##
## approximately exact solution to the 
##   'dustywave' problem, at time t=1.2, for the default
##   parameterfile parameters. note that the solution below
##   is really only exact to ~4 significant figures (the routine
##   used to print this just printed lots more!)
##
## columns are:
##  x-position      x-velocity of dust      x-velocity of gas
##  (velocities here are in units of 1e-4, which is the initial 
##   amplitude of the wave)
##
0.9980490207672119	-0.012927208095788956	-0.2584156394004822
0.9960950016975403	-0.017535850405693054	-0.2617073357105255
0.9941409826278687	-0.02214185893535614	-0.2649596333503723
0.9921870231628418	-0.02674453891813755	-0.2681713402271271
0.9902330040931702	-0.03134319186210632	-0.27134132385253906
0.9882790446281433	-0.035937123000621796	-0.27446889877319336
0.9863250255584717	-0.040525637567043304	-0.27755430340766907
0.9843710064888000	-0.04510805383324623	-0.2805982530117035
0.9824170470237732	-0.049683671444654465	-0.28360140323638916
0.9804630279541016	-0.054251816123723984	-0.28656357526779175
0.9785090684890747	-0.058811791241168976	-0.2894837558269501
0.9765550494194031	-0.06336291134357452	-0.2923606336116791
0.9746010899543762	-0.06790450215339660	-0.29519304633140564
0.9726470708847046	-0.07243586331605911	-0.2979803681373596
0.9706931114196777	-0.07695632427930832	-0.30072247982025146
0.9687390923500061	-0.08146519958972931	-0.3034192621707916
0.9667851328849792	-0.08596180379390717	-0.3060705363750458
0.9648311138153076	-0.09044546633958817	-0.3086759150028229
0.9628771543502808	-0.09491550922393799	-0.3112350106239319
0.9609231948852539	-0.09937126934528351	-0.31374838948249817
0.958969235420227	-0.10381206870079040	-0.31621700525283813
0.9570152163505554	-0.10823722928762436	-0.31862789392471313
0.9550612568855286	-0.11264608800411224	-0.3210001587867737
0.9531072974205017	-0.11703798174858093	-0.32331812381744385
0.9511533379554749	-0.12141226232051850	-0.32559019327163696
0.949199378490448	-0.12576824426651000	-0.3278137445449829
0.9472454190254211	-0.13010528683662415	-0.3299865424633026
0.9452914595603943	-0.13442274928092957	-0.332110196352005
0.9433375000953674	-0.13871996104717255	-0.33418387174606323
0.9413835406303406	-0.14299628138542175	-0.3362070620059967
0.9394295811653137	-0.14725105464458466	-0.33817973732948303
0.9374756217002869	-0.15148366987705230	-0.34010154008865356
0.9355217218399048	-0.15569347143173218	-0.3419721722602844
0.9335677623748779	-0.15987980365753174	-0.34379133582115173
0.9316138625144958	-0.16404208540916443	-0.345558762550354
0.929659903049469	-0.16817964613437653	-0.34727421402931213
0.9277060031890869	-0.17229187488555908	-0.34893736243247986
0.9257520437240601	-0.17637816071510315	-0.3505479693412781
0.923798143863678	-0.18043789267539978	-0.3521057963371277
0.9218442440032959	-0.18447044491767883	-0.3536106050014496
0.9198903441429138	-0.18847520649433136	-0.35506200790405273
0.9179364442825317	-0.19245159626007080	-0.35645991563796997
0.9159825444221497	-0.19639900326728820	-0.35780397057533264
0.9140286445617676	-0.20031681656837463	-0.35909390449523926
0.9120747447013855	-0.20420446991920470	-0.36032968759536743
0.9101208448410034	-0.20806136727333070	-0.3615112006664276
0.9081670045852661	-0.21188691258430480	-0.36263835430145264
0.906213104724884	-0.21568056941032410	-0.3637112081050873
0.9042592644691467	-0.21944172680377960	-0.3647295832633972
0.9023053646087646	-0.22316983342170715	-0.36569327116012573
0.9003515243530273	-0.22686432301998138	-0.36660197377204895
0.89839768409729	-0.23052465915679932	-0.36745530366897583
0.8964438438415527	-0.23415027558803558	-0.3682529628276825
0.8944900035858154	-0.23774063587188720	-0.3689946234226227
0.8925361633300781	-0.24129517376422882	-0.36968034505844116
