A Major Project
The research project assigned by Sun Erxiong is titled "Research Project on Non-Constant Equilibrium Solutions of the Bipolar Non-Isentropic Euler-Poisson Equation".
This project was funded by the National Natural Science Foundation, project number 1137XXXX.
So what exactly does this project research?
The Euler - Poisson Equation equations are commonly used to describe the transport phenomena of charged particle streams in semiconductor materials. They are formed by coupling the bipolar non-isentropic compressible Euler Equation that describe the motion of electron streams and the Poisson Equation that describe changes in the electric field.
It describes the elements in semiconductor materials, such as electrons and ions, density and velocity, absolute temperature, electric potential, doping concentration, pressure difference, and energy.
In short, the research objective of this project is to solve physics problems using mathematical methods.
This suited Shen Qi's taste perfectly; it came at just the right time.
According to available information, a research team at Fudan University is working on a project titled "Research Project on the Quasi-neutrality Limit Problem of High-Dimensional Non-Isentropic Euler-Poisson Systems".
Coincidentally, a research team from Shuimu University applied for a project around the same time: the "Research Project on High-Dimensional Potential Flow in Euler-Poisson Systems".
The project number and project name are transparent and publicly available, and can be found on the official websites of relevant national ministries and research funding institutions.
The project at the other university is not yet finished, and the paper documenting the research results has not been published, but Sun Erxiong and Shen Qi can roughly guess what the other university is doing. The mathematics teams at Tsinghua University and Fudan University seem to be doing similar research projects.
"If Tsinghua and Fudan Universities are doing the same work as us, and they publish their results first, then wouldn't all our work have been for nothing?" Shen Qi thought of this question before officially starting work.
"We are all contributing to the nation's scientific and technological progress; there's no such thing as working for nothing. Whether it's Yenching University, Tsinghua University, or Fudan University, whoever achieves a major scientific breakthrough will be a national hero and will surely be remembered in history," Sun Erxiong said with conviction. "The quantum satellite has been launched, and the Jiaolong submersible has been deployed to the deep sea. A strong science and technology sector means a strong nation. Among the nation's most advanced research teams, there must be a Chief Scientist is proficient in mathematics. I am getting old, but you, Shen Qi, have a bright future. You have talent in this area, and your research career will be very long."
"That's true. Tsinghua and Fudan are prestigious universities after all. The rise of Chinese mathematics requires the joint Chinese Mathematician. We must work hand in hand and heart to heart to create a better tomorrow." Shen Qi was deeply moved. Professor Sun's broad and profound academic vision is worthy of respect. Why does everyone want to study at a prestigious university? The scale and academic atmosphere of prestigious universities are there for all to see.
"Of course, I hope our team from Yenching University will be the first to publish our research findings," Sun Erxiong added.
Shen Qi: "..."
"Shen Qi, aren't you going to focus on Mathematical Physics? This project is in the field of Mathematical Physics, which is perfect for you. You can accumulate academic capital and treat it as practice. This project will be promoted through project management. It has just been approved and has entered the implementation stage. I am the project leader and am fully responsible for this project. You, Shen Qi, are the chief researcher of the project team. I hope you will do your best." Sun Erxiong encouraged him.
"Okay, I'll do my best!" Shen Qi was full of fighting spirit. It was his first time undertaking a major research project, and his fighting spirit was off the charts. "Who are the other members of our team?"
"That's it, just the two of us," Sun Erxiong said.
"Mr. Sun, are you trying to ruin my summer vacation as the chief researcher?"
"Are you incapable of handling this project?"
"No, I will give it my all!"
Driven by a sense of responsibility to the nation and a firm determination to conduct scientific research, Shen Qi took on this important task. He needed this research project, both the internal system settings and his research experience in the real world.
Next, Shen Qi and Sun Erxiong discussed the framework design of the research project.
Through intelligence analysis, Shen Qi discovered that research on the Euler -Poisson model for semiconductors has been increasing year by year over the past decade, with teams both domestically and internationally researching this field, making it a relatively popular area.
"Most of the teams that have published their research results are focused on constant steady-state solutions." After analyzing the international and domestic situation, Shen Qi made a preliminary judgment. "However, information about the research teams at Tsinghua University and Fudan University is very limited. From the limited information, I can only speculate that they are trying to study the Euler - Poisson Equation with isentropic dissipation terms at physical boundaries, and have very likely obtained the global existence of smooth solutions near non-constant horizontal solutions. Therefore, Tsinghua University and Fudan University are ahead of the curve."
