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Annual Review of Condensed Matter Physics

Volume 14, 2023

Odd Viscosity and Odd Elasticity

Abstract

Elasticity typically refers to a material's ability to store energy, whereas viscosity refers to a material's tendency to dissipate it. In this review, we discuss fluids and solids for which this is not the case. These materials display additional linear response coefficients known as odd viscosity and odd elasticity. We first introduce odd viscosity and odd elasticity from a continuum perspective, with an emphasis on their rich phenomenology, including transverse responses, modified dislocation dynamics, and topological waves. We then provide an overview of systems that display odd viscosity and odd elasticity. These systems range from quantum fluids and astrophysical gases to active and driven matter. Finally, we comment on microscopic mechanisms by which odd viscosity and odd elasticity arise.

Keyword(s): active matter, continuum mechanics, fluid mechanics, hydrodynamics, nonequilibrium, rheology
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/content/journals/10.1146/annurev-conmatphys-040821-125506
2023-03-10
2024-06-12
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Literature Cited

  1. 1.
    Truesdell C, Toupin R 1960. Principles of Classical Mechanics and Field Theory S Flügge 226–858. Berlin: Springer-Verlag
     [Google Scholar]
  2. 2.
    Landau LD, Lifshitz EM. 1959. Fluid Mechanics, Vol. 6 Course of Theoretical Physics Oxford, UK: Pergamon. , 1st ed..
     [Google Scholar]
  3. 3.
    Landau LD, Lifshitz EM 1986. Theory of Elasticity, Vol. 7 Course of Theoretical Physics Oxford, UK: Elsevier. , 3rd ed.. Transl. JB Sykes, WH Reid (From Russian)
    [Google Scholar]
  4. 4.
    Khain T, Scheibner C, Fruchart M, Vitelli V. 2022. J. Fluid Mech. 934:A23
     [Google Scholar]
  5. 5.
    Avron JE. 1998. J. Stat. Phys. 92:543–57
     [Google Scholar]
  6. 6.
    Han M, Fruchart M, Scheibner C, Vaikuntanathan S, de Pablo JJ, Vitelli V. 2021. Nat. Phys. 17:1260–69
     [Google Scholar]
  7. 7.
    Condiff DW, Dahler JS. 1964. Phys. Fluids 7:842–54
     [Google Scholar]
  8. 8.
    Goldhirsch I. 2010. Granular Matter 12:239–52
     [Google Scholar]
  9. 9.
    Eringen A. 2012. Microcontinuum Field Theories: I. Foundations and Solids New York: Springer
     [Google Scholar]
  10. 10.
    de Groot SR, Mazur P. 1954. Phys. Rev. 94:218–24
     [Google Scholar]
  11. 11.
    de Groot SR, Mazur P. 1962. Non-Equilibrium Thermodynamics Amsterdam: Dover
     [Google Scholar]
  12. 12.
    Rao P, Bradlyn B. 2021. arXiv:2112.04545
  13. 13.
    Cook CQ, Lucas A. 2021. Phys. Rev. Lett. 127:176603
     [Google Scholar]
  14. 14.
    Rao P, Bradlyn B. 2020. Phys. Rev. X 10:021005
     [Google Scholar]
  15. 15.
    Fruchart M, Han M, Scheibner C, Vitelli V. 2022. arXiv:2202.02037
  16. 16.
    Schofield P, Henderson JR. 1982. Proc. R. Soc. A. Math. Phys. Sci. 379:231–46
     [Google Scholar]
  17. 17.
    Irving JH, Kirkwood JG. 1950. J. Chem. Phys. 18:817–29
     [Google Scholar]
  18. 18.
    Souslov A, Gromov A, Vitelli V. 2020. Phys. Rev. E 101:052606
     [Google Scholar]
  19. 19.
    Hess S. 1986. J. Non Equilibrium Thermodyn. 11:3–4175–94
     [Google Scholar]
  20. 20.
    Jarkova E, Pleiner H, Müller HW, Fink A, Brand H. 2001. Eur. Phys. J. E 5:583–88
     [Google Scholar]
  21. 21.
    Varnavides G, Jermyn AS, Anikeeva P, Felser C, Narang P. 2020. Nat. Commun. 11:4710
     [Google Scholar]
  22. 22.
    Friedman AJ, Cook CQ, Lucas A. 2022. arXiv:2202.08269
  23. 23.
    Huang X, Lucas A. 2022. J. High Energy Phys. 2022:82
     [Google Scholar]
  24. 24.
    Zhao Z, Wang B, Komura S, Yang M, Ye F, Seto R. 2021. Phys. Rev. Res. 3:043229
     [Google Scholar]
  25. 25.
    Nicolis A, Son DT. 2011. arXiv:1103.2137
  26. 26.
    Jensen K, Kaminski M, Kovtun P, Meyer R, Ritz A, Yarom A. 2012. J. High Energy Phys. 2012:102
     [Google Scholar]
  27. 27.
    Gromov A, Son DT. 2017. Phys. Rev. X 7:041032
     [Google Scholar]
  28. 28.
    Salbreux G, Jülicher F, Prost J, Callan-Jones A. 2022. Phys. Rev. Res. 4:033158
     [Google Scholar]
  29. 29.
    Robredo I, Rao P, de Juan F, Bergara A, Mañes JL et al. 2021. Phys. Rev. Res. 3:1032068
     [Google Scholar]
  30. 30.
    Banerjee D, Souslov A, Abanov AG, Vitelli V. 2017. Nat. Commun. 8:1573
     [Google Scholar]
  31. 31.
    Ganeshan S, Abanov AG. 2017. Phys. Rev. Fluids 2:094101
     [Google Scholar]
  32. 32.
    Guyon E, Hulin J, Petit L, Mitescu C. 2015. Physical Hydrodynamics Oxford, UK: Oxford Univ. Press
     [Google Scholar]
  33. 33.
    Beenakker JJM, McCourt FR. 1970. Annu. Rev. Phys. Chem. 21:47–72
     [Google Scholar]
  34. 34.
    McCourt F. 1990. Nonequilibrium Phenomena in Polyatomic Gases New York/Oxford: Clarendon/Oxford Univ. Press
     [Google Scholar]
  35. 35.
    Korving J, Hulsman H, Knaap H, Beenakker J. 1966. Phys. Lett. 21:5–7
     [Google Scholar]
  36. 36.
