Hermione might study the physics of magic. For example, how spells travel through the air, what kind of energy is involved in magic. This could lead to new ways of casting spells more efficiently or even creating new spells. She could set up experiments to measure the speed, force, and range of different spells.
Well, thermodynamics could be another one. In the wizarding world, there are a lot of energy - consuming magic like the Patronus charm. Hermione could use the knowledge of thermodynamics to explain how much energy is required and how it can be conserved during magic casting. Also, she might study the entropy in the magical systems, like how chaos or order is maintained in the Forbidden Forest ecosystem through magic.
She could use her scientific knowledge to improve potions. For example, understanding the chemical reactions better might lead to more effective and less dangerous potion - making. Just like in real science, precision and knowledge of elements could enhance the brewing process.
It could be about Harry using scientific methods to study magic. Maybe he wants to find out the scientific basis behind spells and potions.
Well, he might get training in magical knowledge. Such as learning about different magical plants and their uses. He could be taught by an old wizard in his neighborhood. This knowledge would give him an edge when he starts at Hogwarts, especially in Herbology classes. Also, he could be trained in magical navigation, like how to use a map of the wizarding world or find his way in enchanted forests.
Perhaps the story could revolve around them facing challenges within the Hogwarts faculty. There could be some old - fashioned professors who oppose their modern teaching methods. Harry and Hermione then have to prove that their ways are beneficial for the students. They might also discover new magical abilities in some of the students that were previously overlooked, and help those students develop their skills.
One reason could be to search for a powerful magical artifact outside of Hogwarts that they believe is crucial for defeating a new dark threat. In fanfiction, they might feel that Hogwarts has become too dangerous or restricted in terms of resources for their mission.
One possible reason could be that he was under the influence of a powerful dark magic or a curse that made him lose control. Another reason might be that he was tricked into believing Hogwarts was a threat to the wizarding world in some extreme way. Maybe a powerful enemy manipulated him to think that destroying Hogwarts was the only way to save everyone.
In the fanfiction world, Harry might be the heir to Hogwarts if there was some sort of magical pact made generations ago. For example, perhaps one of his ancestors had a special role in the creation or protection of Hogwarts, and this role was passed down through the family. It could also be that his unique magical abilities, like his ability to resist Voldemort's attacks from a young age, are signs of a deeper connection to Hogwarts itself. This connection could be what designates him as the heir in the fanfiction's plot.
If the new headmaster was someone like Neville, he might focus on making the school more accessible to students from different backgrounds. He could also introduce more hands - on learning in Herbology, perhaps with a new greenhouse dedicated to rare and dangerous plants for advanced students to study.
A PhD was a higher-level degree that usually required applicants to have a solid academic background and research experience. Generally speaking, people who were suitable for a PhD needed to have the following characteristics: 1. Possess solid basic knowledge and professional skills, able to conduct in-depth research and analysis independently. 2. Strong interest and passion in a specific field or research topic, and the ability to continue learning and exploring. Excellent logical thinking and reasoning ability, able to think and solve problems independently. Able to work in a team and cooperate with other researchers to complete research projects. Good communication skills, able to communicate effectively with readers, audiences and other researchers and share research results. Of course, studying for a PhD was not an easy thing. It required enough perseverance, patience, and wisdom. Scientific research was a job that required long-term persistence and constant challenges. It required applicants to have the spirit of continuous improvement and self-transcendence.