Mechanics and mathematical modeling of the profession. Basic physical models and concepts of mechanics. Practice locations

The profession lies at the intersection of mathematics, physics and computer science. Students learn to predict the physical processes occurring in solids ah, liquids, gases and plasma using mathematical modeling methods. To do this, one has to use complex computer programs and sometimes create them yourself. Moreover, if it is impossible to use a computer, graduates should be able to solve the problem in other ways. IN curriculum Much attention is paid to physical disciplines, especially mechanics. Also, students get acquainted with computer science, programming and robotics. Specialization depends on what kind of objects the graduate decides to model: solids, liquids or gases. Such a branch of science as engineering biomechanics is becoming popular - the study of the properties of living tissues and the design of artificial body parts. *

* Kit academic disciplines and learning bias

Basic questions of mechanics

Kinematics

Mechanics studies the simplest forms of motion found in the material world, which are united by the common name, mechanical motion.

Under the mechanical movement we will understand the change in the relative position of one material object in relation to another material object. This is one of the most important properties mechanical motion: its relativity.

The main questions that arise when trying to characterize the mechanical movement of a given material object are as follows:

1. How does this object move?, that is, what is the type and nature of its relative motion?

2. Why does this object move in this way and not otherwise?, that is, what are the reasons that cause this particular type and nature of the movement of the object in question?

The search for an answer to the first of these questions is dealt with by the section of mechanics - kinematics, the second - dynamics.

Conclusions: mechanical movement relatively and is the simplest form of motion of matter. Basic questions of mechanics: How and why does a material object move?

Depending on the properties of a material object, the nature and type of its movement, the simplest physical models are used in mechanics:

material point (particle) - an object (body), the dimensions of which can be neglected in comparison with the characteristic size of the movement in which this object participates.

Here we should pay attention to the relative nature of the concept and its abstractness. Any real object has a finite size, which in this particular situation can be neglected or not.

For example, considering the motion of the Earth around the Sun, it can be considered a material point, since the radius of the Earth R z = 6400 km is much less than the radius of its orbit around the Sun R s = 1.5 × 10 8 km. On the other side,

when considering the daily rotation of the Earth around own axis it is impossible to apply the “material point” model for the Earth.

When studying the motion of a body or a system of bodies, when the concept material point cannot be used, it is often useful to apply another physical model called system of material points.

The essence of this model is that any body or system of bodies, the movement of which needs to be studied, is mentally divided into small sections (material points), the dimensions of which are much smaller than the dimensions of the body or system of bodies. In this case, the study of the motion of a body or a system of bodies is reduced to the study of the motion of individual sections of the system, that is, the material points that make up this system. In this case, one should, of course, take into account whether the material points interact with each other or not.

A particular case of the “system of material points” model in mechanics is the model called solid:

Solid - is a system of material points, mutual arrangement which does not change during this movement.

Pay attention to the relativity of this model.

The limiting case of a rigid body model is an absolutely rigid body. In an absolutely solid body, the distance between any arbitrary particles does not change under any conditions. A perfectly rigid body is an abstract model, since no real body has this property.

To describe the movement of a material point, a model is used - trajectory .

Trajectory of movement An imaginary line along which a given material point moves is called.

If this line is a straight line or its segment, then they say that the motion of the material point is rectilinear, otherwise the motion is curvilinear. To describe the types of motion of a rigid body, models of translational and rotational motion are used.

Translational called such a motion of a rigid body, in which any straight line, fastened to this body, during its movement remains parallel to itself.

characteristic feature Such a movement is that the trajectories of all material points that make up a rigid body have the same shape and size and, with a parallel displacement, can be combined with each other.

rotational called such a motion of a rigid body in which all its material points move in circles. In this case, the centers of these circles are located on one straight line, called the axis of rotation.

Arbitrary motion of a rigid body can always be represented as a set of simultaneous translational and rotational motions.

Conclusions: The main physical models of mechanics are a material point, a system of material points and a rigid body. The movement of a material point is determined by the concept of “trajectory of movement”. Trajectories are either straight or curved. The motion of a rigid body can be reduced to two forms: translational and rotational.

