Xu, Duo; Song, Baofang; Avila, Marc (2021): Optimal perturbation (helical, Re=2000,A=1,Wo=15): snapshot axial vorticity t=tf [dataset]. PANGAEA, https://doi.org/10.1594/PANGAEA.932549
Always quote citation above when using data! You can download the citation in several formats below.
Published: 2021-06-11 • DOI registered: 2022-12-31
Abstract:
The data are obtained via an in-house Matlab script (developed by Dr. Baofang Song) to compute the non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows. In this study, a Newtonian fluid driven by pulsatile and oscillatory flow rate flows in a straight pipe. In pulsatile flow, there are three governing parameters: steady Reynolds number (defined by the steady flow component), pulsation amplitude (ratio of oscillatory and steady flow component) and Womersley number (dimensionless pulsation and oscillation frequency). In oscillatory flow, due to vanishment of steady flow component, oscillatory Reynolds number (defined by the oscillation flow component) and Womersley number. The Reynolds number defined by the thickness of Stokes layer is alternatively used for the oscillatory Reynolds number. The study was carried out in a manner that one governing parameter varies while other governing parameters are fixed.
The data file 'OptimalPerturbation_time_VortZ_helical.dat' shows the streamwise vorticity of the optimal helical perturbation in the radial-radial cross-section.
This file includes three columns: the first two column 'x' and 'y' indicate Cartesian coordinates in the radial-radial cross-section; the third column 'VortZ' indicates streamwise vorticity.
Related to:
Xu, Duo; Song, Baofang; Avila, Marc (accepted): Non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows. Journal of Fluid Mechanics, 907, https://doi.org/10.1017/jfm.2020.940
Comment:
#(k_op,m_op)=( 0.00000000,1)
VARIABLES = "x", "y", "VortZ"
ZONE T="time/period=0.250000", I=96, J=96
Parameter(s):
| # | Name | Short Name | Unit | Principal Investigator | Method/Device | Comment |
|---|---|---|---|---|---|---|
| 1 | r, coordinate, cylindrical, radial component | r | Xu, Duo | |||
| 2 | z, coordinate, cylindrical, axial component | z | Xu, Duo | |||
| 3 | ω_z, vorticity, cylindrical, axial component | ω_z | Xu, Duo |
License:
Creative Commons Attribution 4.0 International (CC-BY-4.0)
Status:
Curation Level: Enhanced curation (CurationLevelC) * Processing Level: PANGAEA data processing level 2 (ProcLevel2)
Size:
27648 data points
Data
| 1 r | 2 z | 3 ω_z |
|---|---|---|
| 0.500000000000 | 0.000000000000 | 91.370576200000 |
| 0.499932366000 | 0.000000000000 | 91.908758100000 |
| 0.499729483000 | 0.000000000000 | 93.431117400000 |
| 0.499391406000 | 0.000000000000 | 95.671019700000 |
| 0.498918227000 | 0.000000000000 | 98.216325800000 |
| 0.498310072000 | 0.000000000000 | 100.554888000000 |
| 0.497567107000 | 0.000000000000 | 102.132593000000 |
| 0.496689533000 | 0.000000000000 | 102.418616000000 |
| 0.495677587000 | 0.000000000000 | 100.971641000000 |
| 0.494531543000 | 0.000000000000 | 97.500461800000 |
| 0.493251711000 | 0.000000000000 | 91.912856500000 |
| 0.491838437000 | 0.000000000000 | 84.347825400000 |
| 0.490292104000 | 0.000000000000 | 75.188213700000 |
| 0.488613130000 | 0.000000000000 | 65.052954900000 |
| 0.486801968000 | 0.000000000000 | 54.770335700000 |
| 0.484859110000 | 0.000000000000 | 45.335316600000 |
| 0.482785081000 | 0.000000000000 | 37.854766100000 |
| 0.480580441000 | 0.000000000000 | 33.484407900000 |
| 0.478245788000 | 0.000000000000 | 33.360560100000 |
