	O
this	O
sort	O
are	O
given	O
in	O
Chapters	O
9	O
and	O
10	O
of	O
Gill	O
[	O
16	O
]	O
.	O
When	O
ω	O
≈	O
ωf	B-Process
,	O
there	O
is	O
a	O
large	O
amplitude	O
near-resonant	O
response	O
,	O
the	O
size	O
of	O
which	O
is	O
sensitive	O
to	O
the	O
weak	B-Process
damping	I-Process
and	O
|	B-Process
ω	I-Process
−	I-Process
ωf	I-Process
|	I-Process
.	O
Thus	O
,	O
in	O
numerical	B-Task
solutions	I-Task
of	O
near-resonantly	B-Material
forced	I-Material
waves	I-Material
,	O
we	O
anticipate	O
that	O
errors	O
in	O
ωf	B-Process
(	O
associated	O
with	O
the	O
spatial	B-Process
discretisation	I-Process
)	O
could	O
lead	O
to	O
non-trivial	O
errors	O
in	O
the	O
forced	O
response	O
.	O

A	O
fully-coupled	B-Process
numerical	I-Process
framework	I-Process
for	O
two-phase	B-Process
flows	I-Process
with	O
an	O
implicit	O
implementation	O
of	O
surface	B-Process
tension	I-Process
has	O
been	O
introduced	O
in	O
this	O
article	O
.	O
This	O
fully-coupled	B-Process
framework	I-Process
has	O
then	O
been	O
used	O
to	O
compare	B-Task
the	I-Task
influence	I-Task
of	O
the	O
surface	B-Process
tension	I-Process
treatment	I-Process
on	O
the	O
time-step	B-Process
restrictions	I-Process
resulting	I-Process
from	I-Process
capillary	I-Process
waves	I-Process
.	O
The	O
conducted	O
study	O
demonstrates	O
that	O
restrictions	B-Process
on	I-Process
the	I-Process
numerical	I-Process
time-step	I-Process
resulting	I-Process
from	I-Process
capillary	I-Process
waves	I-Process
are	O
valid	O
and	O
unchanged	O
regardless	O
of	O
the	O
numerical	B-Process
treatment	I-Process
of	I-Process
surface	I-Process
tension	I-Process
.	O
Since	O
surface	O
tension	O
is	O
not	O
a	O
function	O
of	O
pressure	O
or	O
velocity	O
,	O
the	O
change	O
in	O
implementation	O
does	O
not	O
affect	O
the	O
matrix	O
coefficients	O
of	O
the	O
primitive	O
variables	O
and	O
,	O
thus	O
,	O
numerical	O
stability	O
is	O
independent	O
of	O
the	O
treatment	B-Task
of	I-Task
surface	I-Task
tension	I-Task
.	O
Further	O
analysis	O
shows	O
that	O
the	O
capillary	O
time-step	O
constraint	O
is	O
a	O
requirement	O
imposed	O
by	O
the	O
spatiotemporal	B-Task
sampling	I-Task
of	I-Task
capillary	I-Task
waves	I-Task
,	O
which	O
is	O
independent	O
of	O
the	O
applied	B-Process
numerical	I-Process
methodology	I-Process
.	O

The	O
remainder	O
of	O
our	O
discussion	O
proceeds	O
as	O
follows	O
.	O
In	O
Section	O
2	O
we	O
briefly	O
describe	O
the	O
problem	B-Task
of	I-Task
cell	I-Task
tracking	I-Task
and	O
introduce	B-Task
our	I-Task
approach	I-Task
to	I-Task
cell	I-Task
tracking	I-Task
,	O
which	O
may	O
be	O
regarded	O
as	O
fitting	O
a	O
mathematical	B-Process
model	I-Process
to	O
experimental	B-Material
image	I-Material
data	I-Material
sets	I-Material
.	O
We	O
present	O
the	O
geometric	B-Process
evolution	I-Process
law	I-Process
model	I-Process
we	O
seek	O
to	O
fit	O
,	O
which	O
is	O
a	O
simplification	O
of	O
recently	O
developed	O
models	O
in	O
the	O
literature	O
that	O
show	O
good	O
agreement	O
with	O
experiments	O
[	O
8,10	O
–	O
12,4,13,9	O
]	O
.	O
We	O
finish	O
Section	O
2	O
by	O
reformulating	O
our	B-Process
model	I-Process
into	O
the	O
phase	B-Process
field	I-Process
framework	I-Process
,	O
which	O
appears	O
more	O
suitable	O
for	O
the	O
problem	O
in	O
hand	O
,	O
and	O
we	O
formulate	O
the	O
cell	B-Task
tracking	I-Task
problem	I-Task
as	O
a	O
PDE	B-Task
constrained	I-Task
optimisation	I-Task
problem	I-Task
.	O
In	O
Section	O
3	O
we	O
propose	O
an	O
algorithm	B-Process
for	O
the	O
resolution	O
of	O
the	O
PDE	B-Task
constrained	I-Task
optimisation	I-Task
problem	I-Task
and	O
we	O
discuss	O
some	O
practical	O
aspects	O
related	O
to	O
the	O
implementation	O
.	O
In	O
particular	O
we	O
note	O
that	O
the	O
theoretical	B-Process
and	I-Process
computational	I-Process
framework	I-Process
may	O
be	O
applied	O
directly	O
to	O
multi-cell	B-Material
image	I-Material
data	I-Material
sets	I-Material
and	O
raw	B-Material
image	I-Material
data	I-Material
sets	I-Material
(	O
of	O
sufficient	O
quality	O
)	O
without	O
segmentation	B-Process
.	O
In	O
Section	O
4	O
we	O
present	O
some	O
numerical	O
examples	O
for	O
the	O
case	O
of	O
2d	O
single	O
and	O
multi-cell	O
image	B-Material
data	I-Material
sets	I-Material
.	O
Finally	O
in	O
Section	O
5	O
we	O
present	O
some	O
conclusions	O
of	O
our	O
study	O
and	O
discuss	O
future	O
extensions	O
and	O
applications	O
of	O
the	O
work	O
.	O

The	B-Task
dynamics	I-Task
of	I-Task
various	I-Task
physical	I-Task
phenomena	I-Task
,	O
such	O
as	O
the	O
movement	B-Process
of	I-Process
pendulums	I-Process
,	I-Process
planets	I-Process
,	I-Process
or	I-Process
water	I-Process
waves	I-Process
can	O
be	O
described	O
in	O
a	O
variational	B-Process
framework	I-Process
.	O
The	O
development	O
of	O
variational	B-Process
principles	I-Process
for	O
classical	O
mechanics	O
traces	O
back	O
to	O
Euler	O
,	O
Lagrange	O
,	O
and	O
Hamilton	O
;	O
an	O
overview	O
of	O
this	O
history	O
can	O
be	O
found	O
in	O
[	O
1,19	O
]	O
.	O
This	O
approach	B-Process
allows	O
to	O
express	B-Task
all	I-Task
the	I-Task
dynamics	I-Task
of	I-Task
a	I-Task
system	I-Task
in	O
a	O
single	B-Process
functional	I-Process
–	O
the	O
Lagrangian	B-Process
–	O
which	O
is	O
an	O
action	B-Process
integral	I-Process
.	O
Hamiltonian	B-Process
mechanics	I-Process
is	O
a	O
reformulation	B-Process
of	I-Process
Lagrangian	I-Process
mechanics	I-Process
which	O
provides	O
a	O
convenient	O
framework	B-Material
to	O
study	B-Task
the	I-Task
symmetry	I-Task
properties	I-Task
of	I-Task
a	I-Task
system	I-Task
.	O
This	O
is	O
expressed	O
by	O
Noether	O
's	O
theorem	O
which	O
establishes	O
the	O
direct	O
connection	O
between	O
the	O
symmetry	O
properties	O
of	O
Hamiltonian	B-Process
systems	I-Process
and	O
conservation	O
laws	O
.	O
When	O
one	O
approximates	O
the	O
system	B-Process
numerically	O
,	O
it	O
is	O
advantageous	O
to	O
preserve	O
the	O
Hamiltonian	O
structure	O
also	O
at	O
the	O
discrete	O
level	O
.	O
Given	O
that	O
Hamiltonian	B-Process
systems	I-Process
are	O
abundant	O
in	O
nature	O
,	O
their	O
numerical	B-Task
approximation	I-Task
is	O
therefore	O
a	O
topic	O
of	O
significant	O
relevance	O
.	O

As	O
discussed	O
above	O
,	O
proper	B-Task
inclusion	I-Task
of	I-Task
these	I-Task
interactions	I-Task
requires	O
segment	B-Process
synchronization	I-Process
after	I-Process
every	I-Process
iteration	I-Process
.	O
In	O
order	O
to	O
minimize	B-Task
simulation	I-Task
errors	I-Task
due	O
to	O
incorrect	O
values	O
of	O
the	O
interactions	O
potential	O
,	O
segments	B-Process
are	I-Process
synchronized	I-Process
after	I-Process
every	I-Process
iteration	I-Process
.	O
Although	O
relatively	O
long	O
communication	O
times	O
between	O
remote	O
processors	B-Material
may	O
hinder	O
this	O
process	O
in	O
typical	O
parallel	B-Material
computers	I-Material
,	O
this	O
is	O
not	O
the	O
case	O
for	O
GPGPU	B-Material
architectures	I-Material
.	O
Still	O
,	O
full	O
recalculation	B-Process
of	I-Process
the	I-Process
interaction	I-Process
potential	I-Process
after	O
each	O
iteration	O
is	O
time	O
consuming	O
.	O
Instead	O
,	O
the	O
algorithm	B-Process
corrects	B-Process
the	I-Process
current	I-Process
potential	I-Process
by	O
adding	B-Process
dipole	I-Process
contributions	I-Process
for	O
every	O
nearby	O
charge	O
that	O
hopped	O
during	O
the	O
previous	O
iteration	O
.	O
Full	O
updates	O
of	O
the	O
interaction	B-Process
potential	I-Process
are	O
only	O
required	O
for	O
the	O
grid	O
points	O
that	O
are	O
related	O
to	O
charges	O
that	O
hopped	O
during	O
the	O
last	O
iteration	O
.	O
Accumulative	O
rounding	O
errors	O
that	O
arise	O
due	O
to	O
repetitive	O
addition	O
and	O
subtraction	O
are	O
solve	O
this	O
by	O
rounding	O
all	O
interaction	O
potentials	O
to	O
a	O
uniformly	O
spaced	O
range	O
of	O
floating	O
point	O
numbers	O
.	O

The	O
need	O
to	O
represent	B-Task
scale	I-Task
interactions	I-Task
in	O
weather	B-Process
and	I-Process
climate	I-Process
prediction	I-Process
models	I-Process
has	O
,	O
for	O
many	O
decades	O
,	O
motivated	O
research	O
into	O
the	O
use	O
of	O
adaptive	B-Material
meshes	I-Material
[	O
3,34,38	O
]	O
.	O
R-adaptivity	B-Process
–	O
mesh	B-Material
redistribution	O
–	O
involves	O
deforming	B-Process
a	I-Process
mesh	I-Process
in	O
order	O
to	O
vary	O
local	O
resolution	O
and	O
was	O
first	O
considered	O
for	O
atmospheric	B-Process
modelling	I-Process
more	O
than	O
twenty	O
years	O
ago	O
by	O
Dietachmayer	O
and	O
Droegemeier	O
[	O
14	O
]	O
.	O
It	O
is	O
an	O
attractive	O
form	O
of	O
adaptivity	B-Process
since	O
it	O
does	O
not	O
involve	O
altering	B-Process
the	I-Process
mesh	I-Process
connectivity	I-Process
,	O
does	O
not	O
create	O
load	O
balancing	O
problems	O
because	O
points	O
are	O
never	O
created	O
or	O
destroyed	O
,	O
does	O
not	O
require	O
mapping	B-Process
of	I-Process
solutions	I-Process
between	I-Process
meshes	I-Process
[	O
26	O
]	O
,	O
does	O
not	O
lead	O
to	O
sudden	O
changes	O
in	O
resolution	O
and	O
can	O
be	O
retro-fitted	O
into	O
existing	O
models	O
.	O
Variational	B-Process
methods	I-Process
exist	O
which	O
attempt	O
to	O
control	B-Task
resolution	I-Task
in	I-Task
different	I-Task
directions	I-Task
for	I-Task
r-adaptive	I-Task
meshes	I-Task
(	O
e.g.	O
[	O
23,25	O
])	O
.	O
Alternatively	O
,	O
the	O
solution	O
of	O
the	O
Monge	B-Process
–	I-Process
Ampère	I-Process
equation	I-Process
to	O
generate	O
an	O
optimally	B-Material
transported	I-Material
(	I-Material
OT	I-Material
)	I-Material
mesh	I-Material
based	O
on	O
a	O
scalar	B-Process
valued	I-Process
monitor	I-Process
function	I-Process
is	O
a	O
useful	O
form	O
of	O
r-adaptive	B-Process
mesh	I-Process
generation	I-Process
because	O
it	O
generates	O
a	O
mesh	O
equidistributed	O
with	O
respect	O
to	O
a	O
monitor	B-Process
function	I-Process
and	O
does	O
not	O
lead	O
to	O
mesh	B-Process
tangling	I-Process
[	O
7	O
]	O
.	O
We	O
will	O
see	O
that	O
the	O
optimal	B-Task
transport	I-Task
problem	I-Task
on	I-Task
the	I-Task
sphere	I-Task
leads	O
to	O
a	O
slightly	O
different	O
equation	O
of	O
Monge	B-Process
–	I-Process
Ampère	I-Process
type	O
,	O
which	O
has	O
not	O
before	O
been	O
solved	O
numerically	O
on	O
the	O
surface	O
of	O
a	O
sphere	B-Material
,	O
which	O
would	O
be	O
necessary	O
for	O
weather	B-Task
and	I-Task
climate	I-Task
prediction	I-Task
using	O
r-adaptivity	B-Process
.	O

