References
- Friedrich W, Knipping P, Laue M. Interferenzerscheinungen bei Roentgenstrahlen [X-ray interference phenomena]. Ann Phys. 1913;346(10):971–988. http://tedhuntington.com/ulsf/docs_pd/Laue_Max_19130315.pdf
- Knipping P. Zehn Jahre Röntgenstrahlinterferenzen [Ten years of X-ray scattering]. Naturwissenschaften. 1922;10:366–369. https://link.springer.com/content/pdf/10.1007/BF01565290.pdf
- Bragg WH, Bragg WL. The reflection of X-rays by crystals. Proc R Soc A. 1913;88:428–438. https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1913.0040
- Einstein A. Die plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme [The Planck theory of radiation and the theory of specific heat]. Ann Phys. 1907;22(1):180–190. http://myweb.rz.uni-augsburg.de/∼eckern/adp/history/einstein-papers/1907_22_180–190.pdf
- Born M, von Kármán T. Über Schwingungen in Raumgittern [On vibrations in spatial lattices]. Phys Z. 1912;13:297–309.
- Debye P. Zur Theorie der spezifischen Wärmen [On the theory of specific heats]. Ann Phys. 1912;39(14):789–839. doi:10.1002/andp.19123441404.
- Bloch F. Über die Quantenmechanik der Elektronen in Kristallgittern [The quantum mechanics of electrons in crystal lattices]. Z Phys. 1929;52(7):555–600. doi:10.1007/BF01339455.
- Kléman M. Defects in liquid crystals. Rep Prog Phys. 1989;52:555–654. doi:10.1088/0034-4885/52/5/002.
- Kléman M, Friedel J. Lignes de dislocation dans les cholestériques [Dislocation lines in cholesterics]. J Phys Colloq. 1969;30(C4):C4–C43. https://hal.archives-ouvertes.fr/jpa-00213714
- Friedel J. Les dislocations. Paris: Gauthier-Villars; 1956.
- Friedel J. Dislocations. Oxford (UK): Pergamon Press; 1964. Translation of Ref. [10] by L.F. Vassamillet, with new material added by the author.
- Friedel J. Graine de mandarin (I wish I could translate this!). Paris: Odile Jacob; 1994.
- Duparc OH. La ‘dynastie Friedel’: une grande lignée de scientifiques [The Friedel dynasty: a distinguished scientific lineage]. Reflets Phys. 2015;43:14–17. https://www.refletsdelaphysique.fr/articles/refdp/pdf/2015/01/refdp201543p14.pdf
- Kleman M. Chronologies d'un physicien. Paris: Calvage et Mounet; 2016.
- de Broglie M, Friedel E. La Diffraction des Rayons X Par Les Corps Smectiques [X-ray diffraction by smectic materials]. CRAS. 1923;176:738–741. English translation in Ref. [16], pp. 212–215.
- Sluckin TJ, Dunmur DA, Stegemeyer H. Crystals that flow: classic papers from the history of liquid crystals. London: Taylor & Francis; 2004.
- Dunmur D, Sluckin T. Soap, science, and flat-screen TVs: a history of liquid crystals. Oxford: Oxford University Press; 2011. https://archive.org/details/bub_b_OfZaAAAAQAAJ/page/n1/mode/2up
- Lehmann O. Flüssige Kristalle sowie Plastizität von Kristallen im allgemeinen, molekulare Umlagerung und Aggregatzustandsänderungen [usually known as ‘Liquid Crystals’, because the rest is such a mouthful]. Leipzig, Germany: Wilhelm Engelmann; 1904. https://archive.org/details/bub_b_OfZaAAAAQAAJ/page/n1/mode/2up.
- Friedel G. Les états mésomorphes de la matière [The mesomorphic states of matter]. Ann Phys. 1922;9:273–474. French. This famous article is partly translated into English in Ref. [16], pp. 162–210.
- de Gennes PG, Prost J. The physics of liquid crystals. 2nd ed. Oxford: Clarendon Press; 1993. It is the 1974 first edition by de Gennes alone to which I am referring, rather than this jointly authored version.
- Friedel J. Private communication to the author; 2004.
- As far as the author understands the situation, the transliteration of Kleymann into French in the formal documents of Jules's naturalisation was Kleman (without the accent). Somehow or other (perhaps because it seemed more naturally to follow the rules of French orthography), the normal spelling became Kléman (with the accent). As it had been Jules and not Maurice who had managed this process, Maurice assumed the ‘correct’ version possessed the accent. So in the early part of his career, the author of Maurice's papers is a gentleman called ‘M. Kléman’. However, in the late 1990s Maurice became aware that the official French spelling omits the accent. Thus in papers published after 1997, Maurice, being an obedient sort of fellow, transmutes himself into ‘M. Kleman’. References in this paper try to follow that convention; before 1997: Kléman, after 1997: Kleman. We apologise to readers for the apparent lack of consistency, which in this case is a feature, not a bug.
- Guerraggio A, Paoloni G. Vito Volterra. Rome: Springer-Verlag; 2010 (In Italian).
- Goodstein JR. The Volterra chronicles: the life and times of an extraordinary mathematician, 1860–1940. Providence (Rhode Island): American Mathematical Society; 2007.
- Scott S. Mathematics is the lantern: Vito Volterra, Léon Walras, and Irving Fisher on the mathematization of economics. J Hist Econ Thought. 2018;40(4):513–537. https://www.cambridge.org/core/journals/journal-of-the-history-of-economic-thought/article/mathematics-is-the-lantern-vito-volterra-leon-walras-and-irving-fisher-on-the-mathematization-of-economics/714173C2C82D634FFE66D72CD2B8DD81
- Einstein A. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen [On the motion of particles suspended in liquids at rest, as required by the molecular kinetic theory of heat]. Ann Phys. 1905;4:549–560. doi:10.1002/andp.19053220806.
- Perrin J. Mouvement Brownien et grandeurs moléculaires [Brownian motion and molecular size]. J Radium. 1909;6(12):353–360. https://hal.archives-ouvertes.fr/jpa-00242381/document
- Weingarten J. Sulle superficie di discontinuá nella teoria della elasticità dei corpi solidi [On surfaces of discontinuity in the theory of elasticity of solid bodies]. Rend R Accad Lincei. 1901;10:57–60. http://operedigitali.lincei.it/rendicontiFMN/cliccami.htm
- Lamb H. Hydrodynamics. 2nd ed. Cambridge: Cambridge University Press; 1895. https://archive.org/details/hydrodynamics00lamb/page/n3/mode/2up
- Volterra V. Sull'equilibrio dei corpi elastici più volte connessi. Rend R Accad Lincei. 1905;14:193–202. See also other articles in the original series on distorsioni on pp. 127–137, pp. 350-356, pp. 431-438, pp. 641–654 and Vol. 14 2 pp 329-342. They were translated in toto into French [31] from which version they are usually (but in some sense unfairly) cited. The French version has been translated into English by D.H. Delphenich [32].
- Volterra V. Sur l'équilibre des corps élastiques multiplement connexes [On the equilibrium of multiply connected elastic bodies]. Ann l'École Norm Sup. 1907;24:401–518.
- Delphenich DH. On the equilibrium of multiply-connected elastic bodies. Math Mech Solids. 2020;25(9):1683–1760. Translation of the French version of Volterra's articles [31], themselves translations of the Italian [30]. See (October 2021). doi:10.1177/1081286520928095
- Volterra V, Volterra E. Sur les distorsions des corps élastiques (théorie et applications) [On dislocations in elastic bodies (theory and applications)]. Paris: Gauthier-Villars; 1960. http://www.numdam.org/issue/MSM_1960__147__3_0.pdf
- Acharya A. On Weingarten–Volterra defects. J Elast. 2019;134(1):79–101. doi:10.1007/s10659-018-9681-6
- Somigliana C. Sulla teoria delle distorsioni elastiche. Rend R Accad Naz Lincei. 1914;23:463–472.
