Scientific results:
- Our researchers have proposed a method for obtaining precise solutions of nonlinear differential equations and systems of those.
- We have build new conservation laws for mathematical models described by differential equations of fractional and integer order, solved problems of their group classification, developed methods of their precise and approximate integration.
- Our researchers have developed models of collectors of oil and gas deposits with complex geological structure and permeability, as well as models of filtration of oil and gas in them.
- The Laboratory has developed schemes of 3D visualization for computer models and software that has been tested on a 3D testing bench.
- We have created an intellectual database in group analysis with mathematical models from various domains of natural sciences, engineering, and technology.
- New efficient numerical algorithms have been developed for the computer modeling of processes with memory and spatial nonlocality described by fractional differential equations.
- The Laboratory has created a prototype of software complex for the hydrodynamic modeling of seepage flows in a fractured-porous media possessing the property of power-law memory.
Implemented results of research:
- The proposed mathematical model for friction welding using heat during tight pressing of parts can be applied in technologies of manufacturing of blisks of aircraft engines.
- The developed models for processes of movement of oil and gas in collectors with complex structures allow to predict volumes of hydrocarbon extraction from oil and gas deposits of Russia and are used in scientific and practical work of «RN-UfaNIPINeft» LLC that is a project institute of Rosneft Oil Company.
Education and career development:
- We have organized internships of students, postgraduates and young scientists at leading foreign universities: the Blekinge Institute of Technology (Sweden), the School of Mathematics of the Suranaree University of Technology (Thailand), Brock University (Canada), the University of Cádiz (Spain), and the Shenyang Aerospace University (China PR).
- Two doctoral dissertations and 4 candidate dissertations have been defended.
- We have developed educational courses: «Analytical methods of solving differential equations» (bachelors) and «Mathematical modeling with elements of group analysis» (for masters), and the short-term additional training course «Methods of research of symmetry properties of mathematical models». A masters program in mathematics has been developed, as well as a distance education course in applications of group transformations in mathematical modeling (in Russian and English).
Organizational and structural changes:
- New infrastructure has been build for conducting scientific research and completing applied work in mathematical modeling that is being successfully enhance after the completion of the project.
- A unique bench for 3D visualization for research and education purposes has been created and is currently functioning.
- We are regularly modernizing the university's supercomputer.
- The Laboratory has purchased professional software for computer modeling.
Other results:
We have conducted four international conferences: «Modern Group Analysis» (MOGRAN): MOGRAN-15 (2012, Kemer, Turkey), MOGRAN-16 (2013, Ufa, Russia), MOGRAN-17 (2014, Cádiz, Spain), MOGRAN-18 (2015, Shenyang, China PR).
Collaborations:
- Blekinge Institute of Technology (Sweden): a bilateral agreement for conducting joint scientific research in group analysis of mathematical models, and a trilateral agreement (in collaboration with the Federal University of ABC, Brazil) for partnership in staff training in mathematical modeling and group analysis (we have organized internships of young members of the academic staff of the Laboratory, students, postgraduates and young researchers at the Blekinge Institute of Technology; as a result of research in collaboration with employees of the Institute we have published several articles in journals indexed by the «Web of Science» database).
- University of Cádiz (Spain): a bilateral agreement for joint research in group analysis of differential and integro-differential equations and training staff in applied mathematics (joint participation of two universities in the «Erasmus Mundus» program that resulted in postgraduate exchange, several articles have been published in journals indexed by the «Web of Science» database).
- Federal University of ABC (Brazil): a bilateral agreement for collaborative scientific research in group analysis of mathematical models and a trilateral agreement (in collaboration with the Blekinge Institute of Technology, Sweden) for partnership in staff training in mathematical modeling and group analysis (joint events have been conducted, several articles have been published in journals indexed by the «Web of Science» database).