Benefits of learning

• Fundamental mathematical training, providing the possibility of active work in the most difficult areas modern mechanics; deep knowledge of programming, which allows to carry out computer simulation of processes and phenomena in various systems
• Availability of existing scientific schools that allow students to actively engage research work directly to the University
• An outstanding team of teachers and researchers who provide training in all areas of modern mechanics
• Work on unique experimental facilities in their own laboratories, a combination of theoretical and experimental approaches, allowing graduates to comprehensively explore the most complex problems of mechanics
• Mastering applied programs for solving problems of theoretical mechanics, hydroaeromechanics and elasticity theory (ANSYS, FLUENT, etc.) and creating your own algorithms and programs for specific problems of modern mechanics on the most modern computer technology

Notable teachers

• N. F. Morozov - Head of the Department of Elasticity Theory of St. Petersburg State University, Academician of the Russian Academy of Sciences, Professor, Doctor of Physical and Mathematical Sciences. Specialist in the nonlinear theory of elasticity, mathematical methods of fracture mechanics. Author of over 200 publications in Scopus and Web of Science
• P. E. Tovstik - Head of the Department of Theoretical and Applied Mechanics of St. Petersburg State University, Professor, Doctor of Physical and Mathematical Sciences, laureate of the State Prize of the Russian Federation, Honored Scientist of the Russian Federation, Commander of the Order of Honor, Honorary Professor of St. Petersburg State University. Specialist in the field of asymptotic and numerical methods in theoretical mechanics, the theory of thin-walled structures, solid mechanics and nanomechanics. Author of over 250 scientific works, including ten monographs and textbooks
• Yu. V. Petrov - Professor of St. Petersburg State University, Head of the Department "Extreme States of Materials and Structures" IPME RAS, Corresponding Member of RAS, Professor, Doctor of Physical and Mathematical Sciences. Specialist in the dynamic theory of elasticity and plasticity, physics and mechanics of shock-wave processes, dynamics of deformation and destruction of solids, detonation and explosion. Author of over 200 publications in Scopus and Web of Science
• E. V. Kustova - Head of the Department of Hydroaeromechanics, St. Petersburg State University, Doctor of Physical and Mathematical Sciences, Professor of the Russian Academy of Sciences. Specialist in the field of the kinetic theory of transfer and relaxation processes in non-equilibrium reacting gases, studies of heat and mass transfer on the surface of aircraft entering the atmosphere of Earth and Mars. Author of more than 200 scientific papers, including more than 120 publications in Scopus and Web of Science, five monographs and textbooks

Future career

Practice locations

Education involves the passage of educational, research and industrial practice on the basis of departments and scientific laboratories St. Petersburg State University.

List of key professions

Graduates of the program are ready for success professional activity in research, design and design institutes, in the construction industry, mechanical engineering, in the rocket and space industry, biomechanics, robotics and other areas of technology and natural science related to the development and application of mathematical methods. They can work as specialists in research and development work in the field of mathematical modeling, scientific and applied research for science-intensive high-tech industries, production and technological activities. Pedagogical work in the field of secondary general and vocational education is possible.

Organizations where graduates work

Graduates of the program continue their studies in the master's program at St Petersburg University and other universities, work in institutes Russian Academy sciences, at the enterprises of the State Corporation Roscosmos, at the subsidiaries of PJSC Gazprom Neft, at the enterprises of JSC United Shipbuilding Corporation, JSC Concern VKO Almaz-Antey, at the Krylov State Research Center, the Central Institute of Aviation Motors named after P.I. Baranova (CIAM), enterprises of the Mavis Investment Group of Companies, at the Izhora Plant, at the shipbuilding NPO Almaz, at the Obukhov Plant, at the FGU Rubin.

The most common entrance exams are:

• Russian language
• Mathematics ( a basic level of)
• Physics - a profile subject, at the choice of the university
• Informatics and information and communication technologies (ICT) - at the choice of the university

Professions

"Mechanics and math modeling"- a specialty that allows in the future to make a choice from a fairly large number of interesting professions:

• Researcher,
• engineer,
• mathematician,
• analyst,
• supervisor,
• researcher,
• teacher of physical and mathematical disciplines,
• specialist in mathematical modeling.

Academic bachelors have the opportunity to work in any field of science, industry, production, management related to mathematics, engineering, physics, mechanics and programming.

Description of specialty

During the training, students acquire scientific knowledge on computer modeling of various mechanical processes. Students study computational mathematics, mechanics and biomechanics, the theory of stability of electromechanical devices, the degree of elasticity, density and plasticity of materials. They master the static and dynamic strength of various objects and other sciences, one way or another related to theoretical mechanics, mathematics, engineering, sopromat.