    Korving J, Hulsman H, Scoles G, Knaap H, Beenakker J. 1967. Physica 36:177–97
     [Google Scholar]
  37. 37.
    Hulsman H, Knaap H. 1970. Physica 50:565–72
     [Google Scholar]
  38. 38.
    Hulsman H, Van Waasdijk E, Burgmans A, Knaap H, Beenakker J. 1970. Physica 50:53–76
     [Google Scholar]
  39. 39.
    Banerjee D, Souslov A, Vitelli V. 2022. Phys. Rev. Fluids 7:043301
     [Google Scholar]
  40. 40.
    Souslov A, Dasbiswas K, Fruchart M, Vaikuntanathan S, Vitelli V. 2019. Phys. Rev. Lett. 122:128001
     [Google Scholar]
  41. 41.
    Reynolds D, Monteiro GM, Ganeshan S. 2021. arXiv:2112.03076
  42. 42.
    Holder T, Queiroz R, Stern A. 2019. Phys. Rev. Lett. 123:106801
     [Google Scholar]
  43. 43.
    Delacrétaz LV, Gromov A. 2017. Phys. Rev. Lett. 119:226602
     [Google Scholar]
  44. 44.
    Hosaka Y, Komura S, Andelman D. 2021. Phys. Rev. E 104:064613
     [Google Scholar]
  45. 45.
    Tropea C, Yarin AL, Foss JF. 2007. Springer Handbook of Experimental Fluid Mechanics Berlin/Heidelberg: Springer
     [Google Scholar]
  46. 46.
    Ariman T, Turk M, Sylvester N. 1973. Int. J. Eng. Sci. 11:905–30
     [Google Scholar]
  47. 47.
    Hess S. 2019. Atti Della Accademia Peloritana dei Pericolanti: Classe di Scienze Fisiche, Matematiche e Naturali 97:Suppl. 1A9
     [Google Scholar]
  48. 48.
    Kiselev EI, Schmalian J. 2019. Phys. Rev. B 99:035430
     [Google Scholar]
  49. 49.
    Lucas A, Fong KC. 2018. J. Phys. Condens. Matter 30:053001
     [Google Scholar]
  50. 50.
    Tsai JC, Ye F, Rodriguez J, Gollub JP, Lubensky T. 2005. Phys. Rev. Lett. 94:214301
     [Google Scholar]
  51. 51.
    van Zuiden BC, Paulose J, Irvine WTM, Bartolo D, Vitelli V. 2016. PNAS 113:12919–24
     [Google Scholar]
  52. 52.
    Soni V, Bililign ES, Magkiriadou S, Sacanna S, Bartolo D et al. 2019. Nat. Phys. 15:1188–94
     [Google Scholar]
  53. 53.
    Abanov A, Can T, Ganeshan S. 2018. SciPost Phys. 5:010
     [Google Scholar]
  54. 54.
    Abanov AG, Can T, Ganeshan S, Monteiro GM. 2020. Phys. Rev. Fluids 5:104802
     [Google Scholar]
  55. 55.
    Bogatskiy A, Wiegmann P. 2019. Phys. Rev. Lett. 122:214505
     [Google Scholar]
  56. 56.
    Tauber C, Delplace P, Venaille A. 2019. J. Fluid Mech. 868:R2
     [Google Scholar]
  57. 57.
    Baardink G, Cassella G, Neville L, Milewski PA, Souslov A. 2021. Phys. Rev. E 104:014603
     [Google Scholar]
  58. 58.
    Shankar S, Souslov A, Bowick MJ, Marchetti MC, Vitelli V. 2022. Nat. Rev. Phys. 4:380–98
     [Google Scholar]
  59. 59.
    Fruchart M, Carpentier D. 2013. C. R. Phys. 14:779–815
     [Google Scholar]
  60. 60.
    Kogan E. 2016. Phys. Rev. E 94:043111
     [Google Scholar]
  61. 61.
    Lapa MF, Hughes TL. 2014. Phys. Rev. E 89:043019
     [Google Scholar]
  62. 62.
    Lier R, Duclut C, Bo S, Armas J, Jülicher F, Surówka P. 2022. arXiv:2205.12704
  63. 63.
    Kim S, Karrila SJ. 1991. Microhydrodynamics: Principles and Selected Applications Oxford, UK: Butterworth-Heinemann
     [Google Scholar]
  64. 64.
    Happel J, Brenner H. 2012. Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media Dordrecht, Neth.: Springer
     [Google Scholar]
  65. 65.
    Masoud H, Stone HA. 2019. J. Fluid Mech. 879:P1
     [Google Scholar]
  66. 66.
    Hosaka Y, Komura S, Andelman D. 2021. Phys. Rev. E 103:042610
     [Google Scholar]
  67. 67.
    Charru F. 2011. Hydrodynamic Instabilities Cambridge, UK: Cambridge Univ. Press. Transl. P de Forcrand–Millard
     [Google Scholar]
  68. 68.
    Faganello M, Califano F. 2017. J. Plasma Phys. 83:6535830601
     [Google Scholar]
  69. 69.
    Nagano H. 1979. Planet. Space Sci. 27:881–84
     [Google Scholar]
  70. 70.
    Wolff RS, Goldstein BE, Yeates CM. 1980. J. Geophys. Res. 85:7697–707
     [Google Scholar]
  71. 71.
    Lucas A, Surówka P. 2014. Phys. Rev. E 90:063005
     [Google Scholar]
  72. 72.
    Kirkinis E, Andreev AV. 2019. J. Fluid Mech. 878:169–89
     [Google Scholar]
  73. 73.
    Bao G, Jian Y. 2021. Phys. Rev. E 103:013104
     [Google Scholar]
  74. 74.
    Chattopadhyay S. 2021. Phys. Fluids 33:062106
     [Google Scholar]
  75. 75.
    Samanta A. 2022. J. Fluid Mech. 938:A9
     [Google Scholar]
  76. 76.
    Rosenbluth MN, Krall NA, Rostoker N. 1962. Nuclear Fusion: 1962 Suppl., Pt. 1 Conf. Pap. No. CN-10/170 Int. Atomic Energy Agency Vienna, Aust:.
     [Google Scholar]
  77. 77.
