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Hydrodynamic theory of dry active matter

Chen Lei-Ming

Hydrodynamic theory of dry active matter

Chen Lei-Ming
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  • In this paper we shortly review theoretical progress in the field of active matter, focusing on the continuum theory of dry systems, in which momentum of active particles is not conserved due to the interaction between the particles and a substrate or medium. In particular, we review the phenomenological way of deriving hydrodynamic equations for both polar and apolar systems, and the predictions of these theories such as long-ranged orientational order in two-dimensional polar systems and giant number fluctuations. The comparisons among theoretical predictions, numerical results, and experimental evidence are also summarized.
      Corresponding author: Chen Lei-Ming, leiming@cumt.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11474354).
    [1]

    Schweitzer F 2003 Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences (Berlin: Springer)

    [2]

    Surrey T, Ndlec F, Leibler S, Karsenti E 2001 Science 292 1167

    [3]

    Wolgemuth C, Hoiczyk E, Kaiser D, Oster G 2002 Curr. Biol. 12 369

    [4]

    Toner J, Tu Y 1998 Phys. Rev. E 58 4828

    [5]

    Ramaswamy S, Simha R A, Toner J 2003 Europhys. Lett. 62 196

    [6]

    Yamada D, Hondou T, Sano M 2003 Phys. Rev. E 67 040301

    [7]

    Aranson I S, Tsimring L S 2006 Phys. Rev. E 74 031915

    [8]

    Narayan V, Ramaswamy S, Menon N 2007 Science 317 105

    [9]

    Kudrolli A, Lumay G, Volfson D, Tsimring L S 2008 Phys. Rev. Lett. 100 058001

    [10]

    Deseigne J, Dauchot O, Chate H 2010 Phys. Rev. Lett. 105 098001

    [11]

    Drescher K, Dunkel J, Cisneros L H, Ganguly S, Goldstein R E 2011 Proc. Natl. Acad. Sci. USA 108 10940

    [12]

    Ballerini M, Cabibbo N, Candelier R 2008 Proc. Natl. Acad. Sci. USA 105 1232

    [13]

    Ginelli F, Chate H 2010 Phys. Rev. Lett. 105 168103

    [14]

    Bricard A, Caussin J B, Desreumaux N, Dauchot O, Bartolo D 2013 Nature 503 95

    [15]

    Vicsek T, Czirok A, Ben-Jacob E, Cohen I, Shochet O 1995 Phys. Rev. Lett. 75 1226

    [16]

    Gruler H, Dewald U, Eberhardt M 1999 Eur. Phys. J. B 11 187

    [17]

    Peruani F, Deutsch A, Bar M 2006 Phys. Rev. E 74 030904

    [18]

    Baskaran A, Marchetti M C 2008 Phys. Rev. E 77 011920

    [19]

    Yang Y, Marceau V, Gompper G 2010 Phys. Rev. E 82 031904

    [20]

    Toner J, Tu Y 1995 Phys. Rev. Lett. 75 4326

    [21]

    Toner J, Tu Y, S Ramaswamy 2005 Ann. Phys. 318 170

    [22]

    Mermin N D, Wagner H 1966 Phys. Rev. Lett. 17 1133

    [23]

    Bertin E, Droz M, Gregoire G 2006 Phys. Rev. E 74 022101

    [24]

    Bertin E, Droz M, Gregoire G 2009 J. Phys. A 42 445001.

    [25]

    Ihle T 2011 Phys. Rev. E 83 030901

    [26]

    Mishra S, Baskaran A, Marchetti M C 2010 Phys. Rev. E 81 061916

    [27]

    Gregoire G, Chate H 2004 Phys. Rev. Lett. 92 025702

    [28]

    Chate H, Ginelli F, Gregoire G, Raynaud F 2008 Phys. Rev. E 77 046113

    [29]

    Chen L, Toner J, Lee C F 2015 New J. Phys. 17 042002

    [30]

    Chate H, Ginelli F, Gregoire G, Peruani F, Raynaud F 2008 Eur. Phys. J. B 64 451

    [31]

    Zhang H P, Beer A, Florin E L, Swinney H L 2010 Proc. Natl. Acad. Sci. USA 107 13626

    [32]