| 0.475781752000 | 0.000000000000 | 38.528805500000 |
| 0.473189001000 | 0.000000000000 | 49.871119900000 |
| 0.470468236000 | 0.000000000000 | 68.033141400000 |
| 0.467620193000 | 0.000000000000 | 93.354372800000 |
| 0.464645642000 | 0.000000000000 | 125.805956000000 |
| 0.461545389000 | 0.000000000000 | 164.942645000000 |
| 0.458320271000 | 0.000000000000 | 209.876892000000 |
| 0.454971161000 | 0.000000000000 | 259.282712000000 |
| 0.451498967000 | 0.000000000000 | 311.434629000000 |
| 0.447904625000 | 0.000000000000 | 364.282561000000 |
| 0.444189111000 | 0.000000000000 | 415.557621000000 |
| 0.440353427000 | 0.000000000000 | 462.897662000000 |
| 0.436398613000 | 0.000000000000 | 503.976623000000 |
| 0.432325737000 | 0.000000000000 | 536.619596000000 |
| 0.428135902000 | 0.000000000000 | 558.887067000000 |
| 0.423830242000 | 0.000000000000 | 569.116903000000 |
| 0.419409921000 | 0.000000000000 | 565.920715000000 |
| 0.414876134000 | 0.000000000000 | 548.140706000000 |
| 0.410230110000 | 0.000000000000 | 514.782244000000 |
| 0.405473103000 | 0.000000000000 | 464.944563000000 |
| 0.400606403000 | 0.000000000000 | 397.775947000000 |
| 0.395631324000 | 0.000000000000 | 312.479662000000 |
| 0.390549213000 | 0.000000000000 | 208.392679000000 |
| 0.385361445000 | 0.000000000000 | 85.150731300000 |
| 0.380069423000 | 0.000000000000 | -57.058998300000 |
| 0.374674579000 | 0.000000000000 | -217.172051000000 |
| 0.369178373000 | 0.000000000000 | -392.880368000000 |
| 0.363582291000 | 0.000000000000 | -580.277147000000 |
| 0.357887847000 | 0.000000000000 | -773.581525000000 |
| 0.352096583000 | 0.000000000000 | -965.022765000000 |
| 0.346210064000 | 0.000000000000 | -1144.963680000000 |
| 0.340229882000 | 0.000000000000 | -1302.327520000000 |
| 0.334157657000 | 0.000000000000 | -1425.358200000000 |
| 0.327995031000 | 0.000000000000 | -1502.691350000000 |
| 0.321743671000 | 0.000000000000 | -1524.648500000000 |
| 0.315405267000 | 0.000000000000 | -1484.600260000000 |
| 0.308981536000 | 0.000000000000 | -1380.192310000000 |
| 0.302474214000 | 0.000000000000 | -1214.206810000000 |
| 0.295885062000 | 0.000000000000 | -994.855176000000 |
| 0.289215864000 | 0.000000000000 | -735.369835000000 |
| 0.282468422000 | 0.000000000000 | -452.875437000000 |
| 0.275644563000 | 0.000000000000 | -166.652831000000 |
| 0.268746132000 | 0.000000000000 | 103.966495000000 |
| 0.261774996000 | 0.000000000000 | 341.753409000000 |
| 0.254733041000 | 0.000000000000 | 533.437876000000 |
| 0.247622171000 | 0.000000000000 | 670.975690000000 |
| 0.240444312000 | 0.000000000000 | 752.042982000000 |
| 0.233201403000 | 0.000000000000 | 779.723520000000 |
| 0.225895406000 | 0.000000000000 | 761.501833000000 |
| 0.218528296000 | 0.000000000000 | 707.790328000000 |
| 0.211102066000 | 0.000000000000 | 630.277222000000 |
| 0.203618726000 | 0.000000000000 | 540.376781000000 |
| 0.196080300000 | 0.000000000000 | 448.003093000000 |
| 0.188488828000 | 0.000000000000 | 360.794300000000 |
| 0.180846362000 | 0.000000000000 | 283.812044000000 |
| 0.173154972000 | 0.000000000000 | 219.654036000000 |
| 0.165416737000 | 0.000000000000 | 168.861496000000 |
| 0.157633751000 | 0.000000000000 | 130.482628000000 |
| 0.149808119000 | 0.000000000000 | 102.663948000000 |
| 0.141941959000 | 0.000000000000 | 83.172968900000 |
| 0.134037399000 | 0.000000000000 | 69.796109600000 |
| 0.126096578000 | 0.000000000000 | 60.594113300000 |
| 0.118121642000 | 0.000000000000 | 54.026655200000 |
| 0.110114751000 | 0.000000000000 | 48.975224000000 |
| 0.102078070000 | 0.000000000000 | 44.699473900000 |