In the process of learning, students develop the ability to think analytically, study the basics of economics and production management, learn to put into practice the basics of fundamental mathematics, mechanics, physics and other natural sciences.

A feature of training in the specialty "Mechanics and Mathematical Modeling" is a large number of standard hours devoted to practical work. Where students have a unique opportunity to apply their theoretical knowledge in practice, analyze and synthesize specific information. Some of the workshops are devoted to working with computer-mathematical modeling programs designed to simulate technological processes on a monitor screen.

Graduates find application for their knowledge in engineering centers of industrial companies, gas and oil industries, transnational corporations, research and design bureaus, including foreign ones, involved in the development of new engineering technologies.

The main subjects in training in the specialty

• Mechanics of deformable bodies and media.
• Mathematical modeling and computer engineering.

In addition, students study philosophy, history, foreign language and OBZh (basics of life safety). Compulsory disciplines: Physical Culture and applied physical culture.

Terms of study

The term for obtaining full-time education in the specialty"Mechanics and mathematical modeling" is 4 years (including holidays). Part-time and distance learning, by decision of the administration, can be extended for a period of six months to a year.

Skills and abilities acquired during training

• Ability to solve complex problems using information and communication technologies.
• Usage mathematical analysis in the field of theoretical and applied mechanics, resistance of metals, geometry, differential equations and probability theory.
• Work with specialized programs for modeling and optimization of technological processes.
• Doing research work independently or in a group.
• Solving problems of mechanical modeling without the participation of a PC (if the situation requires it).
• Adapting your knowledge to the organization educational process in the field of their competence (physics, mechanics, mathematics, computer science).
• Organization of pedagogical, scientific, managerial and production-technological activities.

During the training, the bachelor acquires the professional skills necessary for competent engineering and analysis of complex mechanical objects by means of computer and / or physical analysis.

During the training, students acquire scientific knowledge on computer modeling of various mechanical processes, develop the ability to think analytically, learn to put into practice the basics of fundamental mathematics, mechanics, physics and other natural sciences.

Graduates find application for their knowledge in engineering centers of industrial companies, gas and oil industries, transnational corporations, research and design bureaus involved in the development of new engineering technologies.

"Mechanics and Mathematical Modeling" is a direction that allows in the future to make a choice from a fairly large number of interesting professions:

Researcher,

• mathematician,

  analyst,

  supervisor,

  researcher,

  teacher of physical and mathematical disciplines,

  specialist in mathematical modeling.

Direction characteristics

Syllabus

Basic profile disciplines:

• mathematical analysis;
• differential equations;
• theoretical mechanics;
• partial differential equations;
• fluid dynamics;
• numerical methods in continuum mechanics;
• physics of the oil and gas reservoir;
• dynamic systems;
• application software packages;
• dynamics of compressible media;
• computer mathematics systems.

Shalaginov S.D. , Associate Professor, Candidate of Sciences;

Machulis V.V. , associate professor, candidate of sciences;

Mosyagin V.E. , Associate Professor, Candidate of Sciences;

Devyatkov A.P. , Associate Professor, Candidate of Sciences;

Butakova N.N. , Associate Professor, Candidate of Sciences;

practices

Siberian and Ural Branch of the Academy of Sciences of the Russian Federation, OJSC Sberbank of Russia, OJSC Zapsibkombank, Schlumberger, LLC Tyumen Institute of Oil and Gas, LLC TyumenNIPIGIPROGAZ, ITAM SB RAS named after. Khristianovich, VTB-24 Bank, SibNAC OJSC, UNI-CONCORD LLC, Earth Cryosphere Institute of the Siberian Branch of the Russian Academy of Sciences, Rusgazproekt OJSC, Nizhneobsky NIPI OJSC, NPO Sibtechneft, Giprotyumenneftegaz OJSC, INFA CJSC , SurgutNIPIneft, NPO Fundamentstroyarkos, OOO Gazpromproektirovanie, OOO Ingeoservice, OOO KogalymNIPIneft.

Achievements

• The TSU SPE Student Chapter team (as part of D.V. Balin) reached the finals of the student intellectual games PetroBowl in London.
• Victory in the contest of the best student works Danil Balin - "The impact of the auto-fracturing process on the development of the field", scientific. head M.Yu. Danko, Head of Hydrodynamic Modeling Department, CJSC Tyumen Institute of Oil and Gas

Learning Outcomes

Ability to solve complex problems using information and communication technologies.

