Kolodkin logo

Modeling of Disasters Consequences, Digital Safety Systems

Group leader: Prof. Vladimir M. Kolodkin, General Engineering Department, Institute of Civil Defense;

Research abstract: To predict the level of fire hazard in educational institutions (EI), to rank buildings and structures of EI by hazard level, a new technology is proposed based on mathematical modeling methods and modern information technologies. It is proposed to use the capabilities of the problem-oriented Service "EI Risk Analyst". The service supports mathematical modeling of the fire process in the building and the process of evacuating people from the building in a fire. Based on the simulation results, hazard level assessments are calculated. The service is available on the Internet in Russia. The EI Risk Analyst service is a toolkit focused on calculating fire hazard level characteristics in buildings and structures of educational institutions. The software supports the following tasks:

  1. Prediction of the frequency of fire in an educational institution building;
  2. Entering construction plans and characteristics related to the building and to each room in the building;
  3. Modeling fire spreading in a building;
  4. Modeling the evacuation of people from a building in a fire;
  5. Assessments of the fire safety level and the formation of the Certificate.

After processing the data entered by user, the Service forms a set of quantitative characteristics of the danger level, including the value of fire risk. The calculated parameters make sense primarily in terms of ranking buildings by fire hazard level.

Prediction of the consequences of a fire within the framework of the Service is based on the results of mathematical modeling of two main processes: the process of a fire propagation in a building and the process of evacuating people from a building in a fire. When modeling a fire in each room, the values of dangerous fire factors are controlled: temperature, heat flow, loss of visibility, lower oxygen content, increase in the content of CO2, CO, and HCl in the room. To simulate the fire process in a building within the Service, program modules are used that implement the integral and zone models.

When modeling the process of evacuating people from a building in a fire, a hybrid model is used that combines the flow model and the agent behavior model. At each time interval, the coordinates of the agents in the building and the possible trajectories of the agents are monitored. The agent’s behavior model is configured so that the agent seeks to leave the premises in the shortest possible time, taking into account the probability that the agent will pass each of the premises along the evacuation route. The probability of an agent passing through each room is determined by the level of deviation of the values of hazardous fire factors from their critical values. If the values of dangerous factors of the fire in the room exceed critical values, the probability of the agent passing the room becomes zero. At the same time, a new agent evacuation trajectory is constructed, that is, the agent trajectories are changed taking into account the results of the fire simulation.

As part of the EI Risk Analyst Service, a regression model is being constructed that relates the frequency of a fire in a building to the main characteristics of the building and the environment. Based on the results of the calculations, the document “Certificate of fire safety of the educational institution” is formed, which includes the main characteristics of the fire hazard of the EI building:

  1. Characteristics of the most dangerous scenario of fire development in the EI building:
  • predicted frequency,
  • the estimate of possible casualties
  • the amount of possible economic damage;
  1. The probability of evacuating people from the building:
  • in the worst-case scenario of fire development,
  • averaged over all possible scenarios of fire propagation;
  1. Individual fire risk for people in the building:
  • in the worst-case scenario of fire propagation,
  • averaged over all possible scenarios of fire propagation.

The “Safety in the Technosphere” resource is supported by an accessible training system that provides training for users in remote access mode, including the “EI Risk Analyst” Service. The service and the training system provide the tool for careful assessment of the danger level in each educational institution, and also comparative analysis of educational institutions by the level of danger they generate for members of society. The rating of buildings according to the fire hazard level will enable the use of economic, administrative and other resources to control the level of fire hazard. The toolkit is available to Internet users. Technical capabilities of the Service allow the development of up to several hundred Certificates per day.

Partners: Russian Scientific Society for Risk Analysis (Modeling of Fire Consequences in EI Buildings project)

Key publications: V. Kolodkin, B. Chirkov System for Adaptive Fire Emergemncy Management in Buildings // Safety in Technosphere, 2017, iss. № 4(67), С. 58-65. V. Kolodkin, D. Varlamov Special Features of Socio-Technical Rescue Operations at Fire Outbreak in Public Buildings // Technosphere Safety Technologies. – Iss. 1 (83). – 2019. – С. 101-112. DOI: 10.25257/TTS.2019.1.83.101-112.


