Arnold Mong and Josephine Yu, seniors at Montgomery Blair High School in Silver Spring, Md., are among 40 national finalists for the Intel Science Talent Search in 2016. (Montgomery County Public Schools)

Montgomery Blair High School in Silver Spring, Md., has again produced a national finalist — actually, two of the 40 nationwide — for the prestigious Intel Science Talent Search competition that started Friday in Washington.

Arnold Mong and Josephine Yu, 17-year-old seniors in Blair’s math-science-computer science magnet program, are vying for the competition’s top honors with research projects that sound well beyond their years. Take Yu’s “Lattice and Continuum Models of Solitons and Vortices in Bilayer Graphene,” an investigation in theoretical physics.

“Every day was exciting,” the teenager said. “Every day was learning something and creating something at the same time.”

Blair has racked up 34 Intel finalists since 1999, more than any other school in the country. The Montgomery County high school ranks third nationally for total finalists since the pre-college science and math competition began in 1942.

Thomas Jefferson High School for Science and Technology, an elite magnet school in Fairfax County, has boasted 11 finalists since 1999, including this year’s finalist: 17-year-old Kunal Shroff. Students at the school worked on research projects using computer and mathematical modeling and human assistance robots. They investigated cancer and other health-care treatments, the impact of sonar in marine habitats and pollution in food sources.

Shroff — Jefferson’s first Intel finalist since 2010 — praised his school, classmates and teachers.

“I would say I’ve gotten a lot of good luck from them, and I want to do well for my sake and for theirs,” Shroff said. “I want to show people we can still compete in science.”

His biology research focused on the toxic Huntingtin protein and explored the mechanism for how that protein causes cellular death. He found that the protein can lead to an abnormal genome — work that could be important in understanding Huntington’s disease.

Shroff says his interest stems from his great-grandfather’s deteriorating condition as he suffered from Alzheimer’s disease. The older man did not recognize Shroff as a child and then stopped recognizing Shroff’s father as his disease progressed.

The experiences touched off an interest in neurodegenerative diseases, which include Alzheimer’s and Huntington’s diseases, Shroff said.

“I wanted to learn more about what it means, what does it physically mean,” he said.

Shroff found a mentor in 2014 at Catholic University of America — and worked in the laboratory of assistant professor John S. Choy for two summers and the current school year. First he helped with Choy’s cancer research, working on a project that looked at how metabolism might affect the development of gene mutations.

Later Choy gave him the chance to explore his own interests, too — unusual for a high school student, Choy says, but Shroff showed he could work independently. “I really am impressed at how he was committed,” he said.

Choy recalls that early on he asked Shroff to write computer code for data analysis related to a research project, and the teenager came back a day later with code written. “It did exactly what I needed,” he said.

Shroff, of Great Falls, Va., says his parents — his mother is a dentist, his father a businessman — have been strongly supportive, and that at his school, research is part of the culture. TJ, as it is known, had eight Intel semifinalists this year.

“In my opinion, all the research projects at TJ truly are remarkable, and I’m just honored Intel has chosen my project to go all the way to the finals,” he said.

The annual competition is a program of the Society for Science & the Public and includes finalists this year from 38 schools in 18 states.

At Montgomery Blair, Yu says she did much of her research last summer, when she worked with her mentor, Harsh Mathur, an associate professor in physics at Case Western Reserve University. She made a few trips to Cleveland and met weekly with him by Skype.

Yu developed a theoretical model to study two stacked sheets of graphene, a material that holds potential for use in electronics and biomedical applications. Graphene consists of a single layer of carbon atoms.

“She worked really independently,” Mathur said, recalling the time he gave her a book on computing used by graduate students and expected to have to explain the material and work with her. “I got kind of busy, and the next thing I knew she had already mastered the chapters and written the code I was expecting to help her write.”

Josephine Yu, of Potomac, says that while physics can be difficult, “it’s kind of like a puzzle. If you look at it closely enough, or you look at it slowly enough, everything starts to make sense, and I really like that about it.”

Yu’s father is a physicist at the National Institutes of Health, and her mother is an accountant. She says her interest in science deepened when she became part of Blair’s magnet program. Physics has been a longtime interest, too.

“It’s always been in the back of my mind,” she said.

What makes the Blair magnet program so successful might be a combination of talented students who put in a lot of work, teachers who press them to look beyond the scope of a typical class and an area that values academic performance and research, said ­Peter Ostrander, the program’s coordinator.

Ostrander said the program does not track its Intel grand-prize winners — although it had one last year. “There are so many talented students that to just keep track of a few doesn’t do justice to the work of the others,” he said.

The Blair magnet program, with 100 students in each high school grade, graduated its first class in 1989. Those involved do senior research projects, take eight classes a day rather than the typical seven, and go deep in specialized subjects. For example, students interested in biology may take genetics, biochemistry or physiology.

For many Blair students, science has long been a personal passion, as it has been for Intel finalist Arnold Mong, 17, the son of computer scientists.

His project in theoretical physics focused on special properties in entangled states of matter, and he designed a test that could potentially improve the encryption of data in communication by detecting whether transmitted data has been modified or intercepted.

Mong’s work started last summer with his mentor O.W. Greenberg, a research professor in physics at the University of Maryland at College Park.

Greenberg described the teenager as hard-working and highly motivated. “He’s one of the best students at his level I’ve ever mentored in the 54 years I was at University of Maryland,” Greenberg said.

Mong said he was looking forward to the many experiences that come with the annual Intel competition. Astrophysicist Neil deGrasse Tyson is expected to deliver a keynote address. Top honors — three first-place awards of $150,000 each and a total of more than $1 million in prizes — are expected to be announced Tuesday at an evening gala.

Mong said he did not think he would be in the running if not for Montgomery Blair. “It’s an honor more for the school than for myself,” he said.