"That's alright. There's currently no research on the stability of non-constant equilibrium solutions of the bipolar non-isentropic compressible Euler - Poisson Equation, so we'll start from that." Sun Erxiong made a framework-based strategic deployment with a high-level, macro-level perspective.
"The workload is huge; it won't be finished in less than a year and a half." Shen Qi realized that this might be his first and last major research project before going abroad.
Scientific research is not child's play; it's impossible to produce results in one or two months. Not counting the execution process, the application and approval of results alone can take several months.
The total research funding for the project "Research on Non-Constant Equilibrium Solutions of the Bipolar Non-Isentropic Euler-Poisson Equation" is 652,400 yuan, which will be disbursed according to the project schedule.
The initial 10% funding for the project has been secured and is in Sun Erxiong's possession, amounting to over 60,000 yuan.
This project does not involve the purchase of instruments and equipment. In fact, as long as the person doing the project has strong enough academic and theoretical abilities, they can achieve results without conducting experiments.
This is also the main reason why Shen Qi dared to take on this job. The core execution logic of this project is to use the technique of symmetry and the spatiotemporal hybrid derivative iteration method to solve the periodic problem on a three-dimensional spatial ring.
In other words, it uses advanced mathematical skills to help Physics Community innovate a new theoretical basis for semiconductor material research and a new mathematical model for solving applied physics problems.
During project execution, an individual's theoretical research ability is more important than equipment.
In today's academic world, only mathematicians dare to take on major research projects when research funding is limited.
"We are heroes of our time, solving a practical problem worth over 600 million yuan with just over 600,000 yuan." Shen Qi did some quick calculations, thinking, "If this project really yields results, the country will surely award our team, right?"
"Shen Qi, you will be independently responsible for the first half of the research work on this project. We'll follow the rules. Here's your research funding." Sun Erxiong handed over five thousand yuan in research funding to Shen Qi and reminded him, "Remember to get invoices when purchasing research materials related to the project."
Shen Qi accepted the first phase of research funding. Five thousand yuan could buy a truckload of stationery such as pens, paper, and erasers; these were the only research materials he could think of at the moment.
"I'll stay on campus this summer to work on a research project," Shen Qi told his family on the phone. He had just made the decision. He only had time during the summer vacation; he would have to take the TOEFL and GRE exams and earn credits for his physics degree when the next semester started.
As July began, Mathematics Department students gradually returned home.
Shen Qi stayed alone in his dormitory. He drew up a logical framework, and the content of the project he was responsible for was roughly planned, which was divided into four research sections.
The first section is the preparatory work, which involves rewriting a series of matrix forms based on Euler Equation. This is purely mathematical work with a huge amount of computation.
The second section is about proving the required energy estimate, where physics begins to get involved.
The third section then presents iterative relationships, where mathematics and physics intersect closely, making it the most crucial section.
The fourth section provides verification estimates through iteration, proving the global existence of the solution, which is the final step, a section for discussing the results and claiming credit.
The four sections are logically connected; each is a small topic on its own, but together they form a major topic.
"Hoo..." After finishing out the framework, Shen Qi took a deep breath, feeling immense pressure. The execution phase alone would take three to five months to complete.
The research findings will ultimately be presented in the form of a paper, and it is estimated that the paper on this major topic will be completed by the end of the year.
In the project team, Sun Erxiong was the team leader, the project principal investigator, and the Boss the team, in charge of both administrative and technical aspects of the work.
Shen Qi was appointed as the chief researcher of the project, the second-in-command, and the technical director, in charge of overcoming technical challenges.
This team can't just consist of the Boss and the technical director. The Boss also has to take on undergraduate teaching duties, and the technical director has even more mundane responsibilities.
Just then, Shen Qi's phone rang. Ou Ye sent a WeChat message: "I'm going home this afternoon. Let's have lunch together."
Shen Qi carried the folder and walked towards the girls' dormitory building.
Ou Ye stood downstairs, pulling a small suitcase.
"Let's eat in the cafeteria, I don't want to go out." Shen Qi led Ou Ye to the cafeteria.
"Are you going home tomorrow?" Ou Ye asked.
"I'm not going back, I have a project to work on," Shen Qi said, taking out project materials from a folder to show Ou Ye.
"National Natural Science Foundation funded project, impressive." Ou Ye looked at it with longing, but also noticed a problem. "Such an important project, and only two people are working on it?"