Abstract

Oscillatory and excitable systems commonly exhibit formation of dynamic non-equilibrium patterns. For example, rotating spiral patterns are observed in biological, chemical, and physical systems ranging from organization of slime mold cells to Belousov-Zhabotinsky reactions, and to crystal growth from nuclei with screw dislocations. Here we describe spontaneous formation of spiral waves and a large variety of other dynamic patterns in anisotropic soft matter driven by low-intensity light. The unstructured ambient or microscope light illumination of thin liquid crystal films in contact with a self-assembled azobenzene monolayer causes spontaneous formation, rich spatial organization, and dynamics of twisted domains and topological solitons accompanied by the dynamic patterning of azobenzene group orientations within the monolayer. Linearly polarized incident light interacts with the twisted liquid crystalline domains, mimicking their dynamics and yielding patterns in the polarization state of transmitted light, which can be transformed to similar dynamic patterns in its intensity and interference color. This shows that the delicate light-soft-matter interaction can yield complex self-patterning of both. We uncover underpinning physical mechanisms and discuss potential uses.

© 2015 Optical Society of America

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  1. J. Wesfreid, H. Brand, P. Monneville, G. Albinet, and N. Boccara, eds., Propagation in Systems far from Equilibrium (Springer, 1988).
  2. R. J. Field and M. Burger, eds., Oscillations and Traveling Waves in Chemical Systems (Wiley, 1985).
  3. F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, “Spatiotemporal evolution of ventricular fibrillation,” Nature 392(6671), 78–82 (1998).
    [Crossref] [PubMed]
  4. L. B. Smolka, B. Marts, and A. L. Lin, “Effect of inhomogeneities on spiral wave dynamics in the Belousov-Zhabotinsky reaction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056205 (2005).
    [Crossref] [PubMed]
  5. J. Luengviriya, P. Porjai, M. Phantu, M. Sutthiopad, B. Tomapatanaget, S. C. Müller, and C. Luengviriya, “Meandering spiral waves in a bubble-free Belousov–Zhabotinsky reaction with pyrogallol,” Chem. Phys. Lett. 588, 267–271 (2013).
    [Crossref]
  6. A. L. Belmonte, Q. Ouyang, and J.-M. Flesselles, “Experimental survey of spiral dynamics in the Belousov-Zhabotinsky reaction,” Phys. II France 7(10), 1425–1468 (1997).
    [Crossref]
  7. N. Li, J. Delgado, H. O. González-Ochoa, I. R. Epstein, and S. Fraden, “Combined excitatory and inhibitory coupling in a 1-D array of Belousov-Zhabotinsky droplets,” Phys. Chem. Chem. Phys. 16(22), 10965–10978 (2014).
    [Crossref] [PubMed]
  8. K. B. Migler and R. B. Meyer, “Spirals in liquid crystals in a rotating magnetic field,” Physica D 71(4), 412–420 (1994).
    [Crossref]
  9. I. Jánossy, K. Fodor-Csorba, A. Vajda, and L. O. Palomares, “Light-induced spontaneous pattern formation in nematic liquid crystal cells,” Appl. Phys. Lett. 99(11), 111103 (2011).
    [Crossref]
  10. C. Zheng and R. B. Meyer, “Thickness effects on pattern formation in liquid crystals in a rotating magnetic field,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 2882–2887 (1997).
    [Crossref]
  11. K. B. Migler and R. B. Meyer, “Solitons and pattern formation in liquid crystals in a rotating magnetic field,” Phys. Rev. Lett. 66(11), 1485–1488 (1991).
    [Crossref] [PubMed]
  12. S. Nasuno, N. Yoshimo, and S. Kai, “Structural transition and motion of domain walls in liquid crystals under a rotating magnetic field,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1598–1601 (1995).
    [Crossref] [PubMed]
  13. T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, “Spiral waves in liquid crystal,” Phys. Rev. Lett. 72(10), 1471–1474 (1994).
    [Crossref] [PubMed]
  14. J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
    [Crossref] [PubMed]
  15. L. Giomi, M. J. Bowick, X. Ma, and M. C. Marchetti, “Defect annihilation and proliferation in active nematics,” Phys. Rev. Lett. 110(22), 228101 (2013).
    [Crossref] [PubMed]
  16. T. Sanchez, D. T. N. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, “Spontaneous motion in hierarchically assembled active matter,” Nature 491(7424), 431–434 (2012).
    [Crossref] [PubMed]
  17. Y. Zhang, N. Zhou, N. Li, M. Sun, D. Kim, S. Fraden, I. R. Epstein, and B. Xu, “Giant volume change of active gels under continuous flow,” J. Am. Chem. Soc. 136(20), 7341–7347 (2014).
    [Crossref] [PubMed]
  18. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd Ed. (Clarendon, 1993).
  19. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University, 2000).
  20. A. Martinez, H. C. Mireles, and I. I. Smalyukh, “Large-area optoelastic manipulation of colloidal particles in liquid crystals using photoresponsive molecular surface monolayers,” Proc. Natl. Acad. Sci. U.S.A. 108(52), 20891–20896 (2011).
    [Crossref] [PubMed]
  21. I. I. Smalyukh and O. D. Lavrentovich, “Anchoring-mediated interaction of edge dislocations with bounding surfaces in confined cholesteric liquid crystals,” Phys. Rev. Lett. 90(8), 085503 (2003).
    [Crossref] [PubMed]
  22. N. Petit-Garrido, R. P. Trivedi, J. Ignés-Mullol, J. Claret, C. Lapointe, F. Sagués, and I. I. Smalyukh, “Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers,” Phys. Rev. Lett. 107(17), 8163–8170 (2011).
    [Crossref] [PubMed]
  23. N. Petit-Garrido, R. Trivedi, F. Sagués, J. Ignés-Mullol, and I. I. Smalyukh, “Topological defects in cholesteric liquid crystals induced by chiral molecular monolayer domains,” Soft Matter 10, 8163–8170 (2014).
    [Crossref] [PubMed]
  24. P. J. Ackerman, Z. Qi, and I. I. Smalyukh, “Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(2), 021703 (2012).
    [Crossref] [PubMed]
  25. A. Martinez, M. Ravnik, B. Lucero, R. Visvanathan, S. Žumer, and I. I. Smalyukh, “Mutually tangled colloidal knots and induced defect loops in nematic fields,” Nat. Mater. 13(3), 258–263 (2014).
    [Crossref] [PubMed]
  26. C. P. Lapointe, S. Hopkins, T. G. Mason, and I. I. Smalyukh, “Electrically driven multiaxis rotational dynamics of colloidal platelets in nematic liquid crystals,” Phys. Rev. Lett. 105(17), 178301 (2010).
    [Crossref] [PubMed]
  27. Q. Liu, Y. Yuan, and I. I. Smalyukh, “Electrically and optically tunable plasmonic guest-host liquid crystals with long-range ordered nanoparticles,” Nano Lett. 14(7), 4071–4077 (2014).
    [Crossref] [PubMed]
  28. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Willey, New York, 1999).
  29. P.-Y. Wang, W. Lu, D. Yu, and R. G. Harrison, “Excitability and pattern formation in a liquid crystal Fabry-Perot interferometer,” Opt. Commun. 189(1-3), 127–134 (2001).
    [Crossref]
  30. M. Büttiker and R. Landauer, “Nucleation theory of overdamped soliton motion,” Phys. Rev. A 23(3), 1397–1410 (1981).
    [Crossref]
  31. F. Lonberg, S. Fraden, A. J. Hurd, and R. B. Meyer, “Field-induced transient periodic structures in nematic liquid crystals: the twist-Fréedericksz transition,” Phys. Rev. Lett. 52(21), 1903–1906 (1984).
    [Crossref]
  32. M. E. McConney, A. Martinez, V. P. Tondiglia, K. M. Lee, D. Langley, I. I. Smalyukh, and T. J. White, “Topography from topology: photoinduced surface features generated in liquid crystal polymer networks,” Adv. Mater. 25(41), 5880–5885 (2013).
    [Crossref] [PubMed]

