Результаты поиска по 'experimental mathematics':
Найдено статей: 62
  1. Andreeva A.A., Anand M., Lobanov A.I., Nikolaev A.V., Panteleev M.A.
    Using extended ODE systems to investigate the mathematical model of the blood coagulation
    Computer Research and Modeling, 2022, v. 14, no. 4, pp. 931-951

    Many properties of ordinary differential equations systems solutions are determined by the properties of the equations in variations. An ODE system, which includes both the original nonlinear system and the equations in variations, will be called an extended system further. When studying the properties of the Cauchy problem for the systems of ordinary differential equations, the transition to extended systems allows one to study many subtle properties of solutions. For example, the transition to the extended system allows one to increase the order of approximation for numerical methods, gives the approaches to constructing a sensitivity function without using numerical differentiation procedures, allows to use methods of increased convergence order for the inverse problem solution. Authors used the Broyden method belonging to the class of quasi-Newtonian methods. The Rosenbroke method with complex coefficients was used to solve the stiff systems of the ordinary differential equations. In our case, it is equivalent to the second order approximation method for the extended system.

    As an example of the proposed approach, several related mathematical models of the blood coagulation process were considered. Based on the analysis of the numerical calculations results, the conclusion was drawn that it is necessary to include a description of the factor XI positive feedback loop in the model equations system. Estimates of some reaction constants based on the numerical inverse problem solution were given.

    Effect of factor V release on platelet activation was considered. The modification of the mathematical model allowed to achieve quantitative correspondence in the dynamics of the thrombin production with experimental data for an artificial system. Based on the sensitivity analysis, the hypothesis tested that there is no influence of the lipid membrane composition (the number of sites for various factors of the clotting system, except for thrombin sites) on the dynamics of the process.

    Keywords: mathematical models, ODE system, equation in variations, CROS method, Broyden method, blood clotting, thrombin, platelets.
  2. Podryga V.O., Polyakov S.V.
    3D molecular dynamic simulation of thermodynamic equilibrium problem for heated nickel
    Computer Research and Modeling, 2015, v. 7, no. 3, pp. 573-579

    This work is devoted to molecular dynamic modeling of the thermal impact processes on the metal sample consisting of nickel atoms. For the solution of this problem, a continuous mathematical model on the basis of the classical Newton mechanics equations has been used; a numerical method based on the Verlet scheme has been chosen; a parallel algorithm has been offered, and its realization within the MPI and OpenMP technologies has been executed. By means of the developed parallel program, the investigation of thermodynamic equilibrium of nickel atoms’ system under the conditions of heating a sample to desired temperature has been executed. In numerical experiments both optimum parameters of calculation procedure and physical parameters of analyzed process have been defined. The obtained numerical results are well corresponding to known theoretical and experimental data.

    Keywords: molecular dynamic simulation, nickel, EAM, temperature, thermostat, Newton mechanics equations, parallel algorithm and program, MPI and OpenMP technologies.
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