The	O
four	O
bounding	B-Material
PCM	I-Material
wastes	I-Material
,	O
given	O
in	O
Table	O
1	O
,	O
were	O
simulated	O
using	O
the	O
most	O
appropriate	O
materials	O
and	O
geometries	O
.	O
“	B-Material
Mock	I-Material
up	I-Material
”	I-Material
PCM	I-Material
drums	I-Material
were	O
assembled	O
using	O
the	O
following	O
components	O
:	O
PCM	O
drums	O
were	O
simulated	O
using	O
mild	B-Material
steel	I-Material
paint	I-Material
cans	I-Material
and	I-Material
lids	I-Material
(	O
Fenton	O
Packaging	O
Ltd.	O
)	O
;	O
PVC	B-Material
bags	I-Material
were	O
replicated	O
using	O
identical	B-Material
PVC	I-Material
sheeting	I-Material
(	O
Romar	O
Workwear	O
Ltd.	O
)	O
;	O
the	O
metallic	B-Material
waste	I-Material
was	O
simulated	O
using	O
commercial	B-Material
grade	I-Material
18	I-Material
/	I-Material
8	I-Material
stainless	I-Material
steel	I-Material
,	O
aluminium	B-Material
and	O
copper	B-Material
(	O
Avus	O
Metals	O
&	O
Plastics	O
Ltd.	O
)	O
,	O
and	O
lead	B-Material
shot	I-Material
(	O
Aldrich	O
)	O
;	O
the	O
inorganic	B-Material
waste	I-Material
was	O
simulated	O
using	O
waste	B-Material
Pyrex	I-Material
labware	I-Material
,	O
crushed	O
masonry	B-Material
,	O
concrete	B-Material
and	O
window	B-Material
glass	I-Material
;	O
CeO2	B-Material
(	O
from	O
Acros	O
Organics	O
,	O
>	O
99.9	O
%	O
;	O
dried	O
15h	O
at	O
600	O
°	O
C	O
)	O
was	O
used	O
as	O
a	O
PuO2	B-Material
surrogate	I-Material
.	O
Commercially	O
available	O
ground	O
,	O
granulated	O
blast-furnace	B-Material
slag	I-Material
“	I-Material
Calumite	I-Material
”	I-Material
was	O
used	O
as	O
an	O
additive	O
[	O
27	O
]	O
.	O
The	O
analysed	O
chemical	O
composition	O
is	O
given	O
in	O
Table	O
3	O
.	O
Calumite	O
is	O
a	O
powdered	B-Material
material	I-Material
,	O
with	O
a	O
typical	O
particle	B-Material
size	O
distribution	O
between	O
limits	O
of	O
ca	O
.	O
40	O
to	O
ca	O
.	O
400μm	O
.	O

There	O
is	O
still	O
some	O
debate	O
about	O
the	O
crystal	B-Material
structure	O
and	O
composition	O
of	O
the	O
fine	B-Material
oxides	I-Material
found	O
in	O
ODS	B-Material
steels	I-Material
and	O
a	O
number	O
of	O
different	O
phases	O
have	O
been	O
both	O
proposed	O
and	O
identified	O
.	O
A	O
complete	B-Task
characterisation	I-Task
of	I-Task
the	I-Task
oxide	I-Task
particles	I-Task
,	O
including	O
crystal	B-Material
structure	O
and	O
composition	O
,	O
is	O
needed	O
as	O
different	O
phases	O
and	O
chemical	O
variants	O
of	O
a	O
single	O
structure	O
have	O
been	O
shown	O
to	O
respond	O
differently	O
to	O
high	O
temperatures	O
and	O
irradiation	B-Process
.	O
Ribis	O
and	O
de	O
Carlan	O
[	O
6	O
]	O
have	O
studied	O
the	O
coarsening	O
characteristics	O
of	O
Y2O3	B-Material
and	O
Y2Ti2O7	B-Material
oxides	I-Material
at	O
high	O
temperatures	O
.	O
They	O
show	O
that	O
the	O
increase	O
in	O
particle	B-Material
size	O
is	O
greater	O
for	O
the	O
non-Ti	O
containing	O
phase	O
.	O
Similarly	O
,	O
Ratti	O
et	O
al	O
.	O
[	O
9	O
]	O
,	O
although	O
they	O
do	O
not	O
allude	O
to	O
specific	O
oxide	O
phases	O
,	O
have	O
shown	O
that	O
small	O
Ti	B-Material
additions	O
to	O
an	O
18	O
%	O
Cr	O
ODS	O
alloy	O
dramatically	O
reduces	O
the	O
coarsening	O
rates	O
of	O
dispersoids	O
when	O
compared	O
to	O
an	O
equivalent	O
alloy	O
without	O
titanium	O
.	O
For	O
example	O
,	O
Ribis	O
indicates	O
that	O
coarsening	O
rates	O
may	O
be	O
controlled	O
by	O
interfacial	O
energy	O
between	O
the	O
secondary	O
phase	O
particles	O
and	O
the	O
matrix	O
;	O
he	O
points	O
out	O
that	O
the	O
resistance	O
to	O
coarsening	O
observed	O
in	O
the	O
Y	O
,	O
Ti	O
,	O
O	O
system	O
is	O
probably	O
the	O
result	O
of	O
a	O
very	O
low	O
interface	O
energy	O
and	O
this	O
would	O
differ	O
from	O
one	O
phase	O
to	O
another	O
.	O
Whittle	O
et	O
al	O
.	O
[	O
10	O
]	O
have	O
shown	O
that	O
pyrochlore	O
and	O
structures	O
closely	O
related	O
to	O
the	O
pyrochlore	O
structure	O
respond	O
in	O
different	O
ways	O
to	O
irradiation	O
.	O
They	O
revealed	O
that	O
oxide	B-Material
structure	O
and	O
variations	O
in	O
composition	O
can	O
affect	O
their	O
ability	O
to	O
withstand	O
and	O
recover	O
from	O
irradiation	O
induced	O
damage	O
.	O

Zirconium	B-Material
alloys	I-Material
are	O
used	O
as	O
fuel	O
cladding	O
in	O
pressurised	O
and	O
boiling	O
water	O
nuclear	B-Material
reactors	I-Material
.	O
As	O
such	O
these	O
materials	O
are	O
exposed	O
to	O
a	O
large	O
number	O
of	O
environmental	O
factors	O
that	O
will	O
promote	O
degradation	B-Process
mechanisms	I-Process
such	O
as	O
oxidation	B-Process
.	O
At	O
high	O
burn-ups	O
,	O
i.e.	O
extended	O
service	O
life	O
,	O
oxidation	O
and	O
the	O
associated	O
hydrogen	B-Process
pick-up	I-Process
can	O
be	O
a	O
limiting	O
factor	O
in	O
terms	O
of	O
fuel	B-Material
efficiency	O
and	O
safety	O
.	O
The	O
oxidation	B-Process
kinetics	O
for	O
many	O
zirconium	B-Material
alloys	I-Material
are	O
cyclical	O
,	O
demonstrating	O
a	O
series	O
of	O
approximately	O
cubic	O
kinetic	O
curves	O
separated	O
by	O
transitions	O
[	O
1	O
–	O
5	O
]	O
.	O
These	O
transitions	O
are	O
typified	O
by	O
a	O
breakdown	O
in	O
the	O
protective	O
character	O
of	O
the	O
oxide	B-Material
and	O
are	O
potentially	O
linked	O
to	O
a	O
number	O
of	O
mechanical	O
issues	O
.	O
Understanding	B-Task
how	I-Task
these	I-Task
issues	I-Task
influence	I-Task
oxidation	I-Task
is	O
a	O
key	O
to	O
developing	B-Task
a	I-Task
full	I-Task
mechanistic	I-Task
understanding	I-Task
of	I-Task
the	I-Task
corrosion	I-Task
process	I-Task
.	O

The	O
formulation	O
in	O
Table	O
1	O
was	O
derived	O
by	O
an	O
empirical	O
approach	O
and	O
led	O
to	O
a	O
non-classical	B-Material
glass	I-Material
matrix	I-Material
.	O
Carter	O
et	O
al	O
.	O
[	O
3	O
]	O
and	O
Zhang	O
et	O
al	O
.	O
[	O
4	O
]	O
took	O
a	O
more	O
systematic	O
approach	O
to	O
such	O
glass-ceramic	B-Material
wasteforms	I-Material
.	O
These	O
wasteforms	O
were	O
targeted	O
at	O
Hanford	B-Material
K-basin	I-Material
sludges	I-Material
and	O
the	O
immobilisation	B-Task
of	I-Task
the	I-Task
primary	I-Task
waste	I-Task
stream	I-Task
from	I-Task
production	I-Task
of	I-Task
molybdenum-99	I-Task
at	O
the	O
Australian	O
Nuclear	O
Science	O
and	O
Technology	O
Organisation	O
site	O
in	O
Sydney	O
respectively	O
.	O
In	O
the	O
work	O
of	O
Carter	O
et	O
al.	O
and	O
Zhang	O
et	O
al.	O
the	O
intended	O
crystalline	B-Material
phase	O
was	O
the	O
closely	O
related	O
titanate	B-Material
pyrochlore	I-Material
,	O
CaUTi2O7	B-Material
.	O
The	O
glass	B-Material
matrix	I-Material
was	O
formulated	O
such	O
that	O
the	O
trivalent	O
species	O
in	O
the	O
glass	B-Material
network	I-Material
,	O
boron	B-Material
and	O
aluminium	B-Material
,	O
were	O
charge	O
compensated	O
on	O
a	O
molar	O
basis	O
by	O
sodium	B-Material
.	O
The	O
stoichiometric	O
composition	O
of	O
the	O
glass	B-Material
in	O
this	O
wasteform	O
was	O
Na2AlBSi6O16	B-Material
.	O
This	O
glass	B-Material
provides	O
a	O
method	O
by	O
which	O
the	O
glass	B-Material
composition	I-Material
can	O
be	O
varied	O
systematically	O
.	O
Given	O
that	O
the	O
initial	O
observations	O
inferred	O
an	O
important	O
role	O
played	O
by	O
alumina	B-Material
,	O
it	O
was	O
decided	O
to	O
prepare	O
a	O
suite	O
of	O
zirconolite	B-Material
glass-ceramics	I-Material
in	O
which	O
the	O
glass	B-Material
matrix	I-Material
was	O
defined	O
by	O
Na2Al1	B-Material
+	I-Material
xB1	I-Material
–	I-Material
xSi6O16	I-Material
to	O
investigate	B-Task
the	I-Task
role	I-Task
played	I-Task
by	I-Task
glass	I-Task
composition	I-Task
in	I-Task
controlling	I-Task
crystalline	I-Task
phase	I-Task
stability	I-Task
.	O
The	O
x	O
=	O
1	O
end	O
member	O
gives	O
the	O
mineral	B-Material
albite	I-Material
,	O
NaAlSi3O8	B-Material
.	O
The	O
melting	O
point	O
of	O
albite	B-Material
is	O
1120	O
°	O
C	O
[	O
5	O
]	O
and	O
the	O
composition	O
cools	O
to	O
a	O
glass	B-Material
at	O
the	O
cooling	O
rates	O
that	O
occur	O
during	O
a	O
HIP	O
cycle	O
.	O
From	O
the	O
available	O
phase	O
diagrams	O
,	O
[	O
6	O
]	O
no	O
boron	B-Material
analogue	O
for	O
albite	B-Material
was	O
shown	O
,	O
and	O
the	O
liquidus	O
estimated	O
from	O
the	O
relevant	O
phase	O
diagram	O
is	O
1100	O
–	O
1200	O
°	O
C	O
.	O
No	O
phase	O
diagrams	O
for	O
the	O
quaternary	O
system	O
Na2O	B-Material
–	I-Material
Al2O3	I-Material
–	I-Material
B2O3	I-Material
–	I-Material
SiO2	I-Material
could	O
be	O
found	O
.	O

Structural	O
properties	O
are	O
well	O
reproduced	O
by	O
all	O
models	O
(	O
Table	O
2	O
)	O
,	O
but	O
the	O
significant	O
improvement	O
of	O
our	O
potential	O
stands	O
in	O
the	O
elastic	O
constants	O
which	O
relate	O
to	O
how	O
the	O
system	O
responds	O
to	O
stress	O
.	O
Indeed	O
,	O
structure	O
and	O
elasticity	O
are	O
important	O
parameters	O
for	O
elucidating	B-Task
grain	I-Task
boundary	I-Task
stability	I-Task
.	O
All	O
potential	O
models	O
correctly	O
predict	B-Task
the	I-Task
relative	I-Task
stability	I-Task
of	I-Task
the	I-Task
defect	I-Task
energies	I-Task
.	O
The	O
Morelon	B-Process
potential	I-Process
model	I-Process
performed	O
best	O
as	O
it	O
was	O
specifically	O
derived	O
to	O
replicate	B-Task
defect	I-Task
formation	I-Task
energies	I-Task
,	O
but	O
it	O
largely	O
underestimates	O
the	O
bulk	O
modulus	O
.	O
The	O
energies	O
calculated	O
with	O
the	O
Morl	B-Process
and	I-Process
the	I-Process
Arima	I-Process
potential	I-Process
models	I-Process
are	O
overestimated	O
;	O
this	O
is	O
a	O
known	O
disadvantage	O
of	O
using	O
rigid	B-Process
ion	I-Process
models	I-Process
as	O
the	O
ionic	O
polarisability	O
is	O
not	O
taken	O
into	O
account	O
.	O
For	O
completeness	O
,	O
we	O
report	O
two	O
shell	B-Process
models	I-Process
with	O
the	O
best	O
results	O
given	O
by	O
the	O
Catlow	B-Process
potential	I-Process
model	I-Process
.	O
The	O
Morl	B-Process
,	I-Process
along	I-Process
with	I-Process
the	I-Process
Grimes	I-Process
shell	I-Process
potential	I-Process
model	I-Process
,	O
accurately	O
reproduce	B-Task
the	I-Task
activation	I-Task
energy	I-Task
of	I-Task
oxygen	I-Task
migration	I-Task
(	O
the	O
migration	B-Process
path	I-Process
was	O
the	O
lowest	O
energy	O
and	O
most	O
favourable	O
diffusion	B-Process
mechanism	I-Process
observed	O
in	O
bulk	O
UO2	B-Material
[	O
1	O
])	O
.	O
The	O
major	O
deficiency	O
of	O
the	O
Morl	B-Process
potential	I-Process
is	O
that	O
the	O
cation	B-Material
defect	O
energies	O
are	O
high	O
,	O
and	O
hence	O
the	O
number	O
of	O
cation	O
defects	O
will	O
be	O
underestimated	O
.	O
However	O
,	O
this	O
should	O
not	O
be	O
an	O
issue	O
unless	O
this	O
model	O
was	O
applied	O
to	O
processes	O
such	O
as	O
grain	B-Process
growth	I-Process
where	O
cation	O
mobility	O
will	O
contribute	O
.	O