- Michell JH. On the direct determination of stress in an elastic solid, with application to the theory of plates I, II. Proc Lond Math Soc. 1899;1(1):100–124. It is interesting to note that this paper cites sources in French, German and Italian. In those days, it seems, English-speaking scientists were still competent enough to handle several European languages…. doi:10.1112/plms/s1-31.1.100
- Timpe AA. Probleme der Spannungsverteilung in ebenen Systemen: einfach gelöst mit Hilfe der Airyschen Funktion [Problems of stress distribution in plane systems: easily solved with the help of the Airy function] [PhD thesis]. Göttingen; 1905. German.
- Timpe AA. Probleme der Spannungsverteilung in ebenen Systemen: einfach gelöst mit Hilfe der Airyschen Funktion (In German) (Problems of stress distribution in plane systems: easily solved with the help of the Airy function). Z Math Phys. 1905;52:348–383. https://archive.org/details/zeitschriftfurm31unkngoog/page/n363/mode/2up
- Love AEH. A treatise on the mathematical theory of elasticity. 1st ed. Cambridge: Cambridge University Press; 1892. https://archive.org/details/atreatiseonmath01lovegoog/page/n6/mode/2up
- Brock WH, Knight DM. The atomic debates: ‘memorable and interesting evenings in the life of the chemical society’. Isis. 1965;56(1):5–25. https://www.jstor.org/stable/pdf/228455.pdf
- Kubbinga H. Crystallography from Haüy to Laue: controversies on the molecular and atomistic nature of solids. Acta Crystallogr A. 2012;68(1):3–29. https://journals.iucr.org/a/issues/2012/01/00/wx0001/wx0001.pdf
- Ferraris G. Early contributions of crystallography to the atomic theory of matter. Substantia. 2019;3(1):111–118. https://www.torrossa.com/en/catalog/preview/4516912
- Frenkel J. Zur Theorie der Elastizitätsgrenze und der Festigkeit kristallinischer Körper [On the theory of the elastic limit and the strength of crystalline bodies]. Z Phys. 1926;37:572–609. German. doi:10.1007/2FBF01397292
- Dehlinger U. Zur Theorie der Rekristallisation reiner Metalle [On the theory of recrystallisation of pure metals]. Ann Phys. 1929;2:749–793. German. doi:10.1002/andp.19293940702
- Taylor GI. The mechanism of plastic deformation of crystals. Part I. Theoretical. Proc R Soc A. 1934;145:362–87. doi:10.1098/rspa.1934.0106
- Orowan E. Zur Kristallplastizät III: Über die Mechanismus der Gleitvorganges [On crystal plasticity III: sliding]. Z Phys. 1934;89:634–59. German. doi:10.1007/BF01341480
- Polanyi M. Über ein Art Gitterstörung, die einen Kristall plastisch machen könnte [On a type of lattice imperfection which may render a crystal ductile]. Z Phys. 1934;89:660–664. German. doi:10.1007/BF01341481
- Burgers JM. Some considerations of the field of stress connected with dislocations in a regular crystal lattice. Indag Math (NS). 1939;42:293–325 (Part I), 378–399 (Part II).
- Burgers JM. Geometrical considerations concerning the structural irregularities to be assumed in crystals. Proc Phys Soc (London). 1940;52:23–33. doi:10.1088/0959-5309/52/1/304/pdf
- Frenkel J, Kontorova T. Über die Theorie der plastischen Verformung [On the theory of plastic deformation]. Phys Z Sowjetunion. 1938;13:1. German. This is the shorter German version of the Russian papers [51].
- Kontorova TA, Frenkel YI. K teoriyi plastychnoyi deformatsiyi ta podviynosti I [On the theory of plastic deformations and twinning]. Zh Eksp Theor Fiz. 1938;8:89–95. Russian. See also papers II, on pp. 1340–1348, and III on pp. 1349–1358 of the same volume.
- Dipierro S, Poggesi G, Valdinoci E. A quantitative rigidity result for a two-dimensional Frenkel–Kontorova model. Physica D. 2021;419:132871. https://www.sciencedirect.com/science/article/pii/S0167278921000294
- Nabarro FRN. Fifty-year study of the Peierls-Nabarro stress. Mater Sci Eng A. 1997;234:67–76. https://www.sciencedirect.com/science/article/pii/S0921509397001846
- Peierls R. The size of a dislocation. Proc Phys Soc. 1940;52(1):34–37. doi:10.1088/0959-5309/52/1/305/pdf
- Nabarro FRN. Dislocations in a simple cubic lattice. Proc Phys Soc. 1947;59(2):256. doi:10.1088/0959-5309/59/2/309/pdf
- Zener C, Hollomon JH. Problems in non-elastic deformation of metals. J Appl Phys. 1946;17(2):69–82. doi:10.1063/1.1707696
- Peach M, Koehler JS. The forces exerted on dislocations and the stress fields produced by them. Phys Rev. 1950;80(3):436. doi:10.1103/PhysRev.80.436
- Frank FC, van der Merwe JH. One-dimensional dislocations. I. Static theory. Proc R Soc A. 1949;198(1053):205–216. doi:10.1098/rspa.1949.0095.
- Rubinstein J. Sine-Gordon equation. J Math Phys. 1970;11(1):258–266. This is the earliest paper in which I can find the term Sine-Gordon equation mentioned. Rubinstein ‘blames’ the Princeton mathematical physicist Martin Kruskal (1925–2006) for inventing the term, which is a pun on the relativistic quantum mechanical Klein-Gordon equation, of which this equation is a non-linear extension. The equation itself, if not the methods for solving it, goes back further than Frenkel and Kontorova, at least to the mid-19th century. doi:10.1063/1.1665057
- Burton WK, Cabrera N, Frank FC. Role of dislocations in crystal growth. Nature. 1949;163(4141):398–399. https://www.nature.com/articles/163398a0
- Frank FC. The influence of dislocations on crystal growth. Discuss Faraday Soc. 1949;5:48–54. https://www.nature.com/articles/163398a0https://pubs.rsc.org/en/content/articlepdf/1949/df/df9490500048
- Burton WK, Cabrera N, Frank FC. The growth of crystals and the equilibrium structure of their surfaces. Phil Trans R Soc A. 1951;243(866):299–358. doi:10.1098/rsta.1951.0006
- Frank FC, Read Jr WT. Multiplication processes for slow moving dislocations. Phys Rev. 1950;79(4):722. doi:10.1103/PhysRev.79.722
- Friedel J. The mechanism of work-hardening and slip-band formation. Proc R Soc A. 1957;242(1229):147–159. http://www.jstor.org/stable/100300
- Frank FC. Crystal dislocations: elementary concepts and definitions. Phil Mag. 1951;42(331):809–819. doi:10.1080/14786445108561310
- The present author recalls a theoretical physics seminar in Bristol in the late 1970s or early 1980s, in which A.P. Young was presenting work (I think) on the two-dimensional XY model. Sir Charles, who had recently retired, was in the audience, on the front row (as ever, sucking on his pipe). It was necessary somehow to explain the concept of the Burgers vector. The speaker, at that time relatively early in his career, did not know that he was teaching the grandmother how to suck eggs. He got as far as explaining the concept, and then realised that he did not know why the Burgers vector was so named. His sentence petered out, as he guessed wildly, but in hindsight obviously incorrectly, that the Burgers vector had been so named by Burgers himself. At which point, Frank butted in at full volume: ”not by Burgers, but by me, actually”, with a strongly emphasised and megaphonic ”me”. At the time, I thought that the early 1950s were impossibly far off, but now at the other end of my career, I can see that early days of dislocation theory might well have seemed very recent to Frank.