R&D journal

Regular and Chaotic Dynamics

Group leader: Aleksei V. Borisov, Head of the Institute of Computer Science, e-mail:

Research abstract: The institute’s activity focuses on research in the field of modern robotics, mechanics, and control theory; development and implementation of new methods of movement on land and in liquid; problems of increasing the maneuverability of existing vehicles (new types of wheels), the creation of new vehicles used in space and on other planets.

The research performed by the Institute has yielded the following results so far:

  • mathematical models have been developed to describe the dynamics of the following mobile systems: spherical robot in four different modifications, screwless surface and underwater mobile systems, omni-wheel mobile robots. The developed mathematical models are the theoretical basis for constructing algorithms for dynamic control of robots and analysis of the stability areas of mobile devices movement.

  • full-scale prototypes of the above-mentioned mobile systems were created and improved. Control programs have been developed and patented for all samples of the mobile systems. New methods have been developed for analyzing the dynamic behavior of robotic systems, including nonholonomic and friction systems. The developed methods are also widely used in the study of various dynamic systems in related fields of science.

  • Methods have been developed for the experimental study of the motion of bodies in a liquid and on various surfaces. The obtained experimental results for the considered full-scale samples of mobile systems confirm the adequacy of the developed theoretical models of motion.

Over the past 5 years, the Institute’s staff has published over 150 papers in leading peer-reviewed scientific journals, including those indexed in the Web of Science and Scopus systems, defended 3 doctoral and 4 candidate dissertations on research topics.

Partners: Institute of Dynamical Astronomy and Ephemerides Calculation (France) National Autonomous University of Mexico Lougborough University (UK) University of Zielona Gora (Poland) Polytechnical University of Catalonia (Spain) Mathematical Institute of Serbian Academy of Science and Arts (Serbia) Ritsumeikan Asia Pacific University (Japan)

Key publications:

  1. Bizyaev I. A., Borisov A. V., Kuznetsov S. P., The Chaplygin sleigh with friction moving due to periodic oscillations of an internal mass, Nonlinear Dynamics, 2019, vol. 95, no. 1, pp. 699-714
  2. Borisov A. V., García-Naranjo L., Mamaev I. S., Montaldi J., Reduction and relative equilibria for the two-body problem on spaces of constant curvature, Celestial Mechanics and Dynamical Astronomy, 2018, vol. 130, no. 6, pp. 1-36
  3. Borisov A. V., Mamaev I. S., Vetchanin E. V., Self-propulsion of a Smooth Body in a Viscous Fluid Under Periodic Oscillations of a Rotor and Circulation, Regular and Chaotic Dynamics, 2018, vol. 23, no. 7-8, pp. 850-874
  4. Kilin A. A., Pivovarova E. N., Chaplygin Top with a Periodic Gyrostatic Moment, Russian Journal of Mathematical Physics, 2018, vol. 25, no. 4, pp. 509-524
  5. Borisov A. V., Mamaev I. S., Rigid Body Dynamics, Ser. De Gruyter Studies in Mathematical Physics, Vol. 52, Berlin/Boston: Higher Education Press and de Gruyter GmbH, 2018, 526 pp.
  6. Borisov A. V., Kilin A. A., Karavaev Y. L., Retrograde motion of a rolling disk Physics-Uspekhi, 2017, vol. 60, no. 9, pp. 931-934
  7. Borisov A. V., Mamaev I. S., Bizyaev I. A., Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics Russian Mathematical Surveys, 2017, vol. 72, no. 5, pp. 783-840
  8. Bizyaev I. A., Borisov A. V., Kilin A. A., Mamaev I. S., Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups Russian Journal of Nonlinear Dynamics, 2017, vol. 13, no. 1, pp. 129-146

Full list of publications


Petrov logo

Mathematical Theory of Management and Conflict Interaction of Groups of Objects

Group leader: Prof. Nikolai Petrov, Dean of the Institute of Mathematics, Information Technologies and E-mail:

Main areas of research: • Dynamic system of shifts, ergodic theory, controlled systems and differential inclusions • Investigation of the structure of the controllability set and the attainability set of linear controlled systems • Investigation of the positional control structure for the time-optimal problem • Linear controlled systems and the theory of global control by Lyapunov invariants • The development of mainstream processes theory • The development of the theory of controlled systems with near-periodic parameters. • Conflict interaction of groups of managed objects. • Nonantagonistic differential games.