    Newcomb WA, U.S. At. Energy Comm., Lawrence Radiat. Lab. 1966. Dynamics of a gyroviscous plasma Livermore, California: Univ. Calif., Lawrence Radiat. Lab.
     [Google Scholar]
  78. 78.
    Roberts KV, Taylor JB. 1962. Phys. Rev. Lett. 8:197–98
     [Google Scholar]
  79. 79.
    Pottier N. 2010. Nonequilibrium Statistical Physics: Linear Irreversible Processes Oxford, UK: Oxford Univ. Press
     [Google Scholar]
  80. 80.
    Callen HB. 1985. Thermodynamics and an Introduction to Thermostatistics New York: John Wiley & Sons
     [Google Scholar]
  81. 81.
    Epstein JM, Mandadapu KK. 2020. Phys. Rev. E 101:052614
     [Google Scholar]
  82. 82.
    Hargus C, Klymko K, Epstein JM, Mandadapu KK. 2020. J. Chem. Phys. 152:201102
     [Google Scholar]
  83. 83.
    Bradlyn B, Goldstein M, Read N. 2012. Phys. Rev. B 86:245309
     [Google Scholar]
  84. 84.
    Read N, Rezayi EH. 2011. Phys. Rev. B 84:085316
     [Google Scholar]
  85. 85.
    Offertaler B, Bradlyn B. 2019. Phys. Rev. B 99:035427
     [Google Scholar]
  86. 86.
    Krommes JA, Hu G. 1993. Phys. Fluids B: Plasma Phys. 5:3908–41
     [Google Scholar]
  87. 87.
    Coleman BD, Truesdell C. 1960. J. Chem. Phys. 33:28–31
     [Google Scholar]
  88. 88.
    Berdyugin AI, Xu SG, Pellegrino FMD, Kumar RK, Principi A et al. 2019. Science 364:6436162–65
     [Google Scholar]
  89. 89.
    ten Bosch B, Beenakker J, Kuščer I. 1984. Phys. A Stat. Mech. Appl. 123:443–62
     [Google Scholar]
  90. 90.
    Sharipov F. 1994. Phys. A Stat. Mech. Appl. 203:437–56
     [Google Scholar]
  91. 91.
    Sharipov F. 1994. Phys. A Stat. Mech. Appl. 203:457–85
     [Google Scholar]
  92. 92.
    Yamauchi L, Hayata T, Uwamichi M, Ozawa T, Kawaguchi K. 2020. arXiv:2008.10852
  93. 93.
    Barabanov AF, Kagan YM, Maksimov LA, Mikheyenkov AV, Khabarova TV. 2015. Physics-Uspekhi 58:446–54
     [Google Scholar]
  94. 94.
    Strohm C, Rikken GLJA, Wyder P. 2005. Phys. Rev. Lett. 95:155901
     [Google Scholar]
  95. 95.
    Koch DL, Brady JF. 1987. Phys. Fluids 30:642–50
     [Google Scholar]
  96. 96.
    Auriault JL, Moyne C, Amaral Souto HP. 2010. Transport Porous Media 85:771–83
     [Google Scholar]
  97. 97.
    Hargus C, Epstein JM, Mandadapu KK. 2021. Phys. Rev. Lett. 127:178001
     [Google Scholar]
  98. 98.
    Vega Reyes F, López-Castaño MA, Rodríguez-Rivas A. 2022. Commun. Phys. 5:256
     [Google Scholar]
  99. 99.
    Rikken GLJA, van Tiggelen BA. 1996. Nature 381:54–55
     [Google Scholar]
  100. 100.
    van Tiggelen BA. 1995. Phys. Rev. Lett. 75:422–24
     [Google Scholar]
  101. 101.
    Quan L, Yves S, Peng Y, Esfahlani H, Alù A 2021. Nat. Commun. 12:2615
     [Google Scholar]
  102. 102.
    Chaikin PM, Lubensky TC. 1995. Principles of Condensed Matter Physics Cambridge, UK: Cambridge Univ. Press
     [Google Scholar]
  103. 103.
    Anderson PW 1984. Basic Notions of Condensed Matter Physics Boca Raton, FL: CRC
     [Google Scholar]
  104. 104.
    Kole SJ, Alexander GP, Ramaswamy S, Maitra A. 2021. Phys. Rev. Lett. 126:248001
     [Google Scholar]
  105. 105.
    Maitra A, Lenz M, Voituriez R. 2020. Phys. Rev. Lett. 125:238005
     [Google Scholar]
  106. 106.
    Korving J, Hulsman H, Hermans L, de Groot J, Knaap H, Beenakker J. 1966. J. Mol. Spectrosc. 20:294–95
     [Google Scholar]
  107. 107.
    Chapman S, Cowling T. 1990. The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases Cambridge, UK: Cambridge Univ. Press. , 3rd ed..
     [Google Scholar]
  108. 108.
    Braginskii SI. 1958. Sov. Phys. J. Exp. Theor. Phys. 6:358–69
     [Google Scholar]
  109. 109.
    Braginskii SI. 1965. Rev. Plasma Phys. 1:205–311
     [Google Scholar]
  110. 110.
    Ramos JJ. 2005. Phys. Plasmas 12:112301
     [Google Scholar]
  111. 111.
    Kaufman AN. 1960. Phys. Fluids 3:610–16
     [Google Scholar]
  112. 112.
    Steinhauer LC. 2011. Phys. Plasmas 18:070501
     [Google Scholar]
  113. 113.
    Stasiewicz K. 1993. Space Sci. Rev. 65:221–52
     [Google Scholar]
  114. 114.
    Nayyar NK, Trehan SK. 1970. J. Plasma Phys. 4:563–71
     [Google Scholar]
  115. 115.
    Steinhauer LC, Ishida A. 1990. Phys. Fluids B: Plasma Phys. 2:2422–30
     [Google Scholar]
  116. 116.
    Terada N, Machida S, Shinagawa H. 2002. J. Geophys. Res. Space Phys. 107:SMP 30
     [Google Scholar]
  117. 117.
    Ishizawa A, Horiuchi R. 2005. Phys. Rev. Lett. 95:045003
     [Google Scholar]
  118. 118.
    Ferraro NM, Jardin SC. 2006. Phys. Plasmas 13:092101
     [Google Scholar]
  119. 119.
    Bae C, Stacey W, Solomon W. 2013. Nuclear Fusion 53:043011
     [Google Scholar]
  120. 120.