2014 (5)

N. Li, J. Delgado, H. O. González-Ochoa, I. R. Epstein, and S. Fraden, “Combined excitatory and inhibitory coupling in a 1-D array of Belousov-Zhabotinsky droplets,” Phys. Chem. Chem. Phys. 16(22), 10965–10978 (2014).
[Crossref] [PubMed]

Y. Zhang, N. Zhou, N. Li, M. Sun, D. Kim, S. Fraden, I. R. Epstein, and B. Xu, “Giant volume change of active gels under continuous flow,” J. Am. Chem. Soc. 136(20), 7341–7347 (2014).
[Crossref] [PubMed]

N. Petit-Garrido, R. Trivedi, F. Sagués, J. Ignés-Mullol, and I. I. Smalyukh, “Topological defects in cholesteric liquid crystals induced by chiral molecular monolayer domains,” Soft Matter 10, 8163–8170 (2014).
[Crossref] [PubMed]

A. Martinez, M. Ravnik, B. Lucero, R. Visvanathan, S. Žumer, and I. I. Smalyukh, “Mutually tangled colloidal knots and induced defect loops in nematic fields,” Nat. Mater. 13(3), 258–263 (2014).
[Crossref] [PubMed]

Q. Liu, Y. Yuan, and I. I. Smalyukh, “Electrically and optically tunable plasmonic guest-host liquid crystals with long-range ordered nanoparticles,” Nano Lett. 14(7), 4071–4077 (2014).
[Crossref] [PubMed]

2013 (4)

M. E. McConney, A. Martinez, V. P. Tondiglia, K. M. Lee, D. Langley, I. I. Smalyukh, and T. J. White, “Topography from topology: photoinduced surface features generated in liquid crystal polymer networks,” Adv. Mater. 25(41), 5880–5885 (2013).
[Crossref] [PubMed]

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

L. Giomi, M. J. Bowick, X. Ma, and M. C. Marchetti, “Defect annihilation and proliferation in active nematics,” Phys. Rev. Lett. 110(22), 228101 (2013).
[Crossref] [PubMed]

J. Luengviriya, P. Porjai, M. Phantu, M. Sutthiopad, B. Tomapatanaget, S. C. Müller, and C. Luengviriya, “Meandering spiral waves in a bubble-free Belousov–Zhabotinsky reaction with pyrogallol,” Chem. Phys. Lett. 588, 267–271 (2013).
[Crossref]

2012 (2)

T. Sanchez, D. T. N. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, “Spontaneous motion in hierarchically assembled active matter,” Nature 491(7424), 431–434 (2012).
[Crossref] [PubMed]

P. J. Ackerman, Z. Qi, and I. I. Smalyukh, “Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(2), 021703 (2012).
[Crossref] [PubMed]

2011 (3)

A. Martinez, H. C. Mireles, and I. I. Smalyukh, “Large-area optoelastic manipulation of colloidal particles in liquid crystals using photoresponsive molecular surface monolayers,” Proc. Natl. Acad. Sci. U.S.A. 108(52), 20891–20896 (2011).
[Crossref] [PubMed]

I. Jánossy, K. Fodor-Csorba, A. Vajda, and L. O. Palomares, “Light-induced spontaneous pattern formation in nematic liquid crystal cells,” Appl. Phys. Lett. 99(11), 111103 (2011).
[Crossref]

N. Petit-Garrido, R. P. Trivedi, J. Ignés-Mullol, J. Claret, C. Lapointe, F. Sagués, and I. I. Smalyukh, “Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers,” Phys. Rev. Lett. 107(17), 8163–8170 (2011).
[Crossref] [PubMed]

2010 (1)

C. P. Lapointe, S. Hopkins, T. G. Mason, and I. I. Smalyukh, “Electrically driven multiaxis rotational dynamics of colloidal platelets in nematic liquid crystals,” Phys. Rev. Lett. 105(17), 178301 (2010).
[Crossref] [PubMed]

2005 (1)

L. B. Smolka, B. Marts, and A. L. Lin, “Effect of inhomogeneities on spiral wave dynamics in the Belousov-Zhabotinsky reaction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056205 (2005).
[Crossref] [PubMed]

2003 (1)

I. I. Smalyukh and O. D. Lavrentovich, “Anchoring-mediated interaction of edge dislocations with bounding surfaces in confined cholesteric liquid crystals,” Phys. Rev. Lett. 90(8), 085503 (2003).
[Crossref] [PubMed]

2001 (1)

P.-Y. Wang, W. Lu, D. Yu, and R. G. Harrison, “Excitability and pattern formation in a liquid crystal Fabry-Perot interferometer,” Opt. Commun. 189(1-3), 127–134 (2001).
[Crossref]

1998 (1)

F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, “Spatiotemporal evolution of ventricular fibrillation,” Nature 392(6671), 78–82 (1998).
[Crossref] [PubMed]

1997 (2)

A. L. Belmonte, Q. Ouyang, and J.-M. Flesselles, “Experimental survey of spiral dynamics in the Belousov-Zhabotinsky reaction,” Phys. II France 7(10), 1425–1468 (1997).
[Crossref]

C. Zheng and R. B. Meyer, “Thickness effects on pattern formation in liquid crystals in a rotating magnetic field,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 2882–2887 (1997).
[Crossref]

1995 (1)

S. Nasuno, N. Yoshimo, and S. Kai, “Structural transition and motion of domain walls in liquid crystals under a rotating magnetic field,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1598–1601 (1995).
[Crossref] [PubMed]

1994 (2)

T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, “Spiral waves in liquid crystal,” Phys. Rev. Lett. 72(10), 1471–1474 (1994).
[Crossref] [PubMed]

K. B. Migler and R. B. Meyer, “Spirals in liquid crystals in a rotating magnetic field,” Physica D 71(4), 412–420 (1994).
[Crossref]

1991 (1)

K. B. Migler and R. B. Meyer, “Solitons and pattern formation in liquid crystals in a rotating magnetic field,” Phys. Rev. Lett. 66(11), 1485–1488 (1991).
[Crossref] [PubMed]

1984 (1)

F. Lonberg, S. Fraden, A. J. Hurd, and R. B. Meyer, “Field-induced transient periodic structures in nematic liquid crystals: the twist-Fréedericksz transition,” Phys. Rev. Lett. 52(21), 1903–1906 (1984).
[Crossref]

1981 (1)

M. Büttiker and R. Landauer, “Nucleation theory of overdamped soliton motion,” Phys. Rev. A 23(3), 1397–1410 (1981).
[Crossref]

Ackerman, P. J.