| 0.094013772700 | 0.000000000000 | 40.759823400000 |
| 0.085924041800 | 0.000000000000 | 36.931733300000 |
| 0.077811065500 | 0.000000000000 | 33.128129800000 |
| 0.069677038500 | 0.000000000000 | 29.338188900000 |
| 0.061524161500 | 0.000000000000 | 25.584457400000 |
| 0.053354640000 | 0.000000000000 | 21.896387800000 |
| 0.045170684300 | 0.000000000000 | 18.296529000000 |
| 0.036974508300 | 0.000000000000 | 14.795281900000 |
| 0.028768329400 | 0.000000000000 | 11.390669500000 |
| 0.020554367700 | 0.000000000000 | 8.070491410000 |
| 0.012334845300 | 0.000000000000 | 4.815178910000 |
| 0.004111985920 | 0.000000000000 | 1.600461460000 |
| 0.498883439000 | 0.033396316900 | 107.491687000000 |
| 0.498815957000 | 0.033391799400 | 107.896640000000 |
| 0.498613527000 | 0.033378248400 | 109.022231000000 |
| 0.498276205000 | 0.033355667300 | 110.610657000000 |
| 0.497804082000 | 0.033324062400 | 112.264669000000 |
| 0.497197285000 | 0.033283442100 | 113.493145000000 |
| 0.496455979000 | 0.033233817500 | 113.768920000000 |
| 0.495580365000 | 0.033175202100 | 112.593327000000 |
| 0.494570679000 | 0.033107611500 | 109.561066000000 |
| 0.493427194000 | 0.033031064200 | 104.418810000000 |
| 0.492150220000 | 0.032945580900 | 97.111571600000 |
| 0.490740102000 | 0.032851184600 | 87.812246900000 |
| 0.489197222000 | 0.032747900900 | 76.931766200000 |
| 0.487521997000 | 0.032635757800 | 65.109571400000 |
| 0.485714880000 | 0.032514785600 | 53.186248400000 |
| 0.483776361000 | 0.032385017000 | 42.161650900000 |
| 0.481706963000 | 0.032246487100 | 33.142461100000 |
| 0.479507247000 | 0.032099233400 | 27.282828900000 |
| 0.477177807000 | 0.031943295700 | 25.720748200000 |
| 0.474719274000 | 0.031778716300 | 29.511684400000 |
| 0.472132313000 | 0.031605539700 | 39.560212200000 |
| 0.469417623000 | 0.031423812600 | 56.550554300000 |
| 0.466575940000 | 0.031233584300 | 80.878112700000 |
| 0.463608032000 | 0.031034906200 | 112.586146000000 |
| 0.460514702000 | 0.030827832100 | 151.314055000000 |
| 0.457296786000 | 0.030612418000 | 196.265413000000 |
| 0.453955156000 | 0.030388722200 | 246.204029000000 |
| 0.450490715000 | 0.030156805100 | 299.484309000000 |
| 0.446904400000 | 0.029916729600 | 354.117942000000 |
| 0.443197182000 | 0.029668560600 | 407.873070000000 |
| 0.439370064000 | 0.029412365200 | 458.395740000000 |
| 0.435424081000 | 0.029148212700 | 503.338252000000 |
| 0.431360301000 | 0.028876174600 | 540.476314000000 |
| 0.427179823000 | 0.028596324500 | 567.797846000000 |
| 0.422883778000 | 0.028308738100 | 583.550900000000 |
| 0.418473327000 | 0.028013493200 | 586.245878000000 |
| 0.413949666000 | 0.027710669700 | 574.616691000000 |
| 0.409314016000 | 0.027400349500 | 547.554826000000 |
| 0.404567633000 | 0.027082616500 | 504.038022000000 |
| 0.399711800000 | 0.026757556700 | 443.079799000000 |
| 0.394747831000 | 0.026425258100 | 363.726859000000 |
| 0.389677069000 | 0.026085810500 | 265.127841000000 |
| 0.384500886000 | 0.025739305800 | 146.689204000000 |
| 0.379220682000 | 0.025385837800 | 8.322129490000 |
| 0.373837885000 | 0.025025501900 | -149.231072000000 |
| 0.368353953000 | 0.024658395900 | -324.020986000000 |
| 0.362770368000 | 0.024284618800 | -512.515065000000 |
| 0.357088640000 | 0.023904271900 | -709.289319000000 |
| 0.351310308000 | 0.023517458100 | -906.868292000000 |
| 0.345436934000 | 0.023124282000 | -1095.796380000000 |
| 0.339470108000 | 0.022724849900 | -1265.010520000000 |
| 0.333411443000 | 0.022319270000 | -1402.552460000000 |
| 0.327262578000 | 0.021907652000 | -1496.607690000000 |