0.8905823826789856	-0.24481336772441864	-0.3703101575374603
0.8886285424232483	-0.24829469621181488	-0.37088415026664734
0.886674702167511	-0.25173860788345337	-0.3714025616645813
0.8847209215164185	-0.25514462590217590	-0.3718653917312622
0.8827671408653259	-0.25851222872734070	-0.37227264046669006
0.8808133602142334	-0.26184085011482240	-0.37262409925460815
0.8788595795631409	-0.26513007283210754	-0.3729197084903717
0.8769057989120483	-0.26837936043739320	-0.3731593191623688
0.8749520182609558	-0.27158823609352110	-0.3733426332473755
0.8729982376098633	-0.27475616335868835	-0.3734685480594635
0.8710445165634155	-0.27788275480270386	-0.3735351264476776
0.869090735912323	-0.28096744418144226	-0.3735432028770447
0.8671370148658752	-0.28400987386703490	-0.3735124468803406
0.8651832938194275	-0.28700953722000120	-0.3734167814254761
0.8632295727729797	-0.28996592760086060	-0.37325793504714966
0.861275851726532	-0.29287865757942200	-0.37304383516311646
0.8593221306800842	-0.29574728012084960	-0.3727761209011078
0.8573684096336365	-0.29857134819030760	-0.37245237827301025
0.8554147481918335	-0.30135047435760500	-0.3720719516277313
0.8534610271453857	-0.30408418178558350	-0.3716355562210083
0.8515073657035828	-0.30677208304405210	-0.3711431622505188
0.8495537042617798	-0.30941382050514220	-0.37059468030929565
0.8476000428199768	-0.31200891733169556	-0.36999037861824036
0.8456463813781738	-0.31455704569816590	-0.3693302869796753
0.8436927199363708	-0.31705778837203980	-0.3686144948005676
0.8417391180992126	-0.31951075792312620	-0.3678432106971741
0.8397854566574097	-0.32191562652587890	-0.3670164942741394
0.8378318548202515	-0.32427200675010680	-0.3661344647407532
0.8358782529830933	-0.32657954096794130	-0.3651972711086273
0.8339246511459351	-0.32883790135383606	-0.3642050623893738
0.8319710493087769	-0.33104673027992250	-0.3631579577922821
0.8300175070762634	-0.33320569992065430	-0.362056165933609
0.8280639052391052	-0.33531445264816284	-0.36089977622032166
0.8261103630065918	-0.33737269043922424	-0.35968905687332153
0.8241568207740784	-0.33938017487525940	-0.35842403769493103
0.8222032785415649	-0.34133648872375490	-0.3571050763130188
0.8202497363090515	-0.34324145317077637	-0.355732262134552
0.8182961940765381	-0.34509468078613280	-0.35430583357810974
0.8163426518440247	-0.34689596295356750	-0.35282599925994873
0.814389169216156	-0.34864494204521180	-0.35129299759864807
0.8124356865882874	-0.35034143924713135	-0.3497070074081421
0.8104822039604187	-0.35198518633842470	-0.3480682969093323
0.80852872133255	-0.35357588529586790	-0.3463771343231201
0.8065752387046814	-0.35511335730552673	-0.3446337580680847
0.8046218156814575	-0.35659733414649963	-0.34283843636512756
0.8026683330535889	-0.35802760720252990	-0.34099140763282776
0.800714910030365	-0.35940393805503845	-0.33909299969673157
0.7987614870071411	-0.36072614789009094	-0.3371434807777405
0.7968080639839172	-0.36199405789375305	-0.3351430594921112
0.7948546409606934	-0.36320739984512330	-0.33309218287467957
0.7929012775421143	-0.36436608433723450	-0.33099105954170227
0.7909478545188904	-0.36546987295150757	-0.32884007692337036
0.7889944911003113	-0.36651861667633057	-0.32663947343826294
0.7870411276817322	-0.36751216650009155	-0.32438963651657104
0.7850877642631531	-0.36845031380653380	-0.32209086418151855
0.783134400844574	-0.36933302879333496	-0.3197435736656189
0.7811810970306396	-0.37016010284423830	-0.31734803318977356
0.7792277336120605	-0.37093141674995420	-0.31490465998649597
0.7772744297981262	-0.37164685130119324	-0.3124138116836548
0.7753211259841919	-0.37230631709098816	-0.30987587571144104
0.7733678221702576	-0.37290972471237180	-0.3072912096977234
0.771414577960968	-0.37345698475837710	-0.30466023087501526
0.7694612741470337	-0.37394794821739197	-0.3019833266735077
