<span>The task of the research was to build and analyze a model of the dynamics of pollution of a flowing reservoir and systems of communicating reservoirs with and without taking into account water filtration in the soil as a result of external sources (effluents from industrial enterprises). This work was aimed at studying the change in temporal dynamics, taking into account the concentration of impurities in the volumes of three reservoirs during the periods of discharge and completion, lasting 30 days. Numerical experiments were carried out for various flow rates and compositions of filtration coefficients to study the relaxation times of pollution in the system of reservoirs. Also, software was developed that analyzes the change in the concentration of impurities in the system of reservoirs. As a result, it was found that the pollution pattern is more dependent on the topology of the watercourse network.</span>

The computer simulation features of the alpha particle decay and isotope separationare discussed in presented paper. When positively charged alpha particles hit a thin plate of matter, then at a close distance to the nuclei they are repelled from the nucleus of an atom, deviating from a straight line in motion, and can even change the rectilinear motion, strongly repulsing from the nucleus and moving towards the source of alpha particles. These cases are simulated and graphs of the trajectories of alpha particles are plottedusing modern computer mathematical system Mathcad.It is proposed to compose differential equations describing the trajectory of the alpha particle and solve them by using the Bulstoer function in the Mathcad. The simulations perfectly confirm the predicted behavior of particles some of them deviate from their linear motion in the absence of a nucleus, and some of the particles change direction in the opposite one. Particle sensors installed in different parts of the physical device detect such changes in the trajectory, which is a confirmation of the atomic theory of the structure of matter and materials. An application program for describing the spectroscopic method of isotope separation has been developed and discussed in detail. Of course, the described models cannot be considered absolutely accurate. For example, if the particles are aimed exactly at the nucleus, significant errors can occur. If the particle speed is high, then the particles can overcome the repulsive force of the nucleus, causing the particles to be absorbed by them. Such absorption conditions are not taken into account in the developed models. One of the important tasks of nuclear physics is the separation of isotopes. An application program has been developed to describe the spectroscopic method of isotope separation. This method is based on the characteristics of the trajectory of ions that radiate and oscillate under an impact of a magnetic field. A system of differential equations describing the motion of ions is given. The problem of the motion of electrically charged particles in a uniform magnetic field is solved in the Mathcad.

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