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Найдено документов в текущей БД: 2

    Equations of the dynamics of a liquid crystal under the influence of weak mechanical and thermal perturbations
/ V. M. Sadovskii // AIP Conference Proceedings. - 2014. - Vol. 1629: 6th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2014 (26 June 2014 through 1 July 2014, ) Conference code: 109043. - P311-318, DOI 10.1063/1.4902287 . -

Кл.слова (ненормированные):
dynamics -- micropolar medium -- Nematic liquid crystal -- thermal conductivity -- viscoelasticity -- waves of rotational motion

Аннотация: The paper is devoted to the construction of the simplified mathematical model of thermomechanical behavior of a liquid crystal under the influence of weak mechanical and thermal perturbations. This model is based on the nonlinear equations of a micropolar viscoelastic medium with rotating particles. To describe small strains and finite rotations of molecules, the hypothesis of the dependence of potential energy on the volume change, on the angle of relative rotation and on the entropy is used in the framework of the method of internal thermodynamic parameters. The heat conduction process is described taking into account the anisotropy of a material due to the difference in coefficients of thermal conductivity along the axis of orientation of the particles and in the transverse direction. Separate equation for the tangential stress is obtained from the simplified model, which is useful for the analysis of the recently discussed issues of orientational thermoelasticity and resonant excitation of liquid crystals.

Scopus,
Полный текст (доступен только в локальной сети),
WOS

Держатели документа:
Institute of Computational Modeling, SB RAS, Akademgorodok 50/44Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadovskii, V.M.; Садовский, Владимир Михайлович

    Computational algorithm for modeling viscoelastic waves in the Kelvin-Voigt medium
/ V. M. Sadovskii // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) . - 2015. - Vol. 9045: 6th International Conference on Finite Difference Methods, FDM 2014; Lozenetz; Bulgaria; 18 June 2014 through 23 June 2014; Code 156479. - P348-355, DOI 10.1007/978-3-319-20239-6_38 . -
Аннотация: Numerical algorithm for solving dynamic problems of the theory of viscoelastic medium of Kelvin-Voigt is worked out on the basis of Ivanov’s method of constructing finite difference schemes with prescribed dissipative properties. In one-dimensional problem the results of computations are compared with the exact solution, describing the propagation of plane monochromatic waves. When solving two-dimensional problems, the total approximation method based on the splitting of the system with respect to the spatial variables is applied. The algorithm is tested on solving the problem of traveling surface waves. For illustration of the method, the numerical solution of Lamb’s problem about instantaneous action of concentrated force on the boundary of a half-plane is represented in viscoelastic formulation. © Springer International Publishing Switzerland 2015.

Scopus,
WOS

Держатели документа:
Institute of Computational Modeling SB RAS, Akademgorodok 50/44, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Садовский, Владимир Михайлович