Collective behaviors of self-propelled rods under semi-flexible elastic confinement

Zhong Ying; Shi Xia-Qing

doi:10.7498/aps.69.20200561

Abstract

In biological active systems there commonly exist active rod-like particles under elastic confinement. Here in this work, we study the collective behavior of self-propelled rods confined in an elastic semi-flexible ring. By changing the density of particles and noise level in the system, It is clearly shown that the system has an ordered absorbing phase-separated state of self-propelled rods and the transition to a disordered state as well. The radial polar order parameter and asphericity parameter are characterized to distinguish these states. The results show that the gas density near the central region of the elastic confinement has a saturated gas density that co-exists with the absorbed liquid crystal state at the elastic boundary. In the crossover region, the system suffers an abnormal fluctuation that drives the deformation of the elastic ring. The non-symmetric distribution of particles in the transition region contributes significantly to the collective translocation of the elastic ring.

Keywords:

Authors and contacts

Center for Soft Condensed Matter Physics and Interdisciplinary Research, School of Physical Science and Technology, Soochow University, Suzhou 215006, China

Corresponding author: Shi Xia-Qing, sxiaqing@gmail.com

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References

[1]	Cavagna A, Cimarelli A, Giardina I, Parisi G, Santagati R, Stefanini F, Viale M 2010 Proc. Natl. Acad. Sci. U.S.A. 107 11865 Google Scholar
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[3]	Makris N C, Ratilal P, Symonds D T, Jagannathan S, Lee S, Nero R W 2006 Science 311 660 Google Scholar
[4]	Katz Y, Tunstrom K, Ioannou C C, Huepe C, Couzin I D 2011 Proc. Natl. Acad. Sci. U.S.A. 108 18720 Google Scholar
[5]	Ginelli F, Peruani F, Pillot M H, Chate H, Theraulaz G, Bon R 2015 Proc. Natl. Acad. Sci. U.S.A. 112 12729 Google Scholar
[6]	J.-C. Tsai, Fangfu Ye, Juan Rodriguez, J. P. Gollub, Lubensky T C 2005 Phys. Rev. Lett. 94 214301 Google Scholar
[7]	Zhang H P, Be'er A, Florin E L, Swinney H L 2010 Proc. Natl. Acad. Sci. U.S.A. 107 13626 Google Scholar
[8]	陈雷鸣 2016 65 186401 Google Scholar Chen L M 2016 Acta Phys. Sin. 65 186401 Google Scholar
[9]	Fily Y, Marchetti M C 2012 Phys. Rev. Lett. 108 235702 Google Scholar
[10]	Farrell F D, Marchetti M C, Marenduzzo D, Tailleur J 2012 Phys. Rev. Lett. 108 248101 Google Scholar
[11]	Weitz S, Deutsch A, Peruani F 2015 Phys. Rev. E 92 012322
[12]	Abkenar M, Marx K, Auth T, Gompper G 2013 Phys. Rev. E 88 062314
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[14]	Deseigne J, Dauchot O, Chate H 2010 Phys. Rev. Lett. 105 098001 Google Scholar
[15]	Bialke J, Speck T, Lowen H 2012 Phys. Rev. Lett. 108 168301 Google Scholar
[16]	Wysocki A, Elgeti J, Gompper G 2015 Phys. Rev. E 91 050302 Google Scholar
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[21]	Wensink H H, Lowen H 2012 J. Phys. Condens. Matter 24 464130 Google Scholar
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[29]	Lee C F 2013 New J. Phys. 15 055007 Google Scholar
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Cited By

图 1 (a)系统组成的示意图, 颜色代表杆身的取向; (b)杆间碰撞受力示意图

Figure 1. (a) The schematic diagram of this system, and the rods are colored according to their angle with respect to the radial direction; (b) the interaction between rods.

DownLoad: Full-Size Img PowerPoint

图 2 三种典型分布的快照, 自驱动杆粒子数${N_{\rm{r}}}$均为1500, 噪声大小$\eta $分别为0.10, 0.20和0.50, 依次对应　(a)自驱吸附有序态、(b)过渡态和(c)无序态. 粒子颜色代表取向, 同图1

Figure 2. The snapshots of three regions with fixed particle number ${N_{\rm{r}}} = 1500$ for different noise levels, and, respectively, with (a) $\eta = 0.10$, self-propelled particle absorbed ordered region, (b) $\eta = 0.20$ transient region, and (c) $\eta = 0.50$ disordered phase. The color represents the radial direction as Fig.1.