    Stacey WM, Sigmar DJ. 1985. Phys. Fluids 28:2800–7
     [Google Scholar]
  121. 121.
    Stacey WM, Mandrekas J. 2002. Phys. Plasmas 9:1622–28
     [Google Scholar]
  122. 122.
    Stacey WM, Johnson RW, Mandrekas J. 2006. Phys. Plasmas 13:062508
     [Google Scholar]
  123. 123.
    Winske D. 1996. Phys. Plasmas 3:3966–74
     [Google Scholar]
  124. 124.
    Zhu P, Schnack DD, Ebrahimi F, Zweibel EG, Suzuki M et al. 2008. Phys. Rev. Lett. 101:085005
     [Google Scholar]
  125. 125.
    Yajima N. 1966. Prog. Theor. Phys. 36:1–16
     [Google Scholar]
  126. 126.
    Nakagawa Y. 1956. J. Phys. Earth 4:105–11
     [Google Scholar]
  127. 127.
    Sulpizio JA, Ella L, Rozen A, Birkbeck J, Perello DJ et al. 2019. Nature 576:75–79
     [Google Scholar]
  128. 128.
    Ku MJH, Zhou TX, Li Q, Shin YJ, Shi JK et al. 2020. Nature 583:537–41
     [Google Scholar]
  129. 129.
    Bandurin DA, Torre I, Kumar RK, Ben Shalom M, Tomadin A et al. 2016. Science 351:1055–58
     [Google Scholar]
  130. 130.
    Moll PJW, Kushwaha P, Nandi N, Schmidt B, Mackenzie AP. 2016. Science 351:1061–64
     [Google Scholar]
  131. 131.
    Crossno J, Shi JK, Wang K, Liu X, Harzheim A et al. 2016. Science 351:1058–61
     [Google Scholar]
  132. 132.
    de Jong MJM, Molenkamp LW. 1995. Phys. Rev. B 51:13389–402
     [Google Scholar]
  133. 133.
    Zaanen J. 2016. Science 351:1026–27
     [Google Scholar]
  134. 134.
    Vollhardt D, Wolfle P. 2013. The Superfluid Phases of Helium 3 New York: Dover
     [Google Scholar]
  135. 135.
    Volovik GE. 2020. J. Low Temp. Phys. 202:11–28
     [Google Scholar]
  136. 136.
    Furusawa T, Fujii K, Nishida Y. 2021. Phys. Rev. B 103:064506
     [Google Scholar]
  137. 137.
    Fujii K, Nishida Y. 2018. Ann. Phys. 395:170–82
     [Google Scholar]
  138. 138.
    Read N. 2009. Phys. Rev. B 79:045308
     [Google Scholar]
  139. 139.
    Avron JE, Seiler R, Zograf PG. 1995. Phys. Rev. Lett. 75:697–700
     [Google Scholar]
  140. 140.
    Haldane FDM. 2009. arXiv:0906.1854
  141. 141.
    Haldane FDM. 2011. Phys. Rev. Lett. 107:116801
     [Google Scholar]
  142. 142.
    Park Y, Haldane FDM. 2014. Phys. Rev. B 90:045123
     [Google Scholar]
  143. 143.
    Hoyos C, Son DT. 2012. Phys. Rev. Lett. 108:066805
     [Google Scholar]
  144. 144.
    Fürthauer S, Strempel M, Grill SW, Jülicher F. 2012. Eur. Phys. J. E 35:89
     [Google Scholar]
  145. 145.
    Markovich T, Tjhung E, Cates ME. 2019. New J. Phys. 21:112001
     [Google Scholar]
  146. 146.
    Yeo K, Lushi E, Vlahovska PM. 2015. Phys. Rev. Lett. 114:188301
     [Google Scholar]
  147. 147.
    Grzybowski BA, Stone HA, Whitesides GM. 2000. Nature 405:1033–36
     [Google Scholar]
  148. 148.
    Yan J, Bae SC, Granick S. 2015. Soft Matter 11:147–53
     [Google Scholar]
  149. 149.
    Bililign ES, Balboa Usabiaga F, Ganan YA, Poncet A, Soni V et al. 2021. Nat. Phys. 18:2212–18
     [Google Scholar]
  150. 150.
    Denk J, Huber L, Reithmann E, Frey E. 2016. Phys. Rev. Lett. 116:178301
     [Google Scholar]
  151. 151.
    Liebchen B, Levis D. 2017. Phys. Rev. Lett. 119:058002
     [Google Scholar]
  152. 152.
    López-Castaño MA, Seco AM, Seco AM, Álvaro Rodríguez-Rivas, Reyes FV. 2022. Phys. Rev. Res. 4:033230
     [Google Scholar]
  153. 153.
    Scholz C, Engel M, Pöschel T. 2018. Nat. Commun. 9:931
     [Google Scholar]
  154. 154.
    Yang X, Ren C, Cheng K, Zhang HP. 2020. Phys. Rev. E 101:022603
     [Google Scholar]
  155. 155.
    Riedel IH, Kruse K, Howard J. 2005. Science 309:300–3
     [Google Scholar]
  156. 156.
    Petroff AP, Wu XL, Libchaber A. 2015. Phys. Rev. Lett. 114:158102
     [Google Scholar]
  157. 157.
    Tan TH, Mietke A, Li J, Chen Y, Higinbotham H et al. 2022. Nature 607:287–93
     [Google Scholar]
  158. 158.
    Markovich T, Lubensky TC. 2021. Phys. Rev. Lett. 127:048001
     [Google Scholar]
  159. 159.
    Zhao Z, Yang M, Komura S, Seto R. 2022. Front. Phys. 10:951465
     [Google Scholar]
  160. 160.
    Garzó V. 2017. Phys. Rev. E 95:062906
     [Google Scholar]
  161. 161.
    Wiegmann P, Abanov AG. 2014. Phys. Rev. Lett. 113:034501
     [Google Scholar]
  162. 162.
    Yu X, Bradley AS. 2017. Phys. Rev. Lett. 119:185301
     [Google Scholar]
  163. 163.
    Moroz S, Hoyos C, Benzoni C, Son DT. 2018. SciPost Phys. 5:039
     [Google Scholar]
  164. 164.
    Reichhardt CJO, Reichhardt C. 2022. EuroPhys. Lett. 137:66004
     [Google Scholar]
  165. 165.