P. J. Ackerman, Z. Qi, and I. I. Smalyukh, “Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(2), 021703 (2012).
[Crossref] [PubMed]

Belmonte, A. L.

A. L. Belmonte, Q. Ouyang, and J.-M. Flesselles, “Experimental survey of spiral dynamics in the Belousov-Zhabotinsky reaction,” Phys. II France 7(10), 1425–1468 (1997).
[Crossref]

Bowick, M. J.

L. Giomi, M. J. Bowick, X. Ma, and M. C. Marchetti, “Defect annihilation and proliferation in active nematics,” Phys. Rev. Lett. 110(22), 228101 (2013).
[Crossref] [PubMed]

Büttiker, M.

M. Büttiker and R. Landauer, “Nucleation theory of overdamped soliton motion,” Phys. Rev. A 23(3), 1397–1410 (1981).
[Crossref]

Chaikin, P. M.

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

Chen, D. T. N.

T. Sanchez, D. T. N. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, “Spontaneous motion in hierarchically assembled active matter,” Nature 491(7424), 431–434 (2012).
[Crossref] [PubMed]

Claret, J.

N. Petit-Garrido, R. P. Trivedi, J. Ignés-Mullol, J. Claret, C. Lapointe, F. Sagués, and I. I. Smalyukh, “Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers,” Phys. Rev. Lett. 107(17), 8163–8170 (2011).
[Crossref] [PubMed]

Coullet, P.

T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, “Spiral waves in liquid crystal,” Phys. Rev. Lett. 72(10), 1471–1474 (1994).
[Crossref] [PubMed]

DeCamp, S. J.

T. Sanchez, D. T. N. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, “Spontaneous motion in hierarchically assembled active matter,” Nature 491(7424), 431–434 (2012).
[Crossref] [PubMed]

Delgado, J.

N. Li, J. Delgado, H. O. González-Ochoa, I. R. Epstein, and S. Fraden, “Combined excitatory and inhibitory coupling in a 1-D array of Belousov-Zhabotinsky droplets,” Phys. Chem. Chem. Phys. 16(22), 10965–10978 (2014).
[Crossref] [PubMed]

Ditto, W. L.

F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, “Spatiotemporal evolution of ventricular fibrillation,” Nature 392(6671), 78–82 (1998).
[Crossref] [PubMed]

Dogic, Z.

T. Sanchez, D. T. N. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, “Spontaneous motion in hierarchically assembled active matter,” Nature 491(7424), 431–434 (2012).
[Crossref] [PubMed]

Epstein, I. R.

Y. Zhang, N. Zhou, N. Li, M. Sun, D. Kim, S. Fraden, I. R. Epstein, and B. Xu, “Giant volume change of active gels under continuous flow,” J. Am. Chem. Soc. 136(20), 7341–7347 (2014).
[Crossref] [PubMed]

N. Li, J. Delgado, H. O. González-Ochoa, I. R. Epstein, and S. Fraden, “Combined excitatory and inhibitory coupling in a 1-D array of Belousov-Zhabotinsky droplets,” Phys. Chem. Chem. Phys. 16(22), 10965–10978 (2014).
[Crossref] [PubMed]

Flesselles, J.-M.

A. L. Belmonte, Q. Ouyang, and J.-M. Flesselles, “Experimental survey of spiral dynamics in the Belousov-Zhabotinsky reaction,” Phys. II France 7(10), 1425–1468 (1997).
[Crossref]

Fodor-Csorba, K.

I. Jánossy, K. Fodor-Csorba, A. Vajda, and L. O. Palomares, “Light-induced spontaneous pattern formation in nematic liquid crystal cells,” Appl. Phys. Lett. 99(11), 111103 (2011).
[Crossref]

Fraden, S.

N. Li, J. Delgado, H. O. González-Ochoa, I. R. Epstein, and S. Fraden, “Combined excitatory and inhibitory coupling in a 1-D array of Belousov-Zhabotinsky droplets,” Phys. Chem. Chem. Phys. 16(22), 10965–10978 (2014).
[Crossref] [PubMed]

Y. Zhang, N. Zhou, N. Li, M. Sun, D. Kim, S. Fraden, I. R. Epstein, and B. Xu, “Giant volume change of active gels under continuous flow,” J. Am. Chem. Soc. 136(20), 7341–7347 (2014).
[Crossref] [PubMed]

F. Lonberg, S. Fraden, A. J. Hurd, and R. B. Meyer, “Field-induced transient periodic structures in nematic liquid crystals: the twist-Fréedericksz transition,” Phys. Rev. Lett. 52(21), 1903–1906 (1984).
[Crossref]

Frisch, T.

T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, “Spiral waves in liquid crystal,” Phys. Rev. Lett. 72(10), 1471–1474 (1994).
[Crossref] [PubMed]

Giles, W. R.

F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, “Spatiotemporal evolution of ventricular fibrillation,” Nature 392(6671), 78–82 (1998).
[Crossref] [PubMed]

Gilli, J. M.

T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, “Spiral waves in liquid crystal,” Phys. Rev. Lett. 72(10), 1471–1474 (1994).
[Crossref] [PubMed]

Giomi, L.

L. Giomi, M. J. Bowick, X. Ma, and M. C. Marchetti, “Defect annihilation and proliferation in active nematics,” Phys. Rev. Lett. 110(22), 228101 (2013).
[Crossref] [PubMed]

González-Ochoa, H. O.

N. Li, J. Delgado, H. O. González-Ochoa, I. R. Epstein, and S. Fraden, “Combined excitatory and inhibitory coupling in a 1-D array of Belousov-Zhabotinsky droplets,” Phys. Chem. Chem. Phys. 16(22), 10965–10978 (2014).
[Crossref] [PubMed]

Harrison, R. G.

P.-Y. Wang, W. Lu, D. Yu, and R. G. Harrison, “Excitability and pattern formation in a liquid crystal Fabry-Perot interferometer,” Opt. Commun. 189(1-3), 127–134 (2001).
[Crossref]

Heymann, M.

T. Sanchez, D. T. N. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, “Spontaneous motion in hierarchically assembled active matter,” Nature 491(7424), 431–434 (2012).
[Crossref] [PubMed]

Hopkins, S.

C. P. Lapointe, S. Hopkins, T. G. Mason, and I. I. Smalyukh, “Electrically driven multiaxis rotational dynamics of colloidal platelets in nematic liquid crystals,” Phys. Rev. Lett. 105(17), 178301 (2010).
[Crossref] [PubMed]

Hurd, A. J.

F. Lonberg, S. Fraden, A. J. Hurd, and R. B. Meyer, “Field-induced transient periodic structures in nematic liquid crystals: the twist-Fréedericksz transition,” Phys. Rev. Lett. 52(21), 1903–1906 (1984).
[Crossref]

Ignés-Mullol, J.