DownLoad: Full-Size Img PowerPoint

图 3 改变噪声强度$\eta $和弹性环中自驱动杆粒子数${N_{\rm{r}}}$得到的相图　(a)比较径向极性序参${S_{\rm{p}}}$大小得到的热力图; (b)比较非球度$\varDelta $大小得到的热力图, 其中转变区域具有极大值

Figure 3. Phase diagrams for self-propelled rods in elastic-ring with varying the noise strength $\eta $ and the number of self-propelled rods ${N_{\rm{r}}}$, and the order parameter corresponding to (a) the radial polarity ${S_{\rm{P}}}$ and (b) the asphericity $\varDelta $. We have maximal asphericity $\varDelta $ in the transition region.

DownLoad: Full-Size Img PowerPoint

图 4 (a)改变噪声强度$\eta $和自驱动杆粒子数${N_{\rm{r}}}$, 比较约化密度差P得到的热力图; (b)不同噪声强度$\eta $下, 弹性环中心附近粒子数密度随自驱动杆粒子数${N_{\rm{r}}}$的变化趋势

Figure 4. (a) Phase diagram of the reduced density difference P for self-propelled rods with varying the noise strength $\eta $ and the number of self-propelled rods ${N_{\rm{r}}}$; (b) density of central particles, ${\psi _{{\rm{in}}}}$, versus the particle number ${N_{\rm{r}}}$ for different noise strength $\eta $.

DownLoad: Full-Size Img PowerPoint

图 5 弹性环及杆状粒子质心均方位移随时间的变化　(a)粒子数${N_{\rm{r}}}$为1500时, 噪声大小$\eta $为0.10, 0.20和0.50所在三个区区域的比较; (b)粒子数${N_{\rm{r}}}$ = 1000, $\eta $为0.25, 0.30和0.50下无序态时的对比

Figure 5. Mean-squared displacement(MSD)for the center of mass of particle and elastic ring: (a) Noise levels $\eta = 0.10$, $\eta = 0.20$, and $\eta = 0.50$ for ${N_{\rm{r}}} = 1500$; (b) noise levels for $\eta = 0.25$, $\eta = 0.30$, and $\eta = 0.50$ with particle number ${N_{\rm{r}}} = 1000$ in the disordered regime.