| 0.321025178000 | 0.021490107100 | -1536.793110000000 |
| 0.314700929000 | 0.021066748500 | -1515.546740000000 |
| 0.308291542000 | 0.020637690600 | -1429.416600000000 |
| 0.301798752000 | 0.020203049400 | -1280.018360000000 |
| 0.295224315000 | 0.019762942600 | -1074.447930000000 |
| 0.288570010000 | 0.019317489300 | -825.000767000000 |
| 0.281837636000 | 0.018866809900 | -548.158442000000 |
| 0.275029015000 | 0.018411026300 | -262.936154000000 |
| 0.268145989000 | 0.017950262000 | 11.186845600000 |
| 0.261190421000 | 0.017484641400 | 256.439656000000 |
| 0.254164191000 | 0.017014290700 | 458.689132000000 |
| 0.247069201000 | 0.016539337000 | 608.820553000000 |
| 0.239907370000 | 0.016059908800 | 703.367967000000 |
| 0.232680636000 | 0.015576135900 | 744.336521000000 |
| 0.225390954000 | 0.015088149100 | 738.308686000000 |
| 0.218040296000 | 0.014596080400 | 695.047086000000 |
| 0.210630650000 | 0.014100063000 | 625.873636000000 |
| 0.203164021000 | 0.013600231000 | 542.108149000000 |
| 0.195642429000 | 0.013096719700 | 453.796564000000 |
| 0.188067909000 | 0.012589665200 | 368.869051000000 |
| 0.180442510000 | 0.012079204800 | 292.767058000000 |
| 0.172768296000 | 0.011565476600 | 228.489600000000 |
| 0.165047341000 | 0.011048619500 | 176.949030000000 |
| 0.157281735000 | 0.010528773400 | 137.501351000000 |
| 0.149473579000 | 0.010006078800 | 108.522666000000 |
| 0.141624986000 | 0.009480677310 | 87.932011200000 |
| 0.133738078000 | 0.008952710920 | 73.599679500000 |
| 0.125814989000 | 0.008422322520 | 63.618378900000 |
| 0.117857862000 | 0.007889655590 | 56.444695700000 |
| 0.109868851000 | 0.007354854230 | 50.937047400000 |
| 0.101850117000 | 0.006818063120 | 46.323751500000 |
| 0.093803828600 | 0.006279427490 | 42.133562100000 |
| 0.085732163000 | 0.005739093060 | 38.114464900000 |
| 0.077637303900 | 0.005197206000 | 34.157966200000 |
| 0.069521441200 | 0.004653912910 | 30.237972900000 |
| 0.061386770600 | 0.004109360790 | 26.367028700000 |
| 0.053235492700 | 0.003563696930 | 22.568579100000 |
| 0.045069812700 | 0.003017068970 | 18.861897000000 |
| 0.036891939700 | 0.002469624790 | 15.255780600000 |
| 0.028704086300 | 0.001921512490 | 11.747546100000 |
| 0.020508467300 | 0.001372880350 | 8.324674460000 |
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| 0.004102803350 | 0.000274650369 | 1.651140490000 |
| 0.495538744000 | 0.066643477700 | 123.132714000000 |
| 0.495471714000 | 0.066634463000 | 123.402629000000 |
| 0.495270641000 | 0.066607421400 | 124.126425000000 |
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| 0.493863894000 | 0.066418232300 | 125.924514000000 |
| 0.493127559000 | 0.066319204800 | 124.897127000000 |
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| 0.488850667000 | 0.065744018800 | 101.876563000000 |
| 0.487450003000 | 0.065555647800 | 90.884477500000 |
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| 0.482458472000 | 0.064884352200 | 51.364618500000 |
| 0.480532949000 | 0.064625394600 | 38.799680900000 |
| 0.478477425000 | 0.064348953500 | 28.282133900000 |
| 0.476292457000 | 0.064055103800 | 20.959398200000 |
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| 0.468966967000 | 0.063069921300 | 29.072619000000 |
| 0.466270478000 | 0.062707278800 | 44.815398700000 |
| 0.463447846000 | 0.062327671800 | 68.040631300000 |
| 0.460499836000 | 0.061931203000 | 98.863499000000 |
| 0.457427244000 | 0.061517979600 | 137.009659000000 |
| 0.454230903000 | 0.061088113500 | 181.777364000000 |