- Nye JF. Some geometrical relations in dislocated crystals. Acta Metallurgica. 1953;11:53–162. https://www.sciencedirect.com/science/article/abs/pii/0001616053900546
- Bingham EC. Plasticity and elasticity. J Franklin Inst. 1924;197(1):99–115. https://www.sciencedirect.com/science/article/pii/S001600322490500X
- Ariano R. The relationship between forces and deformations. With special reference to rubber. Rubber Chem Technol. 1930;3(1):62–66. https://meridian.allenpress.com/rct/article-abstract/3/1/62/89770/The-Relationship-between-Forces-and-Deformations
- Andrade ENC. On the viscous flow in metals, and allied phenomena. Proc R Soc A. 1910;84(567):1–12. doi:10.1098/rspa.1910.0050
- Mott NF. Bakerian lecture: dislocations, plastic flow and creep. Proc R Soc A. 1953;220(1140):1–14. doi:10.1098/rspa.1953.0167
- Dorn JE. Some fundamental experiments on high temperature creep. J Mech Phys Solids. 1954;3:85–115. https://www.sciencedirect.com/science/article/pii/0022509655900545
- Weertman J. Theory of steady-state creep based on dislocation climb. J Appl Phys. 1955;26(10):1213–1217. doi:10.1063/1.1721875
- Harper J, Dorn JE. Viscous creep of aluminum near its melting temperature. Acta Metallurgica. 1957;5(11):654–665. https://www.sciencedirect.com/science/article/abs/pii/0001616057901128
- Nabarro FRN. The mechanism of Harper-Dorn creep. Acta Metallurgica. 1989;37(8):2217–2222. https://www.sciencedirect.com/science/article/abs/pii/0001616089901478
- Langdon TG. Creep at low stresses: an evaluation of diffusion creep and Harper-Dorn creep as viable creep mechanisms. Metall Mater Trans A. 2002;33(2):249–259. doi:10.1007/s11661-002-0087-4.pdf
- Bragg WL, Nye JF. A dynamical model of a crystal structure. Proc R Soc Lond A Math Phys Sci. 1947;190(1023):474–481. doi:10.1098/rspa.1947.0089
- Hedges JM, Mitchell JW. The observation of polyhedral sub-structures in crystals of silver bromide. Phil Mag. 1953;44(349):223–224. doi:10.1080/14786440208520298
- Hirsch PB, Horne RW, Whelan MJ. Direct observations of the arrangement and motion of dislocations in aluminium. Phil Mag. 1956;1(7):677–684. Reprinted in Phil. Mag. 86 4553–4572 (2006). doi:10.1080/14786430600844674
- Hirth J. A brief history of dislocation theory. Metall Trans A. 1985;16(12):2085–2090. doi:10.1007/BF02670413.pdf
- Frank FC. Crystal growth and dislocations. Adv Phys. 1952;1(1):91–109. doi:10.1080/00018735200101171
- Menzies AWC, Sloat CA. Spiral markings on carborundum crystals. Nature. 1929;163:348–349. https://www.nature.com/articles/123348b0
- Frank FC. On the theory of liquid crystals. Discuss Faraday Soc. 1958;25:19–28. https://pubs.rsc.org/en/content/articlepdf/1958/df/df9582500019
- Oseen CW. The theory of liquid crystals. Trans Faraday Soc. 1933;29(140):883–899. Reprinted in Ref. [16].
- Oseen CW. Die anisotropen Flüssigkeiten: Tatsächen und Theorien. Berlin: Gebrüder Borntraeger; 1929.
- Leslie FM. Some constitutive equations for liquid crystals. Arch Ration Mech Anal. 1968;28(4):265–283. doi:10.1007/BF00251810.pdf
- Frank FC. Quasi-kristalline und kristalline Flussigkeiten [Quasi-crystalline and crystalline fluids]. Phys Z. 1939;39:530–534. German. A rather unsuccessful qualitative attempt at a microscopic theory of nematic rods. A more definitive theory was produced by Onsager a few years later, but probably required more experience than Frank possessed immediately after his PhD.
- Sluckin T. Professor Sir Charles Frank (1911–1998): historical perspectives on the development of liquid crystal continuum theory. Liq Cryst Today. 1998;8(3):1–5. doi:10.1080/13583149808047711
- Sluckin TJ. Some reflections on defects in liquid crystals: from Amerio to Zannoni and beyond. Liq Cryst. 2018;45(13–15):1894–1912. doi:10.1080/02678292.2018.1500652
- Friedel J, De Gennes PG. Boucles de disclination dans les cristaux liquides [Disclination loops in liquid crystals]. C R Acad Sci Paris B. 1969;268:257–259.
- Liquid Crystal Group O. Lignes doubles de désinclinaison dans les cristaux liquides cholestériques à grands pas [Double disclination lines in cholesteric liquid crystals with large pitch]. J Phys Colloq. 1969;30(C4):C4–38.
- Bouligand Y, Kléman M. Paires de disinclinaisons hélicoïdales dans les cholestériques [Helicoidal disclination pairs in cholesterics]. J Phys. 1970;31(11–12):1041–1054. https://hal.archives-ouvertes.fr/jpa-00207000
- Kléman M, Schlenker M. The use of dislocation theory in magnetoelasticity. J Appl Phys. 1972;43(7):3184–3190. doi:10.1063/1.1661683
- Kröner E. In: Collatz L, Lösch F, editors. Kontinuumstheorie der Versetzungen und Eigenspannungen [Continuum theory of dislocations and residual stresses]. Springer; 1958. (Ergebnisse der Angewandten Mathematik [Results in applied mathematics]; vol. 5).
- Dzyaloshinskii IE. Toward a theory of disclinations in liquid crystals. Sov Phys JETP. 1970;31:773–782.
- Cladis PE, Kléman M. Non-singular disclinations of strength S = +1 in nematics. J Phys. 1972;33(5–6):591–598. https://hal.archives-ouvertes.fr/jpa-00207284
- Williams C, Pierański P, Cladis PE. Nonsingular s = +1 screw disclination lines in nematics. Phys Rev Lett. 1972;29(2):90. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.29.90
- Meyer RB. On the existence of even indexed disclinations in nematic liquid crystals. Phil Mag. 1973;27(2):405–424. Submitted in March 1972, only two months after the Cladis-Kléman paper [96]. But whereas ref. [96] was published in the May-June edition (1972) of the Journal de Physique, Meyer had to wait for almost a year before his paper appeared in the following February (1973). The (English) editors of the Philosophical Magazine clearly did not feel that rapid publication was important. doi:10.1080/14786437308227417
- Toulouse G, Kléman M. Principles of a classification of defects in ordered media. J Phys. 1976;37(6):149–151. https://hal.archives-ouvertes.fr/jpa-00231261
- Kléman M, Michel L, Toulouse G. Classification of topologically stable defects in ordered media. J Phys Lett. 1977;38(10):195–197. doi:10.1051/jphyslet:019770038010019500
- Kléman M. Relationship between Burgers circuit, Volterra process and homotopy groups. J Phys Lett. 1977;38(10):199–202. doi:10.1051/jphyslet:019770038010019900
- Kléman M, Michel L. On the classification of defects in the smectic phases Sm A and Sm C. J Phys Lett. 1978;39(2):29–32. https://hal.archives-ouvertes.fr/jpa-00231435
- Poenaru V, Toulouse G. The crossing of defects in ordered media and the topology of 3-manifolds. J Phys. 1977;38(8):887–895. https://hal.archives-ouvertes.fr/jpa-00208655
- Michel L. Symmetry in condensed matter physics. In: Schrader R, Seiler R, Uhlenbrock DA, editors. Mathematical problems in theoretical physics. Springer; 1982. p. 336–347. (Lecture notes in physics; vol. 153). Available from: https://link.springer.com/chapter/10.1007/3-540-11192-1_61
- Landau L. The theory of phase transitions. Nature. 1936;138(3498):840–841. https://www.nature.com/articles/138840a0
- Landau LD. K teorii fasovikh perekhodov I [On the theory of phase transitions. I]. Zh Eksp Teor Fiz. 1937;11:19–32. Paper II in the series is on p. 627 of the same volume. English translations can be found in ref. [107]. Available from: http://archive.ujp.bitp.kiev.ua/files/journals/53/si/53SI08p.pdf
- Landau LD. On the theory of phase transitions I, II. In: Ter Haar D, editor. Collected papers of L. D. Landau. Elsevier; 1965. p. 193–216. Available from: https://www.sciencedirect.com/book/9780080105864/collected-papers-of-l-d-landau
- Toledano P, Toledano JC. Landau theory of phase transitions. In: Application to structural, incommensurate, magnetic and liquid crystal systems. World Scientific Publishing Company; 1987. (World scientific lecture notes in physics; vol. 3).
