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Research Article

From molecular to continuum modelling of bistable liquid crystal devices

ORCID Icon, , , &
Pages 2267-2284 | Received 11 Nov 2016, Accepted 30 Jan 2017, Published online: 21 Feb 2017

References

  • de Gennes PG, Prost J. The Physics of Liquid Crystals. New York (NY): Oxford University Press Inc.; 1974.
  • Virga EG. Variational theories for liquid crystals. Vol. 8. London: Chapman & Hall; 1995.
  • Berardi R, Lintuvuori JS, Wilson MR, et al. Phase diagram of the uniaxial and biaxial soft-core Gay-Berne model. J Chem Phys. 2011;135(13):134119.
  • Care C, Cleaver D. Computer simulation of liquid crystals. Rep Prog Phys. 2005;68(11):2665–2700.
  • Robinson M, Andrews SS, Erban R. Multiscale reaction-diffusion simulations with Smoldyn. Bioinfor- Matics. 2015;31(14):2406–2408.
  • Erban R. Coupling all-atom molecular dynamics simulations of ions in water with Brownian dynamics. Proc R Soc A. 2016;472(2186):20150556.
  • Tsakonas C, Davidson AJ, Brown CV, et al. Multistable alignment states in nematic liquid crystal filled wells. Appl Phys Lett. 2007;90(11):1913.
  • Lewis AH, Garlea I, Alvarado J, et al. Colloidal liquid crystals in rectangular confinement: theory and experiment. Soft Matter. 2014;10(39):7865–7873.
  • Luo C, Majumdar A, Erban R. Multistability in planar liquid crystal wells. Phys Rev E. 2012;85(6):061702.
  • Kusumaatmaja H, Majumdar A. Free energy pathways of a multistable liquid crystal device. Soft Matter. 2015;11(24):4809–4817.
  • Kralj S, Majumdar A. Order reconstruction patterns in nematic liquid crystal wells. Proc R Soc A. 2014;470(2169):20140276.
  • Ladak S, Davidson A, Brown C, et al. Sidewall control of static azimuthal bistable nematic alignment states. J Phys D: Appl Phys. 2009;42(8):085114.
  • Anquetil-Deck C, Cleaver DJ, Atherton TJ. Competing alignments of nematic liquid crystals on square- patterned substrates. Phys Rev E. 2012;86(4):041707.
  • Davidson AJ, Mottram NJ. Conformal mapping techniques for the modelling of liquid crystal devices. Eur J Appl Math. 2012;23(01):99–119.
  • Gˆarlea IC, Mulder BM. Defect structures mediate the isotropicnematic transition in strongly confined liquid crystals. Soft Matter. 2015;11(3):608–614.
  • Slavinec M, Klemen EII, Ambro MDI, et al. Impact of nanoparticles on nematic ordering in square wells. Adv Cond Matter Phys. 2015;2015.
  • Allen MP, Wilson MR. Computer simulation of liquid crystals. J Comput Aided Mol Des. 1989;3(4):335–353.
  • Gay J, Berne B. Modification of the overlap potential to mimic a linear site–site potential. J Chem Phys. 1981;74(6):3316–3319.
  • Lebwohl P, Lasher G. Nematic-liquid-crystal order–A Monte Carlo calculation. Phys Rev A. 1972;6(1):426–429.
  • Erban R. From molecular dynamics to Brownian dynamics. Proc R Soc A. 2014;470(2167):20140036.
  • Berne BJ. Gaussian model potentials for molecular interactions. J Chem Phys. 1972;56(8):4213.
  • Berardi R, Emerson APJ, Zannoni C. Monte Carlo investigations of a Gay-Berne liquid crystal. J Chem Soc Faraday Trans. 1993;89(22):4069–4078.
  • Luckhurst G, Simpson P. Computer simulation studies of anisotropic systems: VIII. the Lebwohl-Lasher model of nematogens revisited. Mol Phys. 1982;47(2):251–265.
  • Chiccoli C, Pasini P, Zannoni C. A Monte Carlo simulation of the inhomogeneous Lebwohl-Lasher lattice model. Liq Cryst. 1987;2(1):39–54.
  • Hastings WK. Monte Carlo sampling methods using Markov chains and their applications. Biometrika. 1970;57(1):97–109.
  • Billeter J, Smondyrev A, Loriot G, et al. Phase-ordering dynamics of the Gay-Berne nematic liquid crystal. Phys Rev E. 1999;60(6):6831–6840.
  • Majumdar A. Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory. Eur J Appl Math. 2010;21(02):181–203.
  • Anquetil-Deck C, Cleaver D. Nematic liquid-crystal alignment on stripe-patterned substrates. Phys Rev E. 2010;82(3):031709.
  • Logg A, Mardal KA, Wells GE. Automated solution of differential equations by the finite element method: the FEniCS book. Vol. 84. Springer Science & Business Media; 2012.
  • Alnæs M, Blechta J, Hake J, et al. The FEniCS project version 1.5. Arch Numer Softw. 2015;3(100):9–23.
  • Mottram NJ, Newton CJ Introduction to Q-tensor theory. arXiv preprint arXiv:14093542. 2014.
  • Majumdar A, Milewski PA, Spicer A. Front propagation at the nematic-isotropic transition temperature. SIAM J Appl Math. 2016;76:1296–1320.
  • Farrell PE, Beentjes CHL, Birkisson A The computation of disconnected bifurcation diagrams. 2016; arXiv:1603.00809 [math.NA].
  • Keller HB. Numerical solution of bifurcation and nonlinear eigenvalue problems. In: Rabinowitz PH, editor. Applications of bifurcation theory. New York: Academic Press; 1977. p. 359–384.
  • Farrell PE, Birkisson A, Funke SW. Deflation techniques for finding distinct solutions of nonlinear partial differential equations. SIAM J Sci Comput. 2015;37(4):A2026–A2045.
  • Adler JH, Emerson DB, Farrell PE, et al. A deflation technique for detecting multiple liquid crystal equilibrium states. arXiv preprint arXiv:160107383. 2016.
  • Lewis A. Defects in liquid crystals: mathematical and experimental studies [dissertation]. University of Oxford; 2016.