Applications of the Peach-Koehler force in liquid crystals

References

• Brandenberger RH. Topological defects and structure formation. Int J Mod Phys A. 1994;9:2117–2189. doi: 10.1142/S0217751X9400090X
   Web of Science ®Google Scholar
• Durrer R, Kunz M, Melchiorri A. Cosmic structure formation with topological defects. Phys Rep. 2002;364(1):1–81. doi: 10.1016/S0370-1573(02)00014-5
   Google Scholar
• Kosterlitz JM, Thouless DJ. Order, metastability and phase transitions in two-dimensional systems. J Phys C. 1973;6:1181–1203. doi: 10.1088/0022-3719/6/7/010
   Web of Science ®Google Scholar
• Agnolet G, McQueeney DF, Reppy JD. Kosterlitz-thouless transition in helium films. Phys Rev B. 1989;39(13):8934. doi: 10.1103/PhysRevB.39.8934
   Web of Science ®Google Scholar
• Chaikin PM, Lubensky TC. Principles of condensed matter physics. Cambridge: Cambridge University Press; 1995.
   Google Scholar
• Frank FC, Read WT. Multiplication processes for slow moving dislocations. Phys Rev. 1950;79(4):722. doi: 10.1103/PhysRev.79.722
   Web of Science ®Google Scholar
• Halperin BI, Nelson DR. Theory of two-dimensional melting. Phys Rev Lett. 1978;41(2):121. doi: 10.1103/PhysRevLett.41.121
   Web of Science ®Google Scholar
• Peng C, Turiv T, Guo Y, et al. Command of active matter by topological defects and patterns. Science. 2016;354(6314):882–885. doi: 10.1126/science.aah6936
   PubMed Web of Science ®Google Scholar
• Genkin MM, Sokolov A, Lavrentovich OD, et al. Topological defects in a living nematic ensnare swimming bacteria. Phys Rev X. 2017;7(1):011029. doi: 10.1103/PhysRevX.7.011029
   Web of Science ®Google Scholar
• Zhang R, Redford SA, Ruijgrok PV, et al. Spatiotemporal control of liquid crystal structure and dynamics through activity patterning. Nat Mater. 2021;20(6):875–882. doi: 10.1038/s41563-020-00901-4
   PubMed Web of Science ®Google Scholar
• Shankar S, Souslov A, Bowick MJ, et al. Topological active matter. Nat Rev Phys. 2022;4(6):380–398. doi: 10.1038/s42254-022-00445-3
   Google Scholar
• Ardaševa A, Doostmohammadi A. Topological defects in biological matter. Nat Rev Phys. 2022;4(6):354–356. doi: 10.1038/s42254-022-00469-9
   Google Scholar
• Peach M, Koehler JS. The forces exerted on dislocations and the stress fields produced by them. Phys Rev. 1950;80(3):436–439. doi: 10.1103/PhysRev.80.436
   Google Scholar
• Anderson PM, Hirth JP, Lothe J. Theory of dislocations. Cambridge: Cambridge University Press; 2017.
   Google Scholar
• de Gennes PG, Prost J. The physics of liquid crystals. Oxford: Oxford University Press; 1993.
   Google Scholar
• Kléman M. Points, lines, and walls: in liquid crystals, magnetic systems, and various ordered media. Chichester: Wiley; 1983.
   Google Scholar
• Eshelby JD. The force on a disclination in a liquid crystal. Philos Mag A. 1980;42(3):359–367. doi: 10.1080/01418618008239363
   Web of Science ®Google Scholar
• Kawasaki K, Brand HR. Gauge theory of continuous media with topological defects: uniaxial nematic liquid crystals and superfluid 4He. Ann Phys. 1985;160(2):420–440. doi: 10.1016/0003-4916(85)90151-4
   Web of Science ®Google Scholar
• Rey AD. Defect controlled dynamics of nematic liquids. Liq Cryst. 1990;7(3):315–334. doi: 10.1080/02678299008033809
   Web of Science ®Google Scholar
• Long C, Tang X, Selinger RLB, et al. Geometry and mechanics of disclination lines in 3D nematic liquid crystals. Soft Matter. 2021;17(8):2265–2278. doi: 10.1039/D0SM01899F
   PubMed Web of Science ®Google Scholar
• Schimming CD, Viñals J. Singularity identification for the characterization of topology, geometry, and motion of nematic disclination lines. Soft Matter. 2022;18(11):2234–2244. doi: 10.1039/D1SM01584B
   PubMed Web of Science ®Google Scholar
• Schimming CD, Viñals J. Kinematics and dynamics of disclination lines in three-dimensional nematics. Proc R Soc A. 2023;479(2273):20230042. doi: 10.1098/rspa.2023.0042
   Google Scholar
• Long C, Deutsch MJ, Angelo J, et al. Frank-read mechanism in nematic liquid crystals; 2022. https://arxiv.org/abs/2212.01316.