- Mermin ND. The topological theory of defects in ordered media. Rev Mod Phys. 1979;51:591–648. https://link.aps.org/pdf/10.1103/RevModPhys.51.591
- Lagerwall ST. On some important chapters in the history of liquid crystals. Liq Cryst. 2013;40(12):1698–1729. doi:10.1080/02678292.2013.831134
- Friedel G, Grandjean F. Les liquides à coniques focales (Focal conic liquids). C R l'Acad Sci. 1910;151:762–765. https://gallica.bnf.fr/ark:/12148/bpt6k31042/f762.item
- Friedel G, Grandjean F. Observations géometriques sur les liquides à coniques focales [Geometric observations of focal conic liquids]. Bull Soc Fr Minéral. 1910;33:409–465.
- Friedel G, Grandjean F. Liquides anisotropes. Observations sur la Note de M. O. Lehmann [Anisotropic liquids: observations on Lehmann's note]. Bull Soc Fr Minéral. 1910;33:466–469.
- Bouligand Y. Recherches sur les textures des états mésomorphes - 1: les arrangements focaux dans les smectiques: rappels et considérations théoriques [Mesomorophic textures 1: focal structures in smectics: review and theoretical considerations]. J Phys Colloq. 1972;33(5–6):525–547. https://hal.archives-ouvertes.fr/jpa-00207280
- Bidaux R, Boccara N, Sarma G, et al. Statistical properties of focal conic textures in smectic liquid crystals. J Phys. 1973;34(7):661–672. https://hal.archives-ouvertes.fr/jpa-00207427
- Kleman M, Lavrentovich OD. Liquids with conics. Liq Cryst. 2009;36(10–11):1085–1099. doi:10.1080/02678290902814718
- Kléman M. Energetics of focal conics of smectic phases. J Phys. 1977;38:1511–1518. https://hal.archives-ouvertes.fr/jpa-00208726
- Boltenhagen P, Lavrentovich OD, Kléman M. Oily streaks and focal conic domains in Lα lyotropic liquid crystals. J Phys II. 1991;1(10):1233–1252. https://hal.archives-ouvertes.fr/jpa-00247586
- Sethna JP, Kléman M. Spheric domains in smectic liquid crystals. Phys Rev A. 1982;26(5):3037–3040. doi:10.1103/PhysRevA.26.3037
- Lavrentovich O. Hierarchy of defect structures in space-filling by flexible smectic-a layers. Sov Phys JETP. 1986;64:984–990. http://www.jetp.ras.ru/cgi-bin/dn/e_064_05_0984.pdf
- Fournier JB, Durand G. Focal conic faceting in smectic-A liquid crystals. J Phys II. 1991;1(7):845–870. https://hal.archives-ouvertes.fr/jpa-00247560
- Williams CE, Kléman M. On the association of screw dislocation lines and focal domains in smectics-A. Phil Mag. 1976;33:213–217. doi:10.1080/14786437608221108
- Meyer C, Kleman M. How do defects transform at the smectic A-nematic phase transition? Mol Cryst Liq Cryst. 2005;437(1):111–119 (1355–1363). doi:10.1080/15421400590955325
- Kleman M, Meyer C, Nastishin YA. Imperfections in focal conic domains: the role of dislocations. Phil Mag. 2006;86:4439–4458. doi:10.1080/14786430600724496
- Nelson DR, Toner J. Bond-orientational order, dislocation loops, and melting of solids and smectic-a liquid crystals. Phys Rev B. 1981;24(1):363. doi:10.1103/PhysRevB.24.363
- Bourdon L, Sommeria J, Kléman M. Sur l'existence de lignes singulières dans les domaines focaux en phases Sm C et Sm C* (On the existence of singular lines in the focal domains of the Sm C and Sm C* phases). J Phys. 1982;43(1):77–96. https://hal.archives-ouvertes.fr/jpa-00209385
- Kleman M, Lavrentovich OD, Nastishin Y.A. Dislocations and disclinations in mesomorphic phases. In: Nabarro FRN, Hirth JP, editors. Dislocations in solids. Vol. 12. Elsevier; 2004. Ch. 66. p. 147–271. Available from: https://doi.org/10.1016/S1572-4859(05)80005-1
- Meyer C, Asnacios S, Bourgaux C, et al. Effects of shear on a lyotropic lamellar phase. Mol Cryst Liq Cryst. 1999;A332(1):531–538. doi:10.1080/10587259908023799
- Meyer C, Asnacios S, Bourgaux C, et al. Rheology of lyotropic and thermotropic lamellar phases. Rheol Acta. 2000;39(3):223–233. doi:10.1007/s003970000075.pdf
- Lelidis I, Kleman M, Martin JL. Static and dynamic observations of dislocations and other defects in smectic Cano wedges. Mol Cryst Liq Cryst A. 2000;351(1):187–196. doi:10.1080/10587250008023268
- Meyer C, Asnacios S, Kleman M. Universal properties of lamellar systems under weak shear. Eur Phys J E. 2001;6(3):245–253. doi:10.1007/s101890170007.pdf
- Blanc C, Zuodar N, Lelidis I, et al. Defect dynamics in a smectic Grandjean-Cano wedge. Phys Rev E. 2004;69(1):011705. doi:10.1103/PhysRevE.69.011705
- Blanc C, Zuodar N, Martin J, et al. Role of microscopic defects in the plasticity of lamellar materials. Mol Cryst Liq Cryst. 2004;412(1):85–92. doi:10.1080/15421400490431903
- Blanc C, Meyer C, Asnacios S, et al. Do lamellar liquid crystals flow like solids? Phil Mag Lett. 2005;85(12):641–648. doi:10.1080/14786430500402482
- Lelidis I, Blanc C, Kléman M. Optical and confocal microscopy observations of screw dislocations in smectic-A liquid crystals. Phys Rev E. 2006;74(5):051710. doi:10.1103/PhysRevE.74.051710
- Horn RG, Kléman M. Observations on shear-induced textures and rheology of a smectic-A phase. Ann Phys. 1978;3:229–234. doi:10.1051/anphys/197803030229
- Oswald P, Béhar J, Kléman M. Observation d'un réseau de paraboles focales sous cisaillement dans un smectique A [Observations of a network of focal parabolas in a smectic A phase under shear]. Phil Mag A. 1982;46(6):899–914. doi:10.1080/01418618208236940
- Mahjoub HF, McGrath KM, Kléman M. Phase transition induced by shearing of a sponge phase. Langmuir. 1996;12(13):3131–3138. doi:10.1021/la950723/2B
- Mahjoub HF, Bourgaux C, Sergot P, et al. Evidence of a sponge-to-lamellar phase transition under shear by x-ray scattering experiments in a couette cell. Phys Rev Lett. 1998;81(10):2076–2079. doi:10.1103/PhysRevLett.81.2076
- Kleman M. The lamellar and sponge phases of dilute surfactant systems: structures and defects at equilibrium and under shear. Pramana. 1999;53(1):107–119. doi:10.1007/S12043-999-0143-3.pdf
- Navier C-LMH. Mémoire sur les lois du mouvement des fluides [Memoir on the laws of fluid motion]. Mém l'Acad R Sci l'Inst France. 1823;6(1823):389–440. https://gallica.bnf.fr/ark:/12148/bpt6k3221x/f577.item.zoom
- Darrigol O. Worlds of flow: a history of hydrodynamics from the Bernoullis to Prandtl. Oxford: Oxford University Press; 2005.
- Stokes GG. On the steady motion of incompressible fluids. Trans Camb Phil Soc. 1842;7:439–454. https://www.cambridge.org/core/books/mathematical-andphysical-papers/on-the-steady-motion-ofincompressible-fluids/FA298D24646A9BF83FF077036A9287A3
- Schenck R. Kristallinische flüssigkeiten und flüssige kristalle [Crystalline fluids and liquid crystals]. Leipzig: W. Engelmann; 1905.
- Mi esowicz M. Influence of a magnetic field on the viscosity of para-azoxyanisol. Nature. 1935;136(3433):261–261. https://www.nature.com/articles/136261a0
- Mi esowicz M. The three coefficients of viscosity of anisotropic liquids. Nature. 1946;158(4001):27–27. https://www.nature.com/articles/158027b0
- Carlsson T, Leslie FM. The development of theory for flow and dynamic effects for nematic liquid crystals. Liq Cryst. 1999;26(9):1267–1280. doi:10.1080/026782999203931
- Stewart IW. The static and dynamic continuum theory of liquid crystals: a mathematical introduction. London: Taylor and Francis; 2004. Available from https://doi.org/10.1201/9781315272580 (pay wall).
