Translation. Region: Russian Federal

Source: State University Higher School of Economics – State University Higher School of Economics –

Created in Nizhny Novgorod campus of HSE International Laboratory of Dynamic Systems and Applications conducts deep theoretical research and applied studies, including the study of ocean waves, solar corona reconnections, volcanic phenomena and ship stability. Its scientists, who have won more than 20 significant scientific grants over the past 5 years, actively collaborate with Russian and foreign colleagues from China, Spain, the USA, Great Britain, Brazil and other countries. The Vyshka.Glavnoe news service spoke with its head, Professor Olga Pochinka, about the work of the laboratory.

— When was the laboratory created?

— Let’s start with 2014, when colleagues from the Mathematics Department of the Moscow HSE suggested creating a department on the Nizhny Novgorod campus, and we were fired up by the idea. Together with five colleagues, we moved from the Nizhny Novgorod State University to the HSE in Nizhny Novgorod, and in 2015 we opened the first intake of undergraduate students for the Mathematics educational program, a total of eight people.

Then the recruitment began to expand, and I began inviting people from UNN. We worked as research fellows at the Laboratory of Theory and Practice of Decision Support and simultaneously taught students.

In 2017, we separated into the Laboratory of Topological Methods of Dynamics, and in 2019, we won a mega-grant from the Government, and this was the only mega-grant in fundamental mathematics won in the Nizhny Novgorod region in the entire history of projects. Our leading scientist Dmitry Turaev is also a former Nizhny Novgorod resident, now a professor at the British Imperial College, a renowned specialist in the field of dynamic systems.

The laboratory began to grow rapidly, and in parallel with the increase in scientific work, we also expanded our educational areas: we created a postgraduate program, a master’s program, and this year we are opening a new bachelor’s program in applied mathematics.

— Tell us about the priority areas of the laboratory’s work.

— Initially, our laboratory was created primarily as a center for fundamental scientific research. Mathematics is a self-sufficient science, and there are always people who are interested in learning its own laws. An equally important activity is to explain how these laws work in practice. Recently, the laboratory team has noticeably expanded with researchers actively engaged in applied developments.

— What applied areas would you highlight?

— We have problems that come from physics. For example, we studied the effects of reconnection in the solar corona. From the point of view of deep mathematical theory, we explained the mechanism of solar flares. If we imagine the surface of the Sun as a two-dimensional sphere, then the magnetic charges on the surface create domes that change their location depending on the configuration of the charges. When the domes collide, so-called separators appear, visually manifesting themselves in the occurrence of a solar flare. The mechanisms of dome reconnection were explained using the bifurcation of the birth of a heteroclinic curve, widely known in the theory of dynamic systems.

We also managed to explain the pattern recognition algorithm by the existence of an energy function in a dynamic system. In general, tasks related to the construction of such functions are very important. All dynamic systems are largely dissipative, that is, they lose energy over time. We managed to establish the relationship between the energy function and the dynamics of the system. That is, a scientist, even without knowing the system, can measure the indicators of its energy function and say a lot about the dynamics of the system.

These are just the applications I have worked with personally. But there are many employees in the lab developing other applied areas.

Efim Pelinovsky and his student Ekaterina Didenkulova conducted a theoretical analysis of internal waves that arise in the ocean during an explosive eruption of an underwater volcano. They calculated the characteristics of the wave field for different ratios between the radius of the explosion source and the depth of the basin. And they showed that the field of internal waves has the form of frequency-modulated groups, of which the head group has the maximum amplitude. The wave of maximum height in this train arrives significantly later than the weak head wave, which makes it possible to prepare for the approach of dangerous waves.

Ioann Melnikov studies the dynamics of waves in both linear and nonlinear weakly dispersive models. In his work with shallow water equations, there is an interesting question about finding non-reflective bottom profiles, due to which a wave can propagate freely over large distances (with conservation of energy), which is important for applications. Together with Efim Pelinovsky, he obtained a countable family of limited bottom profiles and a continuous family in the form of underwater slides. Research into weakly nonlinear and weakly dispersive models (described by Korteweg-de Vries type equations) is also aimed at finding and studying waves that propagate with a constant speed and unchanged shape (in particular, soliton solutions). In this way, a classification of soliton solution shapes was obtained in the generalized Korteweg-de Vries equation, and now the question arises of how this classification can change with a different account of nonlinearity and dispersion.

Fedor Peplin studies computational fluid dynamics, motion dynamics and stability of high-speed vessels. New criteria for the stability of hovercraft have been obtained. A model of the dynamics of an hovercraft with flexible skegs has been constructed, allowing for the design of amphibious vehicles for use in hard-to-reach regions. Issues related to the damping of various types of high-speed vessels have been studied. Work is currently underway to obtain new, more precise criteria for the stability of promising amphibious vehicles, taking into account the design features and operating conditions of the vehicles. Methods for modeling the dynamics of flexible pneumatic structures in a fluid flow are also being developed.

— There are several scientific groups within the laboratory, conducting research in different directions. How did you manage to unite them?

