id	sid	tid	token	lemma	pos
x346d22089x	1	1	the	the	DET
x346d22089x	1	2	method	method	NOUN
x346d22089x	1	3	of	of	ADP
x346d22089x	1	4	slow	slow	ADJ
x346d22089x	1	5	invariant	invariant	ADJ
x346d22089x	1	6	manifolds	manifold	NOUN
x346d22089x	1	7	(	(	PUNCT
x346d22089x	1	8	sims	sim	NOUN
x346d22089x	1	9	)	)	PUNCT
x346d22089x	1	10	,	,	PUNCT
x346d22089x	1	11	as	as	SCONJ
x346d22089x	1	12	developed	develop	VERB
x346d22089x	1	13	to	to	PART
x346d22089x	1	14	model	model	VERB
x346d22089x	1	15	the	the	DET
x346d22089x	1	16	reduced	reduce	VERB
x346d22089x	1	17	kinetics	kinetic	NOUN
x346d22089x	1	18	of	of	ADP
x346d22089x	1	19	spatially	spatially	ADV
x346d22089x	1	20	homogeneous	homogeneous	ADJ
x346d22089x	1	21	reactive	reactive	ADJ
x346d22089x	1	22	systems	system	NOUN
x346d22089x	1	23	,	,	PUNCT
x346d22089x	1	24	is	be	AUX
x346d22089x	1	25	extended	extend	VERB
x346d22089x	1	26	to	to	ADP
x346d22089x	1	27	systems	system	NOUN
x346d22089x	1	28	with	with	ADP
x346d22089x	1	29	diffusion	diffusion	NOUN
x346d22089x	1	30	.	.	PUNCT
x346d22089x	2	1	using	use	VERB
x346d22089x	2	2	a	a	DET
x346d22089x	2	3	galerkin	galerkin	PROPN
x346d22089x	2	4	projection	projection	NOUN
x346d22089x	2	5	,	,	PUNCT
x346d22089x	2	6	the	the	DET
x346d22089x	2	7	governing	govern	VERB
x346d22089x	2	8	partial	partial	ADJ
x346d22089x	2	9	differential	differential	ADJ
x346d22089x	2	10	equations	equation	NOUN
x346d22089x	2	11	are	be	AUX
x346d22089x	2	12	cast	cast	VERB
x346d22089x	2	13	into	into	ADP
x346d22089x	2	14	a	a	DET
x346d22089x	2	15	finite	finite	ADJ
x346d22089x	2	16	system	system	NOUN
x346d22089x	2	17	of	of	ADP
x346d22089x	2	18	ordinary	ordinary	ADJ
x346d22089x	2	19	differential	differential	ADJ
x346d22089x	2	20	equations	equation	NOUN
x346d22089x	2	21	to	to	PART
x346d22089x	2	22	be	be	AUX
x346d22089x	2	23	solved	solve	VERB
x346d22089x	2	24	on	on	ADP
x346d22089x	2	25	an	an	DET
x346d22089x	2	26	approximate	approximate	ADJ
x346d22089x	2	27	inertial	inertial	ADJ
x346d22089x	2	28	manifold	manifold	NOUN
x346d22089x	2	29	.	.	PUNCT
x346d22089x	3	1	the	the	DET
x346d22089x	3	2	sim	sim	NOUN
x346d22089x	3	3	construction	construction	NOUN
x346d22089x	3	4	technique	technique	NOUN
x346d22089x	3	5	of	of	ADP
x346d22089x	3	6	identifying	identify	VERB
x346d22089x	3	7	equilibria	equilibria	NOUN
x346d22089x	3	8	and	and	CCONJ
x346d22089x	3	9	connecting	connect	VERB
x346d22089x	3	10	heteroclinic	heteroclinic	NOUN
x346d22089x	3	11	orbits	orbit	NOUN
x346d22089x	3	12	is	be	AUX
x346d22089x	3	13	extended	extend	VERB
x346d22089x	3	14	by	by	ADP
x346d22089x	3	15	identifying	identify	VERB
x346d22089x	3	16	steady	steady	ADJ
x346d22089x	3	17	state	state	NOUN