N. Petit-Garrido, R. Trivedi, F. Sagués, J. Ignés-Mullol, and I. I. Smalyukh, “Topological defects in cholesteric liquid crystals induced by chiral molecular monolayer domains,” Soft Matter 10, 8163–8170 (2014).
[Crossref] [PubMed]

N. Petit-Garrido, R. P. Trivedi, J. Ignés-Mullol, J. Claret, C. Lapointe, F. Sagués, and I. I. Smalyukh, “Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers,” Phys. Rev. Lett. 107(17), 8163–8170 (2011).
[Crossref] [PubMed]

Jánossy, I.

I. Jánossy, K. Fodor-Csorba, A. Vajda, and L. O. Palomares, “Light-induced spontaneous pattern formation in nematic liquid crystal cells,” Appl. Phys. Lett. 99(11), 111103 (2011).
[Crossref]

Kai, S.

S. Nasuno, N. Yoshimo, and S. Kai, “Structural transition and motion of domain walls in liquid crystals under a rotating magnetic field,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1598–1601 (1995).
[Crossref] [PubMed]

Kim, D.

Y. Zhang, N. Zhou, N. Li, M. Sun, D. Kim, S. Fraden, I. R. Epstein, and B. Xu, “Giant volume change of active gels under continuous flow,” J. Am. Chem. Soc. 136(20), 7341–7347 (2014).
[Crossref] [PubMed]

Landauer, R.

M. Büttiker and R. Landauer, “Nucleation theory of overdamped soliton motion,” Phys. Rev. A 23(3), 1397–1410 (1981).
[Crossref]

Langley, D.

M. E. McConney, A. Martinez, V. P. Tondiglia, K. M. Lee, D. Langley, I. I. Smalyukh, and T. J. White, “Topography from topology: photoinduced surface features generated in liquid crystal polymer networks,” Adv. Mater. 25(41), 5880–5885 (2013).
[Crossref] [PubMed]

Lapointe, C.

N. Petit-Garrido, R. P. Trivedi, J. Ignés-Mullol, J. Claret, C. Lapointe, F. Sagués, and I. I. Smalyukh, “Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers,” Phys. Rev. Lett. 107(17), 8163–8170 (2011).
[Crossref] [PubMed]

Lapointe, C. P.

C. P. Lapointe, S. Hopkins, T. G. Mason, and I. I. Smalyukh, “Electrically driven multiaxis rotational dynamics of colloidal platelets in nematic liquid crystals,” Phys. Rev. Lett. 105(17), 178301 (2010).
[Crossref] [PubMed]

Lavrentovich, O. D.

I. I. Smalyukh and O. D. Lavrentovich, “Anchoring-mediated interaction of edge dislocations with bounding surfaces in confined cholesteric liquid crystals,” Phys. Rev. Lett. 90(8), 085503 (2003).
[Crossref] [PubMed]

Lee, K. M.

M. E. McConney, A. Martinez, V. P. Tondiglia, K. M. Lee, D. Langley, I. I. Smalyukh, and T. J. White, “Topography from topology: photoinduced surface features generated in liquid crystal polymer networks,” Adv. Mater. 25(41), 5880–5885 (2013).
[Crossref] [PubMed]

Leon, L. J.

F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, “Spatiotemporal evolution of ventricular fibrillation,” Nature 392(6671), 78–82 (1998).
[Crossref] [PubMed]

Li, N.

N. Li, J. Delgado, H. O. González-Ochoa, I. R. Epstein, and S. Fraden, “Combined excitatory and inhibitory coupling in a 1-D array of Belousov-Zhabotinsky droplets,” Phys. Chem. Chem. Phys. 16(22), 10965–10978 (2014).
[Crossref] [PubMed]

Y. Zhang, N. Zhou, N. Li, M. Sun, D. Kim, S. Fraden, I. R. Epstein, and B. Xu, “Giant volume change of active gels under continuous flow,” J. Am. Chem. Soc. 136(20), 7341–7347 (2014).
[Crossref] [PubMed]

Lin, A. L.

L. B. Smolka, B. Marts, and A. L. Lin, “Effect of inhomogeneities on spiral wave dynamics in the Belousov-Zhabotinsky reaction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056205 (2005).
[Crossref] [PubMed]

Liu, Q.

Q. Liu, Y. Yuan, and I. I. Smalyukh, “Electrically and optically tunable plasmonic guest-host liquid crystals with long-range ordered nanoparticles,” Nano Lett. 14(7), 4071–4077 (2014).
[Crossref] [PubMed]

Lonberg, F.

F. Lonberg, S. Fraden, A. J. Hurd, and R. B. Meyer, “Field-induced transient periodic structures in nematic liquid crystals: the twist-Fréedericksz transition,” Phys. Rev. Lett. 52(21), 1903–1906 (1984).
[Crossref]

Lu, W.

P.-Y. Wang, W. Lu, D. Yu, and R. G. Harrison, “Excitability and pattern formation in a liquid crystal Fabry-Perot interferometer,” Opt. Commun. 189(1-3), 127–134 (2001).
[Crossref]

Lucero, B.

A. Martinez, M. Ravnik, B. Lucero, R. Visvanathan, S. Žumer, and I. I. Smalyukh, “Mutually tangled colloidal knots and induced defect loops in nematic fields,” Nat. Mater. 13(3), 258–263 (2014).
[Crossref] [PubMed]

Luengviriya, C.

J. Luengviriya, P. Porjai, M. Phantu, M. Sutthiopad, B. Tomapatanaget, S. C. Müller, and C. Luengviriya, “Meandering spiral waves in a bubble-free Belousov–Zhabotinsky reaction with pyrogallol,” Chem. Phys. Lett. 588, 267–271 (2013).
[Crossref]

Luengviriya, J.

J. Luengviriya, P. Porjai, M. Phantu, M. Sutthiopad, B. Tomapatanaget, S. C. Müller, and C. Luengviriya, “Meandering spiral waves in a bubble-free Belousov–Zhabotinsky reaction with pyrogallol,” Chem. Phys. Lett. 588, 267–271 (2013).
[Crossref]

Ma, X.

L. Giomi, M. J. Bowick, X. Ma, and M. C. Marchetti, “Defect annihilation and proliferation in active nematics,” Phys. Rev. Lett. 110(22), 228101 (2013).
[Crossref] [PubMed]

Marchetti, M. C.

L. Giomi, M. J. Bowick, X. Ma, and M. C. Marchetti, “Defect annihilation and proliferation in active nematics,” Phys. Rev. Lett. 110(22), 228101 (2013).
[Crossref] [PubMed]

Martinez, A.

A. Martinez, M. Ravnik, B. Lucero, R. Visvanathan, S. Žumer, and I. I. Smalyukh, “Mutually tangled colloidal knots and induced defect loops in nematic fields,” Nat. Mater. 13(3), 258–263 (2014).
[Crossref] [PubMed]

M. E. McConney, A. Martinez, V. P. Tondiglia, K. M. Lee, D. Langley, I. I. Smalyukh, and T. J. White, “Topography from topology: photoinduced surface features generated in liquid crystal polymer networks,” Adv. Mater. 25(41), 5880–5885 (2013).
[Crossref] [PubMed]

A. Martinez, H. C. Mireles, and I. I. Smalyukh, “Large-area optoelastic manipulation of colloidal particles in liquid crystals using photoresponsive molecular surface monolayers,” Proc. Natl. Acad. Sci. U.S.A. 108(52), 20891–20896 (2011).
[Crossref] [PubMed]

Marts, B.