Hydrides	B-Material
,	O
once	O
precipitated	O
in	O
zirconium	B-Material
,	O
degrade	O
the	O
mechanical	O
properties	O
of	O
a	O
component	O
,	O
leading	O
to	O
reductions	O
in	O
tensile	O
strength	O
,	O
ductility	O
and	O
fracture	O
toughness	O
[	O
35	O
–	O
40	O
]	O
.	O
These	O
changes	O
can	O
ultimately	O
compromise	O
the	O
integrity	O
of	O
cladding	B-Process
during	O
normal	O
operating	O
life	O
,	O
accident	O
conditions	O
and	O
fuel	B-Material
storage	O
[	O
13	O
]	O
.	O
As	O
well	O
as	O
the	O
degradation	O
of	O
mechanical	O
properties	O
,	O
the	O
presence	O
of	O
hydrides	B-Material
can	O
also	O
affect	O
phenomena	O
like	O
pellet	B-Process
cladding	I-Process
mechanical	I-Process
interaction	I-Process
(	O
PCMI	B-Process
)	O
;	O
or	O
introduce	O
mechanisms	O
for	O
failure	O
,	O
such	O
as	O
delayed	B-Process
hydride	I-Process
cracking	I-Process
(	O
DHC	B-Process
)	O
.	O
The	O
former	O
mechanism	O
is	O
the	O
product	O
of	O
thermal	B-Process
expansion	I-Process
in	O
fuel	B-Material
pellets	I-Material
introducing	O
stresses	O
into	O
the	O
cladding	B-Process
,	O
which	O
may	O
then	O
lead	O
to	O
the	O
formation	O
of	O
cracks	O
in	O
areas	O
made	O
brittle	O
by	O
large	O
hydride	B-Material
concentrations	O
[	O
13	O
]	O
.	O
The	O
latter	O
mechanism	O
,	O
DHC	B-Process
,	O
is	O
a	O
sub-critical	O
,	O
time	O
dependent	O
cracking	B-Process
phenomenon	I-Process
that	O
requires	O
long	O
range	O
hydrogen	B-Material
diffusion	O
for	O
repeated	O
local	B-Task
hydride	I-Task
growth	I-Task
and	O
fracture	O
at	O
a	O
hydrostatic	B-Process
tensile	I-Process
stress	I-Process
raiser	I-Process
[	O
5,41,42	O
]	O
.	O
The	O
process	O
occurs	O
over	O
an	O
extended	O
period	O
of	O
time	O
under	O
a	O
continuously	O
applied	O
load	O
that	O
is	O
below	O
the	O
yield	O
stress	O
of	O
the	O
material	O
[	O
5,41,42	O
]	O
.	O

Uranium	B-Material
carbide	I-Material
was	O
traditionally	O
used	O
as	O
fuel	B-Material
kernel	I-Material
for	O
the	O
US	O
version	O
of	O
pebble	B-Material
bed	I-Material
reactors	I-Material
as	O
opposed	O
to	O
the	O
German	O
version	O
based	O
on	O
uranium	B-Material
dioxide	I-Material
.	O
For	O
the	O
Generation	B-Material
IV	I-Material
nuclear	I-Material
systems	I-Material
,	O
mixed	B-Material
uranium	I-Material
–	I-Material
plutonium	I-Material
carbides	I-Material
(	B-Material
U	I-Material
,	I-Material
Pu	I-Material
)	I-Material
C	I-Material
constitute	O
the	O
primary	O
option	O
for	O
the	O
gas	B-Material
fast	I-Material
reactors	I-Material
(	O
GFR	B-Material
)	O
and	O
UCO	B-Material
is	O
the	O
first	O
candidate	O
for	O
the	O
very	B-Material
high	I-Material
temperature	I-Material
reactor	I-Material
(	O
VHTR	B-Material
)	O
.	O
In	O
the	O
former	O
case	O
the	O
fuel	B-Material
high	O
actinide	B-Material
density	O
and	O
thermal	O
conductivity	O
are	O
exploited	O
in	O
view	O
of	O
high	O
burnup	B-Process
performance	O
.	O
In	O
the	O
latter	O
,	O
UCO	B-Material
is	O
a	O
good	O
compromise	O
between	O
oxides	B-Material
and	O
carbides	B-Material
both	O
in	O
terms	O
of	O
thermal	O
conductivity	O
and	O
fissile	O
density	O
.	O
However	O
,	O
in	O
the	O
American	O
VHTR	B-Material
design	O
,	O
the	O
fuel	B-Material
is	O
a	O
3:1	O
ratio	O
of	O
UO2	B-Material
:	O
UC2	B-Material
for	O
one	O
essential	O
reason	O
,	O
well	O
explained	O
by	O
Olander	O
[	O
2	O
]	O
in	O
a	O
recent	O
publication	O
.	O
During	O
burnup	B-Process
,	O
pure	O
UO2	B-Material
fuel	I-Material
tends	O
to	O
oxidize	O
to	O
UO2	B-Material
+	I-Material
x	I-Material
.	O
UO2	O
+	O
x	O
reacts	O
with	O
the	O
pyrocarbon	B-Material
coating	I-Material
layer	I-Material
according	O
to	O
the	O
equilibrium	O
:(	O
1	O
)	O
UO2	B-Material
+	I-Material
x	I-Material
+	O
xC	B-Material
→	O
UO2	B-Material
+	O
xCO	O

The	O
Magnox	B-Material
reactors	I-Material
represent	O
the	O
first	O
generation	O
of	O
gas-cooled	B-Material
reactors	I-Material
in	O
the	O
UK	O
that	O
used	O
carbon	B-Material
dioxide	I-Material
(	O
CO2	B-Material
)	O
as	O
the	O
primary	O
coolant	B-Material
and	O
a	O
honeycomb	B-Material
network	I-Material
of	I-Material
graphite	I-Material
bricks	I-Material
to	O
provide	O
neutron	B-Process
moderation	I-Process
.	O
During	O
reactor	B-Material
operation	O
significant	O
amounts	O
of	O
carbon	B-Material
monoxide	I-Material
(	O
CO	B-Material
)	O
was	O
produced	O
from	O
the	O
CO2	B-Material
coolant	I-Material
.	O
This	O
CO	B-Material
in	O
turn	O
can	O
be	O
radiolytically	B-Process
polymerised	I-Process
to	O
form	B-Task
a	I-Task
carbonaceous	I-Task
deposit	I-Task
on	I-Task
free	I-Task
surfaces	I-Task
[	O
12	O
]	O
.	O
This	O
non-graphitic	B-Material
carbon	I-Material
deposit	I-Material
is	O
significantly	O
more	O
chemically	O
reactive	O
to	O
air	B-Material
than	O
the	O
underlying	O
graphite	B-Material
[	O
12,13	O
]	O
.	O
During	O
the	O
lifetime	O
of	O
some	O
Magnox	B-Material
reactors	I-Material
,	O
small	O
quantities	O
of	O
methane	B-Material
gas	I-Material
were	O
injected	O
into	O
the	O
coolant	B-Material
gas	I-Material
to	O
inhibit	B-Task
weight	I-Task
loss	I-Task
of	I-Task
the	I-Task
graphite	I-Task
core	I-Task
due	I-Task
to	I-Task
radiolytic	I-Task
oxidation	I-Task
[	O
14	O
]	O
.	O
Methane	B-Material
(	O
CH4	B-Material
)	O
is	O
a	O
precursor	O
for	O
carbonaceous	B-Material
deposits	I-Material
that	O
form	O
a	O
sacrificial	O
layer	O
protecting	O
the	O
underlying	O
graphite	B-Material
from	O
excessive	B-Process
weight	I-Process
loss	I-Process
[	O
15	O
]	O
and	O
reduction	B-Process
in	I-Process
mechanical	I-Process
strength	I-Process
[	O
16	O
]	O
.	O
It	O
is	O
assumed	O
nitrogen	B-Material
incorporation	O
during	O
deposit	O
formation	O
is	O
the	O
subsequent	O
production	O
route	O
for	O
the	O
high	O
14C	O
levels	O
observed	O
.	O

An	O
essential	O
part	O
of	O
nuclear	B-Task
reactor	I-Task
analysis	I-Task
is	O
the	O
prediction	B-Task
of	I-Task
the	I-Task
three-dimensional	I-Task
space-time	I-Task
kinetics	I-Task
of	I-Task
neutrons	I-Task
in	O
a	O
relatively	O
large	O
,	O
finite	O
,	O
heterogeneous	O
,	O
three-dimensional	O
reactor	B-Material
core	I-Material
.	O
In	O
a	O
majority	O
of	O
safety	B-Task
analyses	I-Task
the	O
prediction	B-Task
of	I-Task
reactor	I-Task
physics	I-Task
responses	I-Task
is	O
performed	O
using	O
neutron	B-Material
diffusion	O
theory	O
applied	O
to	O
three-dimensional	O
systems	O
,	O
with	O
inputs	O
usually	O
derived	O
from	O
deterministic	B-Process
neutron	I-Process
transport	I-Process
solutions	I-Process
of	O
two-dimensional	B-Process
lattice	I-Process
geometries	I-Process
.	O
There	O
has	O
been	O
increased	O
activity	O
related	O
to	O
uncertainty	O
and	O
sensitivity	O
in	O
reactor	B-Task
physics	I-Task
calculations	I-Task
,	O
and	O
the	O
Organization	O
for	O
Economic	O
Cooperation	O
and	O
Development	O
–	O
Nuclear	O
Energy	O
Agency	O
(	O
OECD-NEA	O
)	O
has	O
sponsored	O
an	O
ongoing	O
benchmark	O
entitled	O
“	O
Uncertainty	B-Material
Analysis	I-Material
in	I-Material
Modelling	I-Material
”	O
(	O
UAM	B-Material
)	O
related	O
to	O
these	O
efforts	O
.	O
The	O
goal	O
of	O
this	O
work	O
is	O
to	O
offer	O
a	O
strategy	B-Task
for	I-Task
computing	I-Task
lattice	I-Task
sensitivities	I-Task
using	O
the	O
DRAGON	B-Material
lattice	I-Material
code	I-Material
and	O
WIMS-D4	B-Material
multi-group	I-Material
library	I-Material
.	O
Results	O
are	O
presented	O
with	O
comparison	O
to	O
those	O
from	O
TSUNAMI	B-Process
,	O
developed	O
by	O
Oak	O
Ridge	O
National	O
Laboratories	O
.	O

The	O
pipes	B-Material
under	O
pressure	O
in	O
the	O
RCS	B-Material
or	O
connected	O
to	O
RCS	O
are	O
usually	O
made	O
of	O
austenitic	B-Material
or	I-Material
austenitic	I-Material
&	I-Material
ferritic	I-Material
stainless	I-Material
steel	I-Material
.	O
Most	O
connections	O
are	O
welded	O
.	O
The	O
pipes	B-Material
may	O
be	O
exposed	O
to	O
various	O
degradation	O
phenomena	O
(	O
diverse	O
hazards	O
,	O
mechanical	O
fatigue	O
,	O
thermal	O
fatigue	O
,	O
stress	O
corrosion	O
,	O
etc.	O
)	O
.	O
Event	B-Task
screening	I-Task
in	O
the	O
databases	O
showed	O
a	O
total	O
of	O
116	O
events	O
(	O
33	O
related	O
to	O
cracks	O
and	O
83	O
to	O
leaks	O
)	O
.	O
Three	O
main	O
causes	O
for	O
failure	O
were	O
identified	O
,	O
namely	O
,	O
fatigue	O
,	O
corrosion	O
and	O
the	O
presence	O
of	O
manufacturing	O
defects	O
.	O
Human	O
factor	O
induced	O
defects	O
proved	O
to	O
have	O
little	O
impact	O
–	O
less	O
than	O
10	O
%	O
of	O
the	O
cases	O
could	O
be	O
attributed	O
to	O
operation	O
errors	O
.	O
Fatigue	O
was	O
found	O
being	O
induced	O
by	O
several	O
factors	O
:	O
excessive	O
vibration	O
,	O
pressure	O
shocks	O
and	O
the	O
thermal	O
regime	O
of	O
operating	O
the	O
pipe	B-Material
,	O
as	O
well	O
as	O
by	O
combinations	O
of	O
these	O
factors	O
.	O
Corrosion	O
was	O
induced	O
,	O
in	O
most	O
of	O
the	O
cases	O
,	O
by	O
a	O
non-appropriate	O
choice	O
of	O
alloys	B-Material
while	O
not	O
taking	O
into	O
account	O
the	O
chemical	O
parameters	O
of	O
the	O
fluid	B-Material
inside	O
pipes	B-Material
.	O
Manufacturing	O
defects	O
mostly	O
dealt	O
with	O
welding	O
related	O
problems	O
and	O
deviation	O
from	O
the	O
design	O
documentation	O
during	O
post-weld	O
heat	O
treatment	O
.	O