x346d22089x	3	18	solutions	solution	NOUN
x346d22089x	3	19	to	to	ADP
x346d22089x	3	20	the	the	DET
x346d22089x	3	21	governing	govern	VERB
x346d22089x	3	22	partial	partial	ADJ
x346d22089x	3	23	differential	differential	ADJ
x346d22089x	3	24	equations	equation	NOUN
x346d22089x	3	25	and	and	CCONJ
x346d22089x	3	26	connecting	connect	VERB
x346d22089x	3	27	analogous	analogous	ADJ
x346d22089x	3	28	orbits	orbit	NOUN
x346d22089x	3	29	in	in	ADP
x346d22089x	3	30	the	the	DET
x346d22089x	3	31	galerkin	galerkin	PROPN
x346d22089x	3	32	-	-	PUNCT
x346d22089x	3	33	projected	project	VERB
x346d22089x	3	34	space	space	NOUN
x346d22089x	3	35	.	.	PUNCT
x346d22089x	4	1	in	in	ADP
x346d22089x	4	2	parametric	parametric	ADJ
x346d22089x	4	3	studies	study	NOUN
x346d22089x	4	4	varying	vary	VERB
x346d22089x	4	5	the	the	DET
x346d22089x	4	6	domain	domain	NOUN
x346d22089x	4	7	length	length	NOUN
x346d22089x	4	8	,	,	PUNCT
x346d22089x	4	9	the	the	DET
x346d22089x	4	10	time	time	NOUN
x346d22089x	4	11	scale	scale	NOUN
x346d22089x	4	12	spectrum	spectrum	NOUN
x346d22089x	4	13	is	be	AUX
x346d22089x	4	14	shifted	shift	VERB
x346d22089x	4	15	,	,	PUNCT
x346d22089x	4	16	and	and	CCONJ
x346d22089x	4	17	various	various	ADJ
x346d22089x	4	18	classes	class	NOUN
x346d22089x	4	19	of	of	ADP
x346d22089x	4	20	non	non	ADJ
x346d22089x	4	21	-	-	ADJ
x346d22089x	4	22	linear	linear	ADJ
x346d22089x	4	23	dynamics	dynamic	NOUN
x346d22089x	4	24	are	be	AUX
x346d22089x	4	25	identified	identify	VERB
x346d22089x	4	26	.	.	PUNCT
x346d22089x	5	1	a	a	DET
x346d22089x	5	2	critical	critical	ADJ
x346d22089x	5	3	length	length	NOUN
x346d22089x	5	4	scale	scale	NOUN
x346d22089x	5	5	is	be	AUX
x346d22089x	5	6	identified	identify	VERB
x346d22089x	5	7	at	at	ADP
x346d22089x	5	8	which	which	PRON
x346d22089x	5	9	a	a	DET
x346d22089x	5	10	bifurcation	bifurcation	NOUN
x346d22089x	5	11	occurs	occur	VERB
x346d22089x	5	12	in	in	ADP
x346d22089x	5	13	the	the	DET
x346d22089x	5	14	equilibria	equilibria	NOUN
x346d22089x	5	15	used	use	VERB
x346d22089x	5	16	to	to	PART
x346d22089x	5	17	construct	construct	VERB
x346d22089x	5	18	the	the	DET
x346d22089x	5	19	one	one	NUM
x346d22089x	5	20	-	-	PUNCT
x346d22089x	5	21	dimensional	dimensional	ADJ
x346d22089x	5	22	sim	sim	NOUN
x346d22089x	5	23	.	.	PUNCT
x346d22089x	6	1	above	above	ADP
x346d22089x	6	2	this	this	DET
x346d22089x	6	3	length	length	NOUN
x346d22089x	6	4	scale	scale	NOUN
x346d22089x	6	5	additional	additional	ADJ
x346d22089x	6	6	real	real	ADJ
x346d22089x	6	7	non	non	ADJ
x346d22089x	6	8	-	-	ADJ
x346d22089x	6	9	singular	singular	ADJ
x346d22089x	6	10	steady	steady	ADJ
x346d22089x	6	11	state	state	NOUN
x346d22089x	6	12	solutions	solution	NOUN
