A note on couette flow of nematic crystals according to the Ericksen–Leslie theory

Rickert, Wilhelm; Иванова, Е. В.; Müller, Wolfgang

doi:10.1002/zamm.201900035

Cited by 4 publications

(3 citation statements)

References 26 publications

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“…According to the Voigt–Reuss Hill (VRH) average scheme, − the aggregate bulk modulus ( B ), the shear modulus ( G ), and Young’s modulus ( E ) are acquired through the elastic constants shown in Figure a. There was a sharp increase in the estimate of the bulk modulus for dopant fixation, while 0.9 dopant focus exhibits a high value of 290 GPa and 0.5 dopant focus has a low value of 53 GPa.…”

Section: Resultsmentioning

confidence: 99%

First-Principles Calculations to Investigate Coupling Fe Doping with Oxygen Vacancies in Stannic Oxide and Their Physical Properties

Ramaraj,

SKS,

Zhang

et al. 2023

J. Phys. Chem. C

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We study the effects of Fe doping on the structural, electronic conductivity, elastic constants, and thermal conductivity of Sn 1−x Fe x O 2 (0 ≥ x ≤ 1) oxides by orbital hybridization as a consequence of charge remuneration of Fe 2+ /Fe 3+ and charge transfer using density functional theory calculations. We derive an effective spin-pseudospin Hamiltonian (H effective ) on the subspace of states with separately involved t 2g orbitals at each Fe site and visualize the combined atomic orbitals to form various molecular orbitals. Here, we determined that the mixed-valence electrons empowered by Fe 2+ −O 2− −Fe 3+ pairings in higher concentrations prevail through the double exchange-coupled pair. Specifically, we examined the oxygen positional parameters, average bond length, octahedral distortion, electronic structure, bulk modulus, shear modulus, Young's modulus, Poisson ratio, and thermal conductivity, which were significantly affected by the concentrations of x (0, 0.1, 0.3, 0.5, 0.7, 0.9, and 1), leading to negative shear and Young's moduli, a large Gruneisen parameter, and a lower Debye temperature. We estimate an ultralow thermal conductivity for Sn 1−x Fe x O 2 of around 0.002−1.5 W m −1 K −1 at 300 K. We also found that fixations of the 0.5 and 0.3 dopants lead to ultralow thermal conductivity. The electronic structure of SnO 2 is 3.582 eV, and the maximum valence band is composed of the O-2p and Sn-5p states, while the conduction band minimum is between the O-2p and Sn-5s states. Fe doping modulates the bond strengths in Sn 1−x Fe x O 2 by introducing intermediate energy levels and increasing the degree of hybridization of the Fe-d, Sn-p, and O-p electron states. The reduced thermal conductivity at ambient temperature makes the material an effective candidate for use in thermal management materials and optoelectronic devices.

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Section: Resultsmentioning

confidence: 99%

First-Principles Calculations to Investigate Coupling Fe Doping with Oxygen Vacancies in Stannic Oxide and Their Physical Properties

Ramaraj,

SKS,

Zhang

et al. 2023

J. Phys. Chem. C

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“…Such models were constructed on the basis of the concept of a liquid crystal as a structurally inhomogeneous medium composed of rotating particles, within the framework of the Cosserat generalized continuum [9] by such researchers as Refs. [10][11][12][13][14]. An acoustic approximation model, which phenomenologically accounts for interaction between sound propagation and nematic molecule orientation, was proposed in the study [15].…”

Section: Mathematical Modelsmentioning

confidence: 99%

“…Equation (14) for the orientation angle of molecules in the rectangle Ω with the appropriate boundary conditions was solved in a similar manner using the fast Fourier transform which by itself ensured periodicity of the solution with respect to the variable 𝑥, based on the discrete variant of the iterative process…”

Section: Computational Algorithmmentioning

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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Cavity Flow of Nematic Liquid Crystals – A Parameter Study

Rickert

Müller

2020

Advanced Problems in Mechanics

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A note on couette flow of nematic crystals according to the Ericksen–Leslie theory

Cited by 4 publications

References 26 publications

First-Principles Calculations to Investigate Coupling Fe Doping with Oxygen Vacancies in Stannic Oxide and Their Physical Properties

First-Principles Calculations to Investigate Coupling Fe Doping with Oxygen Vacancies in Stannic Oxide and Their Physical Properties

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

Cavity Flow of Nematic Liquid Crystals – A Parameter Study

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