DownLoad: Full-Size Img PowerPoint

map

[1]	Cavagna A, Cimarelli A, Giardina I, Parisi G, Santagati R, Stefanini F, Viale M 2010 Proc. Natl. Acad. Sci. U.S.A. 107 11865 Google Scholar
[2]	Ballerini M, Cabibbo N, Candelier R, Cavagna A, Cisbani E, Giardina I, Lecomte V, Orlandi A, Parisi G, Procaccini A, Viale M, Zdravkovic V 2008 Proc. Natl. Acad. Sci. U.S.A. 105 1232 Google Scholar
[3]	Makris N C, Ratilal P, Symonds D T, Jagannathan S, Lee S, Nero R W 2006 Science 311 660 Google Scholar
[4]	Katz Y, Tunstrom K, Ioannou C C, Huepe C, Couzin I D 2011 Proc. Natl. Acad. Sci. U.S.A. 108 18720 Google Scholar
[5]	Ginelli F, Peruani F, Pillot M H, Chate H, Theraulaz G, Bon R 2015 Proc. Natl. Acad. Sci. U.S.A. 112 12729 Google Scholar
[6]	J.-C. Tsai, Fangfu Ye, Juan Rodriguez, J. P. Gollub, Lubensky T C 2005 Phys. Rev. Lett. 94 214301 Google Scholar
[7]	Zhang H P, Be'er A, Florin E L, Swinney H L 2010 Proc. Natl. Acad. Sci. U.S.A. 107 13626 Google Scholar
[8]	陈雷鸣 2016 65 186401 Google Scholar Chen L M 2016 Acta Phys. Sin. 65 186401 Google Scholar
[9]	Fily Y, Marchetti M C 2012 Phys. Rev. Lett. 108 235702 Google Scholar
[10]	Farrell F D, Marchetti M C, Marenduzzo D, Tailleur J 2012 Phys. Rev. Lett. 108 248101 Google Scholar
[11]	Weitz S, Deutsch A, Peruani F 2015 Phys. Rev. E 92 012322
[12]	Abkenar M, Marx K, Auth T, Gompper G 2013 Phys. Rev. E 88 062314
[13]	Surrey T, Nedelec F, Leibler S, Karsenti E 2001 Science 292 1167 Google Scholar
[14]	Deseigne J, Dauchot O, Chate H 2010 Phys. Rev. Lett. 105 098001 Google Scholar
[15]	Bialke J, Speck T, Lowen H 2012 Phys. Rev. Lett. 108 168301 Google Scholar
[16]	Wysocki A, Elgeti J, Gompper G 2015 Phys. Rev. E 91 050302 Google Scholar
[17]	Costanzo A, Di Leonardo R, Ruocco G, Angelani L 2012 J. Phys. Condens. Matter 24 065101 Google Scholar
[18]	Isele-Holder R E, Elgeti J, Gompper G 2015 Soft Matter 11 7181 Google Scholar
[19]	Ginelli F, Peruani F, Bar M, Chate H 2010 Phys. Rev. Lett. 104 184502 Google Scholar
[20]	Gao T, Blackwell R, Glaser M A, Betterton M D, Shelley M J 2015 Phys. Rev. Lett. 114 048101 Google Scholar
[21]	Wensink H H, Lowen H 2012 J. Phys. Condens. Matter 24 464130 Google Scholar
[22]	Ofer N, Mogilner A, Keren K 2011 Proc. Natl. Acad. Sci. U.S.A. 108 20394 Google Scholar
[23]	Prass M, Jacobson K, Mogilner A, Radmacher M 2006 J. Cell Biol. 174 767 Google Scholar
[24]	Weichsel J, Schwarz U S 2013 New J. Phys. 15 035006 Google Scholar
[25]	Theriot J A, Mitchison T J, Tilney L G, Portnoy D A 1992 Nature 357 257 Google Scholar
[26]	Pantaloni D 2001 Science 292 1502 Google Scholar
[27]	Lushi E, Wioland H, Goldstein R E 2014 Proc. Natl. Acad. Sci. U.S.A. 111 9733 Google Scholar
[28]	Wensink H H, Lowen H 2008 Phys. Rev. E 78 031409 Google Scholar
[29]	Lee C F 2013 New J. Phys. 15 055007 Google Scholar
[30]	Yang X, Manning M L, Marchetti M C 2014 Soft Matter 10 6477 Google Scholar
[31]	Abaurrea Velasco C, Dehghani Ghahnaviyeh S, Nejat Pishkenari H, Auth T, Gompper G 2017 Soft Matter 13 5865 Google Scholar
[32]	Tian W D, Gu Y, Guo Y K, Chen K 2017 Chin. Phys. B 26 100502 Google Scholar
[33]	Paoluzzi M, Di Leonardo R, Marchetti M C, Angelani L 2016 Sci. Rep. 6 34146 Google Scholar
[34]	Spellings M, Engel M, Klotsa D, Sabrina S, Drews A M, Nguyen N H, Bishop K J, Glotzer S C 2015 Proc. Natl. Acad. Sci. U.S.A. 112 E4642 Google Scholar
[35]	Zhang R F, Ren C L, Feng J W, Ma Y Q 2019 Sci. China-Phys. Mech. Astron. 62 117012 Google Scholar
[36]	Pesek J, Baerts P, Smeets B, Maes C, Ramon H 2016 Soft Matter 12 3360 Google Scholar
[37]	Lober J, Ziebert F, Aranson I S 2014 Soft Matter 10 1365 Google Scholar
[38]	Opathalage A, Norton M M, Juniper M P N, et al. 2019 PNAS 116 4788 Google Scholar
[39]	Keber F C, Loiseau E, Sanchez T, et al. 2014 Science 345 1135 Google Scholar

20200561-movie1.mp4

20200561-movie2.mp4

20200561-movie3.mp4

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Vol. 69, Issue 8 - 2020-04-20

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