1932

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.

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2023-03-10
2024-04-14
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Literature Cited

  1. 1.
    Truesdell C, Toupin R 1960. Principles of Classical Mechanics and Field Theory S Flügge 226858. Berlin: Springer-Verlag
  2. 2.
    Landau LD, Lifshitz EM. 1959. Fluid Mechanics, Vol. 6 Course of Theoretical Physics Oxford, UK: Pergamon. , 1st ed..
  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)
  4. 4.
    Khain T, Scheibner C, Fruchart M, Vitelli V. 2022. J. Fluid Mech. 934:A23
  5. 5.
    Avron JE. 1998. J. Stat. Phys. 92:54357
  6. 6.
    Han M, Fruchart M, Scheibner C, Vaikuntanathan S, de Pablo JJ, Vitelli V. 2021. Nat. Phys. 17:126069
  7. 7.
    Condiff DW, Dahler JS. 1964. Phys. Fluids 7:84254
  8. 8.
    Goldhirsch I. 2010. Granular Matter 12:23952
  9. 9.
    Eringen A. 2012. Microcontinuum Field Theories: I. Foundations and Solids New York: Springer
  10. 10.
    de Groot SR, Mazur P. 1954. Phys. Rev. 94:21824
  11. 11.
    de Groot SR, Mazur P. 1962. Non-Equilibrium Thermodynamics Amsterdam: Dover
  12. 12.
    Rao P, Bradlyn B. 2021. arXiv:2112.04545
  13. 13.
    Cook CQ, Lucas A. 2021. Phys. Rev. Lett. 127:176603
  14. 14.
    Rao P, Bradlyn B. 2020. Phys. Rev. X 10:021005
  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. 379:23146
  17. 17.
    Irving JH, Kirkwood JG. 1950. J. Chem. Phys. 18:81729
  18. 18.
    Souslov A, Gromov A, Vitelli V. 2020. Phys. Rev. E 101:052606
  19. 19.
    Hess S. 1986. J. Non Equilibrium Thermodyn. 11:3–417594
  20. 20.
    Jarkova E, Pleiner H, Müller HW, Fink A, Brand H. 2001. Eur. Phys. J. E 5:58388
  21. 21.
    Varnavides G, Jermyn AS, Anikeeva P, Felser C, Narang P. 2020. Nat. Commun. 11:4710
  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
  24. 24.
    Zhao Z, Wang B, Komura S, Yang M, Ye F, Seto R. 2021. Phys. Rev. Res. 3:043229
  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
  27. 27.
    Gromov A, Son DT. 2017. Phys. Rev. X 7:041032
  28. 28.
    Salbreux G, Jülicher F, Prost J, Callan-Jones A. 2022. Phys. Rev. Res. 4:033158
  29. 29.
    Robredo I, Rao P, de Juan F, Bergara A, Mañes JL et al. 2021. Phys. Rev. Res. 3:1032068
  30. 30.
    Banerjee D, Souslov A, Abanov AG, Vitelli V. 2017. Nat. Commun. 8:1573
  31. 31.
    Ganeshan S, Abanov AG. 2017. Phys. Rev. Fluids 2:094101
  32. 32.
    Guyon E, Hulin J, Petit L, Mitescu C. 2015. Physical Hydrodynamics Oxford, UK: Oxford Univ. Press
  33. 33.
    Beenakker JJM, McCourt FR. 1970. Annu. Rev. Phys. Chem. 21:4772
  34. 34.
    McCourt F. 1990. Nonequilibrium Phenomena in Polyatomic Gases New York/Oxford: Clarendon/Oxford Univ. Press
  35. 35.
    Korving J, Hulsman H, Knaap H, Beenakker J. 1966. Phys. Lett. 21:57
  36. 36.
    Korving J, Hulsman H, Scoles G, Knaap H, Beenakker J. 1967. Physica 36:17797
  37. 37.
    Hulsman H, Knaap H. 1970. Physica 50:56572
  38. 38.
    Hulsman H, Van Waasdijk E, Burgmans A, Knaap H, Beenakker J. 1970. Physica 50:5376
  39. 39.
    Banerjee D, Souslov A, Vitelli V. 2022. Phys. Rev. Fluids 7:043301
  40. 40.
    Souslov A, Dasbiswas K, Fruchart M, Vaikuntanathan S, Vitelli V. 2019. Phys. Rev. Lett. 122:128001
  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
  43. 43.
    Delacrétaz LV, Gromov A. 2017. Phys. Rev. Lett. 119:226602
  44. 44.
    Hosaka Y, Komura S, Andelman D. 2021. Phys. Rev. E 104:064613
  45. 45.