- de Gennes PG. Viscous flow in smectic A liquid crystals. Phys Fluids. 1974;17(9):1645–1654. doi:10.1063/1.1694950
- Roux D, Nallet F, Diat O. Rheology of lyotropic lamellar phases. Europhys Lett. 1993;24:53–58. doi:10.1209/0295-5075/24/1/009
- Rosenblatt CS, Pindak R, Clark NA, et al. The parabolic focal conic: a new smectic A defect. J Phys. 1977;38(9):1105–1115. https://hal.archives-ouvertes.fr/jpa-00208677/document
- Oswald P, Ben-Abraham SI. Undulation instability under shear in smectic A liquid crystals. J Phys. 1982;43(8):1193–1197. https://hal.archives-ouvertes.fr/jpa-00209496
- Goulian M, Milner ST. Shear alignment and instability of smectic phases. Phys Rev Lett. 1995;74(10):1775. doi:10.1103/PhysRevLett.74.1775
- Auernhammer GK, Brand HR, Pleiner H. Shear-induced instabilities in layered liquids. Phys Rev E. 2002;66(6):061707. doi:10.1103/PhysRevE.66.061707
- Stewart IW, Stewart F. Shear flow in smectic A liquid crystals. J Phys. 2009;21(46):465101. doi:10.1088/0953-8984/21/46/465101/pdf
- Fujii S, Komura S, Lu C-YD. Structural rheology of the smectic phase. Materials. 2014;7(7):5146–5168. https://www.mdpi.com/1996-1944/7/7/5146
- Tiddy GJT. Surfactant-water liquid crystal phases. Phys Rep. 1980;57(1):1–46. https://www.sciencedirect.com/science/article/pii/0370157380900411
- Langevin D. Micelles and microemulsions. Annu Rev Phys Chem. 1992;43(1):341–369. doi:10.1146/annurev.pc.43.100192.002013
- Porte G. Lamellar phases and disordered phases of fluid bilayer membranes. J Phys. 1992;4(45):8649. doi:10.1088/0953-8984/4/45/002/pdf
- Iñiguez-Palomares R, Acuna-Campa H, Maldonado A. Effect of polymer on the elasticity of surfactant membranes: a light scattering study. Phys Rev E. 2011;84(1):011604. doi:10.1103/PhysRevE.84.011604
- Garvey CJ, Lenné T, Koster KL, et al. Phospholipid membrane protection by sugar molecules during dehydration – insights into molecular mechanisms using scattering techniques. Int J Mol Sci. 2013;14(4):8148–8163. https://www.mdpi.com/1422-0067/14/4/8148
- Cates ME, Milner ST. Role of shear in the isotropic-to-lamellar transition. Phys Rev Lett. 1989;62(16):1856. doi:10.1103/PhysRevLett.62.1856
- Bruinsma R, Rabin Y. Shear-flow enhancement and suppression of fluctuations in smectic liquid crystals. Phys Rev A. 1992;45(2):994. doi:10.1103/PhysRevA.45.994
- Butler P. Shear induced structures and transformations in complex fluids. Curr Opin Colloid Interface Sci. 1999;4(3):214–221. https://www.sciencedirect.com/science/article/pii/S1359029499000412
- Butler PD, Porcar L, Hamilton WA, et al. Comment on ‘evidence of a sponge-to-lamellar phase transition under shear by x-ray scattering experiments in a couette cell’. Phys Rev Lett. 2002;88(5):059601. doi:10.1103/PhysRevLett.88.059601
- Kléman M. Curved crystals, defects and disorder. Adv Phys. 1989;38(6):605–667. doi:10.1080/00018738900101152
- Frank FC. Supercooling of liquids. Proc R Soc A. 1952;215:43–46. doi:10.1098/rspa.1952.0194
- Bernal JD. The Bakerian Lecture, 1962. The structure of liquids. Proc R Soc A. 1964;280(1382):299–322. doi:10.1098/rspa.1964.0147
- Sadoc JF, Dixmier J, Guinier A. Theoretical calculation of dense random packings of equal and non-equal sized hard spheres: applications to amorphous metallic alloys. J Non Cryst Solids. 1973;12(1):46–60. https://www.sciencedirect.com/science/article/abs/pii/0022309373900549
- Toulouse G. Theory of the frustration effect in spin glasses I. Commun Phys. 1977;2:115–119. doi:10.1142/9789812799371_0009
- Kléman M, Sadoc JF. A tentative description of the crystallography of amorphous solids. J Phys Lett. 1979;40(21):569–574. https://hal.archives-ouvertes.fr/jpa-00231690
- Kléman M. The geometrical nature of disorder and its elementary excitations. J Phys. 1982;43:1389–1396. https://hal.archives-ouvertes.fr/jpa-00209519
- Kléman M. Dual properties of conjugate disclination segment networks in amorphous material. J Phys Lett. 1983;44:295–302. https://hal.archives-ouvertes.fr/jpa-00232195
- Kléman M, Pavlovitch A. Defects in aperiodic crystals. J Phys Colloq. 1986;47(C3):229–236. https://hal.archives-ouvertes.fr/jpa-00225735
- Kléman M, Gefen Y, Pavlovitch A. Topological defects in non-Haüyan crystallography: the two-dimensional case. Europhys Lett. 1986;1(2):61–69. doi:10.1209/0295-5075/1/2/004/pdf
- Pavlovitch A, Kléman M. Generalised 2D Penrose tilings: structural properties. J Phys A. 1987;20(3):687–702. doi:10.1088/0305-4470/20/3/031/pdf
- Kléman M. Topology of the phase in aperiodic crystals. J Phys. 1990;51(21):2431–2437. https://hal.archives-ouvertes.fr/jpa-00212542
- Kléman M. Dislocations and disvections in aperiodic crystals. J Phys I. 1992;2(1):69–87. https://hal.archives-ouvertes.fr/jpa-00246464
- Kléman M. Disvections: mismatches, dislocations, and non-Abelian properties of quasicrystals. J Phys. 1996;8(49):10263. doi:10.1088/0953-8984/8/49/017/pdf
- Shechtman D, Blech I, Gratias D, et al. Metallic phase with long-range orientational order and no translational symmetry. Phys Rev Lett. 1984;53(20):1951. doi:10.1103/PhysRevLett.53.1951
- Levine D, Steinhardt PJ. Quasicrystals: a new class of ordered structures. Phys Rev Lett. 1984;53(26):2477. doi:10.1103/PhysRevLett.53.2477
- Mackay AL. Crystallography and the Penrose pattern. Physica A. 1982;114(1–3):609–613. https://www.sciencedirect.com/science/article/abs/pii/0378437182903594
- Penrose R. The role of aesthetics in pure and applied mathematical research. Bull Inst Math Appl. 1974;10:266–271.
- Kramer P, Neri R. On periodic and non-periodic space fillings of Em obtained by projection. Acta Crystallogr A. 1984;40(5):580–587. http://scripts.iucr.org/cgi-bin/paper?S0108767384001203
- Dmitrienko VE, Kleman M, Mauri F. Quasicrystal-related phases in tetrahedral semiconductors: structure, disorder, and ab initio calculations. Phys Rev B. 1999;60(13):9383. doi:10.1103/PhysRevB.60.9383
- Dmitrienko VE, Kléman M. Icosahedral order and disorder in semiconductors. Phil Mag Lett. 1999;79(6):359–367. doi:10.1080/095008399177200
- Steurer W. Why are quasicrystals quasiperiodic? Chem Soc Revs. 2012;41(20):6719–6729. https://pubs.rsc.org/en/content/articlepdf/2012/cs/c2cs35063g
- Kléman M. Défauts dans les cristaux liquides (Defects in liquid crystals). Bull Soc Fr Minéral Cristallogr. 1972;95(2):215–230. https://www.persee.fr/doc/bulmi_0037–9328_1972_num_95_2_6671
- Kleman M, Friedel J. Disclinations, dislocations, and continuous defects: a reappraisal. Rev Mod Phys. 2008;80:61–115. doi:10.1103/RevModPhys.80.61
- Kleman M, Lavrentovich OD. Topological point defects in nematic liquid crystals. Phil Mag. 2006;86(25–26):4117–4137. doi:10.1080/14786430600593016
- Kléman M. Points, lignes, parois. Paris: Éd. de Physique; 1977. [English translation: Points, lines and walls in liquid crystals, magnetic systems and various ordered media, London: John Wiley and Sons, 1982].
