Freedericksz Transition in Nematic Liquid Crystal Flows in Dimension Two

Chen, Yuan; Kim, Soojung; Yu, Yong

doi:10.1137/17m1151213

Cited by 7 publications

(4 citation statements)

References 17 publications

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“…The correctness of formulation of boundary problems for the equations of dynamics and statics of liquid crystals, as well as their solution stability was addressed in Refs. [16][17][18][19][20]. The studies [21][22][23][24] focused on application of the finite element method to the analysis of the behavior of liquid crystals under external impacts.…”

Section: Mathematical Modelsmentioning

confidence: 99%

Mathematical modeling of inhomogeneous electric field impact on a liquid crystal layer

Sadovskii

Sadovskaya

2022

Z Angew Math Mech

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The authors analyze the Fréedericksz transition phenomenon of reorientation of molecules in the plane liquid crystal layer in inhomogeneous electric field generated by parallel plate capacitor using the Oseen–Frank mathematical model. The capacitor is a set of short metal plates periodically located on both sides of the extended liquid crystal layer, connected in series in two circuits. When electric charges of different signs appear on opposite plates of the capacitor, the electric field in the periodicity cell turns out to be significantly inhomogeneous both in length and in thickness of the layer. Governing equations of the model represent Euler's variational equations in the problem on minimization of the potential energy of liquid crystal. Numerical solution of the equations uses the authorial variational difference scheme. The Laplace equation for electric potential in the exterior of the liquid crystal layer is solved using the method of lines. The electric field and the patterns of orientation angles of molecules inside the layer are determined by iterating with numerical solution of Poisson's equation using the fast Fourier transform at each iteration step. The algorithm is implemented by means of CUDA technology for computing systems with graphics accelerators. The scale of the mesh to ensure the computation accuracy is selected from calculation of Tsvetkov's order parameter in a rectangular cell pattern. Verification of the algorithm and program is implemented by way of comparing the computational results and the exact solution of the problem on the homogenous electric field with the constant initial orientation angle of liquid crystal molecules. The computations accomplished yield the patterns of the electric potentials and orientation angles of molecules depending on the position of the capacitor plates at uniform and s‐shaped initial distribution of the orientation angles through the thickness of the liquid crystal layer.

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Section: Mathematical Modelsmentioning

confidence: 99%

Mathematical modeling of inhomogeneous electric field impact on a liquid crystal layer

Sadovskii

Sadovskaya

2022

Z Angew Math Mech

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“…In the absence of external forcings f , g and the anisotropic energy potential φ(d), the system (1.2) has extensively studied and several important results have been obtained. In addition to the papers we cited above we refer, among others, to [17,18,[26][27][28]30,41] for results obtained prior to 2013, and to [7,[19][20][21][22]24,25,40,42,43] for results obtained after 2014. For detailed reviews of the literature about the mathematical theory of nematic liquid crystals and other related models, we recommend the review articles [8,15,29] and the recent papers [20,25].…”

Section: Introductionmentioning

confidence: 99%

On the 2D Ericksen–Leslie equations with anisotropic energy and external forces

2021

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In this paper we consider the 2D Ericksen–Leslie equations which describe the hydrodynamics of nematic liquid crystal with external body forces and anisotropic energy modeling the energy of applied external control such as magnetic or electric field. Under general assumptions on the initial data, the external data and the anisotropic energy, we prove the existence and uniqueness of global weak solutions with finitely many singular times. If the initial data and the external forces are sufficiently small, then we establish that the global weak solution does not have any singular times and is regular as long as the data are regular.

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“…791735 "SELEs". 35,45] for results obtained prior to 2013, and to [11,21,22,23,24,29,30,44,46,47] for results obtained after 2014. For detailed reviews of the literature about the mathematical theory of nematic liquid crystals and other related models, we recommend the review articles [34,17,12] and the recent papers [22,30].…”

Section: Introductionmentioning

confidence: 99%

On strong solution to the 2D stochastic Ericksen-Leslie system: A Ginzburg-Landau approximation approach

Brzezniak,

Deugoue,

Razafimandimby

2020

Preprint

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In this manuscript, we consider a highly nonlinear and constrained stochastic PDEs modelling the dynamics of 2-dimensional nematic liquid crystals under random perturbation. This system of SPDEs is also known as the stochastic Ericksen-Leslie equations (SELEs). We discuss the existence of local strong solution to the stochastic Ericksen-Leslie equations. In particular, we study the convergence the stochastic Ginzburg-Landau approximation of SELEs, and prove that the SELEs with initial data in H 1 ×H 2 has at least a martingale, local solution which is strong in PDEs sense.

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Freedericksz Transition in Nematic Liquid Crystal Flows in Dimension Two

Cited by 7 publications

References 17 publications

Mathematical modeling of inhomogeneous electric field impact on a liquid crystal layer

Mathematical modeling of inhomogeneous electric field impact on a liquid crystal layer

On the 2D Ericksen–Leslie equations with anisotropic energy and external forces

On strong solution to the 2D stochastic Ericksen-Leslie system: A Ginzburg-Landau approximation approach

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