    Tropea C, Yarin AL, Foss JF. 2007. Springer Handbook of Experimental Fluid Mechanics Berlin/Heidelberg: Springer
  46. 46.
    Ariman T, Turk M, Sylvester N. 1973. Int. J. Eng. Sci. 11:90530
  47. 47.
    Hess S. 2019. Atti Della Accademia Peloritana dei Pericolanti: Classe di Scienze Fisiche, Matematiche e Naturali 97:Suppl. 1A9
  48. 48.
    Kiselev EI, Schmalian J. 2019. Phys. Rev. B 99:035430
  49. 49.
    Lucas A, Fong KC. 2018. J. Phys. Condens. Matter 30:053001
  50. 50.
    Tsai JC, Ye F, Rodriguez J, Gollub JP, Lubensky T. 2005. Phys. Rev. Lett. 94:214301
  51. 51.
    van Zuiden BC, Paulose J, Irvine WTM, Bartolo D, Vitelli V. 2016. PNAS 113:1291924
  52. 52.
    Soni V, Bililign ES, Magkiriadou S, Sacanna S, Bartolo D et al. 2019. Nat. Phys. 15:118894
  53. 53.
    Abanov A, Can T, Ganeshan S. 2018. SciPost Phys. 5:010
  54. 54.
    Abanov AG, Can T, Ganeshan S, Monteiro GM. 2020. Phys. Rev. Fluids 5:104802
  55. 55.
    Bogatskiy A, Wiegmann P. 2019. Phys. Rev. Lett. 122:214505
  56. 56.
    Tauber C, Delplace P, Venaille A. 2019. J. Fluid Mech. 868:R2
  57. 57.
    Baardink G, Cassella G, Neville L, Milewski PA, Souslov A. 2021. Phys. Rev. E 104:014603
  58. 58.
    Shankar S, Souslov A, Bowick MJ, Marchetti MC, Vitelli V. 2022. Nat. Rev. Phys. 4:38098
  59. 59.
    Fruchart M, Carpentier D. 2013. C. R. Phys. 14:779815
  60. 60.
    Kogan E. 2016. Phys. Rev. E 94:043111
  61. 61.
    Lapa MF, Hughes TL. 2014. Phys. Rev. E 89:043019
  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
  64. 64.
    Happel J, Brenner H. 2012. Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media Dordrecht, Neth.: Springer
  65. 65.
    Masoud H, Stone HA. 2019. J. Fluid Mech. 879:P1
  66. 66.
    Hosaka Y, Komura S, Andelman D. 2021. Phys. Rev. E 103:042610
  67. 67.
    Charru F. 2011. Hydrodynamic Instabilities Cambridge, UK: Cambridge Univ. Press. Transl. P de Forcrand–Millard
  68. 68.
    Faganello M, Califano F. 2017. J. Plasma Phys. 83:6535830601
  69. 69.
    Nagano H. 1979. Planet. Space Sci. 27:88184
  70. 70.
    Wolff RS, Goldstein BE, Yeates CM. 1980. J. Geophys. Res. 85:7697707
  71. 71.
    Lucas A, Surówka P. 2014. Phys. Rev. E 90:063005
  72. 72.
    Kirkinis E, Andreev AV. 2019. J. Fluid Mech. 878:16989
  73. 73.
    Bao G, Jian Y. 2021. Phys. Rev. E 103:013104
  74. 74.
    Chattopadhyay S. 2021. Phys. Fluids 33:062106
  75. 75.
    Samanta A. 2022. J. Fluid Mech. 938:A9
  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:.
  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.
  78. 78.
    Roberts KV, Taylor JB. 1962. Phys. Rev. Lett. 8:19798
  79. 79.
    Pottier N. 2010. Nonequilibrium Statistical Physics: Linear Irreversible Processes Oxford, UK: Oxford Univ. Press
  80. 80.
    Callen HB. 1985. Thermodynamics and an Introduction to Thermostatistics New York: John Wiley & Sons
  81. 81.
    Epstein JM, Mandadapu KK. 2020. Phys. Rev. E 101:052614
  82. 82.
    Hargus C, Klymko K, Epstein JM, Mandadapu KK. 2020. J. Chem. Phys. 152:201102
  83. 83.
    Bradlyn B, Goldstein M, Read N. 2012. Phys. Rev. B 86:245309
  84. 84.
    Read N, Rezayi EH. 2011. Phys. Rev. B 84:085316
  85. 85.
    Offertaler B, Bradlyn B. 2019. Phys. Rev. B 99:035427
  86. 86.
