PC2023-P2 Best solutions and final results

Problem 2 – Phase transitions in a wire

In total, 91 solutions were submitted for problem 2, out of which 25 were correct.
Congratulations to everyone who managed to solve this problem!

The Best Solution Awards were selected from the 7 submissions sent before the second hint was published. Usually, only those solutions are considered that are not based on any hints, but this time, there were too few such solutions, and as a matter of fact, the first hint was very subtle. The Best Solution Award was shared between the solutions that analyzed in detail the heat transfer along the wire near the phase boundary. There were two such solutions, submitted by Luka Passek-Kumerički and Anindya Guria. Both of them derive the temperature profile along the wire, but Luka Passek-Kumerički is the only one who correctly shows the rapid process of power rising from P_0 to \sqrt{\frac 23}P_0 and to \sqrt{\frac 83}P_0 on the graph. Everyone else treats this as a discontinuity which is not correct: the thermalization is fast as compared to the voltage growth time, but not instantaneous. As a result, Luka Passek-Kumerički earns 0.6 of the award, and Anindya Guria – the remaining 0.4. For my taste (JK), Luka Passek-Kumerički has unnecessarily complicated calculations, e.g. his formulae 1-25 and 38; still, these are not wrong, so I overlook this.

Additionally, very well-written solutions were submitted by Vlad-Stefan Oros, Eyal Walach, and Gil Ronen (note that E.W. has a typo in Section 1.3, instead of T_h-T_c=T_c-T_h, there should be T_h-T_c=T_c-T_l). These are well worth reading as they explain in an easy-to-understand way how the phase separation front propagates. All these authors get a publication bonus factor of exp(0.1).

Final results for Problem 2

Pre-university students:

First nameSurnameCountrySchoolP2 date time
DD/MM/YY 00:00:00
P2 Score
Vlad-ȘtefanOrosRomania“Grigore Moisil” Theoretical High School19/12/2022 19:39:002.7949
TomasBabelisLithuaniaVilniaus jėzuitų gimnazija01/01/2023 15:41:002.016
ChenyunWangChinaShanghai High School17/01/2023 10:54:001.5005
DženanMidžićBosnia and HerzegovinaJU Gimnazija “Bihać”22/01/2023 16:07:001.1108
HarshinPosinaIndiaFIITJEE Madhapur26/01/2023 21:05:001.0629
Andrei-DariusDragomirRomaniaInternational Computer Highschool of Bucharest (ICHB)29/01/2023 00:10:000.9663
MateuszKamińskiPolandVI High School in Cracow07/02/2023 16:37:000.6655
FilipBaciakPoland1 LO w Chrzanowie05/02/2023 00:23:000.6588
AlexandarRoussevBulgaria07/02/2023 18:03:000.5748
Elias KoschierMichail OgnyanovAustriaERG Donaustadt12/02/2023 02:16:000.495
VisheshSehrawatIndiaFIITJEE13/02/2023 11:13:000.456
RhythmKediaIndiaMB International13/02/2023 16:49:000.4388
EppuLeinonenFinlandMunkkiniemen yhteiskoulu13/02/2023 17:05:000.3751

University students:

First nameSurnameCountryUniversityP2 date time
DD/MM/YY 00:00:00
P2 Score
AnindyaGuriaIndiaIndian Institute of Science28/12/2022 13:51:003.4297
GilRonenIsraelHebrew University of Jerusalem24/12/2022 23:23:002.8665
LukaPassek-KumeričkiCroatiaUniversity of Zagreb07/01/2023 21:23:002.7599
EyalWalachIsraelBar-Ilan University01/01/2023 00:07:002.1321
ZiyueWangChinaHebei University of Technology01/01/2023 04:10:001.6662
SoumyadeepSarmaIndiaIndian Institute of Science29/01/2023 02:44:000.7827
KerimCherkezovTurkmenistanTurkmen State University03/02/2023 16:09:000.6588
LukasSchichtGermanyUniversity of Rostock05/02/2023 22:45:000.6322
MarinusLehmannGermanyUniversity of Potsdam19/02/2023 22:42:000.5
JerzyGamdzykPolandUniversity of Warsaw20/02/2023 00:48:000.5
KaarelPaalEstoniaTalTech19/02/2023 16:43:000.4826
TejasAcharyaIndiaUniversity of Oxford12/02/2023 12:48:000.4778

The list of countries:
Algeria, Argentina, Armenia, Australia, Austria, Azerbaijan, Bahrain, Bangladesh, Belarus, Belgium, Bosnia and Herzegovina, Brazil, Bulgaria, Cambodia, Cameroon, Canada, China, Croatia, Cuba, Czech Republic, Ecuador, Egypt, El Salvador, Estonia, Finland, France, Georgia, Germany, Greece, Guatemala, Honduras, Hong Kong, Hungary, India, Indonesia, Iran, Israel, Italy, Japan, Kazakhstan, Kenya, Kosovo, Kyrgyzstan, Latvia, Lithuania, Macau, Malaysia, Mexico, Moldova, Montenegro, Nepal, Netherlands, Nigeria, North Korea, North Macedonia, Pakistan, Peru, Philippines, Poland, Romania, Russia, Rwanda, Saudi Arabia, Serbia, Singapore, Slovakia, Slovenia, South Africa, South Korea, Spain, Sri Lanka, Suriname, Sweden, Switzerland, Syria, Taiwan, Tajikistan, Thailand, Turkey, Turkmenistan, Ukraine, United Arab Emirates, United Kingdom, United States, Uzbekistan, Vietnam.