   Google Scholar
• Wang M, Li Y, Yokoyama H. Artificial web of disclination lines in nematic liquid crystals. Nat Commun. 2017;8(1):388. doi: 10.1038/s41467-017-00548-x
   PubMedGoogle Scholar
• Babakhanova G, Golestani YM, Baza H, et al. Dynamically morphing microchannels in liquid crystal elastomer coatings containing disclinations. J Appl Phys. 2020;128(18):184702. doi: 10.1063/5.0022193
   Web of Science ®Google Scholar
• Allender DW, Crawford GP, Doane JW. Determination of the liquid-crystal surface elastic constant K24. Phys Rev Lett. 1991;67(11):1442–1445. doi: 10.1103/PhysRevLett.67.1442
   PubMed Web of Science ®Google Scholar
• Kralj S, Žumer S. The stability diagram of a nematic liquid crystal confined to a cylindrical cavity. Liq Cryst. 1993;15(4):521–527. doi: 10.1080/02678299308036471
   Web of Science ®Google Scholar
• Kralj S, Žumer S. Saddle-splay elasticity of nematic structures confined to a cylindrical capillary. Phys Rev E. 1995;51(1):366–379. doi: 10.1103/PhysRevE.51.366
   Web of Science ®Google Scholar
• Burylov SV. Equilibrium configuration of a nematic liquid crystal confined to a cylindrical cavity. J Exp Theor Phys. 1997;85(5):873–886. doi: 10.1134/1.558425
   Web of Science ®Google Scholar
• Shams A, Yao X, Park JO, et al. Theoretical predictions of disclination loop growth for nematic liquid crystals under capillary confinement. Phys Rev E. 2014;90(4):42501. doi: 10.1103/PhysRevE.90.042501
   Web of Science ®Google Scholar
• De Luca G, Rey AD. Point and ring defects in nematics under capillary confinement. J Chem Phys. 2007;127(10):104902. doi: 10.1063/1.2775451
   PubMed Web of Science ®Google Scholar
• Vafa F, Zhang GH, Nelson DR. Defect absorption and emission for p-atic liquid crystals on cones. Phys Rev E. 2022;106(2):24704. doi: 10.1103/PhysRevE.106.024704
   Web of Science ®Google Scholar
• Kleman M, Lavrentovich OD. Topological point defects in nematic liquid crystals. Philos Mag. 2006;86(25–26):4117–4137. doi: 10.1080/14786430600593016
   Web of Science ®Google Scholar
• Kralj S, Žumer S. Fréedericksz transitions in supra-μm nematic droplets. Phys Rev A. 1992;45(4):2461–2470. doi: 10.1103/PhysRevA.45.2461
   PubMed Web of Science ®Google Scholar
• Terentjev EM. Disclination loops, standing alone and around solid particles, in nematic liquid crystals. Phys Rev E. 1995;51(2):1330–1337. doi: 10.1103/PhysRevE.51.1330
   Web of Science ®Google Scholar
• Fukuda J, Yokoyama H. Stability of a hyperbolic disclination ring in a nematic liquid crystal. Phys Rev E. 2002;66(1):12703. doi: 10.1103/PhysRevE.66.012703
   Web of Science ®Google Scholar
• Wang X, Kim YK, Bukusoglu E, et al. Experimental insights into the nanostructure of the cores of topological defects in liquid crystals. Phys Rev Lett. 2016;116(14):147801. doi: 10.1103/PhysRevLett.116.147801
   PubMed Web of Science ®Google Scholar
• Ettinger S, Slaughter CG, Parra SH, et al. Magnetic-field-driven director configuration transitions in radial nematic liquid crystal droplets. Phys Rev E. 2023;108(2):24704. doi: 10.1103/PhysRevE.108.024704
   Web of Science ®Google Scholar