    Krommes JA, Hu G. 1993. Phys. Fluids B: Plasma Phys. 5:390841
  87. 87.
    Coleman BD, Truesdell C. 1960. J. Chem. Phys. 33:2831
  88. 88.
    Berdyugin AI, Xu SG, Pellegrino FMD, Kumar RK, Principi A et al. 2019. Science 364:643616265
  89. 89.
    ten Bosch B, Beenakker J, Kuščer I. 1984. Phys. A Stat. Mech. Appl. 123:44362
  90. 90.
    Sharipov F. 1994. Phys. A Stat. Mech. Appl. 203:43756
  91. 91.
    Sharipov F. 1994. Phys. A Stat. Mech. Appl. 203:45785
  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 58:44654
  94. 94.
    Strohm C, Rikken GLJA, Wyder P. 2005. Phys. Rev. Lett. 95:155901
  95. 95.
    Koch DL, Brady JF. 1987. Phys. Fluids 30:64250
  96. 96.
    Auriault JL, Moyne C, Amaral Souto HP. 2010. Transport Porous Media 85:77183
  97. 97.
    Hargus C, Epstein JM, Mandadapu KK. 2021. Phys. Rev. Lett. 127:178001
  98. 98.
    Vega Reyes F, López-Castaño MA, Rodríguez-Rivas A. 2022. Commun. Phys. 5:256
  99. 99.
    Rikken GLJA, van Tiggelen BA. 1996. Nature 381:5455
  100. 100.
    van Tiggelen BA. 1995. Phys. Rev. Lett. 75:42224
  101. 101.
    Quan L, Yves S, Peng Y, Esfahlani H, Alù A 2021. Nat. Commun. 12:2615
  102. 102.
    Chaikin PM, Lubensky TC. 1995. Principles of Condensed Matter Physics Cambridge, UK: Cambridge Univ. Press
  103. 103.
    Anderson PW 1984. Basic Notions of Condensed Matter Physics Boca Raton, FL: CRC
  104. 104.
    Kole SJ, Alexander GP, Ramaswamy S, Maitra A. 2021. Phys. Rev. Lett. 126:248001
  105. 105.
    Maitra A, Lenz M, Voituriez R. 2020. Phys. Rev. Lett. 125:238005
  106. 106.
    Korving J, Hulsman H, Hermans L, de Groot J, Knaap H, Beenakker J. 1966. J. Mol. Spectrosc. 20:29495
  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..
  108. 108.
    Braginskii SI. 1958. Sov. Phys. J. Exp. Theor. Phys. 6:35869
  109. 109.
    Braginskii SI. 1965. Rev. Plasma Phys. 1:205311
  110. 110.
    Ramos JJ. 2005. Phys. Plasmas 12:112301
  111. 111.
    Kaufman AN. 1960. Phys. Fluids 3:61016
  112. 112.
    Steinhauer LC. 2011. Phys. Plasmas 18:070501
  113. 113.
    Stasiewicz K. 1993. Space Sci. Rev. 65:22152
  114. 114.
    Nayyar NK, Trehan SK. 1970. J. Plasma Phys. 4:56371
  115. 115.
    Steinhauer LC, Ishida A. 1990. Phys. Fluids B: Plasma Phys. 2:242230
  116. 116.
    Terada N, Machida S, Shinagawa H. 2002. J. Geophys. Res. Space Phys. 107:SMP 30
  117. 117.
    Ishizawa A, Horiuchi R. 2005. Phys. Rev. Lett. 95:045003
  118. 118.
    Ferraro NM, Jardin SC. 2006. Phys. Plasmas 13:092101
  119. 119.
    Bae C, Stacey W, Solomon W. 2013. Nuclear Fusion 53:043011
  120. 120.
    Stacey WM, Sigmar DJ. 1985. Phys. Fluids 28:28007
  121. 121.
    Stacey WM, Mandrekas J. 2002. Phys. Plasmas 9:162228
  122. 122.
    Stacey WM, Johnson RW, Mandrekas J. 2006. Phys. Plasmas 13:062508
  123. 123.
    Winske D. 1996. Phys. Plasmas 3:396674
  124. 124.
    Zhu P, Schnack DD, Ebrahimi F, Zweibel EG, Suzuki M et al. 2008. Phys. Rev. Lett. 101:085005
  125. 125.
    Yajima N. 1966. Prog. Theor. Phys. 36:116
  126. 126.
    Nakagawa Y. 1956. J. Phys. Earth 4:10511
  127. 127.
    Sulpizio JA, Ella L, Rozen A, Birkbeck J, Perello DJ et al. 2019. Nature 576:7579
  128. 128.