    Goldston RJ. 2020. Introduction to Plasma Physics Boca Raton, FL: CRC
     [Google Scholar]
  166. 166.
    Hazeltine R. 2018. The Framework of Plasma Physics Boca Raton, FL: CRC
     [Google Scholar]
  167. 167.
    Kagan Y, Maksimov L. 1962. J. Exp. Theor. Phys. Lett. 14:604–10
     [Google Scholar]
  168. 168.
    Kagan Y, Afanasév AM. 1962. J. Exp. Theor. Phys. Lett. 14:1096–101
     [Google Scholar]
  169. 169.
    Kagan Y, Maksimov L. 1967. J. Exp. Theor. Phys. Lett. 24:1893–908
     [Google Scholar]
  170. 170.
    Moraal H, McCourt F, Knaap HFP 1969. Physica 45:455–68
     [Google Scholar]
  171. 171.
    McCourt F, Knaap H, Moraal H. 1969. Physica 43:485–512
     [Google Scholar]
  172. 172.
    Knaap H, Beenakker J. 1967. Physica 33:643–70
     [Google Scholar]
  173. 173.
    McCourt FR, Snider RF. 1967. J. Chem. Phys. 47:4117–28
     [Google Scholar]
  174. 174.
    Levi A, McCourt F. 1968. Physica 38:415–37
     [Google Scholar]
  175. 175.
    Waldmann L. 1958. Z. Naturforsch. A 13:609–20
     [Google Scholar]
  176. 176.
    Hess S. 2003. Z. Naturforsch. A 58:269–74
     [Google Scholar]
  177. 177.
    Harris S. 2004. An Introduction to the Theory of the Boltzmann Equation New York: Dover
     [Google Scholar]
  178. 178.
    Dorfman J, van Beijeren H, Kirkpatrick T. 2021. Contemporary Kinetic Theory of Matter Cambridge, UK: Cambridge Univ. Press
     [Google Scholar]
  179. 179.
    Morrison PJ. 1998. Rev. Mod. Phys. 70:467–521
     [Google Scholar]
  180. 180.
    Salmon R. 1988. Ann. Rev. Fluid Mech. 20:225–56
     [Google Scholar]
  181. 181.
    Morrison PJ, Caldas IL, Tasso H. 1984. Z. Naturforsch. A 39:1023–27
     [Google Scholar]
  182. 182.
    Lingam M, Morrison P. 2014. Phys. Lett. A 378:3526–32
     [Google Scholar]
  183. 183.
    Morrison PJ. 2005. Phys. Plasmas 12:058102
     [Google Scholar]
  184. 184.
    Morrison PJ, Lingam M, Acevedo R. 2014. Phys. Plasmas 21:082102
     [Google Scholar]
  185. 185.
    Lingam M, Morrison PJ, Wurm A. 2020. J. Plasma Phys. 86:835860501
     [Google Scholar]
  186. 186.
    Lingam M. 2015. Phys. Lett. A 379:1425–30
     [Google Scholar]
  187. 187.
    Monteiro GM, Abanov AG, Ganeshan S. 2021. arXiv:2105.01655
  188. 188.
    Wen XG, Zee A. 1992. Phys. Rev. Lett. 69:953–56
     [Google Scholar]
  189. 189.
    Abanov AG, Gromov A. 2014. Phys. Rev. B 90:014435
     [Google Scholar]
  190. 190.
    Hughes TL, Leigh RG, Parrikar O. 2013. Phys. Rev. D 88:025040
     [Google Scholar]
  191. 191.
    Gromov A, Jensen K, Abanov AG. 2016. Phys. Rev. Lett. 116:126802
     [Google Scholar]
  192. 192.
    Geracie M, Son DT. 2014. J. High Energy Phys. 2014:4
     [Google Scholar]
  193. 193.
    Haehl FM, Loganayagam R, Rangamani M. 2015. J. High Energy Phys. 2015:60
     [Google Scholar]
  194. 194.
    Scheibner C, Souslov A, Banerjee D, Surówka P, Irvine WTM, Vitelli V. 2020. Nat. Phys. 16:475–80
     [Google Scholar]
  195. 195.
    Scheibner C, Irvine WTM, Vitelli V. 2020. Phys. Rev. Lett. 125:118001
     [Google Scholar]
  196. 196.
    Shankar S, Mahadevan L. 2022. bioRxiv 2022.02.20.481216
  197. 197.
    Braverman L, Scheibner C, VanSaders B, Vitelli V. 2021. Phys. Rev. Lett. 127:268001
     [Google Scholar]
  198. 198.
    Nelson D, Halperin B. 1979. Phys. Rev. B 19:2457–84
     [Google Scholar]
  199. 199.
    Ashida Y, Gong Z, Ueda M. 2020. Adv. Phys. 69:249–435
     [Google Scholar]
  200. 200.
    Zubov LM. 1997. Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies, Vol. 47: Lect. Notes Phys. Monogr. Berlin/Heidelberg: Springer
     [Google Scholar]
  201. 201.
    Marsden JE. 1994. Mathematical Foundations of Elasticity New York: Dover
     [Google Scholar]
  202. 202.
    Truesdell CA. 1963. J. Res. Natl. Bureau Standards Sect. B Math. Math. Phys. 67B:285
     [Google Scholar]
  203. 203.
    Nassar H, Yousefzadeh B, Fleury R, Ruzzene M, Alù A et al. 2020. Nat. Rev. Mater. 5:667–85
     [Google Scholar]
  204. 204.
    Rice JR. 1976. Theoretical and Applied Mechanics (Proceedings of the 14th International Congress on Theoretical and Applied Mechanics, Vol. 1 WT Koiter 207–20. Delft, Neth.: North Holland
     [Google Scholar]
  205. 205.
    La Ragione L, Oger L, Recchia G, Sollazzo A 2015. Proc. R. Soc. A Math. Phys. Eng. Sci. 471:20150013
     [Google Scholar]
  206. 206.
    Örs H, Prévost JH. 1995. Acta Mech. 111:181–92
     [Google Scholar]
  207. 207.
    Prévost JH. 1982. Int. J. Numer. Anal. Methods Geomechan. 6:323–38
     [Google Scholar]
  208. 208.
    Piccolroaz A, Bigoni D, Willis JR. 2006. J. Mech. Phys. Solids 54:2391–417
     [Google Scholar]
  209. 209.