- Kleman M, Lavrentovich OD. Soft matter physics: an introduction. Berlin: Springer; 2002.
- James IM. History of topology. London: Elsevier; 1999.
- Nash C. Topology and physics: a historical essay. In: James IM, editor. History of topology. North-Holland; 1999. Chapter 12; p. 359–415. Available from: https://arxiv.org/pdf/hep-th/9709135.pdf
- Monastyrskii MI, Perelomov AM. Concerning the existence of monopoles in gauge field theories. Sov Phys JETP Lett. 1975;21:43–44. http://jetpletters.ru/ps/1460/article_22241.pdf
- Tyupkin YS, Fateev VA, Shvarts AS. Existence of heavy particles in gauge field theories. Sov Phys JETP Lett. 1975;21:91–93. http://jetpletters.ru/ps/1460/article_22240.pdf
- Monastyrsky MI, Retakh VS. Topology of linked defects in condensed matter. Commun Math Phys. 1986;103(3):445–459. doi:10.1007/BF01211760.pdf
- Monastyrsky MI. Riemann, topology, and physics. Boston (MA): BIrkhauser; 1999.
- Monastyrsky MI (ed.). Topology in condensed matter. Berlin: Springer Science & Business Media; 2006.
- Volovik GE, Mineev VP. Vortices with free ends in superfluid He3-A in superfluid He-3. Sov Phys JETP Lett. 1976;23:593–595. The full story of the introduction of homotopy theory in the Soviet school is more complicated than we have space to relate here, and also includes the distinguished Russian quantum field theorist Aleksander Markovich Polyakov [233]. The author is grateful to Professors Mineev and Volovik for correspondence on this issue. Available from: http://jetpletters.ru/ps/1806/article_27600.shtml
- Volovik GE, Mineev VP. Line and point singularities in superfluid He-3. Sov Phys JETP Lett. 1976;24:561–563. http://jetpletters.ru/ps/1818/article_27785.shtml
- Volovik GE, Mineev VP. Investigation of singularities in superfluid He-3 and liquid crystals by homotopic topology methods. Sov Phys JETP. 1977;45:1186–1196. http://www.jetp.ras.ru/cgi-bin/e/index/e/45/6/p1186?a=list
- Rogula D. Large deformations of crystals, homotopy, and defects. In: Fichera G, editor. Trends in applications of pure mathematics to mechanics. Proc. Conf. Lecce 1975. Pitman Publishing; 1976. p. 311–331.
- Kibble TW. Topology of cosmic domains and strings. J Phys A. 1976;9(8):1387–1398. doi:10.1088/0305-4470/9/8/029/meta
- Chuang I, Durrer R, Turok N, et al. Cosmology in the laboratory: defect dynamics in liquid crystals. Science. 1991;251(4999):1336–1342. doi:10.1126/science.251.4999.1336
- Finkelstein D. Kinks. J Math Phys. 1966;7(7):1218–1225. doi:10.1063/1.1705025
- Hooft G. Magnetic monopoles in unified gauge theories. Nucl Phys B. 1974;79(2):276–284. https://www.sciencedirect.com/science/article/abs/pii/0550321374904866
- James IM. Reflections on the history of topology. Sem Mat Fis Milano. 1996;66:87–96. doi:10.1007/BF0292535
- Hilton P. A brief, subjective history of homology and homotopy theory in this century. Math Mag. 1988;61(5):282–291. http://www.jstor.org/stable/2689545
- Listing JB. Vorstudien zu Topologie [Preliminary studies on topology]. Gottingen: Vandenhoeck u. Ruprecht; 1848.
- Flament D. La topologie de Johann Benedict Listing (1808–1882); Résonances dans quelques oeuvres de contemporains [The topology of Johann Benedict Listing (1808–1882); resonances in the work of some contemporaries]. Khronos. 2016;3:123–180. https://www.revistas.usp.br/khronos/article/view/134555
- Poincaré H. Papers on topology: analysis situs and its five supplements. Providence (Rhode Island): AMS and LMS; 2010. https://www.maths.ed.ac.uk/v1ranick/papers/poincare2009.pdf.
- Veblen O. Analysis situs. New York (NY): AMS; 1922.
- Thomson W. (Lord Kelvin), On vortex atoms. Proc R Soc Edinb. 1867;6:94–105. https://zapatopi.net/kelvin/papers/on_vortex_atoms.html
- Tait PG. On knots. In: Scientific papers. Vol. I. Cambridge University Press; 1898. Chapter 39–41; p. 273–347. Reprints of original papers appearing in Proc. Roy. Soc. Edinburgh in 1877, 1884 and 1885. Available from: https://www.archive.org/details/scientificpaper01taituoft
- Knott CG. Life and scientific work of Peter Guthrie Tait. Cambridge: Cambridge University Press; 1911 https://www.maths.ed.ac.uk/v1ranick/papers/taitbio.pdf.
- Kragh H. The vortex atom: a Victorian theory of everything. Centaurus. 2002;44:32–114. doi:10.1034/j.1600-0498.2002.440102.x
- Epple M. Topology, matter, and space, I: Topological notions in 19th-century natural philosophy. Arch Hist Exact Sci. 1998;52:297–392. https://www.jstor.org/stable/27858741
- Silver DS. Knot theory's odd origins. Am Sci. 2006;94(2):158–165. https://els-bib.southalabama.edu/mathstat/personal_pages/silver/Maxwell.pdf
- Silver DS. Knots in the nursery, unpublished. Available from: https://els-bib.southalabama.edu/mathstat/personal_pages/silver/Maxwell.pdf
- Dehn M. Über die Topologie des dreidimensionalen Raumes [On the topology of three dimensional space]. Math Ann. 1910;69:137–168. doi:10.1007/BF01455155. (German).
- Peifer D. Max Dehn and the origins of topology and infinite group theory. Am Math Mon. 2015;122:217–233. doi:10.4169/amer.math.monthly.122.03.217
- Tait PG. Johann Benedict Listing; Listing's Topologie Scientific papers. Vol. II. Cambridge: Cambridge University Press; 1900. p. 273–347. Chapter 65–66; Ch. 65 is Tait's obituary of Listing (originally in Nature 1883). Ch. 66 is the text of a lecture to the Edinburgh Mathematical Society on Listing's work, which appeared in Phil. Mag., 1884. https://www.archive.org/details/scientificpaper02taituoft
- Alexander GP, Chen BG-G, Matsumoto EA, et al. Colloquium: disclination loops, point defects, and all that in nematic liquid crystals. Rev Mod Phys. 2012;84(2):497–515. doi:10.1103/RevModPhys.84.497.
- Alexander GP. Topology in liquid crystal phases. In: Gupta S, Saxena A, editors. The role of topology in materials. Springer; 2018. Chapter 9; p. 229–257. (Springer series in solid-state sciences; vol. 189). Available from: https://link.springer.com/chapter/10.1007/978-3-319-76596-9_9
- Machon T. The topology of knots and links in nematics. Liq Cryst Today. 2019;28(3):58–67. doi:10.1080/1358314X.2019.1681113
- Michel L. Symmetry defects and broken symmetry. Configurations hidden symmetry. Rev Mod Phys. 1980;52(3):617. doi:10.1103/RevModPhys.52.617
- Michel L, Zhilinskiı BI. Symmetry, invariants, topology. Basic tools. Phys Rep. 2001;341(1–6):11–84. https://www.sciencedirect.com/science/article/pii/S0370157300000880
- Poénaru V. Some aspects of the theory of defects of ordered media and gauge fields related to foliations. Commun Math Phys. 1981;80(1):127–136. doi:10.1007/BF01213598.pdf
- Luckhurst GR, Sluckin TJ. Biaxial nematic liquid crystals: theory, simulation and experiment. Chichester: John Wiley & Sons; 2015.