    Ku MJH, Zhou TX, Li Q, Shin YJ, Shi JK et al. 2020. Nature 583:53741
  129. 129.
    Bandurin DA, Torre I, Kumar RK, Ben Shalom M, Tomadin A et al. 2016. Science 351:105558
  130. 130.
    Moll PJW, Kushwaha P, Nandi N, Schmidt B, Mackenzie AP. 2016. Science 351:106164
  131. 131.
    Crossno J, Shi JK, Wang K, Liu X, Harzheim A et al. 2016. Science 351:105861
  132. 132.
    de Jong MJM, Molenkamp LW. 1995. Phys. Rev. B 51:13389402
  133. 133.
    Zaanen J. 2016. Science 351:102627
  134. 134.
    Vollhardt D, Wolfle P. 2013. The Superfluid Phases of Helium 3 New York: Dover
  135. 135.
    Volovik GE. 2020. J. Low Temp. Phys. 202:1128
  136. 136.
    Furusawa T, Fujii K, Nishida Y. 2021. Phys. Rev. B 103:064506
  137. 137.
    Fujii K, Nishida Y. 2018. Ann. Phys. 395:17082
  138. 138.
    Read N. 2009. Phys. Rev. B 79:045308
  139. 139.
    Avron JE, Seiler R, Zograf PG. 1995. Phys. Rev. Lett. 75:697700
  140. 140.
    Haldane FDM. 2009. arXiv:0906.1854
  141. 141.
    Haldane FDM. 2011. Phys. Rev. Lett. 107:116801
  142. 142.
    Park Y, Haldane FDM. 2014. Phys. Rev. B 90:045123
  143. 143.
    Hoyos C, Son DT. 2012. Phys. Rev. Lett. 108:066805
  144. 144.
    Fürthauer S, Strempel M, Grill SW, Jülicher F. 2012. Eur. Phys. J. E 35:89
  145. 145.
    Markovich T, Tjhung E, Cates ME. 2019. New J. Phys. 21:112001
  146. 146.
    Yeo K, Lushi E, Vlahovska PM. 2015. Phys. Rev. Lett. 114:188301
  147. 147.
    Grzybowski BA, Stone HA, Whitesides GM. 2000. Nature 405:103336
  148. 148.
    Yan J, Bae SC, Granick S. 2015. Soft Matter 11:14753
  149. 149.
    Bililign ES, Balboa Usabiaga F, Ganan YA, Poncet A, Soni V et al. 2021. Nat. Phys. 18:221218
  150. 150.
    Denk J, Huber L, Reithmann E, Frey E. 2016. Phys. Rev. Lett. 116:178301
  151. 151.
    Liebchen B, Levis D. 2017. Phys. Rev. Lett. 119:058002
  152. 152.
    López-Castaño MA, Seco AM, Seco AM, Álvaro Rodríguez-Rivas, Reyes FV. 2022. Phys. Rev. Res. 4:033230
  153. 153.
    Scholz C, Engel M, Pöschel T. 2018. Nat. Commun. 9:931
  154. 154.
    Yang X, Ren C, Cheng K, Zhang HP. 2020. Phys. Rev. E 101:022603
  155. 155.
    Riedel IH, Kruse K, Howard J. 2005. Science 309:3003
  156. 156.
    Petroff AP, Wu XL, Libchaber A. 2015. Phys. Rev. Lett. 114:158102
  157. 157.
    Tan TH, Mietke A, Li J, Chen Y, Higinbotham H et al. 2022. Nature 607:28793
  158. 158.
    Markovich T, Lubensky TC. 2021. Phys. Rev. Lett. 127:048001
  159. 159.
    Zhao Z, Yang M, Komura S, Seto R. 2022. Front. Phys. 10:951465
  160. 160.
    Garzó V. 2017. Phys. Rev. E 95:062906
  161. 161.
    Wiegmann P, Abanov AG. 2014. Phys. Rev. Lett. 113:034501
  162. 162.
    Yu X, Bradley AS. 2017. Phys. Rev. Lett. 119:185301
  163. 163.
    Moroz S, Hoyos C, Benzoni C, Son DT. 2018. SciPost Phys. 5:039
  164. 164.
    Reichhardt CJO, Reichhardt C. 2022. EuroPhys. Lett. 137:66004
  165. 165.
    Goldston RJ. 2020. Introduction to Plasma Physics Boca Raton, FL: CRC
  166. 166.
    Hazeltine R. 2018. The Framework of Plasma Physics Boca Raton, FL: CRC
  167. 167.
    Kagan Y, Maksimov L. 1962. J. Exp. Theor. Phys. Lett. 14:60410
  168. 168.
