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Тhe aim of this work is to assess the mechanical behavior of coronary vessels and angioplasty balloons during the angioplasty procedure, based on intravascular ultrasound (IVUS) and angiography data obtained for each patient individually. To treat atherosclerosis, a serious chronic inflammatory disease of the arteries characterized by the formation of atherosclerotic plaques, which causes vessel narrowing and impairs blood supply to tissues and organs, modern medical practice employs a minimally invasive endovascular procedure known as balloon angioplasty. Key aspects of modeling this procedure include understanding the behavior of patients’ arteries and the balloons used during the intervention. Based on intravascular ultrasound and angiography data, a biomechanical model of an artery affected by atherosclerosis is developed. A finite element model of the arterial segment is constructed, accounting for its nonlinear hyperelastic behavior. To simulate the behavior of the angioplasty balloon, a mathematical model of the balloon is developed and validated against experimental data. An assessment of the stress-strain state of a specific patient’s coronary artery and angioplasty balloon is performed. For a full-scale simulation of the angioplasty process, a mathematical model is developed that incorporates all three objects considered above: personalization of the artery model through the use of real patient data; a finite element model of the artery built based on of the personalized model, accounting for its nonlinear behavior; a finite element model of the angioplasty balloon. The developed mathematical models and the results obtained from them will further allow us to derive dependencies of key angioplasty parameters. These dependencies can be used to improve angioplasty techniques based on intravascular imaging data. Furthermore, the application of mathematical modeling methods will help reduce the number of clinical trials in this field.

In this paper we present a mathematical model and numerical results on a propagation of the combustion front of the SHS compound, where the rate of chemical reaction at each point of the SHS sample is determined by solving the problem of diffusion and chemical reaction in the reaction cell. We obtained the dependence of the combustion front on the size of the average element of a heterogeneous structure with different values of the diffusion intensity. These dependences agree qualitatively with the experimental data. We studied the effect of activation energy for diffusion on the propagation velocity of combustion front. It is revealed the propagation of the combustion front transforms to an oscillatory regime at increase in activation energy of diffusion. A transition boundary of the combustion front propagation from the steady-state regime to the oscillatory one is defined.

In the paper we construct the adjoint problem for the explicit and implicit parabolic quazi-linear grid boundary-value problems with one spatial variable; the coefficients of the problems depend on the solution at the same time and earlier times. Dependence on the history of the solution is via the state vector; its evolution is described by the differential equation. Many models of diffusion mass transport are reduced to such boundary-value problems. Having solutions to the direct and adjoint problems, one can obtain the exact value of the gradient of a functional in the space of parameters the problem also depends on. We present solving algorithms, including the parallel one.

In the paper we consider the inverse problem of evaluating kinetic parameters of the model of dehydriding of metal powder using experimental data. The «blind search» in the space of parameters revealed multiple physically reasonable solutions. The solutions were obtained using high–performance computational modeling based on BOINC–grid.

The aim of this article is to study the discrete mathematical model of transport network dynamics, recently built by author. The study showed some drawbacks of the basic model and the ways of overcoming these drawbacks, and an improved version of the model was proposed. Simulation systems, created on the basis of this new model were used to do test calculations similar to those previously done with the help of the basic model. The results of these calculations with both models are compared.

The work deals the implementation of a three-dimensional mathematical model of the nonlinear time-varying temperature control and a numerical method of solving it.

We study the motion and destruction of Chelyabinsk meteoroid using simple physical and mathematical models. We evaluate the parameters of the motion, taking into account the ablation and mechanical destruction of the meteoroid, and compare our results to the observation data.

Mathematical simulation of natural convection and surface radiation in a square air enclosure having isothermal vertical walls with a local heat source of constant temperature has been carried out. Mathematical model has been formulated on the basis of the dimensionless variables such as stream function, vorticity and temperature by using the Boussinesq approximation and diathermancy of air. Distributions of streamlines and isotherms reflecting an effect of Rayleigh number $ 10^3 \leqslant Ra \leqslant 10^6 $, surface emissivity $0 \leqslant ε < 1$, ratio between the length of heat source and the size of enclosure $0.2 \leqslant l/L \leqslant 0.6$ and dimensionless time $0 \leqslant τ \leqslant 100$ on fluid flow and heat transfer have been obtained. Correlations for the average heat transfer coefficient in dependence on $Ra$, $ε$ and $l/L$ have been ascertained.

The purpose of this paper is to develop a macroscopic hydrodynamic model describing the vehicular traffic on a road junction and taking into account the distribution of traffic light phases and the existing road markings.

In this paper, we propose the unified procedure for the development and calibration of mathematical model for multilane urban road traffic flow. We use macroscopic approach, describing traffic flow with the system of second-order nonlinear hyperbolic equations (for traffic density and velocity). We close the resulting model with the equation of vehicle flow as a function of density, obtained empirically for each segment of road network using data from traffic detectors and vehicles’ GPS tracks. We verify the developed new model and calibration methods by using it to model segment of Moscows Ring Road.