Question

"[This word] mixing" is a process in which trajectories in non-linear dynamical systems separate linearly, rather than exponentially. This first (0[1])word in the name of a two-n-dimensional object central to Hamiltonian mechanics is synonymous with "complex argument." In classical mechanics, graphs of momentum versus position that are spanned by the (0[1])coordinates p-comma-q depict (0[2])"[this word] (0[1])(*) space." (10[4]0[1])This word (10[1]0[1])names the value that is multiplied (0[1])by (10[1])i (10[1])in an exponential (0[2])in solutions (0[1])to physical systems. This word names (10[1])a (10[1])quantity that determines whether interference is destructive. (10[1])For 10 points, (10[2])give this word (0[1])for (10[1])an angle-like (0[1])quantity denoted (10[1])"phi" (10[1])that describes (10[1])an offset in the (0[1])frequency (10[2]0[2])of a wave. (10[2]0[3])■END■ (10[9]0[12])

ANSWER: phase [accept phase space or phase diagram or phase factor or phase difference]
<Science - Physics>
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Karthik JayaramWalkerLee's Summit190
Aaryan SumeshThomas Jefferson ALindbergh490
Tarun DeviChattahoochee ALincoln-Way East A520
Ameya BhaleraoDowningtown STEMIrvington520
Reed KarosichCoronadoSolon540
Aadi PudasainiLexingtonCentennial A5510
Beckett PurseyEdinaBelmont5510
Jason YaoMontgomery Blair BNorth Quincy550
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Dev GurungOkemosYukon B5510
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Krish ChintaInnovation Academy AStrake Jesuit B630
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Ray GuanWinston Churchill BRussell6510
Juni LowenharHunter BSeven Lakes680
Darren KellisMiltonParkway West680
Kaiden LeeNorthviewGrosse Pointe South700
Gugan ThuduppathyMontgomery Blair AHerron7610
Kevin QiuWayzataDetroit Catholic Central B7710
Kevin AdlerNorthmontCarmel B8410
Anirudh "Ani" SrinivasanAdlai E. Stevenson ARichard Montgomery8710
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Winnie NutkowitzNorthside College PrepCarmel A930
Hrishi BhoomaThomas Jefferson DWalter Payton A9510
Cormac KennedySaint JosephUni School of Nashville A9610
Everett Van TilHomewood-FlossmoorPark Tudor9810
Tate OsborneAlabama Cyber TechLambert B1020
Maya HulyalkarAdlai E. Stevenson BCentennial B10310
Jeev HoraKane County ATJohns Creek1030
Evan GilesUni School of Nashville BPage10310
Maggie SunHunter AWest Point1030
Tyler MercadoLincoln-Way East AChattahoochee A10610
Danny "Raj" MorrisStrake Jesuit BInnovation Academy A10610
Steven ZhaoHinsdale Central ALambert A1060
Sanjay Shanmuga PerumalLambert AHinsdale Central A1060
Wyatt JohnsonSolonCoronado1060
Adhrit YadavLambert BAlabama Cyber Tech1070
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Kiran PatelBarringtonEastchester10710
Draco QiaoCarmel ANorthside College Prep10710
Samy El-ZahabiChattahoochee BWhite Pigeon10710
Nathan LiangThomas Jefferson CClassen SAS1070
Tyler SongWinston Churchill ADetroit Catholic Central A10710
Dominic SalazarIrvingtonDowningtown STEM10710
Colin MaxworthyDetroit Catholic Central CFairfield County AT1070
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Evan GniadekQuince OrchardVirginia1070
Brodie HenryWest PointHunter A1070

Summary

TournamentEditionExact Match?TUHConv. %Power %Neg %Average Buzz
2025 PACE NSC06/07/2025Y4171%0%0%88.90