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| 0.109132251000 | 0.014676859900 | 52.671373600000 |
| 0.101167277000 | 0.013605675100 | 47.741136000000 |
| 0.093174933700 | 0.012530809500 | 43.319122100000 |
| 0.085157383600 | 0.011452553900 | 39.126968100000 |
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| 0.069055344300 | 0.009287040320 | 31.002706700000 |
| 0.060975211400 | 0.008200368170 | 27.031838400000 |
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| 0.028511643700 | 0.003834443040 | 12.051955300000 |
| 0.020370971100 | 0.002739629090 | 8.541677490000 |
| 0.012224787500 | 0.001644073980 | 5.097392290000 |
| 0.004075296670 | 0.000548074083 | 1.694445130000 |
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| 0.486736722000 | 0.098933593900 | 131.390944000000 |
| 0.485745053000 | 0.098732028400 | 125.235760000000 |
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| 0.483367788000 | 0.098248827900 | 106.186549000000 |
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| 0.268145989000 | -0.017950262000 | 196.281804000000 |
| 0.261190421000 | -0.017484641400 | 425.540808000000 |
| 0.254164191000 | -0.017014290700 | 605.804158000000 |
| 0.247069201000 | -0.016539337000 | 730.134086000000 |
| 0.239907370000 | -0.016059908800 | 797.359190000000 |
| 0.232680636000 | -0.015576135900 | 811.628085000000 |
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| 0.188067909000 | -0.012589665200 | 351.108154000000 |
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| 0.165047341000 | -0.011048619500 | 160.019787000000 |
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| 0.149473579000 | -0.010006078800 | 96.346706900000 |
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| 0.004102803350 | -0.000274650369 | 1.542634370000 |
| 0.500000000000 | 0.000000000000 | 91.370576200000 |
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| 0.493251711000 | 0.000000000000 | 91.912856500000 |
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| 0.480580441000 | 0.000000000000 | 33.484407900000 |
| 0.478245788000 | 0.000000000000 | 33.360560100000 |
| 0.475781752000 | 0.000000000000 | 38.528805500000 |
| 0.473189001000 | 0.000000000000 | 49.871119900000 |
| 0.470468236000 | 0.000000000000 | 68.033141400000 |
| 0.467620193000 | 0.000000000000 | 93.354372800000 |
| 0.464645642000 | 0.000000000000 | 125.805956000000 |
| 0.461545389000 | 0.000000000000 | 164.942645000000 |
| 0.458320271000 | 0.000000000000 | 209.876892000000 |
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| 0.451498967000 | 0.000000000000 | 311.434629000000 |
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| 0.444189111000 | 0.000000000000 | 415.557621000000 |
| 0.440353427000 | 0.000000000000 | 462.897662000000 |
| 0.436398613000 | 0.000000000000 | 503.976623000000 |
| 0.432325737000 | 0.000000000000 | 536.619596000000 |
| 0.428135902000 | 0.000000000000 | 558.887067000000 |
| 0.423830242000 | 0.000000000000 | 569.116903000000 |
| 0.419409921000 | 0.000000000000 | 565.920715000000 |
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| 0.395631324000 | 0.000000000000 | 312.479662000000 |
| 0.390549213000 | 0.000000000000 | 208.392679000000 |
| 0.385361445000 | 0.000000000000 | 85.150731300000 |
| 0.380069423000 | 0.000000000000 | -57.058998300000 |
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| 0.275644563000 | 0.000000000000 | -166.652831000000 |
| 0.268746132000 | 0.000000000000 | 103.966495000000 |
| 0.261774996000 | 0.000000000000 | 341.753409000000 |
| 0.254733041000 | 0.000000000000 | 533.437876000000 |
