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	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