L. B. Smolka, B. Marts, and A. L. Lin, “Effect of inhomogeneities on spiral wave dynamics in the Belousov-Zhabotinsky reaction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056205 (2005).
[Crossref] [PubMed]

Mason, T. G.

C. P. Lapointe, S. Hopkins, T. G. Mason, and I. I. Smalyukh, “Electrically driven multiaxis rotational dynamics of colloidal platelets in nematic liquid crystals,” Phys. Rev. Lett. 105(17), 178301 (2010).
[Crossref] [PubMed]

McConney, M. E.

M. E. McConney, A. Martinez, V. P. Tondiglia, K. M. Lee, D. Langley, I. I. Smalyukh, and T. J. White, “Topography from topology: photoinduced surface features generated in liquid crystal polymer networks,” Adv. Mater. 25(41), 5880–5885 (2013).
[Crossref] [PubMed]

Meyer, R. B.

C. Zheng and R. B. Meyer, “Thickness effects on pattern formation in liquid crystals in a rotating magnetic field,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 2882–2887 (1997).
[Crossref]

K. B. Migler and R. B. Meyer, “Spirals in liquid crystals in a rotating magnetic field,” Physica D 71(4), 412–420 (1994).
[Crossref]

K. B. Migler and R. B. Meyer, “Solitons and pattern formation in liquid crystals in a rotating magnetic field,” Phys. Rev. Lett. 66(11), 1485–1488 (1991).
[Crossref] [PubMed]

F. Lonberg, S. Fraden, A. J. Hurd, and R. B. Meyer, “Field-induced transient periodic structures in nematic liquid crystals: the twist-Fréedericksz transition,” Phys. Rev. Lett. 52(21), 1903–1906 (1984).
[Crossref]

Migler, K. B.

K. B. Migler and R. B. Meyer, “Spirals in liquid crystals in a rotating magnetic field,” Physica D 71(4), 412–420 (1994).
[Crossref]

K. B. Migler and R. B. Meyer, “Solitons and pattern formation in liquid crystals in a rotating magnetic field,” Phys. Rev. Lett. 66(11), 1485–1488 (1991).
[Crossref] [PubMed]

Mireles, H. C.

A. Martinez, H. C. Mireles, and I. I. Smalyukh, “Large-area optoelastic manipulation of colloidal particles in liquid crystals using photoresponsive molecular surface monolayers,” Proc. Natl. Acad. Sci. U.S.A. 108(52), 20891–20896 (2011).
[Crossref] [PubMed]

Müller, S. C.

J. Luengviriya, P. Porjai, M. Phantu, M. Sutthiopad, B. Tomapatanaget, S. C. Müller, and C. Luengviriya, “Meandering spiral waves in a bubble-free Belousov–Zhabotinsky reaction with pyrogallol,” Chem. Phys. Lett. 588, 267–271 (2013).
[Crossref]

Nasuno, S.

S. Nasuno, N. Yoshimo, and S. Kai, “Structural transition and motion of domain walls in liquid crystals under a rotating magnetic field,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1598–1601 (1995).
[Crossref] [PubMed]

Ouyang, Q.

A. L. Belmonte, Q. Ouyang, and J.-M. Flesselles, “Experimental survey of spiral dynamics in the Belousov-Zhabotinsky reaction,” Phys. II France 7(10), 1425–1468 (1997).
[Crossref]

Palacci, J.

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

Palomares, L. O.

I. Jánossy, K. Fodor-Csorba, A. Vajda, and L. O. Palomares, “Light-induced spontaneous pattern formation in nematic liquid crystal cells,” Appl. Phys. Lett. 99(11), 111103 (2011).
[Crossref]

Penkoske, P. A.

F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, “Spatiotemporal evolution of ventricular fibrillation,” Nature 392(6671), 78–82 (1998).
[Crossref] [PubMed]

Petit-Garrido, N.

N. Petit-Garrido, R. Trivedi, F. Sagués, J. Ignés-Mullol, and I. I. Smalyukh, “Topological defects in cholesteric liquid crystals induced by chiral molecular monolayer domains,” Soft Matter 10, 8163–8170 (2014).
[Crossref] [PubMed]

N. Petit-Garrido, R. P. Trivedi, J. Ignés-Mullol, J. Claret, C. Lapointe, F. Sagués, and I. I. Smalyukh, “Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers,” Phys. Rev. Lett. 107(17), 8163–8170 (2011).
[Crossref] [PubMed]

Phantu, M.

J. Luengviriya, P. Porjai, M. Phantu, M. Sutthiopad, B. Tomapatanaget, S. C. Müller, and C. Luengviriya, “Meandering spiral waves in a bubble-free Belousov–Zhabotinsky reaction with pyrogallol,” Chem. Phys. Lett. 588, 267–271 (2013).
[Crossref]

Pine, D. J.

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

Porjai, P.

J. Luengviriya, P. Porjai, M. Phantu, M. Sutthiopad, B. Tomapatanaget, S. C. Müller, and C. Luengviriya, “Meandering spiral waves in a bubble-free Belousov–Zhabotinsky reaction with pyrogallol,” Chem. Phys. Lett. 588, 267–271 (2013).
[Crossref]

Qi, Z.

P. J. Ackerman, Z. Qi, and I. I. Smalyukh, “Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(2), 021703 (2012).
[Crossref] [PubMed]

Ravnik, M.

A. Martinez, M. Ravnik, B. Lucero, R. Visvanathan, S. Žumer, and I. I. Smalyukh, “Mutually tangled colloidal knots and induced defect loops in nematic fields,” Nat. Mater. 13(3), 258–263 (2014).
[Crossref] [PubMed]

Rica, S.

T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, “Spiral waves in liquid crystal,” Phys. Rev. Lett. 72(10), 1471–1474 (1994).
[Crossref] [PubMed]

Sacanna, S.

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

Sagués, F.

N. Petit-Garrido, R. Trivedi, F. Sagués, J. Ignés-Mullol, and I. I. Smalyukh, “Topological defects in cholesteric liquid crystals induced by chiral molecular monolayer domains,” Soft Matter 10, 8163–8170 (2014).
[Crossref] [PubMed]

N. Petit-Garrido, R. P. Trivedi, J. Ignés-Mullol, J. Claret, C. Lapointe, F. Sagués, and I. I. Smalyukh, “Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers,” Phys. Rev. Lett. 107(17), 8163–8170 (2011).
[Crossref] [PubMed]

Sanchez, T.

T. Sanchez, D. T. N. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, “Spontaneous motion in hierarchically assembled active matter,” Nature 491(7424), 431–434 (2012).
[Crossref] [PubMed]

Smalyukh, I. I.