| 0.247622171000 | 0.000000000000 | 670.975690000000 |
| 0.240444312000 | 0.000000000000 | 752.042982000000 |
| 0.233201403000 | 0.000000000000 | 779.723520000000 |
| 0.225895406000 | 0.000000000000 | 761.501833000000 |
| 0.218528296000 | 0.000000000000 | 707.790328000000 |
| 0.211102066000 | 0.000000000000 | 630.277222000000 |
| 0.203618726000 | 0.000000000000 | 540.376781000000 |
| 0.196080300000 | 0.000000000000 | 448.003093000000 |
| 0.188488828000 | 0.000000000000 | 360.794300000000 |
| 0.180846362000 | 0.000000000000 | 283.812044000000 |
| 0.173154972000 | 0.000000000000 | 219.654036000000 |
| 0.165416737000 | 0.000000000000 | 168.861496000000 |
| 0.157633751000 | 0.000000000000 | 130.482628000000 |
| 0.149808119000 | 0.000000000000 | 102.663948000000 |
| 0.141941959000 | 0.000000000000 | 83.172968900000 |
| 0.134037399000 | 0.000000000000 | 69.796109600000 |
| 0.126096578000 | 0.000000000000 | 60.594113300000 |
| 0.118121642000 | 0.000000000000 | 54.026655200000 |
| 0.110114751000 | 0.000000000000 | 48.975224000000 |
| 0.102078070000 | 0.000000000000 | 44.699473900000 |
| 0.094013772700 | 0.000000000000 | 40.759823400000 |
| 0.085924041800 | 0.000000000000 | 36.931733300000 |
| 0.077811065500 | 0.000000000000 | 33.128129800000 |
| 0.069677038500 | 0.000000000000 | 29.338188900000 |
| 0.061524161500 | 0.000000000000 | 25.584457400000 |
| 0.053354640000 | 0.000000000000 | 21.896387800000 |
| 0.045170684300 | 0.000000000000 | 18.296529000000 |
| 0.036974508300 | 0.000000000000 | 14.795281900000 |
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| 0.012334845300 | 0.000000000000 | 4.815178910000 |
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| 0.475781752000 | 0.000000000000 | 38.528805500000 |
| 0.473189001000 | 0.000000000000 | 49.871119900000 |
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| 0.451498967000 | 0.000000000000 | 311.434629000000 |
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| 0.268746132000 | 0.000000000000 | 103.966495000000 |
| 0.261774996000 | 0.000000000000 | 341.753409000000 |
| 0.254733041000 | 0.000000000000 | 533.437876000000 |
| 0.247622171000 | 0.000000000000 | 670.975690000000 |
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| 0.196080300000 | 0.000000000000 | 448.003093000000 |
| 0.188488828000 | 0.000000000000 | 360.794300000000 |
| 0.180846362000 | 0.000000000000 | 283.812044000000 |
| 0.173154972000 | 0.000000000000 | 219.654036000000 |
| 0.165416737000 | 0.000000000000 | 168.861496000000 |
| 0.157633751000 | 0.000000000000 | 130.482628000000 |
| 0.149808119000 | 0.000000000000 | 102.663948000000 |
| 0.141941959000 | 0.000000000000 | 83.172968900000 |
| 0.134037399000 | 0.000000000000 | 69.796109600000 |
| 0.126096578000 | 0.000000000000 | 60.594113300000 |
| 0.118121642000 | 0.000000000000 | 54.026655200000 |
| 0.110114751000 | 0.000000000000 | 48.975224000000 |
| 0.102078070000 | 0.000000000000 | 44.699473900000 |
| 0.094013772700 | 0.000000000000 | 40.759823400000 |
| 0.085924041800 | 0.000000000000 | 36.931733300000 |
| 0.077811065500 | 0.000000000000 | 33.128129800000 |
| 0.069677038500 | 0.000000000000 | 29.338188900000 |
| 0.061524161500 | 0.000000000000 | 25.584457400000 |
| 0.053354640000 | 0.000000000000 | 21.896387800000 |
| 0.045170684300 | 0.000000000000 | 18.296529000000 |
| 0.036974508300 | 0.000000000000 | 14.795281900000 |
| 0.028768329400 | 0.000000000000 | 11.390669500000 |
| 0.020554367700 | 0.000000000000 | 8.070491410000 |
| 0.012334845300 | 0.000000000000 | 4.815178910000 |
| 0.004111985920 | 0.000000000000 | 1.600461460000 |