    Kagan Y, Afanasév AM. 1962. J. Exp. Theor. Phys. Lett. 14:1096101
  169. 169.
    Kagan Y, Maksimov L. 1967. J. Exp. Theor. Phys. Lett. 24:1893908
  170. 170.
    Moraal H, McCourt F, Knaap HFP 1969. Physica 45:45568
  171. 171.
    McCourt F, Knaap H, Moraal H. 1969. Physica 43:485512
  172. 172.
    Knaap H, Beenakker J. 1967. Physica 33:64370
  173. 173.
    McCourt FR, Snider RF. 1967. J. Chem. Phys. 47:411728
  174. 174.
    Levi A, McCourt F. 1968. Physica 38:41537
  175. 175.
    Waldmann L. 1958. Z. Naturforsch. A 13:60920
  176. 176.
    Hess S. 2003. Z. Naturforsch. A 58:26974
  177. 177.
    Harris S. 2004. An Introduction to the Theory of the Boltzmann Equation New York: Dover
  178. 178.
    Dorfman J, van Beijeren H, Kirkpatrick T. 2021. Contemporary Kinetic Theory of Matter Cambridge, UK: Cambridge Univ. Press
  179. 179.
    Morrison PJ. 1998. Rev. Mod. Phys. 70:467521
  180. 180.
    Salmon R. 1988. Ann. Rev. Fluid Mech. 20:22556
  181. 181.
    Morrison PJ, Caldas IL, Tasso H. 1984. Z. Naturforsch. A 39:102327
  182. 182.
    Lingam M, Morrison P. 2014. Phys. Lett. A 378:352632
  183. 183.
    Morrison PJ. 2005. Phys. Plasmas 12:058102
  184. 184.
    Morrison PJ, Lingam M, Acevedo R. 2014. Phys. Plasmas 21:082102
  185. 185.
    Lingam M, Morrison PJ, Wurm A. 2020. J. Plasma Phys. 86:835860501
  186. 186.
    Lingam M. 2015. Phys. Lett. A 379:142530
  187. 187.
    Monteiro GM, Abanov AG, Ganeshan S. 2021. arXiv:2105.01655
  188. 188.
    Wen XG, Zee A. 1992. Phys. Rev. Lett. 69:95356
  189. 189.
    Abanov AG, Gromov A. 2014. Phys. Rev. B 90:014435
  190. 190.
    Hughes TL, Leigh RG, Parrikar O. 2013. Phys. Rev. D 88:025040
  191. 191.
    Gromov A, Jensen K, Abanov AG. 2016. Phys. Rev. Lett. 116:126802
  192. 192.
    Geracie M, Son DT. 2014. J. High Energy Phys. 2014:4
  193. 193.
    Haehl FM, Loganayagam R, Rangamani M. 2015. J. High Energy Phys. 2015:60
  194. 194.
    Scheibner C, Souslov A, Banerjee D, Surówka P, Irvine WTM, Vitelli V. 2020. Nat. Phys. 16:47580
  195. 195.
    Scheibner C, Irvine WTM, Vitelli V. 2020. Phys. Rev. Lett. 125:118001
  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
  198. 198.
    Nelson D, Halperin B. 1979. Phys. Rev. B 19:245784
  199. 199.
    Ashida Y, Gong Z, Ueda M. 2020. Adv. Phys. 69:249435
  200. 200.
    Zubov LM. 1997. Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies, Vol. 47: Lect. Notes Phys. Monogr. Berlin/Heidelberg: Springer
  201. 201.
    Marsden JE. 1994. Mathematical Foundations of Elasticity New York: Dover
  202. 202.
    Truesdell CA. 1963. J. Res. Natl. Bureau Standards Sect. B Math. Math. Phys. 67B:285
  203. 203.
    Nassar H, Yousefzadeh B, Fleury R, Ruzzene M, Alù A et al. 2020. Nat. Rev. Mater. 5:66785
  204. 204.
    Rice JR. 1976. Theoretical and Applied Mechanics (Proceedings of the 14th International Congress on Theoretical and Applied Mechanics, Vol. 1 WT Koiter 20720. 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
  206. 206.
    Örs H, Prévost JH. 1995. Acta Mech. 111:18192
  207. 207.
    Prévost JH. 1982. Int. J. Numer. Anal. Methods Geomechan. 6:32338
  208. 208.
    Piccolroaz A, Bigoni D, Willis JR. 2006. J. Mech. Phys. Solids 54:2391417
  209. 209.
    Bigoni D. 1995. Int. J. Solids Struct. 32:316789
  210. 210.