Use of mathematical analysis in the field of theoretical and applied mechanics, geometry, differential equations and probability theory.

Work with specialized programs for modeling and optimization of technological processes.

Doing research work independently or in a group.

Solving problems of mechanical modeling without the participation of a PC (if the situation requires it).

Adapting your knowledge to the organization of the educational process in the field of your competence (physics, mechanics, mathematics, computer science).

Organization of pedagogical, scientific, managerial and production-technological activities.

Employment and career

Areas of activity:

Bachelors have the opportunity to work in any field of science, industry, production, management related to mathematics, engineering, physics, mechanics and programming.

Places of employment of bachelors:

Siberian and Ural Branch of the Academy of Sciences of the Russian Federation, Central Bank, OJSC Sberbank of Russia, OJSC Zapsibkombank, OJSC Surgutneftegazbank, OJSC SibNIINP, Schlumberger, LLC Tyumen Institute of Oil and Gas, LLC TyumenNIPIGIPROGAZ, OJSC Gazprom Neft, CJSC VostokNefteGazProekt, ITAM SB RAS im. Khristianovich, VTB-24 Bank, SibNAC OJSC, UNI-CONCORD LLC, Earth Cryosphere Institute of the Siberian Branch of the Russian Academy of Sciences, Rusgazproekt OJSC, Nizhneobsky NIPI OJSC, NPO Sibtechneft, Giprotyumenneftegaz OJSC, INFA CJSC , SurgutNIPIneft, NPO Fundamentstroyarkos, OOO Gazpromproektirovanie, OOO Ingeoservice, OOO KogalymNIPIneft.

Internships for students, undergraduates and graduate students:

• Evgeny Popov – Scholarship of the President of the Russian Federation for studying abroad, Center for Cloud Computing, University of Birmingham (Great Britain);
• Artem Vorobyov - Scholarship of the President of the Russian Federation for studying abroad, Nanyang University of Technology(Singapore);
• Alexander Kropotin - Scholarship of the President of the Russian Federation for studying abroad, Ulm University (Germany);
• Alexander Stupnikov - Scholarship of the President of the Russian Federation for studying abroad, Ulm University (Germany);
• Natalia Derevyasnikova - program "Semester Abroad", University of Passau (Germany);
• Artur Romazanov, Evgenia Egorova - program "Semester Abroad", University of Passau (Germany);
• Andrey Rybkin - program "Semester Abroad", Kindai University (Gosaka, Japan);
• Anna Zhikhareva - Global UGRAD student exchange program, University of Idaho at Boise (USA);
• Ekaterina Lobanova – Fulbright FLTA Program, Wheaton College (Norton, USA)
• Alexander Gorbachev - Fulbright Program, State research university(state of New York, USA);
• Natalia Derevyasnikova, Anton Lyachek – internship, Huawei (Shenzhen and Beijing, China);
• Polina Gultyaeva, Vladislav Fishman – Semester Abroad Program, University of Koblenz-Landau (Germany)
• Lusine Harutyunyan, Mikhail Lyapunov – Semester Abroad Program, University of Guadalajara (Mexico)

