Geodesic
Investigation of the orientational thermoelasticity effect using a simplified model of nematic liquid crystal in the acoustic approximation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 18 (2025) no. 3, pp. 337-346.

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Analysis of the orientational thermoelasticity effect using a two-dimensional simplified dynamic model of liquid crystal in the acoustic approximation is presented in the paper. It is assumed that effect occurs when one of the boundaries of a rectangular liquid crystal layer is heated. To solve the system of model equations, the method of two-cycle splitting with respect to spatial variables is used in combination with the finite-difference Godunov scheme for the acoustic equations and the Ivanov scheme with controlled energy dissipation for the heat conduction equation. This combination of finite-difference methods allows one to calculate related thermomechanical processes using the same time and space steps that satisfy the Courant-Friedrichs-Levy criterion. The numerical algorithm was implemented as a parallel program written in C++. Parallelization of computations was performed with NVIDIA graphic accelerators using CUDA technology. Simulations demonstrate that it is impossible to observe the effect of reorientation of liquid crystal molecules under the influence of temperature for the presented simplified model in the acoustic approximation. It was concluded that when surface tension forces are taken into account this effect will be observed for the model used in this work.
Keywords: liquid crystal, thermal conductivity, dynamics, CUDA technology. 
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Irina V. Smolekho. Investigation of the orientational thermoelasticity effect using a simplified model of nematic liquid crystal in the acoustic approximation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 18 (2025) no. 3, pp. 337-346. http://geodesic.mathdoc.fr/item/JSFU_2025_18_3_a5/

[1] L.M. Blinov, Structure and Properties of Liquid Crystals, Springer, Dordrecht, 2011 | DOI

[2] P.G. de Gennes, J.Prost, The Physics of Liquid Crystals, Oxford University Press, New York, 1993

[3] J.L.Ericksen, “Conservation laws for liquid crystals”, Trans. Soc. Rheol., 5:1 (1961), 23–34 | DOI | MR

[4] F.M.Leslie, “Some constitutive equations for liquid crystals”, Arch. Ration. Mech. Anal., 28:4 (1968), 265–283 | DOI | MR

[5] V.M.Sadovskii, O.V.Sadovskaya, I.V.Smolekho, “Modeling of the dynamics of a liquid crystal under the action of weak perturbations”, J. Appl. Mech. Tech. Phys., 62:1 (2021), 193–206 | DOI | MR

[6] S.I.Trashkeev, A.V.Britvin, “Thermal orientation effect in a nematic liquid crystal”, Tech. Phys., 56 (2011), 747–753 | DOI

[7] E.Cosseratm, F.Cosserat, “Théorie des Corps Déformables”, Chwolson's Traité Physique, 2nd ed., 1909, 953–1173

[8] V.M.Sadovskii, O.V.Sadovskaya, I.V.Smolekho, “Parallel implementation of the algorithm describing the behavior of liquid crystals under the action of electric field”, AIP Conf. Proc., 2025 (2018), 070005 | DOI

[9] S.K.Godunov, A.V.Zabrodin, M.Ya.Ivanov, A.N.Kraiko, G.P.Prokopov, Numerical Solving Many-Dimensional Problems of Gas Dynamics, Nauka, M., 1976 (in Russian)

[10] G.V.Ivanov, Yu.M.Volchkov, I.O.Bogulskii, S.A.Anisimov, V.D.Kurguzov, Numerical Solution of Dynamic Elastic-Plastic Problems of Deformable Solids, Sib. Univ. Izd., Novosibirsk, 2002 (in Russian) | MR

[11] R.Farber, CUDA Application Design and Development, Elsevier, Amsterdam–Boston–London–New York–Oxford–Paris–San Francisco–Singapore–Sydney–Tokyo, 2011

[12] K.Skarp, S.T.Lagerwall, B.Stebler, “Measurements of hydrodynamic parameters for nematic 5CB”, Mol. Cryst. Liq. Cryst., 60:3 (1980), 215–236 | DOI

[13] B.A.Belyaev, N.A.Drokin, V.F.Shabanov, V.N.Shepov, “Dielectric anisotropy of 5CB liquid crystal in a decimeter wavelenght range”, Phys. Solid State, 42:3 (2000), 577–579 | DOI