Historically	O
,	O
the	O
interest	O
in	O
accurate	O
measurement	O
of	O
DNI	O
started	O
decades	O
ago	O
.	O
Early	O
studies	O
(	O
e.g.	O
,	O
Linke	O
,	O
1931	O
;	O
Linke	O
and	O
Ulmitz	O
,	O
1940	O
)	O
identified	O
the	O
difficulty	O
of	O
separating	B-Task
the	I-Task
measurement	I-Task
of	I-Task
DNI	I-Task
from	I-Task
that	I-Task
of	I-Task
the	I-Task
diffuse	I-Task
irradiance	I-Task
in	I-Task
the	I-Task
immediate	I-Task
vicinity	I-Task
of	I-Task
the	I-Task
sun	I-Task
,	O
hereafter	O
referred	O
to	O
as	O
circumsolar	O
irradiance	O
.	O
Pastiels	O
(	O
1959	O
)	O
conducted	O
a	O
detailed	O
study	B-Task
of	I-Task
the	I-Task
geometry	I-Task
of	I-Task
pyrheliometers	I-Task
,	I-Task
and	I-Task
how	I-Task
that	I-Task
geometry	I-Task
interacted	I-Task
with	I-Task
circumsolar	I-Task
radiance	I-Task
,	O
using	O
simplified	O
representations	O
of	O
the	O
latter	O
.	O
Various	O
communications	O
were	O
then	O
presented	O
at	O
a	O
WMO	O
Task	O
Group	O
meeting	O
held	O
in	O
Belgium	O
in	O
1966	O
(	O
WMO	O
,	O
1967	O
)	O
to	O
improve	B-Task
the	I-Task
accuracy	I-Task
of	I-Task
pyrheliometric	I-Task
measurements	I-Task
,	I-Task
including	I-Task
estimates	I-Task
of	I-Task
the	I-Task
circumsolar	I-Task
enhancement	I-Task
.	O
Ångström	O
(	O
1961	O
)	O
and	O
Ångström	O
and	O
Rohde	O
(	O
1966	O
)	O
later	O
contributed	O
to	O
the	O
same	O
topic	O
,	O
followed	O
years	O
later	O
by	O
Major	O
(	O
1973	O
,	O
1980	O
)	O
.	O
The	O
whole	O
issue	O
of	O
instrument	O
geometry	O
vs.	O
circumsolar	O
irradiance	O
was	O
complex	O
and	O
confusing	O
at	O
the	O
time	O
because	O
different	O
makes	O
and	O
models	O
of	O
instruments	O
had	O
differing	O
geometries	O
.	O
This	O
was	O
considerably	O
simplified	O
after	O
WMO	O
issued	O
guidelines	O
about	O
the	O
recommended	O
geometry	O
of	O
pyrheliometers	B-Material
,	O
which	O
led	O
to	O
a	O
relatively	O
“	O
standard	O
”	O
geometry	O
used	O
in	O
all	O
recent	O
instruments	O
.	O
The	O
experimental	O
issues	O
related	O
to	O
the	O
measurement	O
of	O
DNI	O
are	O
discussed	O
in	O
Section	O
3.2	O
.	O

The	O
wind	B-Process
speed	I-Process
and	I-Process
cloud	I-Process
height	I-Process
Markov	I-Process
chains	I-Process
are	O
produced	O
accounting	O
for	O
seasonal	O
variations	O
.	O
A	O
Markov	B-Process
chain	I-Process
is	O
used	O
for	O
each	O
variable	O
representing	O
each	O
of	O
the	O
four	O
seasons	O
,	O
capturing	O
the	O
variability	O
at	O
different	O
times	O
of	O
the	O
year	O
,	O
totalling	O
four	O
chains	O
each	O
.	O
The	O
okta	B-Process
number	I-Process
Markov	I-Process
chains	I-Process
also	O
consider	O
the	O
effect	O
of	O
season	O
,	O
with	O
the	O
inclusion	O
of	O
impacts	O
from	O
pressure	O
and	O
diurnal	O
variation	O
.	O
Eight	O
okta	B-Process
Markov	I-Process
chains	I-Process
are	O
produced	O
that	O
are	O
split	O
by	O
above	O
and	O
below	O
average	O
pressure	O
for	O
each	O
season	O
,	O
and	O
four	O
additional	O
morning	O
okta	O
Markov	O
chains	O
are	O
produced	O
to	O
capture	O
the	O
diurnal	O
variation	O
for	O
okta	O
transitions	O
between	O
00:00	O
and	O
05:00am	O
for	O
each	O
season	O
.	O
The	O
intent	O
is	O
to	O
capture	B-Task
the	I-Task
variation	I-Task
in	I-Task
transition	I-Task
probability	I-Task
that	O
occurs	O
as	O
a	O
result	O
of	O
weather	O
changes	O
due	O
to	O
the	O
presence	O
of	O
solar	O
energy	O
.	O
5am	O
is	O
considered	O
the	O
cut-off	O
because	O
it	O
is	O
a	O
typical	O
sunrise	O
in	O
the	O
summer	O
for	O
the	O
applied	O
study	O
locations	O
.	O
5h	O
represents	O
5	O
okta	O
transitions	O
and	O
is	O
considered	O
an	O
appropriate	O
duration	O
for	O
the	O
slight	O
propensity	O
to	O
shift	O
towards	O
an	O
increased	O
okta	O
to	O
be	O
represented	O
,	O
Fig.	O
8	O
demonstrates	O
the	O
diurnal	O
transition	O
differences	O
.	O
Fig.	O
2	O
visually	O
demonstrates	O
the	O
mean	O
okta	B-Process
Markov	I-Process
chain	I-Process
for	O
the	O
entire	O
year	O
,	O
whilst	O
the	O
effect	O
of	O
season	O
can	O
be	O
seen	O
in	O
Fig.	O
11	O
.	O

In	O
addition	O
,	O
the	O
prediction	B-Task
of	I-Task
solar	I-Task
cell	I-Task
’s	I-Task
temperature	I-Task
is	O
very	O
important	O
for	O
the	O
electrical	O
characterisation	O
of	O
CPV	B-Process
modules	O
.	O
Rodrigo	O
et	O
al	O
.	O
(	O
2014	O
)	O
reviewed	O
various	O
methods	O
for	O
the	O
calculation	B-Task
of	I-Task
the	I-Task
cell	I-Task
temperature	I-Task
in	O
High	B-Process
Concentrator	I-Process
PV	I-Process
(	O
HCPV	B-Process
)	O
modules	O
.	O
The	O
methods	O
were	O
categorised	O
based	O
on	O
:	O
(	O
1	O
)	O
heat	O
sink	O
temperature	O
,	O
(	O
2	O
)	O
electrical	O
parameters	O
and	O
(	O
3	O
)	O
atmospheric	O
parameters	O
.	O
The	O
first	O
two	O
categories	O
are	O
based	O
on	O
direct	O
measurements	O
of	O
CPV	B-Process
modules	O
in	O
indoor	O
or	O
outdoor	O
experimental	O
setups	O
and	O
presented	O
the	O
highest	O
degree	O
of	O
accuracy	O
(	O
Root	O
Mean	O
Square	O
Error	O
(	O
RMSE	O
)	O
1.7	O
–	O
2.5K	O
)	O
.	O
Most	O
of	O
the	O
methods	O
reviewed	O
by	O
Rodrigo	O
et	O
al	O
.	O
(	O
2014	O
)	O
calculate	B-Task
the	I-Task
cell	I-Task
temperature	I-Task
at	O
open-circuit	B-Process
conditions	I-Process
.	O
Methods	O
that	O
predict	O
the	O
cell	O
temperature	O
at	O
maximum	B-Process
power	I-Process
point	I-Process
(	O
MPP	B-Process
)	O
operation	O
offer	O
a	O
more	O
realistic	O
approach	O
since	O
they	O
include	O
the	O
electrical	B-Process
energy	I-Process
generation	I-Process
of	O
the	O
solar	B-Material
cells	I-Material
(	O
i.e.	O
real	O
operating	O
conditions	O
)	O
;	O
Yandt	O
et	O
al	O
.	O
(	O
2012	O
)	O
described	O
a	O
method	O
predicting	B-Task
the	I-Task
cell	I-Task
temperature	I-Task
at	I-Task
MPP	I-Task
based	O
on	O
electrical	O
parameters	O
and	O
Fernández	O
et	O
al	O
.	O
(	O
2014b	O
)	O
based	O
on	O
heat	O
sink	O
temperature	O
with	O
absolute	O
RMSE	O
0.55	O
–	O
1.44K	O
.	O
Fernández	O
et	O
al	O
.	O
(	O
2014a	O
)	O
also	O
proposed	O
an	O
artificial	B-Process
neural	I-Process
network	I-Process
model	I-Process
to	O
estimate	B-Task
the	I-Task
cell	I-Task
temperature	I-Task
based	O
on	O
atmospheric	O
parameters	O
and	O
an	O
open-circuit	B-Process
voltage	I-Process
model	I-Process
based	O
on	O
electrical	O
parameters	O
(	O
Fernandez	O
et	O
al.	O
,	O
2013a	O
)	O
offering	O
good	O
accuracy	O
(	O
RMSE	O
3.2K	O
and	O
2.5K	O
respectively	O
(	O
Rodrigo	O
et	O
al.	O
,	O
2014	O
))	O
.	O
The	O
main	O
disadvantage	O
of	O
the	O
aforementioned	O
methods	O
is	O
that	O
an	O
experimental	O
setup	O
is	O
required	O
to	O
obtain	O
the	O
parameters	O
used	O
for	O
the	O
cell	B-Task
temperature	I-Task
calculation	I-Task
.	O

Our	O
procedure	O
does	O
not	O
address	O
the	O
issue	O
of	O
how	O
parameterizations	B-Process
can	O
vary	O
for	O
different	O
flow	B-Process
types	O
.	O
However	O
,	O
Edeling	O
et	O
al	O
.	O
[	O
9	O
]	O
carried	O
out	O
separate	O
calibrations	O
for	O
a	O
set	O
of	O
13	O
boundary-layer	B-Process
flows	I-Process
.	O
They	O
summarized	O
this	O
information	O
across	O
calibrations	O
by	O
computing	O
Highest	B-Process
Posterior-Density	I-Process
(	O
HPD	B-Process
)	O
intervals	O
,	O
and	O
subsequently	O
represent	O
the	O
total	O
solution	O
uncertainty	O
with	O
a	O
probability-box	B-Material
(	O
p-box	B-Material
)	O
.	O
This	O
p-box	O
represents	O
both	O
parameter	O
variability	O
across	O
flows	B-Process
,	O
and	O
epistemic	O
uncertainty	O
within	O
each	O
calibration	O
.	O
A	O
prediction	O
of	O
a	O
new	O
boundary-layer	B-Process
flow	I-Process
is	O
made	O
with	O
uncertainty	O
bars	O
generated	O
from	O
this	O
uncertainty	O
information	O
,	O
and	O
the	O
resulting	O
error	O
estimate	O
is	O
shown	O
to	O
be	O
consistent	O
with	O
measurement	O
data	O
.	O
This	O
approach	O
is	O
helpful	O
,	O
but	O
it	O
might	O
be	O
extended	O
further	O
by	O
modelling	B-Process
proximity	I-Process
across	I-Process
flows	I-Process
through	O
a	O
distance	O
that	O
would	O
relate	O
to	O
the	O
flow	B-Process
characteristics	O
in	O
order	O
to	O
borrow	O
strength	O
across	O
calibrations	O
instead	O
of	O
splitting	B-Process
the	I-Process
calibrations	I-Process
and	I-Process
then	I-Process
merging	I-Process
the	I-Process
outcomes	I-Process
afterwards	O
.	O
This	O
is	O
a	O
challenging	O
but	O
attractive	O
venue	O
for	O
future	O
research	O
.	O