    Bigoni D. 1995. Int. J. Solids Struct. 32:3167–89
     [Google Scholar]
  210. 210.
    Bordiga G, Piccolroaz A, Bigoni D. 2022. J. Mech. Phys. Solids 158:104665
     [Google Scholar]
  211. 211.
    Carol I, Willam K 1996. Int. J. Solids Struct. 33:2939–57
     [Google Scholar]
  212. 212.
    Carol I, Jirásek M, Bažant Z. 2001. Int. J. Solids Struct. 38:2921–31
     [Google Scholar]
  213. 213.
    Challamel N, Halm D, Dragon A. 2006. C. R. Mécan. 334:414–18
     [Google Scholar]
  214. 214.
    Lubensky TC. 2005. Pramana J. Phys. 64:727–42
     [Google Scholar]
  215. 215.
    Warner M, Terentjev EM. 2003. Liquid Crystal Elastomers, Vol. 120 Int. Ser. Monogr. Phys. Oxford, UK: Oxford Univ. Press
     [Google Scholar]
  216. 216.
    Storm C, Pastore JJ, MacKintosh FC, Lubensky TC, Janmey PA. 2005. Nature 435:191–94
     [Google Scholar]
  217. 217.
    Cosserat E, Cosserat F. 1909. Théorie des Corps Déformables Paris: A. Hermann et Fils
     [Google Scholar]
  218. 218.
    Lakes RS, Benedict RL. 1982. Int. J. Eng. Sci. 20:1161–67
     [Google Scholar]
  219. 219.
    Chen Y, Li X, Scheibner C, Vitelli V, Huang G. 2021. Nat. Commun. 12:5935
     [Google Scholar]
  220. 220.
    Brandenbourger M, Scheibner C, Veenstra J, Vitelli V, Coulais C. 2021. arXiv:2108.08837
  221. 221.
    Palacci J, Sacanna S, Kim SH, Yi GR, Pine DJ, Chaikin PM. 2014. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 372:20130372
     [Google Scholar]
  222. 222.
    Briand G, Schindler M, Dauchot O. 2018. Phys. Rev. Lett. 120:208001
     [Google Scholar]
  223. 223.
    Desreumaux N, Florent N, Lauga E, Bartolo D. 2012. Eur. Phys. J. E 35:68
     [Google Scholar]
  224. 224.
    Lavergne FA, Wendehenne H, Bäuerle T, Bechinger C. 2019. Science 364:70–74
     [Google Scholar]
  225. 225.
    Baconnier P, Shohat D, Hernández López C, Coulais C, Démery V et al. 2022. Nat. Phys. 18:1234–39
     [Google Scholar]
  226. 226.
    Guazzelli É, Hinch J. 2011. Annu. Rev. Fluid Mech. 43:97–116
     [Google Scholar]
  227. 227.
    Beatus T, Bar-Ziv R, Tlusty T. 2007. Phys. Rev. Lett. 99:124502
     [Google Scholar]
  228. 228.
    Beatus T, Tlusty T, Bar-Ziv R. 2006. Nat. Phys. 2:743–48
     [Google Scholar]
  229. 229.
    Baek Y, Solon AP, Xu X, Nikola N, Kafri Y. 2018. Phys. Rev. Lett. 120:058002
     [Google Scholar]
  230. 230.
    Uchida N, Golestanian R. 2010. Phys. Rev. Lett. 104:178103
     [Google Scholar]
  231. 231.
    Soto R, Golestanian R. 2014. Phys. Rev. Lett. 112:068301
     [Google Scholar]
  232. 232.
    Saha S, Ramaswamy S, Golestanian R. 2019. New J. Phys. 21:063006
     [Google Scholar]
  233. 233.
    Meredith CH, Moerman PG, Groenewold J, Chiu YJ, Kegel WK et al. 2020. Nat. Chem. 12:1136–42
     [Google Scholar]
  234. 234.
    Ivlev AV, Bartnick J, Heinen M, Du CR, Nosenko V, Löwen H. 2015. Phys. Rev. X 5:011035
     [Google Scholar]
  235. 235.
    Peterson CW, Parker J, Rice SA, Scherer NF. 2019. Nano Lett. 19:897–903
     [Google Scholar]
  236. 236.
    Yifat Y, Coursault D, Peterson CW, Parker J, Bao Y et al. 2018. Light Sci. Appl. 7:105
     [Google Scholar]
  237. 237.
    Han F, Parker JA, Yifat Y, Peterson C, Gray SK et al. 2018. Nat. Commun. 9:4897
     [Google Scholar]
  238. 238.
    Poncet A, Bartolo D. 2022. Phys. Rev. Lett. 128:048002
     [Google Scholar]
  239. 239.
    Nash LM, Kleckner D, Read A, Vitelli V, Turner AM, Irvine WTM. 2015. PNAS 112:14495–500
     [Google Scholar]
  240. 240.
    Bauer A, Pfleiderer C. 2016. Topological Structures in Ferroic Materials, Vol. 228 Springer Ser. Mater. Sci. J Seidel 1–28. Cham: Springer Int.
     [Google Scholar]
  241. 241.
    Koschmieder E, Pallas S. 1974. Int. J. Heat Mass Transf. 17:991–1002
     [Google Scholar]
  242. 242.
    Born M, Huang K. 1954. Dynamical Theory of Crystal Lattices Oxford, UK: Clarendon:
     [Google Scholar]
  243. 243.
    Lutsko JF. 1989. J. Appl. Phys. 65:2991–97
     [Google Scholar]
  244. 244.
    Barrat J-L 2006. Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology, Vol. 2 Lect. Notes Phys., Vol. 704 M Ferraria, G Coccotti, K Binder 287–307. Berlin/Heidelberg: Springer
     [Google Scholar]
  245. 245.
    Fruchart M, Vitelli V. 2020. Phys. Rev. Lett. 124:248001
     [Google Scholar]
  246. 246.
    Chen Z. 2022. arXiv:2204.06587
  247. 247.
    Wang P, Lu L, Bertoldi K. 2015. Phys. Rev. Lett. 115:104302
     [Google Scholar]
  248. 248.
    Zhao Y, Zhou X, Huang G. 2020. J. Mech. Phys. Solids 143:104065
     [Google Scholar]
  249. 249.