Partners: • Department of "Differential Equations", Faculty of Mechanics and Mathematics, Moscow State University, • Department of Optimal Management, VMK Moscow State University, • Faculty of Mathematics and Mechanics, St. Petersburg State University, • Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, • Institute of Mathematics and Mechanics, Ural Branch of RAS, • Institute of System Dynamics and Control Theory of the Russian Academy of Sciences (Irkutsk), • Institute of Mathematics of the Academy of Sciences of Belarus, • Institute of Cybernetics NAS of Ukraine, • Institute of Mathematics, Academy of Sciences of Uzbekistan, • Tashkent University (Uzbekistan), • Faculty of Mathematics, Chelyabinsk University, • Faculty of Mathematics, Nizhny Novgorod University, • Economics, Mechanics and Mathematics faculties of Perm University, • Institute of Applied Mechanics RAS (Izhevsk)

Key publications


Kharanzh logo

Functional Materials and Coatings

Group leader: Prof. Evgenii Kharanzhevskiy, Head of Materials Physics and Chemistry Laboratory: e-mail:

Research abstract: Research is aimed at obtaining new functional materials with improved mechanical, physicochemical and tribotechnical properties. Materials and coatings are formed by high-speed selective laser sintering of ultrafine nanostructured powders. Ultrahigh cooling and crystallization rates of materials during such a laser treatment make it possible to obtain and fix a metastable nanostructured state of a substance, characterized by a highly developed surface and a system of coupled nanostructured pores. To exclude the influence of oxygen, laser sintering is carried out in a vacuum chamber, which allows to obtain any materials, including those with high affinity for oxygen. Unique technologies make it possible to modify the surface layers of parts in order to significantly improve the functional properties of materials without changing the geometry of the part with improved surface roughness. The method allows to obtain coatings on the surface of parts of complex shape with a thickness of up to 1 mm from virtually any material. Scope: production of catalysts, electrodes for hydrogen energy, super capacitors, obtaining coatings with high corrosion and wear resistance, superhard coatings, coatings for electrical contacts. Main research areas:

  1. Materials and coatings with new functional, tribotechnical and electrochemical properties: a. Biocompatible coatings b. Hard alloy coatings VK-10 on the surface of steels and alloys. Coating thickness from 5 to 80 microns. Unique resistance to abrasive and adhesive wear. Hardness 20 GPa. Ideal for contact surfaces of sensors, pressure tools, parts that work in aggressive conditions with high wear. c. Coatings to reduce the contact resistance of materials (steel, silver, copper alloys, etc.). High erosion resistance of contact surfaces of breakable and sliding contacts. d. Corrosion-resistant coatings based on conductive metal-metalloid systems. e. Coatings for the cathodic evolution of hydrogen in hydrogen energy. f. Active materials of super capacitors electrodes.
  2. Obtaining laser-induced nanostructures on the surface of steels: a. Saturation of the surface of steels with graphite up to 20 wt.% b. A decrease in the coefficient of friction of slip pairs by 2-3 times with dry friction and friction with lubricant.
  3. Laser processing of materials: a. Laser welding of steels, non-ferrous alloys (aluminum, copper, etc.), titanium b. Laser hardening c. Laser cutting of steels and non-ferrous alloys d. Laser marking of organic and inorganic materials
  4. Experimental studies in the field of material sciences a. X-ray diffraction b. Transmission Electron Microscopy (TEM) c. Scanning Electron Microscopy (SEM) d. BET measurement of specific surface and porosity of materials e. Raman spectroscopy

Partners (joint research):

Key publications