One	O
of	O
the	O
most	O
important	O
outcomes	O
of	O
the	O
comparative	B-Task
analysis	I-Task
is	O
the	O
fact	O
that	O
in	O
all	O
tested	O
cases	O
the	O
use	O
of	O
FM	B-Process
is	O
associated	O
with	O
a	O
dramatic	O
reduction	O
in	O
computational	O
time	O
when	O
compared	O
with	O
FE	B-Process
,	O
generally	O
being	O
in	O
the	O
order	O
of	O
seconds	O
for	O
FM	B-Process
and	O
in	O
the	O
order	O
of	O
hours	O
for	O
FE	B-Process
.	O
Table	O
1	O
reports	O
the	O
timings	O
of	O
the	O
simulations	O
for	O
both	O
methods	O
.	O
Free	O
expansion	O
is	O
the	O
fastest	O
case	O
,	O
where	O
FM	B-Process
reaches	O
the	O
load-free	O
configuration	O
in	O
just	O
2	O
s	O
,	O
while	O
simulations	B-Process
inside	O
the	O
vessels	B-Material
with	O
the	O
diameter	O
of	O
around	O
30	O
mm	O
take	O
approximately	O
30	O
s	O
.	O
Most	O
of	O
the	O
execution	O
time	O
of	O
the	O
FM	B-Process
deployment	I-Process
algorithm	I-Process
is	O
dedicated	O
to	O
the	O
contact	O
check	O
and	O
calculations	O
of	O
the	O
implications	O
the	O
vessel	B-Material
wall	I-Material
has	O
on	O
the	O
stent	O
structure	O
.	O
Interestingly	O
,	O
in	O
both	O
methods	O
,	O
the	O
highest	O
computational	O
time	O
(	O
i.e.	O
,	O
curved	B-Material
vessels	I-Material
)	O
is	O
not	O
associated	O
with	O
the	O
most	O
complex	O
geometry	O
(	O
i.e.	O
,	O
patient-specific	O
case	O
of	O
aortic	O
dissection	O
)	O
.	O
Another	O
fact	O
worth	O
mentioning	O
is	O
the	O
relation	O
of	O
the	O
computational	O
time	O
to	O
the	O
diameter	O
of	O
the	O
vessel	B-Material
in	O
both	O
methods	O
.	O
While	O
the	O
computational	O
time	O
of	O
FM	B-Process
appeared	O
to	O
be	O
directly	O
related	O
to	O
the	O
diameter	O
of	O
the	O
vessel	B-Material
,	O
no	O
immediate	O
relation	O
was	O
found	O
for	O
the	O
FE	B-Process
simulations	I-Process
.	O
Such	O
outcome	O
is	O
probably	O
related	O
to	O
the	O
simplified	B-Process
contact	I-Process
model	I-Process
used	O
by	O
FM	B-Process
,	O
which	O
makes	O
the	O
stent-graft	B-Process
expansion	I-Process
terminate	O
once	O
the	O
nodes	B-Material
come	O
in	O
contact	O
with	O
the	O
vessel	B-Material
wall	I-Material
.	O
On	O
the	O
contrary	O
,	O
it	O
is	O
well	O
known	O
that	O
the	O
contact	B-Process
algorithm	I-Process
used	O
in	O
the	O
FE	B-Process
analyses	I-Process
increases	O
the	O
computational	O
cost	O
of	O
the	O
simulations	B-Process
.	O

Gas	B-Process
sorption	I-Process
,	I-Process
storage	I-Process
and	I-Process
separation	I-Process
in	O
carbon	B-Material
materials	I-Material
are	O
mainly	O
based	O
on	O
physisorption	B-Process
on	O
the	O
surfaces	O
and	O
particularly	O
depend	O
on	O
the	O
electrostatic	B-Process
and	I-Process
dispersion	I-Process
(	I-Process
i.e.	I-Process
,	I-Process
vdW	I-Process
)	I-Process
interactions	I-Process
.	O
The	O
former	O
can	O
be	O
tuned	O
by	O
introducing	B-Process
charge	I-Process
variations	I-Process
in	I-Process
the	I-Process
material	I-Process
,	O
and	O
the	O
latter	O
by	O
chemical	B-Process
substitution	I-Process
.	O
The	O
strength	O
of	O
the	O
interaction	O
is	O
determined	O
by	O
the	O
surface	O
characteristics	O
of	O
the	O
adsorbent	B-Material
and	O
the	O
properties	O
of	O
targeted	O
adsorbate	B-Material
molecule	I-Material
,	O
including	O
but	O
not	O
limited	O
to	O
the	O
size	O
and	O
shape	O
of	O
the	O
adsorbate	O
molecule	O
along	O
with	O
its	O
polarizability	O
,	O
magnetic	O
susceptibility	O
,	O
permanent	O
dipole	O
moment	O
,	O
and	O
quadrupole	O
moment	O
.	O
Li	O
et	O
al.	O
summarise	O
the	O
adsorption-related	O
physical	O
parameters	O
of	O
many	O
gas	B-Material
or	I-Material
vapour	I-Material
adsorbates	I-Material
,	O
and	O
herein	O
Table	O
1	O
we	O
show	O
a	O
few	O
of	O
those	O
of	O
interest	O
,	O
H2	B-Material
,	O
N2	B-Material
,	O
CO	B-Material
,	O
CO2	B-Material
,	O
CH4	B-Material
,	O
NH3	B-Material
,	O
SO2	B-Material
and	O
H2S	B-Material
[	O
90	O
]	O
.	O
For	O
instance	O
,	O
an	O
adsorbent	B-Material
with	O
a	O
high	O
specific	O
surface	O
area	O
is	O
a	O
good	O
candidate	O
for	O
adsorption	O
of	O
a	O
molecule	B-Material
with	O
high	O
polarizability	O
but	O
no	O
polarity	O
.	O
Adsorbents	B-Material
with	O
highly	O
polarised	O
surfaces	O
are	O
good	O
for	O
adsorbate	B-Material
molecules	I-Material
with	O
a	O
high	O
dipole	O
moment	O
.	O
The	O
adsorbents	B-Material
with	O
high	O
electric	O
field	O
gradient	O
surfaces	O
are	O
found	O
to	O
be	O
ideal	O
for	O
the	O
high	B-Material
quadrupole	I-Material
moment	I-Material
adsorbate	I-Material
molecules	I-Material
[	O
91	O
]	O
.	O
Normally	O
,	O
the	O
binding	O
or	O
adsorption	O
strength	O
with	O
a	O
carbon	O
nanostructure	O
is	O
relatively	O
low	O
for	O
H2	B-Material
and	O
N2	B-Material
;	O
intermediate	O
for	O
CO	B-Material
,	O
CH4	B-Material
and	O
CO2	B-Material
;	O
and	O
relatively	O
high	O
for	O
H2S	B-Material
,	O
NH3	B-Material
and	O
H2O	B-Material
.	O
Thus	O
,	O
surface	B-Process
modifications	I-Process
,	O
such	O
as	O
doping	B-Process
,	O
functionalization	B-Process
and	O
improving	B-Process
the	I-Process
pore	I-Process
structure	I-Process
and	I-Process
specific	I-Process
surface	I-Process
area	I-Process
of	I-Process
nanocarbons	I-Process
,	O
are	O
important	O
to	O
enhance	B-Task
gas	I-Task
adsorption	I-Task
.	O
For	O
this	O
purpose	O
,	O
graphene	B-Material
offers	O
a	O
great	O
scope	O
for	O
tailor-made	O
carbonaceous	B-Material
adsorbents	I-Material
.	O

When	O
dominated	O
by	O
surface	B-Process
shadowing	I-Process
mechanisms	I-Process
,	O
the	O
aggregation	B-Process
of	I-Process
vapor	I-Process
particles	I-Process
onto	I-Process
a	I-Process
surface	I-Process
is	O
a	O
complex	O
,	O
non-local	O
phenomenon	O
.	O
In	O
the	O
literature	O
,	O
there	O
have	O
been	O
many	O
attempts	O
to	O
analyze	B-Task
the	I-Task
growth	I-Task
mechanism	I-Task
by	O
means	O
of	O
pure	O
geometrical	B-Process
considerations	I-Process
;	O
i.e.	O
,	O
by	O
assuming	O
that	O
vapor	B-Material
particles	I-Material
arrive	O
at	O
the	O
film	B-Material
surface	I-Material
along	O
a	O
single	B-Process
angular	I-Process
direction	I-Process
[	O
38,41	O
]	O
.	O
Continuum	B-Process
approaches	I-Process
,	O
which	O
are	O
based	O
on	O
the	O
fact	O
that	O
the	O
geometrical	B-Process
features	I-Process
of	O
the	O
film	B-Material
(	O
i.e.	O
,	O
the	O
nanocolumns	B-Process
)	O
are	O
much	O
larger	O
than	O
the	O
typical	O
size	O
of	O
an	O
atom	B-Material
[	O
42,266,267	O
]	O
,	O
have	O
been	O
also	O
explored	O
.	O
For	O
instance	O
,	O
Poxson	O
et	O
al	O
.	O
[	O
228	O
]	O
developed	O
an	O
analytic	B-Process
model	I-Process
that	O
takes	O
into	O
account	O
geometrical	B-Process
factors	I-Process
as	O
well	O
as	O
surface	B-Process
diffusion	I-Process
.	O
This	O
model	O
accurately	O
predicted	O
the	O
porosity	O
and	O
deposition	O
rate	O
of	O
thin	B-Material
films	I-Material
using	O
a	O
single	O
input	O
parameter	O
related	O
to	O
the	O
cross-sectional	O
area	O
of	O
the	O
nanocolumns	B-Material
,	O
the	O
volume	O
of	O
material	O
and	O
the	O
thickness	O
of	O
the	O
film	B-Material
.	O
Moreover	O
,	O
in	O
Ref	O
.	O
[	O
39	O
]	O
,	O
an	O
analytical	B-Process
semi-empirical	I-Process
model	I-Process
was	O
presented	O
to	O
quantitatively	B-Task
describe	I-Task
the	I-Task
aggregation	I-Task
of	I-Task
columnar	I-Task
structures	I-Task
by	O
means	O
of	O
a	O
single	O
parameter	O
dubbed	O
the	O
fan	O
angle	O
.	O
This	O
material-dependent	O
quantity	O
can	O
be	O
experimentally	O
obtained	O
by	O
performing	O
deposition	O
at	O
normal	O
incidence	O
on	O
an	O
imprinted	O
groove	B-Material
seeded	I-Material
substrate	I-Material
,	O
and	O
then	O
measuring	O
the	O
increase	O
in	O
column	O
diameter	O
with	O
film	B-Material
thickness	O
.	O
This	O
model	O
was	O
tested	O
under	O
various	O
conditions	O
[	O
40	O
]	O
,	O
which	O
returned	O
good	O
results	O
and	O
an	O
accurate	O
prediction	B-Task
of	I-Task
the	I-Task
relation	I-Task
between	I-Task
the	I-Task
incident	I-Task
angle	I-Task
of	I-Task
the	I-Task
deposition	I-Task
flux	I-Task
and	I-Task
the	I-Task
tilt	I-Task
angle	I-Task
of	I-Task
the	I-Task
columns	I-Task
for	O
several	O
materials	O
.	O

A	O
bond	B-Process
failure	I-Process
is	O
thought	O
of	O
as	O
a	O
micro-crack	B-Process
nucleation	I-Process
,	O
specifically	O
as	O
a	O
separation	B-Process
between	I-Process
the	I-Process
adjacent	I-Process
cells	I-Process
in	I-Process
the	I-Process
cellular	I-Process
structure	I-Process
along	I-Process
their	I-Process
common	I-Process
face	I-Process
.	O
Initially	O
,	O
the	O
micro-cracks	B-Material
may	O
be	O
dispersed	O
in	O
the	O
model	O
reflecting	O
the	O
random	O
distribution	O
of	O
pore	B-Material
sizes	O
and	O
the	O
low	O
level	O
of	O
interaction	O
due	O
to	O
force	O
redistribution	O
.	O
Interaction	O
and	O
coalescence	O
may	O
follow	O
as	O
the	O
population	O
of	O
micro-cracks	B-Material
increases	O
.	O
These	O
situations	O
are	O
illustrated	O
in	O
Fig.	O
3.	O
The	O
structure	O
of	O
the	O
failed	B-Material
surface	I-Material
can	O
be	O
represented	O
with	O
a	O
mathematical	B-Process
graph	I-Process
,	O
where	O
graph	O
nodes	O
represent	O
failed	B-Material
faces	I-Material
and	O
graph	O
edges	O
exist	O
between	O
failed	O
faces	O
with	O
common	O
triple	O
line	O
in	O
the	O
cellular	B-Material
structure	I-Material
,	O
i.e.	O
where	O
two	O
micro-cracks	B-Material
formed	O
a	O
continuous	O
larger	O
crack	B-Material
.	O
With	O
reference	O
to	O
Fig.	O
3	O
,	O
each	O
failed	B-Material
face	I-Material
is	O
a	O
graph	O
node	O
and	O
each	O
pair	O
of	O
neighbouring	O
failed	B-Material
faces	I-Material
is	O
a	O
graph	O
edge	O
.	O

Half	B-Material
metallic	I-Material
ferromagnets	I-Material
(	O
HMF	B-Material
)	O
have	O
attracted	O
enormous	O
interest	O
due	O
to	O
their	O
applications	O
in	O
spintronic	B-Task
devices	I-Task
[	O
1	O
]	O
.	O
Dilute	B-Material
magnetic	I-Material
semiconductors	I-Material
(	O
DMSs	B-Material
)	O
are	O
considered	O
to	O
be	O
the	O
best	O
materials	B-Material
to	I-Material
show	I-Material
half	I-Material
metallicity	I-Material
.	O
These	O
materials	O
have	O
two	O
components	O
,	O
one	O
being	O
a	O
semiconducting	B-Material
material	I-Material
with	O
diamagnetic	O
properties	O
while	O
the	O
other	O
is	O
a	O
magnetic	B-Material
dopant	I-Material
such	O
as	O
transition	B-Material
metal	I-Material
having	O
un-paired	B-Material
d	I-Material
electrons	I-Material
[	O
2	O
]	O
.	O
The	O
major	O
advantage	O
of	O
these	O
materials	O
is	O
utilization	B-Process
of	I-Process
electron	I-Process
's	I-Process
spin	I-Process
as	I-Process
information	I-Process
carrier	I-Process
since	O
advanced	O
functionalities	O
in	O
spintronic	B-Task
devices	I-Task
can	O
be	O
viable	O
by	O
the	O
use	O
of	O
spin	O
degree	O
of	O
freedom	O
along	O
with	O
the	O
charge	O
of	O
electrons	B-Material
[	O
3	O
]	O
.	O
The	O
major	O
issue	O
regarding	O
the	O
applicability	O
of	O
these	O
materials	O
is	O
to	O
enhance	B-Task
the	I-Task
Curie	I-Task
temperature	I-Task
above	I-Task
room	I-Task
temperature	I-Task
.	O
That	O
's	O
why	O
the	O
research	O
interest	O
shifted	O
towards	O
large	B-Material
band	I-Material
gap	I-Material
materials	I-Material
.	O
A	O
lot	O
of	O
work	O
has	O
been	O
reported	O
on	O
DMSs	B-Material
with	O
different	O
II	B-Material
–	I-Material
VI	I-Material
and	I-Material
III	I-Material
–	I-Material
V	I-Material
semiconductors	I-Material
as	O
host	B-Material
material	I-Material
such	O
as	O
,	O
ZnS	B-Material
,	O
CdS	B-Material
,	O
GaN	B-Material
,	O
ZnO	B-Material
,	O
ZnSe	B-Material
,	O
ZnTe	B-Material
,	O
TiO2	B-Material
,	O
SnO2	B-Material
[	O
4	O
–	O
12	O
]	O
.	O

