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Neural-network approach to modeling liquid crystals in complex confinement

T. Santos-Silva1, P. I. C. Teixeira2,3, C. Anquetil-Deck4,*, and D. J. Cleaver4

  • 1Faculdade de Engenharia, Universidade Católica Portuguesa, Estrada de Talaíde, P-2635-631 Rio de Mouro, Portugal
  • 2Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro 1, P-1950-062 Lisbon, Portugal
  • 3Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisbon, Portugal
  • 4Materials and Engineering Research Institute, Sheffield Hallam University, Pond Street, Sheffield S1 1WB, United Kingdom

  • *Present address: Karlsruhe Institute of Technology, Institute for Meteorology and Climate Research, Atmospheric Aerosol Research Department (IMK-AAF), Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany.
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Phys. Rev. E 89, 053316 – Published 28 May, 2014

DOI: https://doi.org/10.1103/PhysRevE.89.053316

Abstract

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy minimization. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the multilayer perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible, and refinable. Furthermore, it can be readily generalized to the richer experimental patterned-substrate geometries that are now experimentally realizable but very problematic to conventional theoretical treatments.

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References (50)

  1. http://www.displaybank.com/eng/.
  2. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford University Press, Oxford, 1992).
  3. B. Jérôme, Rep. Prog. Phys. 54, 391 (1991).
  4. T. J. Sluckin, Contemp. Phys. 41, 37 (2000).
  5. G. P. Bryan-Brown, E. L. Wood, and I. C. Sage, Nature (London) 399, 338 (1999).
  6. C. V. Brown, M. J. Towler, V. C. Hui, and G. P. Bryan-Brown, Liq. Cryst. 27, 233 (2000).
  7. N. A. Lockwood and N. L. Abbott, Current Opinion Coll. Interf. Sci. 10, 111 (2005).
  8. P. Poulin, H. Stark, T. C. Lubensky, and D. A. Weitz, Science 275, 1770 (1997).
  9. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, 2nd ed. (Academic, London, 1986).
  10. M. M. Telo da Gama, Mol. Phys. 52, 611 (1984).
  11. A. Chrzanowska, P. I. C. Teixeira, H. Eherentraut, and D. J. Cleaver, J. Phys.: Condens. Matter 13, 4715 (2001).
  12. D. de las Heras, L. Mederos, and E. Velasco, Phys. Rev. E 68, 031709 (2003).
  13. D. de las Heras, E. Velasco, and L. Mederos, J. Chem. Phys. 120, 4949 (2004).
  14. J. P. Bramble, S. D. Evans, J. R. Henderson, C. Anquetil, D. J. Cleaver, and N. J. Smith, Liq. Cryst. 34, 1059 (2007).
  15. Y. Yi, V. Khire, C. Bowman, J. Maclennan, and N. Clark, J. Appl. Phys. 103, 093518 (2008).
  16. C. Anquetil-Deck and D. J. Cleaver, Phys. Rev. E 82, 031709 (2010).
  17. C. Anquetil-Deck, D. J. Cleaver, and T. J. Atherton, Phys. Rev. E 86, 041707 (2012).
  18. S. Kitson and A. Giesow, Appl. Phys. Lett. 80, 3635 (2002).
  19. C. Tsoktas, A. J. Davidson, C. V. Brown, and N. J. Mottram, Appl. Phys. Lett. 90, 111913 (2007).
  20. G. G. Wells and C. V. Brown, Appl. Phys. Lett. 91, 223506 (2007).
  21. S. Haykin, Neural Networks: A Comprehensive Foundation, 2nd ed. (Prentice-Hall, New Jersey, 1998).
  22. K. Hornik, M. Stinchcombe, and H. White, Neural Networks 2, 359 (1989).
  23. P. I. C. Teixeira, F. Barmes, and D. J. Cleaver, J. Phys.: Condens. Matter 16, S1969 (2004).
  24. P. I. C. Teixeira, F. Barmes, C. Anquetil-Deck, and D. J. Cleaver, Phys. Rev. E 79, 011709 (2009).
  25. H. Bourlard, N. Morgan, and S. Renals, Speech Commun. 11, 237 (1992).
  26. J. Gutiérrez and Ali S. Hadi, Expert Systems and Probabilistic Network Models (Springer, Berlin, 1997).
  27. P. J. Cheng and S. C. Lin, Int. J. Machine Tools Manufact. 40, 1185 (2000).
  28. N. Intrator, Neural Comput. 4, 98 (1992).
  29. M. Gardner and S. Dorling, Atmos. Environ. 34, 21 (2000).
  30. F. Rosenblatt, Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms (Spartan, Washington DC, 1962).
  31. C. M. Care and D. J. Cleaver, Rep. Prog. Phys. 68, 2665 (2005).
  32. M. Rigby, Mol. Phys. 68, 687 (1989).
  33. J. W. Perram and M. S. Wertheim, J. Comput. Phys. 58, 409 (1985); J. W. Perram, J. Rasmussen, E. Praestgaard, and J. L. Lebowitz, Phys. Rev. E 54, 6565 (1996).
  34. M. P. Allen, G. T. Evans, D. Frenkel, and B. M. Mulder, in Advances in Chemical Physics, edited by I. Prigogine and S. A. Rice (John Wiley and Sons, Hoboken, NJ, USA, 1993), Vol. 86, pp. 1–166.
  35. V. R. Bhethanabotla and W. Steele, Mol. Phys. 60, 249 (1987).
  36. S. L. Huang and V. R. Bhethanabotla, Int. J. Mod. Phys. C 10, 361 (1999).
  37. E. Velasco and L. Mederos, J. Chem. Phys. 109, 2361 (1998).
  38. D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001).
  39. R. Evans, Adv. Phys. 28, 143 (1979).
  40. A. Poniewierski, Phys. Rev. E 47, 3396 (1993).
  41. J. D. Parsons, Phys. Rev. A 19, 1225 (1979); S. D. Lee, J. Chem. Phys. 78, 4972 (1987).
  42. A. M. Somoza and P. Tarazona, J. Chem. Phys. 91, 517 (1989); E. Velasco, L. Mederos, and D. E. Sullivan, Phys. Rev. E 62, 3708 (2000).
  43. A. Chrzanowska, J. Comput. Phys. 191, 265 (2003).
  44. W. McCulloch and W. Pitts, Bull. Math. Biophys. 7, 115 (1943).
  45. D. F. Specht, Neural Networks 3, 109 (1990).
  46. D. S. Modha and Y. Fainman, IEEE Trans. Neural Networks 5, 519 (1994).
  47. See, e.g., W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, 1993).
  48. H. Hansen-Goos and K. Mecke, Phys. Rev. Lett. 102, 018302 (2009).
  49. R. Wittmann and K. Mecke, J. Chem. Phys. 140, 104703 (2014).
  50. M. F. Møller, Neural Networks 6, 525 (1993).

Outline

Information

Phys. Rev. E 89, 053316– Published 28 May, 2014
  • Received 10 November 2012
  • Revised 20 April 2014

©2014 American Physical Society

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