and Computational Methods

doi: 10.18698/2309-3684-2017-4-316

The article presents a mathematical model of the alloys nanoparticles structure rearrangement dynamics after the instantaneous thermal influence (heating or cooling). The model is based on using the method of molecular dynamics of multicomponent alloys with the Lennard-Jones and Morse interatomic potentials as well as the initial conditions of momentary expansion or compression of the alloy nanoparticle regular crystalline structure. We computationally investigate the regularities of rearranging the initially regular atomic structure of a nanoparticle over time. It is shown that depending on the number of atoms in a nanoparticle various finite settled forms of the alloys nanoparticle are possible, both amorphous and new crystalline structures different from the alloy original crystalline nanostructure. We provide numerical results for the titanium nanoparticles and the titanium-nickel alloy (nitinol).

Krasnov I.K., Mozzhorina T.Yu., Balanin A.N. Numerical modeling of alloys nanostructure rearrangement by means of molecular dynamics methods. Маthematical Modeling and Computational Methods, 2017, №4 (16), pp. 3-16

doi: 10.18698/2309-3684-2017-2-94106

We conducted a numerical experiment in applying the shooting method to solve problems of optimal control with switching. We used the problem of lunar soft-landing to test an algorithm that ensures convergence of Newton's method in problems of this type. We analysed the accuracy of our computations.

Mozzhorina T. Yu. Numerical solution to problems of optimal control with switching by means of the shooting method. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 94-106

doi: 10.18698/2309-3684-2017-3-7182

The article considers the application of the direct statistical simulation method to the problems of gas dynamics in a rarefied region. An analytical method for assignment and taking into account complex boundary conditions associated with the geometry of the body located in the computational domain is proposed. An algorithm for the rational description of a body streamlined by a gas is developed.

Krasnov I.K.,Mozzhorina T.Yu., Dzhus D.V. Numerical statistical simulation of the process of rarefied gas flow over an aircraft .Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 71–82

doi: 10.18698/2309-3684-2014-2-327

The paper considers two-dimensional boundary value problem of propagation of plane electromagnetic wave through a periodic stratified medium with one-dimensional photonic crystal structure. The structure contains a finite number of slabs. Each periodicity cell consists of two layers with different real values of constant dielectric permittivity and different thicknesses. We show that under certain additional condition, which connects the angle of incidence of the plane wave, thicknesses of the layers, frequencies and dielectric permittivity of the layers, we can solve the problem completely and explicitly, the solution leading to simple expressions for both the field reflected from the structure, and the field which has passed through it. Herewith in case of H-polarized field, unlike E-polarization, properties of this medium depend on the ratio of thickness of the layers multiplied by their dielectric permittivity (with E-polarization they depend on thickness ratio only). As a result, depending on the field frequency, photonic crystal can behave as perfectly reflecting structure, while with the same ratio of thicknesses of the layers in case of E-polarization, it becomes a wave guiding structure, and vice-versa. We have compared numerical computations with those for cases of E-polarization.

Apeltsin V., Mozzhorina T. Properties of one-dimensional photonic crystal as a reflective or wave guiding structure when excited by H-polarization. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 3-27

doi: 10.18698/2309-3684-2014-3-7488

We examined effects of typical for different climatic zones atmospheric conditions on flight program optimization for a subsonic long-haul passenger aircraft. Simulation of flight and power plant performance was based on current traditional approaches used in solving problems of this kind. The acceleration-climb flight segment has been optimized by minimizing fuel consumption at this flight segment. The cruising flight segment has been optimized considering operating limitations accepted for civil aviation. The in-built model of bypass turbojet engine was used for simulating the flight. This model allows calculating power plant performances under any flight conditions. The flight of subsonic aircraft has been examined in one vertical plane. Calculations have been performed for 6 standard air temperature variations with altitude (depending on climatic zone). Atmospheric pressure variation near Earth surface was considered and effects of atmospheric conditions on flight program optimization were estimated.

Mozzhorina T., Gubareva E. Simulating atmospheric conditions influence on flight program optimization for a subsonic passenger aircraft. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 74-88

doi: 10.18698/2309-3684-2020-2-8194

In this paper, we consider one of the possible feedback algorithms for the vertical landing of the returned first stage of the spacecraft for its reuse in the future. It is proposed to use for thrust correction not correction engines, but the main engine of the power plant of the spacecraft, which can be throttled to 60% of the maximum thrust value. A numerical experiment using the Monte Carlo method is performed to evaluate the performance of this algorithm. A soft landing is a landing with a speed of zero or no more than a few meters per second. The last section of the vertical landing is subject to investigation. The optimal program control in this problem statement in terms of minimum fuel consumption is free fall, then turning the engine on at full power until the moment of landing. It is assumed that such parameters as the speed and mass of the spacecraft's return module at an altitude of 2000 m, the specific impulse, as well as the air density and the coefficient of aerodynamic drag can be randomly deviated from the calculated values. It is assumed that these random variables are distributed according to the normal law, are independent, and their deviations from the calculated values do not exceed 1% for the engine pulse and 5% for all other variables. The landing speed is a random value for which the distribution parameters are calculated. The results of the calculation are analyzed.

Мозжорина Т.Ю., Осипов В.В. Моделирование и синтез оптимального управления вертикальной посадкой возвращаемых космических модулей. Математическое моделирование и численные методы. 2020. № 2. с. 81–94.