It	O
has	O
been	O
known	O
[	O
9,14,18,22	O
]	O
that	O
the	O
fragmentation	B-Process
processes	I-Process
in	O
polyatomic	B-Material
molecules	I-Material
induced	O
by	O
an	O
intense	B-Material
ultrafast	I-Material
laser	I-Material
field	I-Material
can	O
sometimes	O
exhibit	O
sensitive	O
dependence	O
on	O
the	O
instantaneous	O
phase	O
characteristics	O
of	O
the	O
laser	O
field	O
.	O
Depending	O
on	O
the	O
change	O
in	O
sign	O
the	O
chirped	B-Material
laser	I-Material
pulses	I-Material
,	O
fragmentation	B-Task
could	O
be	O
either	O
enhanced	O
or	O
suppressed	O
[	O
14,18,22	O
]	O
.	O
Controlling	O
the	O
outcome	O
of	O
such	O
laser	B-Process
induced	I-Process
molecular	I-Process
fragmentation	I-Process
with	O
chirped	B-Material
femtosecond	I-Material
laser	I-Material
pulses	I-Material
has	O
brought	O
forth	O
a	O
number	O
of	O
experimental	O
and	O
theoretical	O
effects	O
in	O
the	O
recent	O
years	O
.	O
However	O
,	O
efforts	O
are	O
continuing	O
for	O
a	O
specific	O
fragment	B-Task
channel	I-Task
enhancement	I-Task
,	O
which	O
is	O
difficult	O
since	O
it	O
also	O
is	O
a	O
function	O
of	O
the	O
molecular	B-Process
system	I-Process
under	O
study	O
[	O
20,22	O
–	O
24	O
]	O
.	O
Here	O
we	O
report	O
the	O
observation	B-Task
of	I-Task
a	I-Task
coherently	I-Task
enhanced	I-Task
fragmentation	I-Task
pathway	I-Task
of	O
n-propyl	B-Material
benzene	I-Material
,	O
which	O
seems	O
to	O
have	O
such	O
specific	O
fragmentation	B-Material
channel	I-Material
available	O
.	O
We	O
found	O
that	O
for	O
n-propyl	B-Material
benzene	I-Material
,	O
the	O
relative	O
yield	O
of	O
C3H3	B-Material
+	I-Material
is	O
extremely	O
sensitive	O
to	O
the	O
phase	O
of	O
the	O
laser	B-Material
pulse	I-Material
as	O
compared	O
to	O
any	O
of	O
the	O
other	O
possible	O
channels	B-Material
.	O
In	O
fact	O
,	O
there	O
is	O
almost	O
an	O
order	O
of	O
magnitude	O
enhancement	O
in	O
the	O
yield	O
of	O
C3H3	B-Material
+	I-Material
when	O
negatively	B-Material
chirped	I-Material
pulses	I-Material
are	O
used	O
,	O
while	O
there	O
is	O
no	O
effect	O
with	O
the	O
positive	B-Material
chirp	I-Material
.	O
Moreover	O
,	O
the	O
relative	O
yield	O
of	O
all	O
the	O
other	O
heavier	B-Material
fragment	I-Material
ions	I-Material
resulting	O
from	O
interaction	O
of	O
the	O
strong	O
field	O
with	O
the	O
molecule	B-Material
is	O
not	O
sensitive	O
to	O
the	O
sign	O
of	O
the	O
chirp	B-Material
,	O
within	O
the	O
noise	O
level	O
.	O

The	O
vibrational	O
spectra	O
of	O
l-cysteine	B-Material
have	O
been	O
recorded	O
and	O
assigned	O
in	O
both	O
solution	O
[	O
8,9	O
]	O
and	O
the	O
solid	O
state	O
[	O
10	O
–	O
14	O
]	O
.	O
Spectral	B-Process
assignments	I-Process
have	O
been	O
made	O
using	O
empirical	B-Process
force	I-Process
fields	I-Process
[	O
15	O
]	O
,	O
Hartree	B-Process
–	I-Process
Fock	I-Process
calculations	I-Process
[	O
10,16,17	O
]	O
based	O
on	O
the	O
isolated	B-Process
molecule	I-Process
approximation	I-Process
.	O
For	O
systems	O
that	O
exhibit	O
strong	O
intermolecular	O
interactions	O
,	O
this	O
approximation	O
often	O
leads	O
to	O
poor	O
agreement	O
between	O
experiment	O
and	O
theory	O
.	O
A	O
striking	O
example	O
is	O
purine	B-Material
[	O
18	O
]	O
,	O
where	O
a	O
study	B-Task
of	I-Task
the	I-Task
solid	I-Task
state	I-Task
vibrational	I-Task
spectra	I-Task
by	O
isolated	B-Process
molecule	I-Process
and	I-Process
periodic	I-Process
calculations	I-Process
,	O
gave	O
almost	O
quantitative	O
agreement	O
between	O
theory	O
and	O
experiment	O
for	O
the	O
latter	O
,	O
whereas	O
the	O
former	O
gave	O
only	O
modest	O
agreement	O
and	O
was	O
unable	O
to	O
distinguish	O
between	O
the	O
tautomers	B-Material
.	O
In	O
the	O
present	O
case	O
,	O
where	O
the	O
structure	O
consists	O
of	O
ions	B-Material
linked	O
by	O
hydrogen	B-Material
bonds	O
,	O
periodic	B-Process
calculations	I-Process
based	O
on	O
the	O
complete	B-Material
primitive	I-Material
cell	I-Material
are	O
essential	O
[	O
19	O
]	O
.	O
The	O
only	O
work	O
[	O
20	O
]	O
that	O
includes	O
some	O
solid	O
state	O
effects	O
used	O
molecular	B-Process
dynamics	I-Process
but	O
from	O
which	O
it	O
is	O
difficult	O
to	O
extract	O
assignments	O
.	O
The	O
aim	O
of	O
this	O
paper	O
is	O
to	O
provide	B-Task
a	I-Task
complete	I-Task
assignment	I-Task
of	I-Task
the	I-Task
vibrational	I-Task
spectra	I-Task
of	I-Task
l-cysteine	I-Task
in	O
both	O
the	O
orthorhombic	O
and	O
monoclinic	O
forms	O
by	O
the	O
use	O
of	O
a	O
combination	O
of	O
computational	B-Process
and	I-Process
experimental	I-Process
methods	I-Process
.	O

It	O
is	O
critical	O
to	O
the	O
success	O
of	O
the	O
NPD	B-Process
technique	I-Process
that	O
the	O
MOF	B-Material
complex	I-Material
adsorbs	O
a	O
significant	O
amount	O
of	O
D2	B-Material
to	O
boost	O
the	O
observed	O
signal	O
.	O
This	O
technique	O
therefore	O
has	O
disadvantages	O
when	O
studying	O
the	O
binding	B-Process
interaction	I-Process
within	O
MOFs	B-Material
with	O
low	O
uptakes	O
.	O
Furthermore	O
,	O
static	B-Task
crystallographic	I-Task
studies	I-Task
cannot	O
provide	O
insights	O
into	O
the	O
dynamics	O
of	O
the	O
adsorbed	B-Material
gas	I-Material
molecules	I-Material
.	O
Thus	O
,	O
it	O
is	O
very	O
challenging	O
to	O
probe	O
experimentally	O
the	O
H2	B-Process
binding	I-Process
interactions	I-Process
within	O
a	O
porous	O
host	O
system	O
which	O
has	O
very	O
low	O
gas	B-Material
uptake	O
due	O
to	O
the	O
lack	O
of	O
suitable	O
characterisation	B-Process
techniques	I-Process
.	O
We	O
report	O
herein	O
the	O
application	O
of	O
the	O
in	B-Process
situ	I-Process
inelastic	I-Process
neutron	I-Process
scattering	I-Process
(	O
INS	B-Process
)	O
technique	O
to	O
permit	B-Task
direct	I-Task
observation	I-Task
of	I-Task
the	I-Task
dynamics	I-Task
of	I-Task
the	I-Task
binding	I-Task
interactions	I-Task
between	O
adsorbed	B-Material
H2	I-Material
molecules	I-Material
and	O
an	O
aluminium-based	B-Material
porous	I-Material
MOF	I-Material
,	O
NOTT-300	B-Material
,	O
exhibiting	O
moderate	O
porosity	O
,	O
narrow	O
pore	O
window	O
and	O
very	O
low	O
uptake	O
of	O
H2	B-Material
.	O
This	O
neutron	B-Task
spectroscopy	I-Task
study	O
reveals	O
that	O
adsorbed	B-Material
H2	I-Material
molecules	I-Material
do	O
not	O
interact	O
with	O
the	O
organic	B-Material
ligand	I-Material
within	O
the	O
pore	O
channels	O
,	O
and	O
form	O
very	O
weak	O
interactions	O
with	O
[	B-Material
Al	I-Material
(	I-Material
OH	I-Material
)	I-Material
2O4	I-Material
]	I-Material
moieties	I-Material
via	O
a	O
type	O
of	O
through-spacing	B-Process
interaction	I-Process
(	O
Al-O	B-Process
⋯	I-Process
H2	I-Process
)	O
.	O
Interestingly	O
,	O
the	O
very	O
low	O
H2	B-Process
adsorption	I-Process
has	O
been	O
successfully	O
characterised	O
as	O
weak	B-Process
binding	I-Process
interactions	I-Process
and	O
,	O
for	O
the	O
first	O
time	O
,	O
we	O
have	O
found	O
that	O
the	O
adsorbed	B-Material
H2	I-Material
in	O
the	O
pore	O
channel	O
has	O
a	O
liquid	B-Material
type	O
recoil	O
motion	O
at	O
5K	O
(	O
below	O
its	O
melting	O
point	O
)	O
as	O
a	O
direct	O
result	O
of	O
this	O
weak	B-Process
interaction	I-Process
to	O
the	O
MOF	B-Material
host	O
.	O

The	O
sodium	B-Material
trimer	I-Material
has	O
a	O
long	O
history	O
of	O
theoretical	O
and	O
experimental	O
studies	O
.	O
A	O
pioneering	O
theoretical	O
paper	O
of	O
Martin	O
and	O
Davidson	O
published	O
in	O
1978	O
showed	O
that	O
the	O
obtuse	B-Process
isosceles	I-Process
geometry	I-Process
is	O
lower	O
in	O
energy	O
than	O
the	O
linear	B-Process
conformation	I-Process
[	O
6	O
]	O
.	O
Several	O
extended	O
PES	B-Process
scans	I-Process
of	O
Na3	B-Material
and	O
other	O
alkali	B-Material
trimers	I-Material
followed	O
this	O
initial	O
study	O
,	O
employing	O
DFT	B-Process
[	O
7	O
]	O
,	O
complete	B-Process
active	I-Process
space	I-Process
SCF	I-Process
[	O
8	O
]	O
,	O
or	O
a	O
configuration	B-Process
interaction	I-Process
approach	I-Process
based	O
on	O
valence	B-Process
bond	I-Process
wave	I-Process
functions	I-Process
[	O
9	O
]	O
.	O
Recently	O
,	O
the	O
applicability	O
of	O
density	B-Process
functional	I-Process
theory	I-Process
(	O
DFT	B-Process
)	O
to	O
JT-distorted	B-Process
systems	I-Process
has	O
also	O
been	O
tested	O
for	O
Na3	B-Material
[	O
10	O
]	O
,	O
and	O
the	O
B-X	B-Process
transition	I-Process
has	O
been	O
revisited	O
as	O
well	O
,	O
applying	O
state-averaged	B-Process
multi-reference	I-Process
configuration	I-Process
interaction	I-Process
with	O
a	O
large	O
active	O
space	O
in	O
order	O
to	O
derive	B-Task
more	I-Task
accurate	I-Task
non-adiabatic	I-Task
coupling	I-Task
terms	I-Task
for	O
an	O
improved	O
interpretation	O
of	O
photoabsorption	B-Material
spectra	I-Material
[	O
11	O
–	O
13	O
]	O
.	O