N. Petit-Garrido, R. Trivedi, F. Sagués, J. Ignés-Mullol, and I. I. Smalyukh, “Topological defects in cholesteric liquid crystals induced by chiral molecular monolayer domains,” Soft Matter 10, 8163–8170 (2014).
[Crossref] [PubMed]

A. Martinez, M. Ravnik, B. Lucero, R. Visvanathan, S. Žumer, and I. I. Smalyukh, “Mutually tangled colloidal knots and induced defect loops in nematic fields,” Nat. Mater. 13(3), 258–263 (2014).
[Crossref] [PubMed]

Q. Liu, Y. Yuan, and I. I. Smalyukh, “Electrically and optically tunable plasmonic guest-host liquid crystals with long-range ordered nanoparticles,” Nano Lett. 14(7), 4071–4077 (2014).
[Crossref] [PubMed]

M. E. McConney, A. Martinez, V. P. Tondiglia, K. M. Lee, D. Langley, I. I. Smalyukh, and T. J. White, “Topography from topology: photoinduced surface features generated in liquid crystal polymer networks,” Adv. Mater. 25(41), 5880–5885 (2013).
[Crossref] [PubMed]

P. J. Ackerman, Z. Qi, and I. I. Smalyukh, “Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(2), 021703 (2012).
[Crossref] [PubMed]

N. Petit-Garrido, R. P. Trivedi, J. Ignés-Mullol, J. Claret, C. Lapointe, F. Sagués, and I. I. Smalyukh, “Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers,” Phys. Rev. Lett. 107(17), 8163–8170 (2011).
[Crossref] [PubMed]

A. Martinez, H. C. Mireles, and I. I. Smalyukh, “Large-area optoelastic manipulation of colloidal particles in liquid crystals using photoresponsive molecular surface monolayers,” Proc. Natl. Acad. Sci. U.S.A. 108(52), 20891–20896 (2011).
[Crossref] [PubMed]

C. P. Lapointe, S. Hopkins, T. G. Mason, and I. I. Smalyukh, “Electrically driven multiaxis rotational dynamics of colloidal platelets in nematic liquid crystals,” Phys. Rev. Lett. 105(17), 178301 (2010).
[Crossref] [PubMed]

I. I. Smalyukh and O. D. Lavrentovich, “Anchoring-mediated interaction of edge dislocations with bounding surfaces in confined cholesteric liquid crystals,” Phys. Rev. Lett. 90(8), 085503 (2003).
[Crossref] [PubMed]

Smolka, L. B.

L. B. Smolka, B. Marts, and A. L. Lin, “Effect of inhomogeneities on spiral wave dynamics in the Belousov-Zhabotinsky reaction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056205 (2005).
[Crossref] [PubMed]

Spano, M. L.

F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, “Spatiotemporal evolution of ventricular fibrillation,” Nature 392(6671), 78–82 (1998).
[Crossref] [PubMed]

Steinberg, A. P.

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

Sun, M.

Y. Zhang, N. Zhou, N. Li, M. Sun, D. Kim, S. Fraden, I. R. Epstein, and B. Xu, “Giant volume change of active gels under continuous flow,” J. Am. Chem. Soc. 136(20), 7341–7347 (2014).
[Crossref] [PubMed]

Sutthiopad, M.

J. Luengviriya, P. Porjai, M. Phantu, M. Sutthiopad, B. Tomapatanaget, S. C. Müller, and C. Luengviriya, “Meandering spiral waves in a bubble-free Belousov–Zhabotinsky reaction with pyrogallol,” Chem. Phys. Lett. 588, 267–271 (2013).
[Crossref]

Tomapatanaget, B.

J. Luengviriya, P. Porjai, M. Phantu, M. Sutthiopad, B. Tomapatanaget, S. C. Müller, and C. Luengviriya, “Meandering spiral waves in a bubble-free Belousov–Zhabotinsky reaction with pyrogallol,” Chem. Phys. Lett. 588, 267–271 (2013).
[Crossref]

Tondiglia, V. P.

M. E. McConney, A. Martinez, V. P. Tondiglia, K. M. Lee, D. Langley, I. I. Smalyukh, and T. J. White, “Topography from topology: photoinduced surface features generated in liquid crystal polymer networks,” Adv. Mater. 25(41), 5880–5885 (2013).
[Crossref] [PubMed]

Trivedi, R.

N. Petit-Garrido, R. Trivedi, F. Sagués, J. Ignés-Mullol, and I. I. Smalyukh, “Topological defects in cholesteric liquid crystals induced by chiral molecular monolayer domains,” Soft Matter 10, 8163–8170 (2014).
[Crossref] [PubMed]

Trivedi, R. P.

N. Petit-Garrido, R. P. Trivedi, J. Ignés-Mullol, J. Claret, C. Lapointe, F. Sagués, and I. I. Smalyukh, “Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers,” Phys. Rev. Lett. 107(17), 8163–8170 (2011).
[Crossref] [PubMed]

Vajda, A.

I. Jánossy, K. Fodor-Csorba, A. Vajda, and L. O. Palomares, “Light-induced spontaneous pattern formation in nematic liquid crystal cells,” Appl. Phys. Lett. 99(11), 111103 (2011).
[Crossref]

Visvanathan, R.

A. Martinez, M. Ravnik, B. Lucero, R. Visvanathan, S. Žumer, and I. I. Smalyukh, “Mutually tangled colloidal knots and induced defect loops in nematic fields,” Nat. Mater. 13(3), 258–263 (2014).
[Crossref] [PubMed]

Wang, P.-Y.

P.-Y. Wang, W. Lu, D. Yu, and R. G. Harrison, “Excitability and pattern formation in a liquid crystal Fabry-Perot interferometer,” Opt. Commun. 189(1-3), 127–134 (2001).
[Crossref]

White, T. J.

M. E. McConney, A. Martinez, V. P. Tondiglia, K. M. Lee, D. Langley, I. I. Smalyukh, and T. J. White, “Topography from topology: photoinduced surface features generated in liquid crystal polymer networks,” Adv. Mater. 25(41), 5880–5885 (2013).
[Crossref] [PubMed]

Winfree, A. T.

F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, “Spatiotemporal evolution of ventricular fibrillation,” Nature 392(6671), 78–82 (1998).
[Crossref] [PubMed]

Witkowski, F. X.

F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, “Spatiotemporal evolution of ventricular fibrillation,” Nature 392(6671), 78–82 (1998).
[Crossref] [PubMed]

Xu, B.

Y. Zhang, N. Zhou, N. Li, M. Sun, D. Kim, S. Fraden, I. R. Epstein, and B. Xu, “Giant volume change of active gels under continuous flow,” J. Am. Chem. Soc. 136(20), 7341–7347 (2014).
[Crossref] [PubMed]

Yoshimo, N.

S. Nasuno, N. Yoshimo, and S. Kai, “Structural transition and motion of domain walls in liquid crystals under a rotating magnetic field,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1598–1601 (1995).
[Crossref] [PubMed]

Yu, D.

P.-Y. Wang, W. Lu, D. Yu, and R. G. Harrison, “Excitability and pattern formation in a liquid crystal Fabry-Perot interferometer,” Opt. Commun. 189(1-3), 127–134 (2001).
[Crossref]

Yuan, Y.

Q. Liu, Y. Yuan, and I. I. Smalyukh, “Electrically and optically tunable plasmonic guest-host liquid crystals with long-range ordered nanoparticles,” Nano Lett. 14(7), 4071–4077 (2014).
[Crossref] [PubMed]

Zhang, Y.