- Kurik MV, Lavrentovich O. Defects in liquid crystals: homotopy theory and experimental studies. Sov Phys Uspekhi. 1988;31(3):196–224. doi:10.1070/PU1988v031n03ABEH005710/pdf
- Mermin ND. E Pluribus Boojum: the physicist as neologist. Phys Today. 1981;34(4):46–53. doi:10.1063/1.2914510
- Polyakov AM. Isomeric states of quantum fields. Sov Phys JETP. 1975;68(6):988–995. http://www.jetp.ras.ru/cgi-bin/dn/e_041_06_0988.pdf
- Zurek WH. Cosmological experiments in superfluid helium? Nature. 1985;317(6037):505–508. https://www.nature.com/articles/317505a0
- Chuang I, Turok N, Yurke B. Late-time coarsening dynamics in a nematic liquid crystal. Phys Rev Lett. 1991;66(19):2472–2475. doi:10.1103/PhysRevLett.66.2472
- Bowick MJ, Chandar L, Schiff EA, et al. The cosmological Kibble mechanism in the laboratory: string formation in liquid crystals. Science. 1994;263(5149):943–945. doi:10.1126/science.263.5149.943
- Schopohl N, Sluckin TJ. Hedgehog structure in nematic and magnetic systems. J Phys. 1988;49(7):1097–1101. https://hal.archives-ouvertes.fr/jpa-00210792
- Mkaddem S, Gartland Jr EC. Fine structure of defects in radial nematic droplets. Phys Rev E. 2000;62(5):6694–6705. doi:10.1103/PhysRevE.62.6694
- Jänich K. Topological properties of ordinary nematics in 3-space. Acta Appl Math. 1987;8(1):65–74. doi:10.1007/BF00046687.pdf
- Machon T, Alexander GP. Knotted defects in nematic liquid crystals. Phys Rev Lett. 2014;113:027801. doi:10.1103/PhysRevLett.113.027801
- Machon T, Alexander GP. Global defect topology in nematic liquid crystals. Proc R Soc A. 2016;472(2191):20160265. doi:10.1098/rspa.2016.0265
- Čopar S, Dennis MR, Kamien RD, et al. Singular values, nematic disclinations, and emergent biaxiality. Phys Rev E. 2013;87(5):050504. doi:10.1103/PhysRevE.87.050504
- Ruhwandl RW, Terentjev EM. Monte Carlo simulation of topological defects in the nematic liquid crystal matrix around a spherical colloid particle. Phys Rev E. 1997;56(5):5561–5565. doi:10.1103/PhysRevE.56.5561
- Tkalec U, Ravnik M, Čopar S, et al. Reconfigurable knots and links in chiral nematic colloids. Science. 2011;333(6038):62–65. doi:10.1126/science.1205705
- Gu Y, Abbott NL. Observation of Saturn-ring defects around solid microspheres in nematic liquid crystals. Phys Rev Lett. 2000;85(22):4719–4722. doi:10.1103/PhysRevLett.85.4719
- Ravnik M, Škarabot M, Žumer S, et al. Entangled nematic colloidal dimers and wires. Phys Rev Lett. 2007;99(24):247801. doi:10.1103/PhysRevLett.99.247801
- Smalyukh II. Knots and other new topological effects in liquid crystals and colloids. Rep Prog Phys. 2020;83(10):106601. doi:10.1088/1361-6633/abaa39
- Doostmohammadi A, Ladoux B. Physics of liquid crystals in cell biology. Trends Cell Biol (in press). doi:10.1016/j.tcb.2021.09.012
- I am indebted to Oleg Lavrentovich for his personal reminiscence of these conversations.
- Kléman M. The coexistence of cholesteric and 2-dimensional orders. J Phys. 1985;46:1193–1203. https://hal.archives-ouvertes.fr/file/index/docid/210060/filename/ajp-jphys_1985_46_7_1193_0.pdf
- Vinograd J, Lebowitz J, Radloff R, et al. The twisted circular form of polyoma viral DNA. Proc Natl Acad Sci. 1965;53(5):1104–1111. There is, of course, a enormous literature, but this seems to have been the paper which introduced the idea of supercoiling. doi:10.1073/pnas.53.5.1104
- Bateson W. Materials for the study of variation: treated with especial regard to discontinuity in the origin of species. London: Macmillan and Company; 1894. http://www.esp.org/books/bateson/materials/facsimile/contents/ch-23-i.pdf
- D'Arcy Wentworth Thompson. On growth and form. Cambridge: Cambridge University Press; 1917. https://archive.org/details/ongrowthform1917thom
- Prosser S, Pelletier L. Mitotic spindle assembly in animal cells: a fine balancing act. Nat Rev Mol Cell Biol. 2017;18:187–201. doi:10.1038/nrm.2016.162
- Nédélec F, Surrey T, Maggs AC, et al. Self-organization of microtubules and motors. Nature. 1997;389(6648):305–308. https://www.nature.com/articles/38532
- Bouligand Y. Sur une architecture torsadée répandue dans de nombreuses cuticules d'Arthropodes [On the twisted architecture commonly seen in arthropod cuticle]. CRAS. 1965;261:4864–4867. https://gallica.bnf.fr/ark:/12148/bpt6k40266/f1417.item
- Frank R, Frank P, Klein M, et al. L'os compact humain normal au microscope électronique [Normal human compact bone under an electron microscope]. Arch Anat Microsc Morphol Exp. 1955;44:191–206.
- Bouligand Y. Sur une disposition fibrillaire torsadée commune à plusieurs structures biologiques [On the twisted fibre tendency common to many biological structures]. CRAS. 1965;261:3665–3668. https://gallica.bnf.fr/ark:/12148/bpt6k40266/f168.item
- Bouligand Y, Soyer MO, Puiseux-Dao S. La structure fibrillaire et l'orientation des chromosomes chez les dinoflagellés [The fibril structure and orientation of chromosomes in dinoflagellates]. Chromosoma. 1968;24(3):251–287. doi:10.1007/BF00336195
- Bouligand Y. François Grandjean, physicist. Acarologia. 1977;19(1):5–11. https://hal.archives-ouvertes.fr/jpa-00216235
- Bouligand Y, Kléman M. Topologie des lignes singulières des smectiques C non chiraux [Singular line topology in non-chiral smectic C]. J Phys. 1979;40(1):79–97. https://www1.montpellier.inra.fr/CBGP/acarologia/article.php?id=3041
- Bouligand Y. Defects and textures in cholesteric analogues given by some biological systems. J Phys Colloq. 1975;36(C1):331–336. https://hal.archives-ouvertes.fr/jpa-00208887
- Mitov M. Cholesteric liquid crystals in living matter. Soft Matter. 2017;13(23):4176–4209. https://hal.archives-ouvertes.fr/hal-01994869/file/SoftMatter_2017.pdf
- Marchetti MC, Joanny J-F, Ramaswamy S, et al. Hydrodynamics of soft active matter. Rev Mod Phys. 2013;85(3):1143. doi:10.1103/RevModPhys.85.1143
- Rey AD. Liquid crystal models of biological materials and processes. Soft Matter. 2010;6(15):3402–3429. https://pubs.rsc.org/en/content/articlehtml/2010/sm/b921576j
- Zhao J, Gulan U, Horie T, et al. Advances in biological liquid crystals. Small. 2019;15(18):1900019. doi:10.1002/smll.201900019
- Tyson JJ. What everyone should know about the Belousov-Zhabotinsky reaction. In: Frontiers in mathematical biology. Springer; 1994. p. 569–587. (Lecture notes in biomathematics; vol. 100). Available from: https://link.springer.com/chapter/10.1007/978-3-642-50124-1_33
- Müller SC, Plesser T, Hess B. The structure of the core of the spiral wave in the Belousov-Zhabotinskii reaction. Science. 1985;230(4726):661–663. doi:10.1126/science.230.4726.661
- Turing AM. The chemical basis of morphogenesis. Bull Math Biol. 1990;52(1):153–197. Reprinted from Phil. Trans. Roy. Soc. B 237, 37–72 (1952). doi:10.1007/BF02459572.pdf
- Turing AM. Morphogenesis, collected works of A.M. Turing. North Holland; 1992. The famous article [269], plus unpublished notes by Turing, edited with commentary by P.T. Saunders.