Alternatively	O
to	O
H-atom	B-Process
photodetachment	I-Process
from	O
the	O
intermediate	B-Material
radicals	I-Material
,	O
the	O
latter	O
may	O
serve	O
as	O
reducing	B-Material
agents	I-Material
.	O
Evidence	O
has	O
been	O
reported	O
in	O
recent	O
years	O
that	O
the	O
pyridinyl	B-Material
radical	I-Material
(	O
PyH	B-Material
)	O
is	O
an	O
exceptionally	O
strong	O
reducing	B-Material
agent	I-Material
which	O
can	O
even	O
reduce	O
CO2	B-Material
to	O
formaldehyde	B-Material
,	O
formic	B-Material
acid	I-Material
or	O
methanol	B-Material
with	O
suitable	O
catalyzers	B-Material
[	O
27	O
–	O
29	O
]	O
,	O
albeit	O
the	O
mechanisms	O
of	O
these	O
reactions	O
are	O
currently	O
poorly	O
understood	O
[	O
30	O
–	O
32	O
]	O
.	O
The	O
theoretically	O
predicted	O
dissociation	O
thresholds	O
of	O
the	O
AcH	B-Material
,	I-Material
AOH	I-Material
and	I-Material
BAH	I-Material
radicals	I-Material
are	O
about	O
2.7eV	O
,	O
2.5eV	O
and	O
3.0eV	O
,	O
respectively	O
(	O
see	O
Fig.	O
4	O
)	O
,	O
while	O
the	O
predicted	O
dissociation	O
threshold	O
of	O
the	O
pyridinyl	B-Material
radical	I-Material
is	O
much	O
lower	O
,	O
about	O
1.7eV	O
[	O
1	O
]	O
.	O
Pyridinyl	B-Material
is	O
thus	O
a	O
significantly	O
stronger	O
reductant	B-Material
than	O
acridinyl	B-Material
and	O
related	O
radicals	B-Material
.	O
It	O
is	O
therefore	O
not	O
expected	O
that	O
the	O
latter	O
will	O
be	O
able	O
to	O
reduce	B-Task
carbon	I-Task
dioxide	I-Task
in	I-Task
dark	I-Task
reactions	I-Task
.	O

As	O
already	O
discussed	O
,	O
in	O
dilute	B-Material
flows	I-Material
the	O
choice	O
between	O
the	O
hard	B-Process
sphere	I-Process
and	I-Process
soft	I-Process
sphere	I-Process
models	I-Process
largely	O
depends	O
on	O
the	O
computational	O
time	O
spent	O
to	O
solve	B-Task
the	I-Task
particle	I-Task
equation	I-Task
of	I-Task
motion	I-Task
.	O
For	O
very	O
dilute	B-Material
flows	I-Material
,	O
the	O
hard	B-Process
sphere	I-Process
model	I-Process
is	O
the	O
most	O
natural	O
choice	O
.	O
However	O
,	O
when	O
the	O
collisions	O
can	O
no	O
longer	O
be	O
assumed	O
as	O
binary	O
and	O
instantaneous	O
,	O
the	O
soft	B-Process
sphere	I-Process
model	I-Process
is	O
the	O
only	O
realistic	O
option	O
.	O
It	O
is	O
interesting	O
to	O
know	O
whether	O
the	O
choice	O
of	O
the	O
collision	B-Process
model	I-Process
affects	O
the	O
statistics	O
.	O
Fig.	O
14	O
compares	O
the	O
mean	O
velocity	O
obtained	O
from	O
both	O
models	O
with	O
the	O
experimental	O
data	O
.	O
The	O
same	O
comparison	O
is	O
performed	O
for	O
the	O
smooth	B-Material
walls	I-Material
.	O
The	O
differences	O
between	O
the	O
hard	B-Process
and	I-Process
soft	I-Process
sphere	I-Process
models	I-Process
for	O
the	O
smooth	B-Material
walls	I-Material
are	O
almost	O
negligible	O
.	O
However	O
,	O
the	O
differences	O
between	O
the	O
hard	B-Process
and	I-Process
soft	I-Process
sphere	I-Process
models	I-Process
for	O
the	O
rough	B-Material
walls	I-Material
are	O
minor	O
.	O
This	O
is	O
because	O
the	O
rough	B-Task
wall	I-Task
treatment	I-Task
in	O
the	O
soft	B-Process
sphere	I-Process
implementation	I-Process
adds	O
extra	O
virtual	B-Material
walls	I-Material
during	O
the	O
collision	O
of	O
a	O
particle	B-Material
with	O
a	O
wall	B-Material
,	O
which	O
is	O
a	O
more	O
realistic	O
representation	O
of	O
a	O
rough	B-Material
wall	I-Material
compared	O
to	O
the	O
hard	B-Task
sphere	I-Task
rough	I-Task
wall	I-Task
treatment	I-Task
where	O
one	O
random	B-Material
wall	I-Material
is	O
considered	O
.	O
This	O
is	O
because	O
,	O
a	O
soft	B-Process
sphere	I-Process
collision	I-Process
is	O
not	O
instantaneous	O
and	O
occurs	O
over	O
a	O
finite	O
amount	O
of	O
time	O
.	O
Similarly	O
,	O
the	O
same	O
effects	O
are	O
observed	O
on	O
the	O
fluid	B-Material
statistics	O
.	O
However	O
,	O
Fig.	O
15	O
,	O
which	O
compares	O
the	O
particle	B-Material
velocity	O
fluctuations	O
,	O
shows	O
that	O
the	O
differences	O
are	O
somewhat	O
larger	O
.	O
Additionally	O
,	O
the	O
differences	O
in	O
both	O
particle	O
mean	O
and	O
RMS	O
velocity	O
profiles	O
are	O
because	O
the	O
hard	B-Process
sphere	I-Process
collisions	I-Process
are	O
unfortunately	O
heavily	O
dependent	O
on	O
the	O
tangential	O
coefficient	O
of	O
restitution	O
(	O
ψ	O
)	O
;	O
the	O
effects	O
by	O
varying	O
this	O
quantity	O
are	O
shown	O
in	O
Figs.	O
16	O
and	O
17	O
.	O

In	O
the	O
current	O
CLSVOF	B-Process
method	I-Process
,	O
the	O
normal	O
vector	O
is	O
calculated	O
directly	O
by	O
discretising	O
the	O
LS	B-Process
gradient	O
using	O
a	O
finite	B-Process
difference	I-Process
scheme	I-Process
.	O
By	O
appropriately	O
choosing	O
one	O
of	O
three	O
finite	B-Process
difference	I-Process
schemes	I-Process
(	O
central	B-Process
,	I-Process
forward	I-Process
,	I-Process
or	I-Process
backward	I-Process
differencing	I-Process
)	O
,	O
it	O
has	O
been	O
demonstrated	O
that	O
thin	B-Material
liquid	I-Material
ligaments	I-Material
can	O
be	O
well	O
resolved	O
see	O
Xiao	O
(	O
2012	O
)	O
.	O
Although	O
a	O
high	B-Process
order	I-Process
discretisation	I-Process
scheme	I-Process
(	O
e.g.	O
5th	B-Process
order	I-Process
WENO	I-Process
)	O
has	O
been	O
found	O
necessary	O
for	O
LS	B-Process
evolution	O
in	O
pure	O
LS	B-Process
methods	I-Process
to	O
reduce	B-Task
mass	I-Task
error	I-Task
,	O
low	B-Process
order	I-Process
LS	I-Process
discretisation	I-Process
schemes	I-Process
(	O
2nd	O
order	O
is	O
used	O
here	O
)	O
can	O
produce	O
accurate	O
results	O
when	O
the	O
LS	O
equation	O
is	O
solved	O
and	O
constrained	O
as	O
indicated	O
above	O
in	O
a	O
CLSVOF	B-Process
method	I-Process
(	O
see	O
Xiao	O
,	O
2012	O
)	O
,	O
since	O
the	O
VOF	B-Process
method	I-Process
maintains	O
2nd	O
order	O
accuracy	O
.	O
This	O
is	O
a	O
further	O
reason	O
to	O
adopt	O
the	O
CLSVOF	B-Process
method	I-Process
,	O
which	O
has	O
been	O
used	O
for	O
all	O
the	O
following	O
simulations	B-Task
of	I-Task
liquid	I-Task
jet	I-Task
primary	I-Task
breakup	I-Task
.	O

The	O
aim	O
of	O
this	O
paper	O
is	O
to	O
investigate	B-Task
the	I-Task
influence	I-Task
of	I-Task
the	I-Task
particle	I-Task
shape	I-Task
on	I-Task
interacting	I-Task
particles	I-Task
flowing	I-Task
in	I-Task
a	I-Task
horizontal	I-Task
turbulent	I-Task
channel	I-Task
flow	I-Task
,	O
for	O
particles	O
with	O
a	O
significant	O
Stokes	O
number	O
.	O
To	O
achieve	O
this	O
,	O
large	B-Process
eddy	I-Process
simulations	I-Process
(	O
LES	B-Process
)	O
of	O
a	O
horizontal	B-Process
turbulent	I-Process
channel	I-Process
flow	I-Process
laden	O
with	O
five	O
different	O
particle	B-Material
shapes	O
,	O
incorporating	O
the	O
drag	B-Process
,	I-Process
lift	I-Process
and	I-Process
toque	I-Process
model	I-Process
derived	O
in	O
Zastawny	O
et	O
al	O
.	O
(	O
2012	O
)	O
,	O
are	O
performed	O
.	O
The	O
well-documented	O
horizontal	B-Process
channel	I-Process
flow	I-Process
case	O
described	O
in	O
Kussin	O
and	O
Sommerfeld	O
(	O
2002	O
)	O
,	O
who	O
study	O
spherical	B-Material
particles	I-Material
,	O
is	O
used	O
as	O
a	O
reference	O
case	O
.	O
The	O
measurements	O
in	O
their	O
work	O
was	O
done	O
with	O
phase	B-Process
Doppler	I-Process
anemometry	I-Process
(	O
PDA	B-Process
)	O
,	O
to	O
measure	O
the	O
fluid	B-Material
and	O
particle	B-Material
velocity	O
simultaneously	O
.	O
The	O
numerical	B-Process
framework	I-Process
applied	O
in	O
this	O
paper	O
has	O
been	O
previously	O
validated	O
for	O
spherical	B-Material
particles	I-Material
in	O
Mallouppas	O
and	O
van	O
Wachem	O
(	O
2013	O
)	O
.	O
In	O
that	O
paper	O
,	O
it	O
is	O
shown	O
that	O
the	O
comprehensive	B-Process
discrete	I-Process
element	I-Process
model	I-Process
(	O
DEM	B-Process
)	O
is	O
more	O
accurate	O
in	O
determining	B-Task
the	I-Task
behaviour	I-Task
of	I-Task
the	I-Task
particles	I-Task
in	I-Task
this	I-Task
horizontal	I-Task
gas	I-Task
–	I-Task
solid	I-Task
channel	I-Task
flow	I-Task
that	O
the	O
hard-sphere	B-Process
model	I-Process
.	O
Moreover	O
,	O
this	O
paper	O
showed	O
that	O
the	O
fluid	B-Material
mechanics	O
are	O
accurately	O
modelled	O
using	O
the	O
LES	B-Process
framework	I-Process
.	O
In	O
the	O
current	O
paper	O
,	O
this	O
framework	O
is	O
extended	O
to	O
account	O
for	O
non-spherical	B-Material
particles	I-Material
.	O

The	O
Statistical	B-Process
Associating	I-Process
Fluid	I-Process
Theory	I-Process
(	O
SAFT	B-Process
)	O
is	O
a	O
well-developed	O
perturbation	B-Process
theory	I-Process
used	O
to	O
describe	O
quantitatively	O
the	O
volumetric	O
properties	O
of	O
fluids	B-Material
.	O
The	O
reader	O
is	O
referred	O
to	O
several	O
reviews	O
on	O
the	O
topic	O
which	O
describe	O
the	O
various	O
stages	O
of	O
its	O
development	O
and	O
the	O
multiple	O
versions	O
available	O
[	O
50	O
–	O
53	O
]	O
.	O
The	O
fundamental	O
difference	O
between	O
the	O
versions	O
is	O
in	O
the	O
underlying	O
intermolecular	B-Process
potential	I-Process
employed	O
to	O
describe	O
the	O
unbounded	B-Material
constituent	I-Material
particles	I-Material
.	O
Hard	B-Material
spheres	I-Material
,	O
square	B-Material
well	I-Material
fluids	I-Material
,	O
LJ	B-Material
fluids	I-Material
,	O
argon	B-Material
,	O
alkanes	B-Material
have	O
all	O
been	O
employed	O
as	O
reference	B-Material
fluids	I-Material
in	O
the	O
different	O
incarnations	O
of	O
SAFT	B-Process
.	O
For	O
the	O
purpose	O
of	O
this	O
work	O
we	O
will	O
center	O
on	O
a	O
particular	O
version	O
of	O
the	O
SAFT	B-Process
EoS	I-Process
,	O
i.e.	O
the	O
SAFT-VR	B-Process
Mie	I-Process
recently	O
proposed	O
by	O
Laffitte	O
et	O
al	O
.	O
[	O
54	O
]	O
and	O
expanded	O
into	O
a	O
group	B-Process
contribution	I-Process
approach	I-Process
,	O
SAFT-γ	B-Process
,	O
by	O
Papaioannou	O
et	O
al	O
.	O
[	O
55	O
]	O
.	O
This	O
particular	O
version	O
of	O
SAFT	B-Process
provides	O
a	O
closed	B-Process
form	I-Process
EoS	I-Process
that	O
describes	O
the	O
macroscopical	O
properties	O
of	O
the	O
Mie	B-Process
potential	I-Process
[	O
56	O
]	O
,	O
also	O
known	O
as	O
the	O
(	B-Process
m,n	I-Process
)	I-Process
potential	I-Process
;	O
a	O
generalized	O
form	O
of	O
the	O
LJ	B-Process
potential	I-Process
(	O
albeit	O
predating	O
it	O
by	O
decades	O
)	O
.	O
The	O
Mie	B-Process
potential	I-Process
has	O
the	O
form	O
(	O
1	O
)	O
ϕ	O
(	O
r	O
)=	O
Cεσrλr	O
−	O
σrλawhere	O
C	O
is	O
an	O
analytical	O
function	O
of	O
the	O
repulsive	O
and	O
attractive	O
exponents	O
,	O
λa	O
and	O
λr	O
,	O
respectively	O
,	O
σ	O
is	O
a	O
parameter	O
that	O
defines	O
the	O
length	O
scale	O
and	O
is	O
loosely	O
related	O
to	O
the	O
average	O
diameter	O
of	O
a	O
Mie	O
bead	B-Material
;	O
ɛ	O
defines	O
the	O
energy	O
scale	O
and	O
corresponds	O
to	O
the	O
minimum	O
potential	O
energy	O
between	O
two	O
isolated	O
beads	B-Material
;	O
expressed	O
here	O
as	O
a	O
ratio	O
to	O
the	O
Boltzmann	O
constant	O
,	O
kB	O
.	O
The	O
Mie	O
function	O
,	O
as	O
written	O
above	O
,	O
deceivingly	O
suggests	O
that	O
four	O
parameters	O
are	O
needed	O
to	O
characterize	O
the	O
behaviour	O
of	O
an	O
isotropic	B-Material
molecule	I-Material
,	O
however	O
the	O
exponents	O
λa	O
and	O
λr	O
are	O
intimately	O
related	O
,	O
and	O
for	O
fluid	B-Material
phase	O
equilibria	O
,	O
one	O
needs	O
not	O
consider	O
them	O
as	O
independent	O
parameters	O
[	O
57	O
]	O
.	O
Accordingly	O
,	O
we	O
choose	O
herein	O
to	O
fix	O
the	O
attractive	O
exponent	O
to	O
λa	O
=	O
6	O
which	O
would	O
be	O
expected	O
to	O
be	O
representative	O
of	O
the	O
dispersion	O
scaling	O
of	O
most	O
simple	B-Material
fluids	I-Material
and	O
refer	O
from	O
here	O
on	O
to	O
the	O
repulsive	O
parameter	O
as	O
λ	O
=	O
λr	O
.	O
The	O
potential	O
simplifies	O
to	O
(	O
2	O
)	O
ϕ	O
(	O
r	O
)=	O
λλ	O
−	O
6λ66	O
/(	O
λ	O
−	O
6	O
)	O
εσrλ	O
−	O
σr6	O

