The directions of the research work of the department are very diverse. The objects of research are physical, mathematical, economic, social and other systems. Under the guidance of teachers and graduate students of the department there are students of various specialties who submit 15-25 reports annually at scientific and technical conferences at SSU and other higher educational institutions, as well as several reports at international scientific and technical conferences. Teachers and graduate students of the department annually publish scientific articles in specialized journals and collections of scientific papers, including articles that are counted in the Scopus database.

Every year students of the specialty take part in the All-Ukrainian competition of student research papers in the areas of "Computer Science and Cybernetics", "Mathematical Sciences", "Physics", "Information Security", "Mathematical Methods, Models in Economics" and "Military Sciences".

Directions of scientific research of the department:

1. Statistical theory and molecular dynamics of non-equilibrium nonlinear systems (Prof. O. Khomenko).
2. Mechanics of adhesive dynamic contact of nonhomogeneous materials with rough surfaces (Prof. Ia. Lyashenko).
3. Modeling of nonlinear processes in relativistic plasma-like systems (Prof. A. Lysenko)
4. The formation processes of nanostructured film systems, the study of nanocrystalline films of borides, nitrides and boridonitridov transition metals (Prof. A. Goncharov).
5. Modeling of processes in complex special-purpose systems (Associate Professor I. Koplyk).
6. Formation and investigation of structural and morphological properties of porous metal and carbon nanosystems formed under conditions close to thermodynamic equilibrium (Associate Professor A. Kornyushchenko).
7. Research of ordering and pattern formation processes in complex spatially extended systems (Senior Lecturer A. Dvornichenko).
8. Ellipsometric studies of the surfaces of amorphous alloys (Associate Professor V. Karpusha).

Recent dissertations:

• Volk I. I. Multiharmonic two-stream superheterodyne FELs with helical electron beams. scientific director – A. V. Lysenko. 2019.
• Badalyan A.Yu. Formation and modes of motion of ensembles of nanoparticles in the framework of statistical theory. Scientific director – O. V. Yushchenko. 2018.
• Troshchenko D. S. Nonequilibrium evolutionary thermodynamics of metals fragmentation with taking into account stochasticity. Scientific director – Doctor of Physics and Mat. Sciences, Professor of AM&CSM Department, SSU, O. Khomenko. 2018.
• Lyashenko I. A. Phase transitions between kinetic modes of boundary friction. Scientific director – Doctor of Physics and Mat. Sciences, Professor of AM&CSM Department, SSU, O. Khomenko. 2018.
• Oleksiienko G. A. Multiharmonic interaction in plasma-beam superheterodyne free electron lasers with helical electron beams. Scientific director – Doctor of Physics and Mat. Sciences, Professor of AM&CSM Department, SSU, A. Lysenko. 2017.
• Shovkoplyas O. A. The influence of forming and thermoradiation processing conditions on the structure and properties of Ti-W-B and Ti-W-C system coatings. Scientific director – Doctor of Physics and Mat. Sciences, Professor, O. Sobol. 2016.
• Zaskoka A. M. Phase transitions in ultrathin solid-like lubricant films at the boundary friction. Scientific director – Associate Professor, Candidate Phys.-Mat. Sciences, I. Lyashenko. 2016.
• Manko N. N. Synergetic representation of stick-slip regime of boundary friction. Scientific director – Associate Professor, Candidate Phys.-Mat. Sciences, I. Lyashenko. 2015.
• Shvets U. S. The influence of plastic deformation and ion irradiation on amorphization and optical properties of Fe and Ni based amorphous alloys. Scientific director – Associate Professor, V. Karpusha, 2014.