# 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:

University students:

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.