    Bordiga G, Piccolroaz A, Bigoni D. 2022. J. Mech. Phys. Solids 158:104665
  211. 211.
    Carol I, Willam K 1996. Int. J. Solids Struct. 33:293957
  212. 212.
    Carol I, Jirásek M, Bažant Z. 2001. Int. J. Solids Struct. 38:292131
  213. 213.
    Challamel N, Halm D, Dragon A. 2006. C. R. Mécan. 334:41418
  214. 214.
    Lubensky TC. 2005. Pramana J. Phys. 64:72742
  215. 215.
    Warner M, Terentjev EM. 2003. Liquid Crystal Elastomers, Vol. 120 Int. Ser. Monogr. Phys. Oxford, UK: Oxford Univ. Press
  216. 216.
    Storm C, Pastore JJ, MacKintosh FC, Lubensky TC, Janmey PA. 2005. Nature 435:19194
  217. 217.
    Cosserat E, Cosserat F. 1909. Théorie des Corps Déformables Paris: A. Hermann et Fils
  218. 218.
    Lakes RS, Benedict RL. 1982. Int. J. Eng. Sci. 20:116167
  219. 219.
    Chen Y, Li X, Scheibner C, Vitelli V, Huang G. 2021. Nat. Commun. 12:5935
  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
  222. 222.
    Briand G, Schindler M, Dauchot O. 2018. Phys. Rev. Lett. 120:208001
  223. 223.
    Desreumaux N, Florent N, Lauga E, Bartolo D. 2012. Eur. Phys. J. E 35:68
  224. 224.
    Lavergne FA, Wendehenne H, Bäuerle T, Bechinger C. 2019. Science 364:7074
  225. 225.
    Baconnier P, Shohat D, Hernández López C, Coulais C, Démery V et al. 2022. Nat. Phys. 18:123439
  226. 226.
    Guazzelli É, Hinch J. 2011. Annu. Rev. Fluid Mech. 43:97116
  227. 227.
    Beatus T, Bar-Ziv R, Tlusty T. 2007. Phys. Rev. Lett. 99:124502
  228. 228.
    Beatus T, Tlusty T, Bar-Ziv R. 2006. Nat. Phys. 2:74348
  229. 229.
    Baek Y, Solon AP, Xu X, Nikola N, Kafri Y. 2018. Phys. Rev. Lett. 120:058002
  230. 230.
    Uchida N, Golestanian R. 2010. Phys. Rev. Lett. 104:178103
  231. 231.
    Soto R, Golestanian R. 2014. Phys. Rev. Lett. 112:068301
  232. 232.
    Saha S, Ramaswamy S, Golestanian R. 2019. New J. Phys. 21:063006
  233. 233.
    Meredith CH, Moerman PG, Groenewold J, Chiu YJ, Kegel WK et al. 2020. Nat. Chem. 12:113642
  234. 234.
    Ivlev AV, Bartnick J, Heinen M, Du CR, Nosenko V, Löwen H. 2015. Phys. Rev. X 5:011035
  235. 235.
    Peterson CW, Parker J, Rice SA, Scherer NF. 2019. Nano Lett. 19:897903
  236. 236.
    Yifat Y, Coursault D, Peterson CW, Parker J, Bao Y et al. 2018. Light Sci. Appl. 7:105
  237. 237.
    Han F, Parker JA, Yifat Y, Peterson C, Gray SK et al. 2018. Nat. Commun. 9:4897
  238. 238.
    Poncet A, Bartolo D. 2022. Phys. Rev. Lett. 128:048002
  239. 239.
    Nash LM, Kleckner D, Read A, Vitelli V, Turner AM, Irvine WTM. 2015. PNAS 112:14495500
  240. 240.
    Bauer A, Pfleiderer C. 2016. Topological Structures in Ferroic Materials, Vol. 228 Springer Ser. Mater. Sci. J Seidel 128. Cham: Springer Int.
  241. 241.
    Koschmieder E, Pallas S. 1974. Int. J. Heat Mass Transf. 17:9911002
  242. 242.
    Born M, Huang K. 1954. Dynamical Theory of Crystal Lattices Oxford, UK: Clarendon:
  243. 243.
    Lutsko JF. 1989. J. Appl. Phys. 65:299197
  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 287307. Berlin/Heidelberg: Springer
  245. 245.
    Fruchart M, Vitelli V. 2020. Phys. Rev. Lett. 124:248001
  246. 246.
    Chen Z. 2022. arXiv:2204.06587
  247. 247.
    Wang P, Lu L, Bertoldi K. 2015. Phys. Rev. Lett. 115:104302
  248. 248.