    Carta G, Brun M, Movchan A, Movchan N, Jones I. 2014. Int. J. Solids Struct. 51:2213–25
     [Google Scholar]
  250. 250.
    Hassanpour S. 2014. Dynamics of gyroelastic continua PhD Thesis Univ. Waterloo
     [Google Scholar]
  251. 251.
    Carta G, Jones IS, Movchan NV, Movchan AB, Nieves MJ. 2017. Sci. Rep. 7:26
     [Google Scholar]
  252. 252.
    Mitchell NP, Nash LM, Irvine WTM. 2018. Phys. Rev. B 98:174301
     [Google Scholar]
  253. 253.
    Mitchell NP, Nash LM, Irvine WTM. 2018. Phys. Rev. B 97:100302
     [Google Scholar]
  254. 254.
    Mitchell NP, Nash LM, Hexner D, Turner AM, Irvine WTM. 2018. Nat. Phys. 14:380–85
     [Google Scholar]
  255. 255.
    Brun M, Jones IS, Movchan AB. 2012. Proc. R. Soc. A Math. Phys. Eng. Sci. 468:3027–46
     [Google Scholar]
  256. 256.
    Benzoni C, Jeevanesan B, Moroz S. 2021. Phys. Rev. B 104:024435
     [Google Scholar]
  257. 257.
    Huang P, Schönenberger T, Cantoni M, Heinen L, Magrez A et al. 2020. Nat. Nanotechnol. 15:761–67
     [Google Scholar]
  258. 258.
    Ochoa H, Kim SK, Tchernyshyov O, Tserkovnyak Y. 2017. Phys. Rev. B 96:020410
     [Google Scholar]
  259. 259.
    Mühlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A et al. 2009. Science 323:915–19
     [Google Scholar]
  260. 260.
    Yu XZ, Onose Y, Kanazawa N, Park JH, Han JH et al. 2010. Nature 465:901–4
     [Google Scholar]
  261. 261.
    Brearton R, Turnbull LA, Verezhak JAT, Balakrishnan G, Hatton PD et al. 2021. Nat. Commun. 12:2723
     [Google Scholar]
  262. 262.
    Sonin EB. 1987. Rev. Mod. Phys. 59:87–155
     [Google Scholar]
  263. 263.
    Gifford SA, Baym G. 2008. Phys. Rev. A 78:043607
     [Google Scholar]
  264. 264.
    Nguyen DX, Gromov A, Moroz S. 2020. SciPost Phys. 9:76
     [Google Scholar]
  265. 265.
    Moroz S, Hoyos C, Benzoni C, Son DT. 2018. SciPost Phys. 5:39
     [Google Scholar]
  266. 266.
    Fetter AL. 2009. Rev. Mod. Phys. 81:647–91
     [Google Scholar]
  267. 267.
    Blatter G, Feigel'man MV, Geshkenbein VB, Larkin AI, Vinokur VM 1994. Rev. Mod. Phys. 66:1125–388
     [Google Scholar]
  268. 268.
    Tkachenko VK. 1969. J. Exp. Theor. Phys. 29:945
     [Google Scholar]
  269. 269.
    Tkachenko V. 1966. Sov. Phys. J. Exp. Theor. Phys. 22:1282–86
     [Google Scholar]
  270. 270.
    Tkachenko V. 1966. Sov. Phys. J. Exp. Theor. Phys. 23:1049–56
     [Google Scholar]
  271. 271.
    Petroff AP, Wu XL, Libchaber A. 2015. Phys. Rev. Lett. 114:158102
     [Google Scholar]
  272. 272.
    Drescher K, Leptos KC, Tuval I, Ishikawa T, Pedley TJ, Goldstein RE. 2009. Phys. Rev. Lett. 102:168101
     [Google Scholar]
  273. 273.
    Goldman A, Cox R, Brenner H. 1967. Chem. Eng. Sci. 22:637–51
     [Google Scholar]
  274. 274.
    Happel J, Brenner H. 1981. Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media, Mechanics of Fluids and Transport Processes Dordrecht, Neth: Springer
     [Google Scholar]
  275. 275.
    Jäger S, Klapp SHL. 2011. Soft Matter 7:6606–16
     [Google Scholar]
  276. 276.
    Timoshenko S. 1940. Strength of Materials New York: D. Van Nostrand Co. , 2nd ed..
     [Google Scholar]
  277. 277.
    Cheng W, Hu G. 2021. Sci. China Phys., Mech. Astron. 64:11114612
     [Google Scholar]
  278. 278.
    Salbreux G, Jülicher F. 2017. Phys. Rev. E 96:032404
     [Google Scholar]
  279. 279.
    Fossati M, Scheibner C, Fruchart M, Vitelli V. 2022. arXiv:2210.03669 [cond-mat.soft]
  280. 280.
    Zahalak GI. 1996. J. Theor. Biol. 182:59–84
     [Google Scholar]
  281. 281.
    Cross MC, Meiron D, Tu Y. 1994. Chaos Interdiscip. J. Nonlinear Sci. 4:607–19
     [Google Scholar]
  282. 282.
    Cross M, Greenside H. 2009. Pattern Formation and Dynamics in Nonequilibrium Systems Cambridge, UK: Cambridge Univ. Press
     [Google Scholar]
  283. 283.
    Pismen L. 2010. Patterns and Interfaces in Dissipative Dynamics Berlin/Heidelberg: Springer
     [Google Scholar]
  284. 284.
    Busse FH, Heikes KE. 1980. Science 208:173–75
     [Google Scholar]
  285. 285.
    Bodenschatz E, Pesch W, Ahlers G. 2000. Annu. Rev. Fluid Mech. 32:709–78
     [Google Scholar]
  286. 286.
    Ahlers G. 2006. Springer Tracts Mod. Phys. 207:67–94
     [Google Scholar]
  287. 287.
    Guarino A, Vidal V. 2004. Phys. Rev. E 69:066311
     [Google Scholar]
  288. 288.
    Fruchart M, Hanai R, Littlewood PB, Vitelli V. 2021. Nature 592:363–69
     [Google Scholar]
  289. 289.
    Nardini C, Fodor E, Tjhung E, van Wijland F, Tailleur J, Cates ME. 2017. Phys. Rev. X 7:021007
     [Google Scholar]
  290. 290.