    Chate H, Ginelli F, Montagne R 2006 Phys. Rev. Lett. 96 180602

    [33]

    Tailleur J, Cates M E 2008 Phys. Rev. Lett. 100 218103

    [34]

    Cates M E 2012 Rep. Prog. Phys. 75 042601

    [35]

    Fily Y, Baskaran A, Marchetti M C 2012 Soft Matter 8 3002

    [36]

    Tu Y, Ulm M, Toner J 1998 Phys. Rev. Lett. 80 4819

    [37]

    Toner J 2012 Phys. Rev. Lett. 108 088102

    [38]

    Chen L, Toner J, Lee C F 2016 Nature Communications 7 12215

    [39]

    Mishra S, Ramaswamy S 2006 Phys. Rev. Lett. 97 090602

    [40]

    Simha R A, Ramaswamy S 2002 Phys. Rev. Lett. 89 058101

    [41]

    Ahmadi A, Marchetti M C, Liverpool T B 2006 Phys. Rev. E 74 061913

    [42]

    Mishra S 2009 Ph. D. Dissertation (Bangalore: Indian Institute of Science)

    [43]

    Shi X, Chate H, Ma Y 2014 New J. Phys. 16 035003

    [44]

    Bertin E, Chate H, Ginelli F, Mishra S, Peshkov A, Ramaswamy S 2013 New J. Phys. 15 085032

    [45]

    Gruler H, Dewald U, Eberhardt M 1999 Eur. Phys. J. B 11 187

    [46]

    Aranson I S, Snezhko A, Olafsen J S, Urbach J S 2008 Science 320 612

    [47]

    Narayan V, Ramaswamy S, Menon N 2008 Science 320 612

    [48]

    Chen L, Toner J 2013 Phys. Rev. Lett. 111 088701

    [49]

    Adhyapak T C, Ramaswamy S, Toner J 2013 Phys. Rev. Lett. 110 118102

    [50]

    Romanczuk P, Chate H, Chen L, Ngo S, Toner J 2015 New J. Phys. 18 063015

  • [1]

    Schweitzer F 2003 Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences (Berlin: Springer)

    [2]

    Surrey T, Ndlec F, Leibler S, Karsenti E 2001 Science 292 1167

    [3]

    Wolgemuth C, Hoiczyk E, Kaiser D, Oster G 2002 Curr. Biol. 12 369

    [4]

    Toner J, Tu Y 1998 Phys. Rev. E 58 4828

    [5]

    Ramaswamy S, Simha R A, Toner J 2003 Europhys. Lett. 62 196

    [6]

    Yamada D, Hondou T, Sano M 2003 Phys. Rev. E 67 040301

    [7]

    Aranson I S, Tsimring L S 2006 Phys. Rev. E 74 031915

    [8]

    Narayan V, Ramaswamy S, Menon N 2007 Science 317 105

    [9]

    Kudrolli A, Lumay G, Volfson D, Tsimring L S 2008 Phys. Rev. Lett. 100 058001

    [10]

    Deseigne J, Dauchot O, Chate H 2010 Phys. Rev. Lett. 105 098001

    [11]

    Drescher K, Dunkel J, Cisneros L H, Ganguly S, Goldstein R E 2011 Proc. Natl. Acad. Sci. USA 108 10940

    [12]

    Ballerini M, Cabibbo N, Candelier R 2008 Proc. Natl. Acad. Sci. USA 105 1232

    [13]

    Ginelli F, Chate H 2010 Phys. Rev. Lett. 105 168103

    [14]

    Bricard A, Caussin J B, Desreumaux N, Dauchot O, Bartolo D 2013 Nature 503 95

    [15]

    Vicsek T, Czirok A, Ben-Jacob E, Cohen I, Shochet O 1995 Phys. Rev. Lett. 75 1226

    [16]

    Gruler H, Dewald U, Eberhardt M 1999 Eur. Phys. J. B 11 187

    [17]

    Peruani F, Deutsch A, Bar M 2006 Phys. Rev. E 74 030904

    [18]

    Baskaran A, Marchetti M C 2008 Phys. Rev. E 77 011920

    [19]

    Yang Y, Marceau V, Gompper G 2010 Phys. Rev. E 82 031904

    [20]

    Toner J, Tu Y 1995 Phys. Rev. Lett. 75 4326

    [21]

    Toner J, Tu Y, S Ramaswamy 2005 Ann. Phys. 318 170

    [22]

    Mermin N D, Wagner H 1966 Phys. Rev. Lett. 17 1133

    [23]

    Bertin E, Droz M, Gregoire G 2006 Phys. Rev. E 74 022101

    [24]

    Bertin E, Droz M, Gregoire G 2009 J. Phys. A 42 445001.