The	O
data	B-Process
acquisition	I-Process
strategies	I-Process
must	O
balance	O
the	O
relevant	O
scales	O
and	O
volumes	O
of	O
the	O
datasets	O
to	O
be	O
used	O
in	O
the	O
physical	B-Task
and	I-Task
statistical	I-Task
modeling	I-Task
.	O
Approaches	O
for	O
extraction	B-Task
of	I-Task
the	I-Task
necessary	I-Task
information	I-Task
must	O
be	O
able	O
to	O
disregard	O
spurious	O
information	O
,	O
so	O
as	O
to	O
develop	O
a	O
working	O
network	B-Process
of	I-Process
models	I-Process
for	O
each	O
active	O
mechanism	O
related	O
to	O
each	O
degradation	O
pathway	O
on	O
the	O
mesoscopic	O
physical	O
level	O
and	O
the	O
data-driven	O
statistical	B-Process
model	I-Process
level	O
.	O
To	O
capture	B-Task
the	I-Task
temporal	I-Task
evolution	I-Task
of	O
the	O
energy	B-Material
material	I-Material
over	O
long	O
time	O
frames	O
,	O
appropriate	B-Process
informatics	I-Process
methods	I-Process
are	O
needed	O
to	O
balance	O
data	O
volume	O
(	O
e.g.	O
,	O
simple	O
univariate	B-Material
time-series	I-Material
data	I-Material
streams	I-Material
with	O
high-dimensional	B-Material
volumetric	I-Material
imaging	I-Material
datasets	I-Material
)	O
while	O
considering	O
their	O
respective	O
information	O
contents	O
[	O
68,69	O
]	O
.	O
The	O
raw	O
data	O
and	O
extracted	O
information	O
must	O
be	O
accessible	O
for	O
query	B-Task
and	O
modeling	B-Task
.	O
Similarly	O
,	O
the	O
modeling	B-Process
approaches	I-Process
used	O
to	O
understand	O
and	O
parameterize	O
active	O
mechanisms	O
and	O
phenomena	O
over	O
lifetime	O
fall	O
into	O
the	O
broad	O
categories	O
of	O
micro	B-Process
-	I-Process
,	I-Process
meso	I-Process
-	I-Process
and	I-Process
macroscopic	I-Process
approaches	I-Process
.	O
Laboratory	B-Task
and	I-Task
real-world	I-Task
experimentation	I-Task
,	O
informatics	B-Task
,	O
analytics	B-Task
,	O
and	O
the	O
development	B-Task
of	I-Task
network	I-Task
models	I-Task
for	O
mesoscopic	O
evolution	O
of	O
energy	B-Material
materials	I-Material
over	O
lifetime	O
together	O
constitute	O
the	O
field	O
of	O
degradation	B-Task
science	I-Task
.	O

There	O
are	O
some	O
relevant	O
studies	O
on	O
information	B-Task
dissemination	I-Task
in	I-Task
transportation	I-Task
systems	I-Task
using	O
simulations	B-Process
.	O
One	O
category	O
of	O
studies	O
look	O
at	O
how	O
either	O
local	O
information	O
(	O
only	O
about	O
the	O
neighbours	O
)	O
or	O
global	O
information	O
(	O
about	O
the	O
entire	O
network	O
)	O
affects	O
the	O
global	O
network	O
performance	O
.	O
Our	O
approach	O
is	O
different	O
in	O
the	O
sense	O
that	O
we	O
investigate	B-Process
the	I-Process
impact	I-Process
of	I-Process
information	I-Process
on	I-Process
the	I-Process
global	I-Process
network	I-Process
performance	I-Process
depending	O
on	O
the	O
fraction	O
of	O
people	O
that	O
receive	O
information	O
.	O
We	O
analyse	B-Task
what	I-Task
is	I-Task
the	I-Task
effect	I-Task
of	I-Task
real	I-Task
time	I-Task
information	I-Task
dissemination	I-Task
and	O
explain	O
why	O
this	O
effect	O
appears	O
.	O
Information	O
is	O
disseminated	O
in	O
real	O
time	O
and	O
contains	O
global	O
details	O
about	O
how	O
congested	O
the	O
roads	O
are	O
.	O
This	O
approach	O
is	O
important	O
as	O
it	O
gives	O
insights	O
on	O
the	O
impact	O
that	O
massive	B-Process
use	I-Process
of	I-Process
real-time	I-Process
information	I-Process
can	O
have	O
on	O
traffic	O
.	O
This	O
can	O
be	O
useful	O
for	O
building	B-Task
more	I-Task
intelligent	I-Task
traffic	I-Task
control	I-Task
mechanisms	I-Task
where	O
information	O
is	O
a	O
steering	O
tool	O
.	O

Generalized	B-Process
polynomial	I-Process
chaos	I-Process
expansions	I-Process
.	O
One	O
approach	O
to	O
model	B-Task
densities	I-Task
with	O
stochastically	O
dependent	O
components	O
numerically	O
,	O
is	O
to	O
reformulate	O
the	O
uncertainty	B-Task
problem	I-Task
as	O
a	O
set	O
of	O
independent	O
components	O
through	O
generalised	B-Process
polynomial	I-Process
chaos	I-Process
expansion	I-Process
[	O
34	O
]	O
.	O
As	O
described	O
in	O
detail	O
in	O
Section	O
3.1	O
,	O
a	O
Rosenblatt	B-Process
transformation	I-Process
allows	O
for	O
the	O
mapping	O
between	O
any	O
domain	O
and	O
the	O
unit	O
hypercube	O
[	O
0	O
,	O
1	O
]	O
D	O
.	O
With	O
a	O
double	O
transformation	O
we	O
can	O
reformulate	O
the	O
response	O
function	O
f	O
asf	O
(	O
x,t,Q	O
)=	O
f	O
(	O
x,t,TQ	O
−	O
1	O
(	O
TR	O
(	O
R	O
)))≈	O
fˆ	O
(	O
x,t,R	O
)=∑	O
n	O
∈	O
INcn	O
(	O
x,t	O
)	O
Φn	O
(	O
R	O
)	O
,	O
where	O
R	O
is	O
any	O
random	O
variable	O
drawn	O
from	O
pR	O
,	O
which	O
for	O
simplicity	O
is	O
chosen	O
to	O
consists	O
of	O
independent	O
components	O
.	O
Also	O
,	O
{	O
Φn	O
}	O
n	O
∈	O
IN	O
is	O
constructed	O
to	O
be	O
orthogonal	O
with	O
respect	O
to	O
LR	O
,	O
not	O
LQ	O
.	O
In	O
any	O
case	O
,	O
R	O
is	O
either	O
selected	O
from	O
the	O
Askey-Wilson	B-Process
scheme	I-Process
,	O
or	O
calculated	O
using	O
the	O
discretized	B-Process
Stieltjes	I-Process
procedure	I-Process
.	O
We	O
remark	O
that	O
the	O
accuracy	O
of	O
the	O
approximation	O
deteriorate	O
if	O
the	O
transformation	O
composition	O
TQ	O
−	O
1	O
∘	O
TR	O
is	O
not	O
smooth	O
[	O
34	O
]	O
.	O
Dakota	O
,	O
Turns	O
,	O
and	O
Chaospy	O
all	O
support	O
generalized	B-Process
polynomial	I-Process
chaos	I-Process
expansions	I-Process
for	O
independent	O
stochastic	O
variables	O
and	O
the	O
Normal	O
/	O
Nataf	O
copula	O
listed	O
in	O
Table	O
2	O
.	O
Since	O
Chaospy	O
has	O
the	O
Rosenblatt	B-Process
transformation	I-Process
underlying	O
the	O
computational	B-Material
framework	I-Material
,	O
generalized	B-Process
polynomial	I-Process
chaos	I-Process
expansions	I-Process
are	O
in	O
fact	O
available	O
for	O
all	O
densities	O
.	O

The	O
main	O
drawback	O
of	O
thermo-oxidation	B-Process
in	O
most	O
actual	O
devices	O
and	O
ITER	B-Material
is	O
its	O
limitation	O
to	O
maintenance	O
periods	O
,	O
when	O
the	O
vessel	B-Material
walls	O
can	O
be	O
heated	O
up	O
around	O
300	O
–	O
400	O
°	O
C	O
by	O
hot	O
helium	B-Material
injection	O
through	O
the	O
cooling	B-Material
system	I-Material
[	O
19,20	O
]	O
,	O
and	O
also	O
because	O
of	O
the	O
required	O
reconditioning	B-Task
of	O
the	O
walls	O
before	O
plasma	B-Task
operation	I-Task
to	O
remove	O
the	O
absorbed	O
oxygen	B-Material
[	O
10	O
]	O
.	O
However	O
,	O
the	O
temperature	O
achieved	O
is	O
not	O
homogeneous	O
over	O
the	O
vessel	B-Material
,	O
as	O
it	O
is	O
limited	O
to	O
the	O
distance	O
to	O
the	O
cooling	B-Material
tubes	I-Material
,	O
and	O
thus	O
to	O
the	O
device	O
design	O
.	O
The	O
analysis	O
of	O
this	O
study	O
is	O
a	O
continuation	O
of	O
previous	O
works	O
done	O
for	O
the	O
treatment	B-Task
of	I-Task
ITER	I-Task
carbon	I-Task
co-deposits	I-Task
[	O
1	O
–	O
3	O
]	O
,	O
so	O
the	O
temperatures	O
studied	O
are	O
in	O
the	O
range	O
of	O
350	O
°	O
C	O
for	O
divertor	B-Material
and	O
200	O
–	O
275	O
°	O
C	O
for	O
main	B-Material
wall	I-Material
and	O
remote	B-Material
parts	I-Material
.	O
At	O
present	O
,	O
due	O
to	O
budget	O
restrains	O
as	O
well	O
as	O
due	O
to	O
tritium	B-Material
trapped	O
in	O
co-deposited	O
carbon	B-Material
layers	I-Material
,	O
ITER	B-Material
will	O
not	O
use	O
carbon	B-Material
materials	I-Material
at	O
the	O
divertor	B-Material
strike	O
points	O
in	O
spite	O
of	O
their	O
excellent	O
resilience	O
against	O
large	O
heat	O
loads	O
.	O
Nevertheless	O
,	O
many	O
present	O
experimental	O
nuclear	B-Material
fusion	I-Material
devices	I-Material
(	O
DIII-D	B-Material
,	O
TCV	B-Material
,	O
etc.	O
)	O
and	O
new	O
ones	O
(	O
JT-60SA	B-Material
,	O
KSTAR	B-Material
,	O
Wenderstein-7X	B-Material
)	O
use	O
carbon	B-Material
elements	I-Material
,	O
so	O
the	O
removal	B-Task
of	I-Task
carbon	I-Task
co-deposits	I-Task
is	O
still	O
necessary	O
for	O
a	O
better	O
device	O
operation	O
—	O
plasma	B-Task
density	I-Task
control	I-Task
,	O
dust	B-Material
events	O
,	O
etc	O
.	O
The	O
temperatures	O
used	O
in	O
this	O
work	O
are	O
not	O
very	O
different	O
from	O
the	O
ones	O
achievable	O
in	O
present	O
devices	O
,	O
such	O
that	O
the	O
results	O
can	O
be	O
extrapolated	O
to	O
them	O
.	O
Moreover	O
,	O
even	O
for	O
ITER	B-Material
this	O
study	O
could	O
be	O
useful	O
if	O
carbon	B-Material
materials	I-Material
have	O
to	O
be	O
eventually	O
installed	O
in	O
the	O
case	O
that	O
operation	O
with	O
tungsten	B-Material
tiles	I-Material
at	O
the	O
strike	O
points	O
is	O
precluded	O
by	O
unexpected	O
reasons	O
.	O