x346d22089x	6	13	are	be	AUX
x346d22089x	6	14	found	find	VERB
x346d22089x	6	15	which	which	PRON
x346d22089x	6	16	lead	lead	VERB
x346d22089x	6	17	to	to	ADP
x346d22089x	6	18	a	a	DET
x346d22089x	6	19	diffusion	diffusion	NOUN
x346d22089x	6	20	-	-	PUNCT
x346d22089x	6	21	modified	modify	VERB
x346d22089x	6	22	sim	sim	NOUN
x346d22089x	6	23	.	.	PUNCT
x346d22089x	7	1	at	at	ADP
x346d22089x	7	2	these	these	DET
x346d22089x	7	3	longer	long	ADJ
x346d22089x	7	4	lengths	length	NOUN
x346d22089x	7	5	,	,	PUNCT
x346d22089x	7	6	the	the	DET
x346d22089x	7	7	spectral	spectral	ADJ
x346d22089x	7	8	gap	gap	NOUN
x346d22089x	7	9	in	in	ADP
x346d22089x	7	10	the	the	DET
x346d22089x	7	11	time	time	NOUN
x346d22089x	7	12	scales	scale	NOUN
x346d22089x	7	13	indicates	indicate	VERB
x346d22089x	7	14	that	that	SCONJ
x346d22089x	7	15	an	an	DET
x346d22089x	7	16	appropriate	appropriate	ADJ
x346d22089x	7	17	manifold	manifold	NOUN
x346d22089x	7	18	for	for	ADP
x346d22089x	7	19	a	a	DET
x346d22089x	7	20	reduction	reduction	NOUN
x346d22089x	7	21	technique	technique	NOUN
x346d22089x	7	22	is	be	AUX
x346d22089x	7	23	higher	high	ADJ
x346d22089x	7	24	than	than	ADP
x346d22089x	7	25	one	one	NUM
x346d22089x	7	26	-	-	PUNCT
x346d22089x	7	27	dimensional	dimensional	ADJ
x346d22089x	7	28	.	.	PUNCT
x346d22089x	8	1	this	this	PRON
x346d22089x	8	2	is	be	AUX
x346d22089x	8	3	shown	show	VERB
x346d22089x	8	4	for	for	ADP
x346d22089x	8	5	three	three	NUM
x346d22089x	8	6	examples	example	NOUN
x346d22089x	8	7	in	in	ADP
x346d22089x	8	8	closed	closed	ADJ
x346d22089x	8	9	reaction	reaction	NOUN
x346d22089x	8	10	-	-	PUNCT
x346d22089x	8	11	diffusion	diffusion	NOUN
x346d22089x	8	12	systems	system	NOUN
x346d22089x	8	13	:	:	PUNCT
x346d22089x	8	14	a	a	DET
x346d22089x	8	15	generic	generic	ADJ
x346d22089x	8	16	chemical	chemical	ADJ
x346d22089x	8	17	reaction	reaction	NOUN
x346d22089x	8	18	mechanism	mechanism	NOUN
x346d22089x	8	19	,	,	PUNCT
x346d22089x	8	20	an	an	DET
x346d22089x	8	21	oxygen	oxygen	NOUN
x346d22089x	8	22	dissociation	dissociation	NOUN
x346d22089x	8	23	reaction	reaction	NOUN
x346d22089x	8	24	mechanism	mechanism	NOUN
x346d22089x	8	25	,	,	PUNCT
x346d22089x	8	26	and	and	CCONJ
x346d22089x	8	27	the	the	DET
x346d22089x	8	28	zel'dovich	zel'dovich	NOUN
x346d22089x	8	29	reaction	reaction	NOUN
x346d22089x	8	30	mechanism	mechanism	NOUN
x346d22089x	8	31	of	of	ADP
x346d22089x	8	32	no	no	DET
x346d22089x	8	33	production	production	NOUN
x346d22089x	8	34	.	.	PUNCT
x346d22089x	9	1	the	the	DET
x346d22089x	9	2	extension	extension	NOUN
x346d22089x	9	3	of	of	ADP
x346d22089x	9	4	sims	sim	NOUN
x346d22089x	9	5	to	to	ADP
x346d22089x	9	6	adiabatic	adiabatic	ADJ