    [25]

    Ihle T 2011 Phys. Rev. E 83 030901

    [26]

    Mishra S, Baskaran A, Marchetti M C 2010 Phys. Rev. E 81 061916

    [27]

    Gregoire G, Chate H 2004 Phys. Rev. Lett. 92 025702

    [28]

    Chate H, Ginelli F, Gregoire G, Raynaud F 2008 Phys. Rev. E 77 046113

    [29]

    Chen L, Toner J, Lee C F 2015 New J. Phys. 17 042002

    [30]

    Chate H, Ginelli F, Gregoire G, Peruani F, Raynaud F 2008 Eur. Phys. J. B 64 451

    [31]

    Zhang H P, Beer A, Florin E L, Swinney H L 2010 Proc. Natl. Acad. Sci. USA 107 13626

    [32]

    Chate H, Ginelli F, Montagne R 2006 Phys. Rev. Lett. 96 180602

    [33]

    Tailleur J, Cates M E 2008 Phys. Rev. Lett. 100 218103

    [34]

    Cates M E 2012 Rep. Prog. Phys. 75 042601

    [35]

    Fily Y, Baskaran A, Marchetti M C 2012 Soft Matter 8 3002

    [36]

    Tu Y, Ulm M, Toner J 1998 Phys. Rev. Lett. 80 4819

    [37]

    Toner J 2012 Phys. Rev. Lett. 108 088102

    [38]

    Chen L, Toner J, Lee C F 2016 Nature Communications 7 12215

    [39]

    Mishra S, Ramaswamy S 2006 Phys. Rev. Lett. 97 090602

    [40]

    Simha R A, Ramaswamy S 2002 Phys. Rev. Lett. 89 058101

    [41]

    Ahmadi A, Marchetti M C, Liverpool T B 2006 Phys. Rev. E 74 061913

    [42]

    Mishra S 2009 Ph. D. Dissertation (Bangalore: Indian Institute of Science)

    [43]

    Shi X, Chate H, Ma Y 2014 New J. Phys. 16 035003

    [44]

    Bertin E, Chate H, Ginelli F, Mishra S, Peshkov A, Ramaswamy S 2013 New J. Phys. 15 085032

    [45]

    Gruler H, Dewald U, Eberhardt M 1999 Eur. Phys. J. B 11 187

    [46]

    Aranson I S, Snezhko A, Olafsen J S, Urbach J S 2008 Science 320 612

    [47]

    Narayan V, Ramaswamy S, Menon N 2008 Science 320 612

    [48]

    Chen L, Toner J 2013 Phys. Rev. Lett. 111 088701

    [49]

    Adhyapak T C, Ramaswamy S, Toner J 2013 Phys. Rev. Lett. 110 118102

    [50]

    Romanczuk P, Chate H, Chen L, Ngo S, Toner J 2015 New J. Phys. 18 063015

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  • Received Date:  05 August 2016
  • Accepted Date:  09 September 2016
  • Published Online:  20 September 2016

Hydrodynamic theory of dry active matter

    Corresponding author: Chen Lei-Ming, leiming@cumt.edu.cn
  • 1. College of Sciences, China University of Mining and Technology, Xuzhou 221116, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11474354).

Abstract: In this paper we shortly review theoretical progress in the field of active matter, focusing on the continuum theory of dry systems, in which momentum of active particles is not conserved due to the interaction between the particles and a substrate or medium. In particular, we review the phenomenological way of deriving hydrodynamic equations for both polar and apolar systems, and the predictions of these theories such as long-ranged orientational order in two-dimensional polar systems and giant number fluctuations. The comparisons among theoretical predictions, numerical results, and experimental evidence are also summarized.

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