0.7675080299377441	-0.37438261508941650	-0.2992608845233917
0.7655547857284546	-0.37476092576980590	-0.2964933216571808
0.763601541519165	-0.37508276104927063	-0.2936810553073883
0.7616482973098755	-0.37534812092781067	-0.2908245325088501
0.7596950531005859	-0.37555691599845886	-0.287924200296402
0.7577418684959412	-0.37570920586586000	-0.284980446100235
0.7557886838912964	-0.3758048713207245	-0.2819937467575073
0.7538354992866516	-0.37584397196769714	-0.2789645195007324
0.7518823146820068	-0.3758264183998108	-0.2758932113647461
0.7499291300773621	-0.3757523000240326	-0.2727803587913513
0.7479760050773621	-0.37562158703804016	-0.26962634921073914
0.7460228204727173	-0.3754342496395111	-0.2664317190647125
0.7440696954727173	-0.3751904368400574	-0.2631969153881073
0.7421165704727173	-0.3748900890350342	-0.25992244482040405
0.7401634454727173	-0.3745332658290863	-0.256608784198761
0.7382103800773621	-0.3741200864315033	-0.2532564401626587
0.7362572550773621	-0.37365052103996277	-0.24986593425273895
0.7343041896820068	-0.3731246888637543	-0.24643775820732117
0.7323511242866516	-0.37254267930984497	-0.2429724484682083
0.7303980588912964	-0.37190455198287964	-0.23947051167488098
0.7284449934959412	-0.37121036648750305	-0.23593248426914215
0.7264919877052307	-0.3704603314399719	-0.2323588728904724
0.7245389223098755	-0.3696545362472534	-0.22875027358531952
0.722585916519165	-0.3687930107116699	-0.22510717809200287
0.7206329107284546	-0.36787596344947815	-0.22143018245697021
0.7186799049377441	-0.36690348386764526	-0.21771979331970215
0.7167268991470337	-0.365875780582428	-0.21397660672664642
0.714773952960968	-0.36479297280311584	-0.21020115911960602
0.7128210067749023	-0.3636552393436432	-0.20639406144618988
0.7108680605888367	-0.36246272921562195	-0.202555850148201
0.708915114402771	-0.36121562123298645	-0.1986870914697647
0.7069621682167053	-0.3599141240119934	-0.19478842616081238
0.7050092220306396	-0.35855838656425476	-0.19086039066314697
0.7030563354492188	-0.3571487069129944	-0.18690362572669983
0.7011033892631531	-0.3556852340698242	-0.18291866779327393
0.6991505026817322	-0.3541681468486786	-0.1789061576128006
0.6971976161003113	-0.35259780287742615	-0.1748667061328888
0.6952447891235352	-0.35097429156303406	-0.17080092430114746
0.6932919025421143	-0.34929797053337097	-0.16670940816402435
0.6913390755653381	-0.3475690186023712	-0.16259276866912842
0.6893861889839172	-0.3457877039909363	-0.158451646566391
0.6874333620071411	-0.3439543545246124	-0.15428666770458221
0.6854805946350098	-0.34206917881965637	-0.15009842813014984
0.6835277676582336	-0.3401325047016144	-0.1458875983953476
0.6815749406814575	-0.33814460039138794	-0.14165478944778442
0.6796221733093262	-0.3361057639122009	-0.13740067183971405
0.6776694059371948	-0.334016352891922	-0.13312584161758423
0.6757166385650635	-0.33187657594680786	-0.12883098423480988
0.6737638711929321	-0.32968688011169434	-0.12451673299074173
0.6718111038208008	-0.3274475336074829	-0.12018372863531113
0.6698583364486694	-0.32515883445739746	-0.11583264172077179
0.6679056286811829	-0.3228212296962738	-0.11146412044763565
0.6659529209136963	-0.32043495774269104	-0.10707880556583405
0.6640001535415649	-0.3180004358291626	-0.10267739742994308
0.6620475053787231	-0.3155180513858795	-0.0982605367898941
0.6600947976112366	-0.31298813223838806	-0.09382888674736023
0.65814208984375	-0.31041109561920166	-0.08938313275575638
0.6561894416809082	-0.30778729915618896	-0.08492393046617508
0.6542367339134216	-0.3051171898841858	-0.08045195788145065
0.6522840857505798	-0.3024010956287384	-0.07596788555383682
0.650331437587738	-0.2996394634246826	-0.0714723989367485
0.6483787894248962	-0.29683274030685425	-0.06696617603302002
0.6464261412620544	-0.29398131370544434	-0.06244988366961479
