**Scientific results:**

- The Laboratory has experimentally and numerically researched the mechanism of the formation of submerged jets during surface and volume boiling of liquid near the end of a light waveguide through which laser radiation passes. It has been demonstrated that the interaction of a collapsing bubble with the end of a light waveguide leads to the formation of a hot jet of liquid. The influence of the parameters of the fluid, the geometry of the light-emitting diode and the intensity of laser radiation on the speed of the jet has been studied. The achieved results are highly significant for the development of new surgical medical technologies for the laser surgical treatment of a broad range of widespread diseases. We have solved an inverse problem (a problem of optimal control) for a quasi-linear radiation-conductivity model of heat transfer in endovenous laser ablation. We have proposed an algorithm for solving the problem of optical control and demonstrated its efficiency on a numerical example.

- Within a combined research of the propagation of waves of zoo- and phytoplankton, we have numerically studied the propagation of one-dimensional and two-dimensional waves of populations as part of the «predator-prey» model with the Arditi–Ginzburg trophic function. We reviewed the propagation of population waves of predators and prey as well as the propagation of waves of co-existing populations. The modeling showed that even in the case of an unstable quasi-equilibrium state of the system that establishes itself behind the front of a running wave, the speed of the propagation of a shared wave of settlement are a strictly defined function. The computed mean velocity of propagation of a cellular non-stationary wavefront is unambiguously determined for the specified set of parameters of the problem. Estimates of the speed of the propagation of waves were obtained for both for the cases of flat and cellular wavefronts of populations. The structure and speed of a circular cellular wave that propagates outward are researched to refine the influence of the local curvature and the scaling on the dynamics of the wave.
- We have quantitative researched the conditions that determine the emergence of chaotic or rotating dynamic regimes during the propagation of flames in narrow cylindrical samples of energy materials within two models that differ in their description of heat loss of the sample. It has been demonstrated that the main factor determining the wave dynamics is the thickness of the sample. In sufficiently thin samples the axisymmetric instability mode prevails, while the dynamics of the flame depends on the intensity of heat loss. With an increase of their intensity, the self-oscillation dynamics first transforms into a chaotic one via the doubling of the period of the Feigenbaum cascade, while with a subsequent increase of heat losses dynamic attenuation occurs. However, if the sample is sufficiently thick, the most stable mode is the mode with a non-zero azimuthal wave number, which leads to the formation of rotating structures.
- Our researchers have conducted a numerical modeling of filtration combustion of gases with a detailed review of the processes of combustion and heat transfer in a porous matrix consisting of solid spheres packed into one layer. To verify the numerical results, we created a special burner that allows to collect experimental data on the processes of combustion and the temparature of the solid phase occurring in the interporous space. The results demonstrate that the propagation of a filtration combustion wave for gases is accompanied by oscillations of two types that are clearly separated in frequencies and amplitudes of oscillations. Data of the numerical computations are in good agreement with experimental data in terms of frequencies and amplitudes of oscillations of the flame. The obtained results have a high importance for the understanding of detailed processes pf combustion of gases in radiation burners with filtration combustion of gases that are developed for the creation of new technologies in power generation.

**Implementation of research results:**
- The results of the research of filtration combustion accounting for radiation heat transfer found their reflection in the development of a pre-production model of a device for combined combustion of coal and gas. The device is planned for implementation at power generation facilities of Primorsky Krai.
- The results of the experimental and numerical research of the physical foundations of laser surgery found their applications in medical technologies for the laser surgical treatment of pathologically altered vessels and cysts.

**Education and retraining of personnel:**

In collaboration with the Far Eastern Federal University we have developed and successfully implemented into the education process an updated education program for master’s degree students in the training direction «Applied mathematics».

**Infrastructure transformations:**

We have created a universal computation platform that allows to efficiently model the dynamic behavior of complex reaction-diffusion systems with phase transitions such as combustion waves, interfaces during boiling and condensation of fluids, fronts of the propagation of biological populations and others. The computational capability created within the project at the Institute of Applied Mathematics of the Far Eastern Branch of the Russian Academy of Sciences allow to modernize the existing distributed computation environment of the Far Eastern region of Russia.

**Collaborations:**

- Tohoku University (Japan): joint research, publications in leading academic journals, participation in joint scientific projects.
- Lebedev Physical Institute of the Russian Academy of Sciences (Russia): joint research, publications in leading academic journals, organization and staging of joint scientific events, participation in collaborative projects.
- Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences, Far Eastern Federal University (Russia): joint research, publications in leading international academic journals.
- Vladivostok State University (Russia): joint research, publications in leading international academic journals, organization and staging of joint scientific events