x346d22089x	9	7	reaction	reaction	NOUN
x346d22089x	9	8	systems	system	NOUN
x346d22089x	9	9	is	be	AUX
x346d22089x	9	10	also	also	ADV
x346d22089x	9	11	considered	consider	VERB
x346d22089x	9	12	,	,	PUNCT
x346d22089x	9	13	and	and	CCONJ
x346d22089x	9	14	results	result	NOUN
x346d22089x	9	15	are	be	AUX
x346d22089x	9	16	shown	show	VERB
x346d22089x	9	17	for	for	ADP
x346d22089x	9	18	the	the	DET
x346d22089x	9	19	zel'dovich	zel'dovich	NOUN
x346d22089x	9	20	mechanism	mechanism	NOUN
x346d22089x	9	21	.	.	PUNCT
x346d22089x	10	1	finally	finally	ADV
x346d22089x	10	2	,	,	PUNCT
x346d22089x	10	3	two	two	NUM
x346d22089x	10	4	open	open	ADJ
x346d22089x	10	5	chemical	chemical	NOUN
x346d22089x	10	6	systems	system	NOUN
x346d22089x	10	7	are	be	AUX
x346d22089x	10	8	considered	consider	VERB
x346d22089x	10	9	:	:	PUNCT
x346d22089x	10	10	the	the	DET
x346d22089x	10	11	gray	gray	ADJ
x346d22089x	10	12	-	-	PUNCT
x346d22089x	10	13	scott	scott	PROPN
x346d22089x	10	14	reaction	reaction	NOUN
x346d22089x	10	15	mechanism	mechanism	NOUN
x346d22089x	10	16	,	,	PUNCT
x346d22089x	10	17	and	and	CCONJ
x346d22089x	10	18	a	a	DET
x346d22089x	10	19	hydrogen	hydrogen	NOUN
x346d22089x	10	20	-	-	PUNCT
x346d22089x	10	21	air	air	NOUN
x346d22089x	10	22	reaction	reaction	NOUN
x346d22089x	10	23	mechanism	mechanism	NOUN
x346d22089x	10	24	.	.	PUNCT
x346d22089x	11	1	multiple	multiple	ADJ
x346d22089x	11	2	branches	branch	NOUN
x346d22089x	11	3	of	of	ADP
x346d22089x	11	4	the	the	DET
x346d22089x	11	5	sim	sim	NOUN
x346d22089x	11	6	are	be	AUX
x346d22089x	11	7	identified	identify	VERB
x346d22089x	11	8	,	,	PUNCT
x346d22089x	11	9	complicating	complicate	VERB
x346d22089x	11	10	the	the	DET
x346d22089x	11	11	implementation	implementation	NOUN
x346d22089x	11	12	of	of	ADP
x346d22089x	11	13	the	the	DET
x346d22089x	11	14	sim	sim	NOUN
x346d22089x	11	15	as	as	ADP
x346d22089x	11	16	a	a	DET
x346d22089x	11	17	reduction	reduction	NOUN
x346d22089x	11	18	technique	technique	NOUN
x346d22089x	11	19	.	.	PUNCT
x346d22089x	12	1	limit	limit	NOUN
x346d22089x	12	2	cycles	cycle	NOUN
x346d22089x	12	3	are	be	AUX
x346d22089x	12	4	studied	study	VERB
x346d22089x	12	5	and	and	CCONJ
x346d22089x	12	6	a	a	DET
x346d22089x	12	7	projection	projection	NOUN
x346d22089x	12	8	to	to	ADP
x346d22089x	12	9	the	the	DET
x346d22089x	12	10	sim	sim	NOUN
x346d22089x	12	11	across	across	ADP
x346d22089x	12	12	a	a	DET
x346d22089x	12	13	basin	basin	NOUN
x346d22089x	12	14	of	of	ADP
x346d22089x	12	15	attraction	attraction	NOUN
x346d22089x	12	16	is	be	AUX
x346d22089x	12	17	shown	show	VERB
x346d22089x	12	18	to	to	PART
x346d22089x	12	19	provide	provide	VERB
x346d22089x	12	20	erroneous	erroneous	ADJ
x346d22089x	12	21	results	result	NOUN