- Moffatt HK. G.K. Batchelor and the homogenization of turbulence. Annu Rev Fluid Mech. 2002;34(1):19–35. doi:10.1146/annurev.fluid.34.081701.134821
- de Gennes P-G. Short range order effects in the isotropic phase of nematics and cholesterics. Mol Cryst Liq Cryst. 1971;12(3):193–214.
- Olmsted PD, Goldbart P. Theory of the nonequilibrium phase transition for nematic liquid crystals under shear flow. Phys Rev A. 1990;41(8):4578. doi:10.1103/PhysRevA.41.4578
- Beris AN, Edwards BJ. Thermodynamics of flowing systems with internal microstructure. Oxford: Oxford University Press; 1994.
- Mottram NJ, Newton CJ. Introduction to Q-tensor theory. Preprint; 2014. Available from: https://arxiv.org/pdf/1409.3542.pdf
- Elgeti J, Cates ME, Marenduzzo D. Defect hydrodynamics in 2D polar active fluids. Soft Matter. 2011;7(7):3177–3185. https://pubs.rsc.org/en/content/articlehtml/2011/sm/c0sm01097a
- Ravnik M, Yeomans JM. Confined active nematic flow in cylindrical capillaries. Phys Rev Lett. 2013;110(2):026001. doi:10.1103/PhysRevLett.110.026001
- Thampi S, Yeomans JM. Active turbulence in active nematics. Eur Phys J. 2016;225(4):651–662. doi:10.1140/epjst/e2015-50324-3
- Wensink HH, Dunkel J, Heidenreich S, et al. Meso-scale turbulence in living fluids. Proc Natl Acad Sci. 2012;109(36):14308–14313.
- Aranson IS. Topological defects in active liquid crystals. Phys Uspekhi. 2019;62:892–909. doi:10.3367/UFNe.2018.10.038433
- Reinitzer F. Beiträge zur Kenntnis des Cholesterins [Contributions to understanding cholesterol]. Monatsh Chem. 1888;9:421–441. (Different) English versions can be found in ref. [16] and in Liquid Crystal 5, 7–18 (1989). doi:10.1080/02678298908026349
- Lehmann O. Scheinbar lebende Kristalle und Myelinformen [Apparently living crystals and myelin shapes]. Arch Entwicklungsmech Org. 1908;26(3):483–489. doi:10.1007/BF02161557.pdf
- Lehmann O. Die Saugkraft quellbarer myelinartiger flüssiger Kristalle (The suction of swellable myelin-like liquid crystals). Ann Phys. 1914;349(14):969–976. https://ia800708.us.archive.org/view_archive.php?archive=/28/items/crossref-pre-1923-scholarly-works/10.1002%252Fandp.19123420414.zip&file=10.1002%252Fandp.19143491407.pdf
- Lehmann O. Die scheinbar lebenden Kristalle [Crystals which seem to be alive]. Munich: Schreiber; 1907.
- Lehmann O. Flüssige Kristalle und die Theorien des Lebens [Liquid crystals and theories of life]. Leipzig: JA Barth; 1908.
- Bawden FC, Pirie NW, Bernal JD, et al. Liquid crystalline substances from virus-infected plants. Nature. 1936;138:1051–1052. Also included in the collection [16]. Available from: https://www.nature.com/articles/1381051a0
- Elsdale TR. Parallel orientation of fibroblasts in vitro. Exp Cell Res. 1968;51(2–3):439–450. https://www.sciencedirect.com/science/article/abs/pii/0014482768901341
- Roland JC, Reis D, Vian B, et al. Morphogenesis of plant cell walls at the supramolecular level: internal geometry and versatility of helicoidal expression. Protoplasma. 1987;140(2–3):75–91. doi:10.1007/BF01273716.pdf
- Reis D, Roland JC, Mosiniak M, et al. The sustained and warped helicoidal pattern of a xylan-cellulose composite: the stony endocarp model. Protoplasma. 1992;166(1–2):21–34. doi:10.1007/BF01320139.pdf
- Kemkemer R, Kling D, Kaufmann D, et al. Elastic properties of nematoid arrangements formed by amoeboid cells. Eur Phys J E. 2000;1(2–3):215–225. doi:10.1007/s101890050024.pdf
- Vollrath F, Knight DP. Liquid crystalline spinning of spider silk. Nature. 2001;410(6828):541–548. https://www.nature.com/articles/35069000
- De Luca G, Rey AD. Dynamic interactions between nematic point defects in the spinning extrusion duct of spiders. J Chem Phys. 2006;124(14):144904. doi:10.1063/1.2186640
- Gruler H, Schienbein M, Franke K, et al. Migrating cells: living liquid crystals. Mol Cryst Liq Cryst A. 1995;260(1):565–574. doi:10.1080/10587259508038729
- Gupta G, Rey AD. Texture rules for concentrated filled nematics. Phys Rev Lett. 2005;95(12):127802. doi:10.1103/PhysRevLett.95.127802
- Murugesan YK, Rey AD. Modeling textural processes during self-assembly of plant-based chiral-nematic liquid crystals. Polymers. 2010;2:766–785. https://www.mdpi.com/2073-4360/wen2/4/766
- Saw TB, Doostmohammadi A, Nier V, et al. Topological defects in epithelia govern cell death and extrusion. Nature. 2017;544(7649):212–216. https://www.nature.com/articles/nature21718
- Maroudas-Sacks Y, Garion L, Shani-Zerbib L, et al. Topological defects in the nematic order of actin fibres as organization centres of hydra morphogenesis. Nat Phys. 2021;17(2):251–259. https://www.nature.com/articles/s41567-020-01083-1
- Copenhagen K, Alert R, Wingreen NS, et al. Topological defects promote layer formation in myxococcus xanthus colonies. Nat Phys. 2021;17(2):211–215. https://www.nature.com/articles/s41567-020-01056-4
- Hoffmann LA, Carenza LN, Eckert J, et al. Theory of defect-mediated morphogenesis. Science Advances. 2022;8(15):eabk2712. https://arxiv.org/pdf/2105.15200.pdf
- Turiv T, Krieger J, Babakhanova G, et al. Topology control of human fibroblast cells monolayer by liquid crystal elastomer. Sci Adv. 2020;6(20):eaaz6485. doi:10.1126/sciadv.aaz6485
- Endresen KD, Kim M, Pittman M, et al. Topological defects of integer charge in cell monolayers. Soft Matter. 2021;17:5878–5887. doi:10.1039/d1sm00100k
- Rocker S. Why Baruch Spinoza is still excommunicated. London: Jewish Chronicle; (Newspaper article November 2016) [cited 2021 Dec 22]. Available from: https://www.thejc.com/judaism/features/why-baruch-spinoza-is-still-excommunicated-1.56419
- Kleman M. Book review of ‘Spinoza: a life’, by S. Nadler (Cambridge University Press 1998). Eur Rev. 2000;8(2):263–267. https://www.cambridge.org/core/journals/european-review/article/spinoza-a-lifenadler-scambridge-university-press-cambridge-1998-350-pages-2295-hardback-isbn-0521552109/7A46E11E625B5E6A76CD6A9E9DC3A00C
- Nadler S. Baruch Spinoza: heretic, lens grinder. Arch Ophthalmol. 2000;118(10):1425–1427. https://jamanetwork.com/journals/jamaophthalmology/fullarticle/413771
- Spinoza B. Letter XXXII. Spinoza to Blyenbergh. In: Elwes RHM, editors. The chief works of Benedict de Spinoza. Vol. II. G. Bell and Sons; 1891. p. 331–335. Reissued as a Dover edition 1951. Available from: https://oll-resources.s3.us-east-2.amazonaws.com/oll3/store/titles/1711/1321.02_Bk.pdf
- Kleman M, Robbins JM. Tubes of magnetic flux and electric current in space physics. Sol Phys. 2014;289(4):1173–1192. doi:10.1007/s11207-013-0399-0
- Pieranski P, Godinho MH. Liquid crystals: new perspectives. Wiley; 2021. Available from: https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781119850809
- Sluckin T. Vito Volterra at 150. Math Today. 2011;47:46–48. https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781119850809