Результаты поиска по 'multiscale mathematical modeling':
Найдено статей: 2
  1. Polyakov S.V., Podryga V.O.
    A study of nonlinear processes at the interface between gas flow and the metal wall of a microchannel
    Computer Research and Modeling, 2022, v. 14, no. 4, pp. 781-794

    The work is devoted to the study of the influence of nonlinear processes in the boundary layer on the general nature of gas flows in microchannels of technical systems. Such a study is actually concerned with nanotechnology problems. One of the important problems in this area is the analysis of gas flows in microchannels in the case of transient and supersonic flows. The results of this analysis are important for the gas-dynamic spraying techique and for the synthesis of new nanomaterials. Due to the complexity of the implementation of full-scale experiments on micro- and nanoscale, they are most often replaced by computer simulations. The efficiency of computer simulations is achieved by both the use of new multiscale models and the combination of mesh and particle methods. In this work, we use the molecular dynamics method. It is applied to study the establishment of a gas microflow in a metal channel. Nitrogen was chosen as the gaseous medium. The metal walls of the microchannels consisted of nickel atoms. In numerical experiments, the accommodation coefficients were calculated at the boundary between the gas flow and the metal wall. The study of the microsystem in the boundary layer made it possible to form a multicomponent macroscopic model of the boundary conditions. This model was integrated into the macroscopic description of the flow based on a system of quasi-gas-dynamic equations. On the basis of such a transformed gas-dynamic model, calculations of microflow in real microsystem were carried out. The results were compared with the classical calculation of the flow, which does not take into account nonlinear processes in the boundary layer. The comparison showed the need to use the developed model of boundary conditions and its integration with the classical gas-dynamic approach.

    Keywords: gas-dynamic microflows in channels with real wall structure, multiscale mathematical modeling, boundary conditions problem, combination of microscopic and macroscopic approaches, parallel computing.
  2. Bratsun D.A., Zakharov A.P., Pismen L.M.
    Multiscale mathematical modeling occurrence and growth of a tumour in an epithelial tissue
    Computer Research and Modeling, 2014, v. 6, no. 4, pp. 585-604

    In this paper we propose a mathematical model of cancer tumour occurrence in a quasi twodimensional epithelial tissue. Basic model of the epithelium growth describes the appearance of intensive movement and growth of tissue when it is damaged. The model includes the effects of division of cells and intercalation. It is assumed that the movement of cells is caused by the wave of mitogen-activated protein kinase (MAPK), which in turn activated by the chemo-mechanical signal propagating along tissue due to its local damage. In this paper it is assumed that cancer cells arise from local failure of spatial synchronization of circadian rhythms. The study of the evolutionary dynamics of the model could determine the chemo-physical properties of a tumour, and spatial relationship between the occurrence of cancer cells and development of the entire tissue parameters coordinating its evolution through the exchange of chemical and mechanical signals.

    Keywords: mathematical modeling, cancer growth, circadian rhythms, gene regulation, synchronization, complex systems.
    Views (last year): 10. Citations: 12 (RSCI).

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