x346d22089x	12	22	.	.	PUNCT
x346d22089x	13	1	low	low	ADJ
x346d22089x	13	2	-	-	PUNCT
x346d22089x	13	3	dimensional	dimensional	ADJ
x346d22089x	13	4	galerkin	galerkin	PROPN
x346d22089x	13	5	projections	projection	NOUN
x346d22089x	13	6	are	be	AUX
x346d22089x	13	7	shown	show	VERB
x346d22089x	13	8	to	to	PART
x346d22089x	13	9	provide	provide	VERB
x346d22089x	13	10	correct	correct	ADJ
x346d22089x	13	11	order	order	NOUN
x346d22089x	13	12	of	of	ADP
x346d22089x	13	13	magnitude	magnitude	NOUN
x346d22089x	13	14	predictions	prediction	NOUN
x346d22089x	13	15	for	for	ADP
x346d22089x	13	16	length	length	NOUN
x346d22089x	13	17	scales	scale	NOUN
x346d22089x	13	18	in	in	ADP
x346d22089x	13	19	patterns	pattern	NOUN
x346d22089x	13	20	.	.	PUNCT
x346d22089x	14	1	the	the	DET
x346d22089x	14	2	examples	example	NOUN
x346d22089x	14	3	are	be	AUX
x346d22089x	14	4	evaluated	evaluate	VERB
x346d22089x	14	5	in	in	ADP
x346d22089x	14	6	the	the	DET
x346d22089x	14	7	spatially	spatially	ADV
x346d22089x	14	8	homogeneous	homogeneous	ADJ
x346d22089x	14	9	case	case	NOUN
x346d22089x	14	10	(	(	PUNCT
x346d22089x	14	11	a	a	DET
x346d22089x	14	12	one	one	NUM
x346d22089x	14	13	-	-	PUNCT
x346d22089x	14	14	term	term	NOUN
x346d22089x	14	15	projection	projection	NOUN
x346d22089x	14	16	)	)	PUNCT
x346d22089x	14	17	,	,	PUNCT
x346d22089x	14	18	a	a	DET
x346d22089x	14	19	two	two	NUM
x346d22089x	14	20	-	-	PUNCT
x346d22089x	14	21	term	term	NOUN
x346d22089x	14	22	projection	projection	NOUN
x346d22089x	14	23	capturing	capture	VERB
x346d22089x	14	24	the	the	DET
x346d22089x	14	25	coarsest	coarse	ADJ
x346d22089x	14	26	effects	effect	NOUN
x346d22089x	14	27	of	of	ADP
x346d22089x	14	28	diffusion	diffusion	NOUN
x346d22089x	14	29	,	,	PUNCT
x346d22089x	14	30	and	and	CCONJ
x346d22089x	14	31	a	a	DET
x346d22089x	14	32	high	high	ADJ
x346d22089x	14	33	order	order	NOUN
x346d22089x	14	34	projection	projection	NOUN
x346d22089x	14	35	that	that	PRON
x346d22089x	14	36	is	be	AUX
x346d22089x	14	37	fully	fully	ADV
x346d22089x	14	38	resolved	resolve	VERB
x346d22089x	14	39	.	.	PUNCT
x346d22089x	15	1	the	the	DET
x346d22089x	15	2	results	result	NOUN
x346d22089x	15	3	cast	cast	VERB
x346d22089x	15	4	into	into	ADP
x346d22089x	15	5	doubt	doubt	NOUN
x346d22089x	15	6	the	the	DET
x346d22089x	15	7	sim	sim	NOUN
x346d22089x	15	8	as	as	ADP
x346d22089x	15	9	a	a	DET
x346d22089x	15	10	robust	robust	ADJ
x346d22089x	15	11	rational	rational	ADJ
x346d22089x	15	12	reduction	reduction	NOUN
x346d22089x	15	13	technique	technique	NOUN
x346d22089x	15	14	for	for	ADP
x346d22089x	15	15	reaction	reaction	NOUN
x346d22089x	15	16	dynamics	dynamic	NOUN
x346d22089x	15	17	.	.	PUNCT