0.6444735527038574	-0.2910856008529663	-0.057924214750528336
0.6425209045410156	-0.28814607858657837	-0.05338985472917557
0.6405683159828186	-0.28516313433647156	-0.04884748533368111
0.6386157274246216	-0.2821372449398041	-0.044297780841588974
0.6366631388664246	-0.2790689170360565	-0.03974144905805588
0.6347105503082275	-0.2759585380554199	-0.03517916426062584
0.6327579617500305	-0.2728065848350525	-0.030611610040068626
0.6308054327964783	-0.2696135938167572	-0.026039477437734604
0.6288528442382812	-0.2663799524307251	-0.021463459357619286
0.626900315284729	-0.26310625672340393	-0.01688423752784729
0.6249477863311768	-0.25979292392730713	-0.012302503921091557
0.6229952573776245	-0.2564404308795929	-0.007718960288912058
0.6210427284240723	-0.253049373626709	-0.0031342888250947
0.61909019947052	-0.2496201992034912	0.0014508088352158666
0.6171376705169678	-0.24615344405174255	0.006035638973116875
0.6151852011680603	-0.2426496148109436	0.010619507171213627
0.6132326722145081	-0.23910926282405853	0.015201731584966183
0.6112802028656006	-0.23553287982940674	0.019781628623604774
0.6093277335166931	-0.23192104697227478	0.024358505383133888
0.6073752641677856	-0.22827430069446564	0.028931694105267525
0.6054227948188782	-0.2245931774377823	0.03350049629807472
0.6034703254699707	-0.2208782136440277	0.038064226508140564
0.6015178561210632	-0.21713002026081085	0.04262218251824379
0.5995654463768005	-0.2133491337299347	0.047173671424388885
0.5976129770278931	-0.2095361053943634	0.05171797797083855
0.5956605672836304	-0.20569154620170593	0.056254398077726364
0.5937081575393677	-0.20181600749492645	0.06078225001692772
0.591755747795105	-0.19791007041931152	0.06530086696147919
0.5898033380508423	-0.1939743608236313	0.06980957835912704
0.5878509283065796	-0.19000941514968872	0.07430773973464966
0.5858985185623169	-0.18601588904857635	0.0787947028875351
0.5839461088180542	-0.18199434876441956	0.08326982706785202
0.5819936990737915	-0.17794539034366608	0.0877324566245079
0.5800413489341736	-0.17386965453624725	0.09218188375234604
0.5780889391899109	-0.16976773738861084	0.0966174378991127
0.576136589050293	-0.16564026474952698	0.1010383889079094
0.574184238910675	-0.16148784756660461	0.10544399917125702
0.5722318291664124	-0.1573111116886139	0.10983356833457947
0.5702794790267944	-0.15311071276664734	0.11420638859272003
0.5683271288871765	-0.1488872468471527	0.11856181174516678
0.5663747787475586	-0.14464135468006134	0.12289921939373016
0.5644224286079407	-0.14037369191646576	0.12721799314022064
0.5624701380729675	-0.1360849142074585	0.13151758909225464
0.5605177879333496	-0.1317756325006485	0.1357974261045456
0.5585654377937317	-0.1274465173482895	0.14005693793296814
0.5566131472587585	-0.1230982169508934	0.14429549872875214
0.5546607971191406	-0.11873138695955276	0.14851246774196625
0.5527085065841675	-0.11434667557477951	0.15270715951919556
0.5507561564445496	-0.10994476079940796	0.15687887370586395
0.5488038659095764	-0.10552628338336945	0.16102689504623413
0.5468515753746033	-0.10109192132949829	0.16515052318572998
0.5448992848396301	-0.09664233773946762	0.16924911737442017
0.542946994304657	-0.09217821061611176	0.17332196235656738
0.5409946441650391	-0.08770020306110382	0.17736849188804626
0.5390423536300659	-0.08320900052785873	0.18138809502124786
0.5370900630950928	-0.07870526611804962	0.18538020551204681
0.5351378321647644	-0.0741896852850914	0.18934421241283417
0.5331855416297913	-0.06966294348239899	0.19327965378761292
0.5312332510948181	-0.0651257187128067	0.19718587398529053
0.529280960559845	-0.060578688979148865	0.20106245577335358
0.5273286700248718	-0.05602254346013069	0.20490874350070953
0.5253764390945435	-0.0514579713344574	0.2087242603302002
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