Y. Zhang, N. Zhou, N. Li, M. Sun, D. Kim, S. Fraden, I. R. Epstein, and B. Xu, “Giant volume change of active gels under continuous flow,” J. Am. Chem. Soc. 136(20), 7341–7347 (2014).
[Crossref] [PubMed]

Zheng, C.

C. Zheng and R. B. Meyer, “Thickness effects on pattern formation in liquid crystals in a rotating magnetic field,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 2882–2887 (1997).
[Crossref]

Zhou, N.

Y. Zhang, N. Zhou, N. Li, M. Sun, D. Kim, S. Fraden, I. R. Epstein, and B. Xu, “Giant volume change of active gels under continuous flow,” J. Am. Chem. Soc. 136(20), 7341–7347 (2014).
[Crossref] [PubMed]

Žumer, S.

A. Martinez, M. Ravnik, B. Lucero, R. Visvanathan, S. Žumer, and I. I. Smalyukh, “Mutually tangled colloidal knots and induced defect loops in nematic fields,” Nat. Mater. 13(3), 258–263 (2014).
[Crossref] [PubMed]

Adv. Mater. (1)

M. E. McConney, A. Martinez, V. P. Tondiglia, K. M. Lee, D. Langley, I. I. Smalyukh, and T. J. White, “Topography from topology: photoinduced surface features generated in liquid crystal polymer networks,” Adv. Mater. 25(41), 5880–5885 (2013).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

I. Jánossy, K. Fodor-Csorba, A. Vajda, and L. O. Palomares, “Light-induced spontaneous pattern formation in nematic liquid crystal cells,” Appl. Phys. Lett. 99(11), 111103 (2011).
[Crossref]

Chem. Phys. Lett. (1)

J. Luengviriya, P. Porjai, M. Phantu, M. Sutthiopad, B. Tomapatanaget, S. C. Müller, and C. Luengviriya, “Meandering spiral waves in a bubble-free Belousov–Zhabotinsky reaction with pyrogallol,” Chem. Phys. Lett. 588, 267–271 (2013).
[Crossref]

J. Am. Chem. Soc. (1)

Y. Zhang, N. Zhou, N. Li, M. Sun, D. Kim, S. Fraden, I. R. Epstein, and B. Xu, “Giant volume change of active gels under continuous flow,” J. Am. Chem. Soc. 136(20), 7341–7347 (2014).
[Crossref] [PubMed]

Nano Lett. (1)

Q. Liu, Y. Yuan, and I. I. Smalyukh, “Electrically and optically tunable plasmonic guest-host liquid crystals with long-range ordered nanoparticles,” Nano Lett. 14(7), 4071–4077 (2014).
[Crossref] [PubMed]

Nat. Mater. (1)

A. Martinez, M. Ravnik, B. Lucero, R. Visvanathan, S. Žumer, and I. I. Smalyukh, “Mutually tangled colloidal knots and induced defect loops in nematic fields,” Nat. Mater. 13(3), 258–263 (2014).
[Crossref] [PubMed]

Nature (2)

T. Sanchez, D. T. N. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, “Spontaneous motion in hierarchically assembled active matter,” Nature 491(7424), 431–434 (2012).
[Crossref] [PubMed]

F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, “Spatiotemporal evolution of ventricular fibrillation,” Nature 392(6671), 78–82 (1998).
[Crossref] [PubMed]

Opt. Commun. (1)

P.-Y. Wang, W. Lu, D. Yu, and R. G. Harrison, “Excitability and pattern formation in a liquid crystal Fabry-Perot interferometer,” Opt. Commun. 189(1-3), 127–134 (2001).
[Crossref]

Phys. Chem. Chem. Phys. (1)

N. Li, J. Delgado, H. O. González-Ochoa, I. R. Epstein, and S. Fraden, “Combined excitatory and inhibitory coupling in a 1-D array of Belousov-Zhabotinsky droplets,” Phys. Chem. Chem. Phys. 16(22), 10965–10978 (2014).
[Crossref] [PubMed]

Phys. II France (1)

A. L. Belmonte, Q. Ouyang, and J.-M. Flesselles, “Experimental survey of spiral dynamics in the Belousov-Zhabotinsky reaction,” Phys. II France 7(10), 1425–1468 (1997).
[Crossref]

Phys. Rev. A (1)

M. Büttiker and R. Landauer, “Nucleation theory of overdamped soliton motion,” Phys. Rev. A 23(3), 1397–1410 (1981).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

P. J. Ackerman, Z. Qi, and I. I. Smalyukh, “Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86(2), 021703 (2012).
[Crossref] [PubMed]

L. B. Smolka, B. Marts, and A. L. Lin, “Effect of inhomogeneities on spiral wave dynamics in the Belousov-Zhabotinsky reaction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056205 (2005).
[Crossref] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (2)

C. Zheng and R. B. Meyer, “Thickness effects on pattern formation in liquid crystals in a rotating magnetic field,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(3), 2882–2887 (1997).
[Crossref]

S. Nasuno, N. Yoshimo, and S. Kai, “Structural transition and motion of domain walls in liquid crystals under a rotating magnetic field,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1598–1601 (1995).
[Crossref] [PubMed]

Phys. Rev. Lett. (7)

T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, “Spiral waves in liquid crystal,” Phys. Rev. Lett. 72(10), 1471–1474 (1994).
[Crossref] [PubMed]

K. B. Migler and R. B. Meyer, “Solitons and pattern formation in liquid crystals in a rotating magnetic field,” Phys. Rev. Lett. 66(11), 1485–1488 (1991).
[Crossref] [PubMed]

L. Giomi, M. J. Bowick, X. Ma, and M. C. Marchetti, “Defect annihilation and proliferation in active nematics,” Phys. Rev. Lett. 110(22), 228101 (2013).
[Crossref] [PubMed]

I. I. Smalyukh and O. D. Lavrentovich, “Anchoring-mediated interaction of edge dislocations with bounding surfaces in confined cholesteric liquid crystals,” Phys. Rev. Lett. 90(8), 085503 (2003).
[Crossref] [PubMed]

N. Petit-Garrido, R. P. Trivedi, J. Ignés-Mullol, J. Claret, C. Lapointe, F. Sagués, and I. I. Smalyukh, “Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers,” Phys. Rev. Lett. 107(17), 8163–8170 (2011).
[Crossref] [PubMed]

C. P. Lapointe, S. Hopkins, T. G. Mason, and I. I. Smalyukh, “Electrically driven multiaxis rotational dynamics of colloidal platelets in nematic liquid crystals,” Phys. Rev. Lett. 105(17), 178301 (2010).
[Crossref] [PubMed]

F. Lonberg, S. Fraden, A. J. Hurd, and R. B. Meyer, “Field-induced transient periodic structures in nematic liquid crystals: the twist-Fréedericksz transition,” Phys. Rev. Lett. 52(21), 1903–1906 (1984).
[Crossref]

Physica D (1)

K. B. Migler and R. B. Meyer, “Spirals in liquid crystals in a rotating magnetic field,” Physica D 71(4), 412–420 (1994).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

A. Martinez, H. C. Mireles, and I. I. Smalyukh, “Large-area optoelastic manipulation of colloidal particles in liquid crystals using photoresponsive molecular surface monolayers,” Proc. Natl. Acad. Sci. U.S.A. 108(52), 20891–20896 (2011).
[Crossref] [PubMed]

Science (1)

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

Soft Matter (1)

N. Petit-Garrido, R. Trivedi, F. Sagués, J. Ignés-Mullol, and I. I. Smalyukh, “Topological defects in cholesteric liquid crystals induced by chiral molecular monolayer domains,” Soft Matter 10, 8163–8170 (2014).
[Crossref] [PubMed]

Other (5)

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Willey, New York, 1999).