    Wittkowski R, Tiribocchi A, Stenhammar J, Allen RJ, Marenduzzo D, Cates ME. 2014. Nat. Commun. 5:4351
     [Google Scholar]
  291. 291.
    Kozyreff G, Tlidi M. 2007. Chaos: Interdiscip. J. Nonlinear Sci. 17:037103
     [Google Scholar]
  292. 292.
    Coullet P, Lega J, Houchmanzadeh B, Lajzerowicz J. 1990. Phys. Rev. Lett. 65:1352–55
     [Google Scholar]
  293. 293.
    Coullet P, Goldstein RE, Gunaratne GH. 1989. Phys. Rev. Lett. 63:1954–57
     [Google Scholar]
  294. 294.
    Pomeau Y, Zaleski S, Manneville P. 1983. Phys. Rev. A 27:2710–26
     [Google Scholar]
  295. 295.
    Bodenschatz E, Cannell DS, de Bruyn JR, Ecke R, Hu YC et al. 1992. Phys. D: Nonlinear Phenom. 61:77–93
     [Google Scholar]
  296. 296.
    Clerc MG, Petrossian A, Residori S. 2005. Phys. Rev. E 71:015205
     [Google Scholar]
  297. 297.
    Siggia ED, Zippelius A. 1981. Phys. Rev. A 24:1036–49
     [Google Scholar]
  298. 298.
    Colinet P, Nepomnyashchy AA, Legros JC. 2002. Europhys. Lett. 57:480–86
     [Google Scholar]
  299. 299.
    Tsimring LS. 1996. Phys. D Nonlinear Phenom. 89:368–80
     [Google Scholar]
  300. 300.
    Houghton SM, Knobloch E. 2011. Phys. Rev. E 84:016204
     [Google Scholar]
  301. 301.
    You Z, Baskaran A, Marchetti MC. 2020. PNAS 117:19767–72
     [Google Scholar]
  302. 302.
    Saha S, Agudo-Canalejo J, Golestanian R. 2020. Phys. Rev. X 10:041009
     [Google Scholar]
  303. 303.
    Frohoff-Hülsmann T, Holl MP, Knobloch E, Gurevich SV, Thiele U. 2022. arXiv:2205.14364
  304. 304.
    Clerc MG, Verschueren N. 2013. Phys. Rev. E 88:052916
     [Google Scholar]
  305. 305.
    Coullet P, Emilsson K. 1992. Phys. D Nonlinear Phenom. 61:119–31
     [Google Scholar]
  306. 306.
    Cates ME. 2019. arXiv:1904.01330
  307. 307.
    Loos SAM, Hermann SM, Klapp SHL. 2019. arXiv:1910.08372
  308. 308.
    Loos SAM, Klapp SHL. 2020. New J. Phys. 22:123051
     [Google Scholar]
  309. 309.
    Echebarria B, Pérez-García C. 1998. Europhys. Lett. 43:35–40
     [Google Scholar]
  310. 310.
    Echebarria B, Riecke H. 2000. Phys. D Nonlinear Phenom. 139:97–108
     [Google Scholar]
  311. 311.
    Echebarria B, Riecke H. 2000. Phys. D Nonlinear Phenom. 143:187–204
     [Google Scholar]
  312. 312.
    Marder M. 2010. Condensed Matter Physics Hoboken, NJ: John Wiley & Sons
     [Google Scholar]
  313. 313.
    Nelson DR. 2002. Defects and Geometry in Condensed Matter Physics Cambridge/New York: Cambridge Univ. Press
     [Google Scholar]
  314. 314.
    Weertman J, Weertman JR. 1964. Elementary Dislocation Theory New York: Macmillan
     [Google Scholar]
  315. 315.
    Ishimoto K, Moreau C, Yasuda K. 2022. Phys. Rev. E 105:064603
     [Google Scholar]
  316. 316.
    Zhou D, Zhang J. 2020. Phys. Rev. Res. 2:023173
     [Google Scholar]
  317. 317.
    Strogatz S. 2019. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering Boca Raton, FL: CRC
     [Google Scholar]
  318. 318.
    Tedrake R. 2022. Underactuated robotics: algorithms for walking, running, swimming, flying, and manipulation Course Notes for MIT 6.832 Mass. Inst. Technol. Cambridge: Accessed Oct. 10. https://underactuated.csail.mit.edu/
    [Google Scholar]
  319. 319.
    Yasuda K, Hosaka Y, Sou I, Komura S. 2021. J. Phys. Soc. Jpn. 90:075001
     [Google Scholar]
  320. 320.
    Yasuda K, Kobayashi A, Lin LS, Hosaka Y, Sou I, Komura S. 2022. J. Phys. Soc. Jpn. 91:015001
     [Google Scholar]
  321. 321.
    Yasuda K, Ishimoto K, Kobayashi A, Lin LS, Sou I et al. 2022. J. Chem. Phys. 157:095101
     [Google Scholar]
  322. 322.
    Oswald P. 2014. Rheophysics: The Deformation and Flow of Matter Cambridge, UK: Cambridge Univ. Press
     [Google Scholar]
  323. 323.
    Landau LD, Lifshitz EM 1984. Electrodynamics of Continuous Media, Vol. 8 Course of Theoretical Physics Oxford, UK: Pergamon. , 2nd ed.. Transl. JB Sykes, JS Bell, MJ Kearsley (From Russian)
    [Google Scholar]
  324. 324.
    Banerjee D, Vitelli V, Jülicher F, Surówka P. 2021. Phys. Rev. Lett. 126:138001
     [Google Scholar]
  325. 325.
    Muhlestein MB, Sieck CF, Alù A, Haberman MR. 2016. Proc. R. Soc. A Math. Phys. Eng. Sci. 472:20160604
     [Google Scholar]
  326. 326.
    Day WA. 1971. Arch. Ration. Mech. Anal. 40:155–59
     [Google Scholar]
  327. 327.
    Srivastava A. 2015. Proc. R. Soc. A Math. Phys. Eng. Sci. 471:20150256
     [Google Scholar]
  328. 328.
    Lier R, Armas J, Bo S, Duclut C, Jülicher F, Surówka P. 2022. Phys. Rev. E 105:054607
     [Google Scholar]
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Odd Viscosity and Odd Elasticity
Annual Review of Condensed Matter Physics 14, 471 (2023); https://doi.org/10.1146/annurev-conmatphys-040821-125506
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