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Relevant bibliographies by topics / Liquid crystals Calculus of tensors

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Academic literature on the topic 'Liquid crystals Calculus of tensors'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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Journal articles on the topic "Liquid crystals Calculus of tensors"

1

Chen, Yannan, Liqun Qi, and Epifanio G. Virga. "Octupolar tensors for liquid crystals." Journal of Physics A: Mathematical and Theoretical 51, no. 2 (2017): 025206. http://dx.doi.org/10.1088/1751-8121/aa98a8.

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Carolina Sparavigna, Amelia. "Elasticity Tensors in Nematic Liquid Crystals." International Journal of Sciences 2, no. 07 (2016): 54–65. http://dx.doi.org/10.18483/ijsci.1117.

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Tang, Xingzhou, and Jonathan V. Selinger. "Orientation of topological defects in 2D nematic liquid crystals." Soft Matter 13, no. 32 (2017): 5481–90. http://dx.doi.org/10.1039/c7sm01195d.

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Blenk, S., H. Ehrentraut, and W. Muschik. "Orientation-Balances for Liquid Crystals and Their Representation by Alignment Tensors." Molecular Crystals and Liquid Crystals 204, no. 1 (1991): 133–41. http://dx.doi.org/10.1080/00268949108046600.

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Matteis, Giovanni De, André M. Sonnet, and Epifanio G. Virga. "Landau theory for biaxial nematic liquid crystals with two order parameter tensors." Continuum Mechanics and Thermodynamics 20, no. 6 (2008): 347–74. http://dx.doi.org/10.1007/s00161-008-0086-9.

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Kirste, B. "EPR and ENDOR Investigations of a Cholestane Spin Probe in Liquid Crystals." Zeitschrift für Naturforschung A 42, no. 11 (1987): 1296–304. http://dx.doi.org/10.1515/zna-1987-1112.

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A detailed ENDOR study of anisotropic proton hyperfine shifts in the nitroxide spin probe 3-doxylcholestane (CSL) in liquid-crystalline solution is described. The data are interpreted by means of theoretically calculated proton hyperfine tensors (McConnell-Strathdee-Derbyshire treatment), providing an independent check of the ordering matrix. The orientational order and the dynamic behavior of the nematic and smectic phases of the liquid crystals (40,6), (50,6), and 8CB are investigated by EPR using CSL and phenalenyl as spin probes.

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Mennucci, Benedetta, and Roberto Cammi. "Ab initio model to predict NMR shielding tensors for solutes in liquid crystals." International Journal of Quantum Chemistry 93, no. 2 (2003): 121–30. http://dx.doi.org/10.1002/qua.10541.

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Rubailo, V. I., and A. N. Vtyurin. "Connection of micro and macro parameters of uniaxial liquid crystals - irreducible tensors approach." Applied Physics B Lasers and Optics 60, no. 6 (1995): 535–41. http://dx.doi.org/10.1007/bf01080932.

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Benzi, Caterina, Maurizio Cossi, and Vincenzo Barone. "Accurate prediction of electron-paramagnetic-resonance tensors for spin probes dissolved in liquid crystals." Journal of Chemical Physics 123, no. 19 (2005): 194909. http://dx.doi.org/10.1063/1.2102870.

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Lin, Junyu, and Chen Zou. "Existence of solutions to the biaxial nematic liquid crystals with two order parameter tensors." Mathematical Methods in the Applied Sciences 43, no. 10 (2020): 6430–53. http://dx.doi.org/10.1002/mma.6387.

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Dissertations / Theses on the topic "Liquid crystals Calculus of tensors"

1

Mehta, Ketan. "NLCViz tensor visualization and defect detection in nematic liquid crystals /." Master's thesis, Mississippi State : Mississippi State University, 2006. http://sun.library.msstate.edu/ETD-db/ETD-browse/browse.

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Bedford, Stephen James. "Calculus of variations and its application to liquid crystals." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:a2004679-5644-485c-bd35-544448f53f6a.

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The thesis concerns the mathematical study of the calculus of variations and its application to liquid crystals. In the first chapter we examine vectorial problems in the calculus of variations with an additional pointwise constraint so that any admissible function <strong>n</strong> ε W<sup>1,1</sup>(ΩM), and M is a manifold of suitable regularity. We formulate necessary and sufficient conditions for any given state <strong>n</strong> to be a strong or weak local minimiser of I. This is achieved using a nearest point projection mapping in order to use the more classical results which apply in the absence of a constraint. In the subsequent chapters we study various static continuum theories of liquid crystals. More specifically we look to explain a particular cholesteric fingerprint pattern observed by HP Labs. We begin in Chapter 2 by focusing on a specific cholesteric liquid crystal problem using the theory originally derived by Oseen and Frank. We find the global minimisers for general elastic constants amongst admissible functions which only depend on a single variable. Using the one-constant approximation for the Oseen-Frank free energy, we then show that these states are global minimisers of the three-dimensional problem if the pitch of the cholesteric liquid crystal is sufficiently long. Chapter 3 concerns the application of the results from the first chapter to the situations investigated in the second. The local stability of the one-dimensional states are quantified, analytically and numerically, and in doing so we unearth potential shortcomings of the classical Oseen-Frank theory. In Chapter 4, we ascertain some equivalence results between the continuum theories of Oseen and Frank, Ericksen, and Landau and de Gennes. We do so by proving lifting results, building on the work of Ball and Zarnescu, which relate the regularity of line and vector fields. The results prove to be interesting as they show that for a director theory to respect the head to tail symmetry of the liquid crystal molecules, the appropriate function space for the director field is S BV<sup>2</sup> (Ω,S<sup>2,/sup>). We take this idea and in the final chapter we propose a mathematical model of liquid crystals based upon the Oseen-Frank free energy but using special functions of bounded variation. We establish the existence of a minimiser, forms of the Euler-Lagrange equation, and find solutions of the Euler-Lagrange equation in some simple cases. Finally we use our proposed model to re-examine the same problems from Chapter 2. By doing so we extend the analysis we were able to achieve using Sobolev spaces and predict the existence of multi-dimensional minimisers consistent with the known experimental properties of high-chirality cholesteric liquid crystals.