• Maria Rudzevich, Director of the Informatization Department Tyumen region
• Garif Romashkin, manager of the regional bank VTB24
• Evgeny Popov, Research Fellow at the Cloud Computing Center at the University of Birmingham (Great Britain), holder of grants from the President of the Russian Federation, the Potanin Foundation, Governor's Scholarships, Winner of IT-Planet and WorldSkills Russia competencies "Network and system administration"
• Mikhail Fuchko, WorldSkills Russia National Expert in Network and System Administration, coach of the WorldSkills Russia National Team, Head. laboratory of network and system administration of Tyumen State University.
• Elena Tolubaeva, head of department information technologies Federal Tax Service of Russia for the Kurgan Region
• Ivan Karyakin, director of IT company Mintrocket
• Pavel Mostovoy, Leading Specialist of the Large Exploration Projects Support Department, Gazprom Neft Science and Technology Center
• Anna Semenova, specialist of the information and analytical department of the MAOU "Information and Methodological Center"
• Olga Chuenko, Deputy Director of the GKU TO "Center for Information Technologies of the Tyumen Region"
• Maria Krovatkina, network engineer, Schlumberger Logelco inc (Europe and Africa)
• Inna Grigorieva, head of Department of Business Process Automation (based on the 1C:Enterprise platform), Ph.D.
• Vladislav Shkabura, developer, Schlumberger
• Alexander Blazhenskikh, developer at Yandex.Cloud
• Mikhail Grigoriev, National Expert of WorldSkills Russia, Associate Professor of the Department of Software and Systems Engineering, Ph.D.
• Yulia Boganyuk, head. IMiKN computer laboratories, winner of the regional competition of scientific works, winner of the contest "Miss IT of the Tyumen Region", WorldSkills Russia expert in the "Machine Learning and BigData" competency
• Igor Mashchitsky, Data Processing Specialist at SAP IT-SERVICE LLC (SIBUR)
• Andrey Sorokin, Head of the Processing Group, Operational Support for Seismic Surveys, Gazpromneft NTC LLC
• Sergey Glazunov, one of the most famous white hat hackers in Russia. For his work on finding Chrome vulnerabilities, Google paid him more than $80,000,
• Andrey Labunets, specialist of the information security department of Facebook
• Alexander Gorbachev, winner and prize-winner of national championships, WorldSkills World Championship, European Championship in the nomination of system administration, grant holder for master's studies in the USA.
• Irina Prudaeva, Deputy Director of the Department for the implementation of programs and projects Information and methodological center
• Elena Sycheva, Development Engineer, Tyumen Institute of Oil and Gas
• Tatyana Yuferova, winner of the WorldSkills Russia Tyumen, WorldSkills Russia Ural, WorldSkills Russia National Championships in the Business Software Solutions competency
• Andrey Evdokimov, Technical Specialist, Department of Technological Support for Standardized Procedures for Assessing Student Achievements, TOGIRRO
• Yuri Egorov, Leading Development Engineer at Baspro Group of Companies
• Anna Kozhevnikova, Software Engineer, IMS Service under the Administration of Gazprom Dobycha Urengoy
• Evgeny Kabardinsky, Software Engineer at Leadex Systems
• Konstantin Borisov, Chief Specialist of the Department of Master Planning and Production Calculation, Gazpromneft-Yamal LLC
• Nikita Pogodin, Java developer at Luxoft
• Abdullah Bashiru, Alsart Software Manager (Lagos/Nigeria)
• N.S. Bakhtiy, Head of the Department of Mathematical Modeling of Oil and Gas Fields, SurgutNIPIneft, Ph.D.
• A.A. Zolotov, Development Director of the Club of IT Directors of the Tyumen Region, Head of the Development Department information systems OOO "Concord Soft"
• I.N. Polishchuk, director of the Tyumen branch of JSC "GIS-ASUproject", Ph.D.
• V.V. Trofimov, Development Director, PJSC Rostelecom branch in the Tyumen and Kurgan regions
• A. Parkhomtsev, director of Luis+ LLC Western Siberia»
• A.P. Devyatkov, Associate Professor, Department of Fundamental Mathematics and Mechanics, IMiKN, Ph.D.

• Northeastern Pedagogical University(China).
• Qufu State Pedagogical University (China).
• University of Passau (Germany).
• University of Münster (Germany).
• graduate School administrative sciences, Speyer (Germany).
• Tallinn University (Estonia).
• Daugavpils University (Latvia).
• Novobolgarsky University of Sofia (Bulgaria).
• University. Humboldt in Berlin.
• University of Navarra (Spain).
• University of Strasbourg (France).
• University of Lorraine, Metz (France).
• University of Toulouse 2 - Le Miray (France).
• Bodo University College (Norway).
• University of Oslo (Norway).
• University of Wolverhampton (UK).
• University of California, Los Angeles (USA).
• Federal University Fluminense (Brazil).
• Cooperation agreement between federal agency Commonwealth Office independent states, compatriots living abroad, and for international humanitarian cooperation (Rossotrudnichestvo).
• Eurasian humanitarian Institute(The Republic of Kazakhstan).
• Yerevan public university(Republic of Armenia).
• Tashkent University of Information Technologies.
• University of Informatics and Information Technologies. Apostle Paul, Ohrid.
• University of Lüneburg.

• Microsoft, Samsung
• Zapsibkombank
• SKB Kontur
• OOO "Tyumen Institute of Oil and Gas"
• Base Group Labs

Institute of Mathematics and Computer Science