    Zhao Y, Zhou X, Huang G. 2020. J. Mech. Phys. Solids 143:104065
  249. 249.
    Carta G, Brun M, Movchan A, Movchan N, Jones I. 2014. Int. J. Solids Struct. 51:221325
  250. 250.
    Hassanpour S. 2014. Dynamics of gyroelastic continua PhD Thesis Univ. Waterloo
  251. 251.
    Carta G, Jones IS, Movchan NV, Movchan AB, Nieves MJ. 2017. Sci. Rep. 7:26
  252. 252.
    Mitchell NP, Nash LM, Irvine WTM. 2018. Phys. Rev. B 98:174301
  253. 253.
    Mitchell NP, Nash LM, Irvine WTM. 2018. Phys. Rev. B 97:100302
  254. 254.
    Mitchell NP, Nash LM, Hexner D, Turner AM, Irvine WTM. 2018. Nat. Phys. 14:38085
  255. 255.
    Brun M, Jones IS, Movchan AB. 2012. Proc. R. Soc. A Math. Phys. Eng. Sci. 468:302746
  256. 256.
    Benzoni C, Jeevanesan B, Moroz S. 2021. Phys. Rev. B 104:024435
  257. 257.
    Huang P, Schönenberger T, Cantoni M, Heinen L, Magrez A et al. 2020. Nat. Nanotechnol. 15:76167
  258. 258.
    Ochoa H, Kim SK, Tchernyshyov O, Tserkovnyak Y. 2017. Phys. Rev. B 96:020410
  259. 259.
    Mühlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A et al. 2009. Science 323:91519
  260. 260.
    Yu XZ, Onose Y, Kanazawa N, Park JH, Han JH et al. 2010. Nature 465:9014
  261. 261.
    Brearton R, Turnbull LA, Verezhak JAT, Balakrishnan G, Hatton PD et al. 2021. Nat. Commun. 12:2723
  262. 262.
    Sonin EB. 1987. Rev. Mod. Phys. 59:87155
  263. 263.
    Gifford SA, Baym G. 2008. Phys. Rev. A 78:043607
  264. 264.
    Nguyen DX, Gromov A, Moroz S. 2020. SciPost Phys. 9:76
  265. 265.
    Moroz S, Hoyos C, Benzoni C, Son DT. 2018. SciPost Phys. 5:39
  266. 266.
    Fetter AL. 2009. Rev. Mod. Phys. 81:64791
  267. 267.
    Blatter G, Feigel'man MV, Geshkenbein VB, Larkin AI, Vinokur VM 1994. Rev. Mod. Phys. 66:1125388
  268. 268.
    Tkachenko VK. 1969. J. Exp. Theor. Phys. 29:945
  269. 269.
    Tkachenko V. 1966. Sov. Phys. J. Exp. Theor. Phys. 22:128286
  270. 270.
    Tkachenko V. 1966. Sov. Phys. J. Exp. Theor. Phys. 23:104956
  271. 271.
    Petroff AP, Wu XL, Libchaber A. 2015. Phys. Rev. Lett. 114:158102
  272. 272.
    Drescher K, Leptos KC, Tuval I, Ishikawa T, Pedley TJ, Goldstein RE. 2009. Phys. Rev. Lett. 102:168101
  273. 273.
    Goldman A, Cox R, Brenner H. 1967. Chem. Eng. Sci. 22:63751
  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
  275. 275.
    Jäger S, Klapp SHL. 2011. Soft Matter 7:660616
  276. 276.
    Timoshenko S. 1940. Strength of Materials New York: D. Van Nostrand Co. , 2nd ed..
  277. 277.
    Cheng W, Hu G. 2021. Sci. China Phys., Mech. Astron. 64:11114612
  278. 278.
    Salbreux G, Jülicher F. 2017. Phys. Rev. E 96:032404
  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. 182:5984
  281. 281.
    Cross MC, Meiron D, Tu Y. 1994. Chaos Interdiscip. J. Nonlinear Sci. 4:60719
  282. 282.
    Cross M, Greenside H. 2009. Pattern Formation and Dynamics in Nonequilibrium Systems Cambridge, UK: Cambridge Univ. Press
  283. 283.
    Pismen L. 2010. Patterns and Interfaces in Dissipative Dynamics Berlin/Heidelberg: Springer
  284. 284.
    Busse FH, Heikes KE. 1980. Science 208:17375
  285. 285.
    Bodenschatz E, Pesch W, Ahlers G. 2000. Annu. Rev. Fluid Mech. 32:70978
  286. 286.
    Ahlers G. 2006. Springer Tracts Mod. Phys. 207:6794
  287. 287.