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3

Lu, Zijun. "Theoretical and Numerical Analysis of Phase Changes in Soft Condensed Matter." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case15620007885239.

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Lamy, Xavier. "Autour des singularités d’applications vectorielles en physique de la matière condensée." Thesis, Lyon 1, 2015. http://www.theses.fr/2015LYO10085/document.

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Cette thèse est consacrée principalement à l'analyse mathématique de modèles issus de la physique des cristaux liquides et de la supraconductivité. Ces modèles ont en commun de faire intervenir des systèmes elliptiques dont les solutions présentent des singularités : défauts optiques dans les cristaux liquides, défauts de vorticité en supraconductivité. Les cristaux liquides se composent de molécules allongées qui, tout en étant distribuées « au hasard » comme dans un liquide, tendent à s'aligner dans une direction commune : cet « ordre d'orientation » leur confère des propriétés optiques similaires à celles d'un cristal, à l'origine de leurs nombreuses applications industrielles. On démontre différents résultats liés à la symétrie locale de cet alignement autour des singularités. On présente aussi dans cette thèse différents résultats liés au modèle de Ginzburg-Landau pour les supraconducteurs de type II, et aux « défauts de vorticité » : points isolés autour desquels la supraconductivité est détruite. Une dernière partie de cette thèse traite de la caractérisation de la régularité d'une fonction f à travers la vitesse de convergence de f ∗ ρε pour un certain noyau ρ. Dans un travail commun avec Petru Mironescu, on s'intéresse à la question de la régularité des noyaux ρ qui permettent une telle caractérisation<br>The present thesis is devoted mainly to the mathematical analysis of models arising in the physics of liquid crystals and superconductivity. A common feature of these models is that one has to deal with elliptic systems whose solutions have singularities: optical defects in liquid crystals, vorticity defects in superconductivity. The rod-like molecules in a liquid crystals, while being (as in a liquid) “randomly” distributed, tend to align in a common direction: this “orientational order” enhances crystal-like optical properties, which are responsible for their many industrial applications. We demonstrate different results related to the local symmetry of this alignement near singularities. We also present some results related to the Ginzburg-Landau model for type II superconductivity, and to “vortices”: isolated points at which superconductivity is destroyed. The last part of this thesis addresses regularity characterization for a function f through the convergence rate of f ∗ ρε, for some kernel ρ. In a joint work with Petru Mironescu we study the minimal regularity of ρ that allows such characterization

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Books on the topic "Liquid crystals Calculus of tensors"

1

Lovett, D. R. Tensor properties of crystals. 2nd ed. Institute of Physics Pub., 1999.

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Lovett, D. R. Tensor properties of crystals. Adam Hilger, 1989.

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3

Nye, J. F. Physical properties of crystals: Their representation by tensors and matrices. Clarendon Press, 1985.

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Nye, J. F. Physical Properties of Crystals: Their Representation by Tensors and Matrices. Oxford University Press, USA, 1985.

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Book chapters on the topic "Liquid crystals Calculus of tensors"

1

Hess, Siegfried. "Liquid Crystals and Other Anisotropic Fluids." In Tensors for Physics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12787-3_15.

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2

Hardt, Robert, David Kinderlehrer, and Mitchell Luskin. "Remarks about the mathematical theory of liquid crystals." In Calculus of Variations and Partial Differential Equations. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0082891.

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3

"VARIATIONAL CALCULUS." In An Elementary Course on the Continuum Theory for Nematic Liquid Crystals. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812813671_0001.

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4

Newnham, Robert E. "Thermal conductivity." In Properties of Materials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198520757.003.0020.

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When different portions of a solid are at different temperatures, thermal energy is transported from the warmer to the cooler regions. The thermal conductivity coefficient provides a quantitative measure of the rate at which thermal energy is transported along the thermal gradient. Thermal conductivity coefficients k relate the heat flux h [W/m2] to temperature gradient dT/dZ. In tensor form, The minus sign appears because heat flows from hot to cold. Thermal conductivity is measured in units of W/m K. Four contributions to thermal conductivity are illustrated in Fig. 18.1. The two principal mechanisms are from conduction electrons and from lattice vibration phonons. In transparent solids, especially at high temperature, photon transport can also be important. In porous media, convection currents from gas or liquid molecules can contribute to the thermal conductivity. Thermal conductivity is a polar second rank tensor like electric permittivity, magnetic susceptibility, and electrical resistivity but there is a basic question regarding the symmetry of transport properties such as electrical and thermal conductivity. The symmetry of tensors is partly dictated by geometrical considerations through Neumann’s Principle, and partly through thermodynamic arguments. For triclinic crystals there are nine nonzero conductivity coefficients kij . If the tensor is symmetric then kij = kji, and there are only six independent coefficients to be determined. For the dielectric constant it was shown that Kij = Kji, based on thermostatic energy arguments (Section 9.2). This argument does not hold for transport properties, but there is another principle based on irreversible thermodynamics. Onsager’s Theorem states that for transport properties, involving the flow of charge, heat, or atomic species, then . . . kij = kji. . . . The proof of Onsager’s Theorem depends on statistical mechanics and is beyond the scope of this book. From a practical point of view, Onsager’s Theorem is not very important because most transport experiments are performed on high symmetry metals, semiconductors, and insulators.

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