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd Ed. (Clarendon, 1993).

P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University, 2000).

J. Wesfreid, H. Brand, P. Monneville, G. Albinet, and N. Boccara, eds., Propagation in Systems far from Equilibrium (Springer, 1988).

R. J. Field and M. Burger, eds., Oscillations and Traveling Waves in Chemical Systems (Wiley, 1985).

Supplementary Material (18)

» Media 1: AVI (9937 KB)     
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Figures (7)

Fig. 1
Fig. 1

Pattern-forming photo-responsive LC cell construction. (a-f) Three types of LC cells constructed with (a, d) one substrate coated with a film of rubbed polyimide (with easy axis along the yellow arrow) and another coated with a monolayer of the photo-responsive DMR, or (b, e) with both substrates coated with DMR, or (c,f) with one substrate coated with DMOAP to yield homeotropic anchoring and another coated with DMR. The cells are shown in two states: (a, b, c) at the first moment of illumination with linearly polarized blue light (along P 0) and (d, e, f) in an evolved dynamic state sometime later when the second substrate is adaptively reorienting due to the photo-induced torque on n d caused by polarized-light illumination, e.g. to drive n d away from P d in (a). The polarization of the output light is, in general, elliptical and oriented with its long axis at some angle with respect to the director at the output plane, n d. In the “dynamic equilibrium”, the boundary condition n d for the director at the exit substrate is constantly adjusted to be orthogonal to the long axis of the polarization ellipse orientation of which is dependent on the twist of director throughout the cell while this, in turn, adjusts the amount of director twist and, subsequently, further alters the polarization state, thus providing the nonlinear response and a feedback mechanism needed for the pattern formation.

Fig. 2
Fig. 2

Dynamic Archimedes spirals. (a, b) A series of polarizing micrographs extracted from a video, with elapsed time marked on them, for (a) two spiral patterns shown between crossed polarizers along black double arrows marked by “P” and “A” (Media 1) and (b) with an additional 530 nm wave-plate inserted between the polarizers and having the slow axis oriented along the blue double arrow (Media 2). The spiral arms in series (a) undergo 2π rotation over about 2 seconds while the spiral arms in series (b) undergo π rotation over about 1.2 seconds. (c) Schematic of the experimental setup.

Fig. 3
Fig. 3

Analysis of dynamic Archimedes spiral patterns in optically driven nematic cells. (a) A polar plot of the spiraling Néel wall coordinates in the r-θ cylindrical coordinate system at a constant time, as measured experimentally for the two spiral arms (red and blue filled circles). (b) Linear plots of r versus θ for each arm. The linear red and blue lines in (a,b) are fits of experimental data to an expression r = r 0 + Λθ/(2π) defining the Archimedes spiral geometric configuration. The distance between consecutive solitons (wavelength) for a given spiral arm is denoted as Λ, and is defined in the inset of (b). The fits of two spiraling arms yield wavelengths Λ 1 = 19.03 μm and Λ 2 = 18.5 μm. (c) Coordinates of the “center of mass” of the spiraling pattern tracked over time and color-coded according to the time-color scale on the right to illustrate the meandering behavior similar to that of Archimedes spirals in chemical reaction diffusion systems.

Fig. 4
Fig. 4

Dependence of pattern dynamics on the color of illumination light. (a-c) Three frames of a single time series showing the dependence of defect dynamics on the color of illumination light (Media 3). (a) The pattern is driven by white microscope light at a rate of ~0.37 Hz. (b) the pattern is also effectively driven by blue light to which DMR is highly sensitive, although the rate decreases slightly upon insertion of a blue color filter due to the decreased overall intensity. (c) An optical micrograph showing a static pattern obtained upon insertion of a red color filter: since the interaction of the DMR with red light is negligible, the initially dynamic pattern “freezes” under red illumination. The crossed polarizers are oriented along black double arrows marked by “P” and “A” in (a) and rotation rates are marked on images.

Fig. 5
Fig. 5

Summary of dynamic and static patterns in addition to the propagating Archimedes spiral waves. (a-l) Twelve examples of different species of observed dynamic patterns, all driven with linearly polarized white light and viewed between crossed polarizers oriented along the image edges (Media 4, Media 5, Media 6, Media 7, Media 8, Media 9, Media 10, Media 11, Media 12, Media 13, Media 14, and Media 15). The patterns (a-g) arise in thinner cells of thickness d = 1-2 μm while the patterns (h-l) are observed in thicker cells of d = 2-4 μm.

Fig. 6
Fig. 6

Director structure of the inter-domain solitonic Néel wall regions. (a) Numerically simulated equilibrium director field configurations corresponding to the inter-domain pattern regions with different directions of ± 80° twist. (b) Computer-simulated director field configurations corresponding to the inter-domain regions with different 270° and 80° twist across the cell. The field configurations correspond to initially dynamic patterns that are “frozen” by removing blue and ultraviolet components of illumination light, as in the example shown in Fig. 4(c).

Fig. 7
Fig. 7

Dynamic light-driven patterns in hybrid DMOAP-DMR wedge cells in presence of lateral confinement of the illuminated area. (a-c) Square regions illuminated with linearly polarized blue light viewed between crossed polarizer and analyzer oriented along white double arrows marked with “P” and “A” in (b) (Media 16, Media 17, and Media 18). Time series (a) shows an illuminated region at the thick side of the wedge-shaped cell (d≈4 μm), while the frame series (b) and (c) are obtained in a cell region at the thin side (d≈1 μm). Series (a) and (b) show the illuminated cell region during successively evolved states (with elapsed time marked on the frames extracted from a video) under constant illumination. The transformation of dynamic patterns shown in (c) was initiated by a π-rotation of the linear polarization of incident light beginning from the orientation of this linear polarization P 0 along the vertical edge of the corresponding video frames.

Equations (8)

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F LPDSA = [ W 0 ( I ) / 2 ] ( P 0 n 0 ) 2 d S + [ W d ( I , ε ) / 2 ] ( P d n d ) 2 d S ,
F elastic = { K 11 2 ( n ) 2 + K 22 2 [ n ( × n ) + 2 π p ] 2 + K 33 2 [ n × ( × n ) ] 2 K 24 [ [ n ( n ) + n × ( × n ) ] ] } d V ,
Γ v = n × δ F δ n ,
Γ v = γ 1 ( n × n t ) .
ε = tan ( 1 2 sin 1 [ Ω ϕ X 2 sin 2 X ] )
tan 2 ψ = 2 ϕ X tan X X 2 ( ϕ 2 Ω 2 / 4 ) tan 2 X ,
ξ 2 α τ α t + ω τ sin ( 2 α ) = 0.
ξ 2 τ 2 α 2 r + v w τ α r + ω τ sin ( 2 α ) = 0.

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