— The forming direction is dynamic systems, but almost all phenomena in the world fall under the definition of “dynamic systems”. Thus, Natalia Stankevich uses them for research in biology and medicine, and Alexey Kazakov is engaged in numerical calculation for specific systems of differential equations describing such phenomena as turbulence, Celtic stone, Chaplygin’s top, etc.

Under the umbrella of dynamic systems in the laboratory, specialists in such fundamental mathematical areas as algebra, geometry, topology, function theory, etc., which are not directly related to dynamic systems, also feel great. There is a very strong group of physicists involved in fluid mechanics. Often, such scientific symbiosis brings unexpected results at the junction of research areas.

— How do you attract such diverse specialists?

— As a rule, a young or established scientist appears in the laboratory as a participant in some won grant or project. The laboratory management does everything possible to create comfortable conditions for the employees, welcoming any creative initiative. People appreciate this and in most cases remain in the team after the end of the project, some even move to Nizhny Novgorod for permanent residence.

Another source of promising researchers is educational activity. Since the laboratory serves several educational programs, the range of which is expanding every year, the number of professors and teachers naturally increases. Due to the presence of a scientific department, teachers have a smaller workload than in their previous places of work. The newly arrived employees are happy to devote their free time to scientific research.

The main source of influx of personnel, of course, are students of our program “Fundamental and Applied Mathematics”.

We try not only to attract students to scientific research, but also to track their emerging interest in a timely manner. We offer to work as an intern, some come in the first year of the bachelor’s degree. We involve them in active scientific life, grants, schools, conferences. The overwhelming majority stay in the laboratory, and this is a huge driving force

We have now reached a staff of 60 employees, almost like a small research institute.

— How important do you consider mentoring and personal example to be in science?

— Extremely important. Specifically for our team, we managed to ensure the continuity of generations. In our laboratory, we have employees who are over 75–80 years old, very experienced scientists, some of whom studied with Academician Alexander Andronov, his closest associates and students. There are not so many middle-aged scientists (like me), but we managed to show young people scientists with a high academic culture, such as my scientific supervisor Vyacheslav Grines and his colleagues from the school of nonlinear oscillations.

Let me remind you that the scientific school of nonlinear oscillations was created in Gorky (now Nizhny Novgorod) by young scientists who moved to the then closed city, headed by the future academician Alexander Andronov. A physicist by profession, he sought to describe mathematical models of physical processes and phenomena, to translate them into mathematical language. He created the radiophysics department at Gorky University, then the Institute of Applied Mathematics and Cybernetics was organized, and a scientific school was formed, known in the world as the school of dynamic systems.

— How do you manage to find resources for research?

— We constantly apply for grants and development programs — for established researchers, young people, external and internal to HSE. Over the past 5 years, we have won 21 grants — that’s a lot for a relatively small team. Thanks to young and experienced colleagues who go through the very labor-intensive application process. In general, the main rule of an ambitious team is to never stop at what has been achieved. Even if it seems that today you already have everything you wanted, you must constantly set new goals for yourself.

— How was the international academic cooperation project formed and how does it work?

— The project with Shanghai Tongji University is a joint Russian-Chinese grant, it began in 2024 and is designed for three years. The project mainly involves fundamental research in the qualitative theory of dynamic systems. We met the Chinese co-director of the project, Bin Yu, back in 2010 in France, where we worked together with world-class dynamist Christian Bonatti. To date, we have already written several joint articles.

International scientific cooperation, exchange of ideas is always great. Our young employees went to China, and everyone really liked the atmosphere at the partner university. It is a great joy to have the opportunity to discuss your scientific ideas with interested people.

— Do the laboratory and its staff work outside the university, implementing the educational function of HSE?

— The annual international conference “Topological Methods in Dynamics” has been gathering like-minded scientists from all over the world within the walls of the Nizhny Novgorod HSE for 9 years now.

This year we are holding another scientific conference dedicated to the 30th anniversary of the Nizhny Novgorod Mathematical Society, of which I am currently the president.

For 6 years now, every March we have been holding a school for students called “Mathematical Spring”, inviting different lecturers and speakers, and judging by the students’ feedback, this is a very interesting format for them.

For the second year in a row, we are organizing a student school at the Sirius Mathematical Center together with colleagues from Moscow State University and Moscow Institute of Physics and Technology.

A good initiative was the holding of the All-Russian review of students’ diploma works, which will be held for the fifth time this year.

In June-July we hold a thematic shift for schoolchildren called “Intellectual”. The children are immersed in mathematics, including applied mathematics, computer science, and artificial intelligence. It has been held for the tenth time, in recent years – in the “Salut” camp in the Nizhny Novgorod region.

Throughout the school year, we have a “Mathematical Academy”, where schoolchildren gain their first experience working with scientific research. Our scientists generously share interesting tasks with young talents, and under their guidance, students annually become winners of the “Scientific Society of Students” research paper competition.

I would like to emphasize once again that all this would be impossible without our youth with their energy and enthusiasm. It is great that we have them and that there are more and more of them.

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