    Guarino A, Vidal V. 2004. Phys. Rev. E 69:066311
  288. 288.
    Fruchart M, Hanai R, Littlewood PB, Vitelli V. 2021. Nature 592:36369
  289. 289.
    Nardini C, Fodor E, Tjhung E, van Wijland F, Tailleur J, Cates ME. 2017. Phys. Rev. X 7:021007
  290. 290.
    Wittkowski R, Tiribocchi A, Stenhammar J, Allen RJ, Marenduzzo D, Cates ME. 2014. Nat. Commun. 5:4351
  291. 291.
    Kozyreff G, Tlidi M. 2007. Chaos: Interdiscip. J. Nonlinear Sci. 17:037103
  292. 292.
    Coullet P, Lega J, Houchmanzadeh B, Lajzerowicz J. 1990. Phys. Rev. Lett. 65:135255
  293. 293.
    Coullet P, Goldstein RE, Gunaratne GH. 1989. Phys. Rev. Lett. 63:195457
  294. 294.
    Pomeau Y, Zaleski S, Manneville P. 1983. Phys. Rev. A 27:271026
  295. 295.
    Bodenschatz E, Cannell DS, de Bruyn JR, Ecke R, Hu YC et al. 1992. Phys. D: Nonlinear Phenom. 61:7793
  296. 296.
    Clerc MG, Petrossian A, Residori S. 2005. Phys. Rev. E 71:015205
  297. 297.
    Siggia ED, Zippelius A. 1981. Phys. Rev. A 24:103649
  298. 298.
    Colinet P, Nepomnyashchy AA, Legros JC. 2002. Europhys. Lett. 57:48086
  299. 299.
    Tsimring LS. 1996. Phys. D Nonlinear Phenom. 89:36880
  300. 300.
    Houghton SM, Knobloch E. 2011. Phys. Rev. E 84:016204
  301. 301.
    You Z, Baskaran A, Marchetti MC. 2020. PNAS 117:1976772
  302. 302.
    Saha S, Agudo-Canalejo J, Golestanian R. 2020. Phys. Rev. X 10:041009
  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
  305. 305.
    Coullet P, Emilsson K. 1992. Phys. D Nonlinear Phenom. 61:11931
  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
  309. 309.
    Echebarria B, Pérez-García C. 1998. Europhys. Lett. 43:3540
  310. 310.
    Echebarria B, Riecke H. 2000. Phys. D Nonlinear Phenom. 139:97108
  311. 311.
    Echebarria B, Riecke H. 2000. Phys. D Nonlinear Phenom. 143:187204
  312. 312.
    Marder M. 2010. Condensed Matter Physics Hoboken, NJ: John Wiley & Sons
  313. 313.
    Nelson DR. 2002. Defects and Geometry in Condensed Matter Physics Cambridge/New York: Cambridge Univ. Press
  314. 314.
    Weertman J, Weertman JR. 1964. Elementary Dislocation Theory New York: Macmillan
  315. 315.
    Ishimoto K, Moreau C, Yasuda K. 2022. Phys. Rev. E 105:064603
  316. 316.
    Zhou D, Zhang J. 2020. Phys. Rev. Res. 2:023173
  317. 317.
    Strogatz S. 2019. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering Boca Raton, FL: CRC
  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/
  319. 319.
    Yasuda K, Hosaka Y, Sou I, Komura S. 2021. J. Phys. Soc. Jpn. 90:075001
  320. 320.
    Yasuda K, Kobayashi A, Lin LS, Hosaka Y, Sou I, Komura S. 2022. J. Phys. Soc. Jpn. 91:015001
  321. 321.
    Yasuda K, Ishimoto K, Kobayashi A, Lin LS, Sou I et al. 2022. J. Chem. Phys. 157:095101
  322. 322.
    Oswald P. 2014. Rheophysics: The Deformation and Flow of Matter Cambridge, UK: Cambridge Univ. Press
  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)
  324. 324.
    Banerjee D, Vitelli V, Jülicher F, Surówka P. 2021. Phys. Rev. Lett. 126:138001
  325. 325.
    Muhlestein MB, Sieck CF, Alù A, Haberman MR. 2016. Proc. R. Soc. A Math. Phys. Eng. Sci. 472:20160604
  326. 326.
    Day WA. 1971. Arch. Ration. Mech. Anal. 40:15559
  327. 327.
    Srivastava A. 2015. Proc. R. Soc. A Math. Phys. Eng. Sci. 471:20150256
  328. 328.
    Lier R, Armas J, Bo S, Duclut C, Jülicher F, Surówka P. 2022. Phys. Rev. E 105:054607
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