Труды сотрудников ИВМ СО РАН

/ V. M. Sadovskii, O. V. Sadovskaya // Physical Mesomechanics. - 2013. - Vol. 16, № 4. - P312-318, DOI 10.1134/S102995991304005X . - ISSN 1029-9599
Аннотация: Based on dynamic equations of a heterogeneous elastic medium which take into account rotational degrees of freedom of microstructure particles, a simplified mathematical model was constructed to describe the wave motions of a nematic liquid crystal under weak mechanical and temperature perturbations. It is shown that in the medium under plane deformation, the tangential stress obeys the Klein-Gordon equation of oscillatory particle rotation. Consideration is given to the possibility of initiating rotational waves in a nematic liquid crystal, which change its optical properties, due to heat sources acting at its boundary. © 2013 Pleiades Publishing, Ltd.

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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Sadovskaya, O.V.; Садовская, Оксана Викторовна; Sadovsky V.M.

/ 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 . -
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.

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

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

/ V. Sadovskii, O. Sadovskaya // Advances in Mechanics of Microstructured Media and Structures : Springer Verlag, 2018. - Vol. 87. - P297-341, DOI 10.1007/978-3-319-73694-5_17 . -
Аннотация: A simplified mathematical model of thermomechanical behavior of a liquid crystal in nematic phase under weak mechanical and thermal perturbations as a micropolar viscoelastic medium with rotating particles is constructed. This model is based on the assumption that potential energy of elastic deformation depends on four parameters—the change in volume, angle of relative rotation of particles, first invariant of curvature measure and entropy. 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 particles and in the transverse direction. Influence of electric field on the layer of a liquid crystal is modeled by means of the equations of electrostatics for an inhomogeneous anisotropic medium. In the plane formulation, the parallel computational algorithm is worked out on the basis of splitting method with respect to spatial variables, Godunov’s gap decay method, Ivanov’s method of constructing finite-difference schemes with controlled dissipation properties and method of straight lines for finding electric field. The algorithm is implemented using the CUDA technology for computer systems with graphics accelerators. Results of computations of wave motions demonstrating the efficiency of proposed method and algorithm are represented. It is shown that the effect of orientational thermoelasticity of a liquid crystal in the form of re-orientation of particles in an inhomogeneous temperature field can only be evident in the presence of tangential stresses at the boundary. The modes of resonance excitation in a liquid crystal at the eigenfrequency of rotational motion of particles are analyzed numerically. © Springer International Publishing AG, part of Springer Nature 2018.

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Держатели документа:
Siberian Branch of the Russian Academy of Sciences, Institute of Computational Modeling, Akademgorodok 50/44, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadovskii, V.; Sadovskaya, O.