Near equilibrium dynamics and one-dimensional spatial-temporal structures of polar active liquid crystals

doi:10.1088/1674-1056/23/11/118701

中国物理B ›› 2014, Vol. 23 ›› Issue (11): 118701-118701.doi: 10.1088/1674-1056/23/11/118701

• SPECIAL TOPIC—Non-equilibrium phenomena in soft matters • 上一篇下一篇

Near equilibrium dynamics and one-dimensional spatial-temporal structures of polar active liquid crystals

杨小刚^a, M. Gregory Forest^b, 王奇^{a c d}

a School of Mathematical Sciences, Nankai University, Tianjin 300071, China;
b Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA;
c Department of Mathematics, Interdisciplinary Mathematics Institute and NanoCenter at USC, University of South Carolina, Columbia, SC 29028, USA;
d Beijing Computational Science Research Center, Beijing 100083, China

收稿日期:2014-05-29 修回日期:2014-09-24 出版日期:2014-11-15 发布日期:2014-11-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. DMS-1200487, DMR-1122483, and NIH 2R01GM078994-05A1), the Air Force Office of Scientific Research (AFOSR) (Grant No. FA9550-12-1-0178), and the Army Research Office (Grant Nos. ARO-12-60317-MS and SC EPSCoR GEAR (CI and CRP)).

Near equilibrium dynamics and one-dimensional spatial-temporal structures of polar active liquid crystals

Yang Xiao-Gang (杨小刚)^a, M. Gregory Forest^b, Wang Qi (王奇)^{a c d}

a School of Mathematical Sciences, Nankai University, Tianjin 300071, China;
b Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA;
c Department of Mathematics, Interdisciplinary Mathematics Institute and NanoCenter at USC, University of South Carolina, Columbia, SC 29028, USA;
d Beijing Computational Science Research Center, Beijing 100083, China

Received:2014-05-29 Revised:2014-09-24 Online:2014-11-15 Published:2014-11-15
Contact: Yang Xiao-Gang, M. Gregory Forest, Wang Qi E-mail:nkyxg@mail.nankai.edu.cn;forest@unc.edu;qwang@math.sc.edu
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. DMS-1200487, DMR-1122483, and NIH 2R01GM078994-05A1), the Air Force Office of Scientific Research (AFOSR) (Grant No. FA9550-12-1-0178), and the Army Research Office (Grant Nos. ARO-12-60317-MS and SC EPSCoR GEAR (CI and CRP)).

摘要/Abstract

摘要：

We systematically explore near equilibrium, flow-driven, and flow-activity coupled dynamics of polar active liquid crystals using a continuum model. Firstly, we re-derive the hydrodynamic model to ensure the thermodynamic laws are obeyed and elastic stresses and forces are consistently accounted. We then carry out a linear stability analysis about constant steady states to study near equilibrium dynamics around the steady states, revealing long-wave instability inherent in this model system and how active parameters in the model affect the instability. We then study model predictions for onedimensional (1D) spatial-temporal structures of active liquid crystals in a channel subject to physical boundary conditions. We discuss the model prediction in two selected regimes, one is the viscous stress dominated regime, also known as the flow-driven regime, while the other is the full regime, in which all active mechanisms are included. In the viscous stress dominated regime, the polarity vector is driven by the prescribed flow field. Dynamics depend sensitively on the physical boundary condition and the type of the driven flow field. Bulk-dominated temporal periodic states and spatially homogeneous states are possible under weak anchoring conditions while spatially inhomogeneous states exist under strong anchoring conditions. In the full model, flow-orientation interaction generates a host of planar as well as out-of-plane spatial-temporal structures related to the spontaneous flows due to the molecular self-propelled motion. These results provide contact with the recent literature on active nematic suspensions. In addition, symmetry breaking patterns emerge as the additional active viscous stress due to the polarity vector is included in the force balance. The inertia effect is found to limit the long-time survival of spatial structures to those with small wave numbers, i.e., an asymptotic coarsening to long wave structures. A rich set of mechanisms for generating and limiting the flow structures as well as the spatial-temporal structures predicted by the model are displayed.

关键词: active liquid crystals, active particles, spatial-temporal structures, spontaneous flows

Abstract:

Key words: active liquid crystals, active particles, spatial-temporal structures, spontaneous flows

中图分类号: (Ordinary differential equations (ODE), partial differential equations (PDE), integrodifferential models)

87.10.Ed

87.23.Cc (Population dynamics and ecological pattern formation) 87.23.Kg (Dynamics of evolution)

杨小刚, M. Gregory Forest, 王奇. Near equilibrium dynamics and one-dimensional spatial-temporal structures of polar active liquid crystals[J]. 中国物理B, 2014, 23(11): 118701-118701.

Yang Xiao-Gang (杨小刚), M. Gregory Forest, Wang Qi (王奇). Near equilibrium dynamics and one-dimensional spatial-temporal structures of polar active liquid crystals[J]. Chin. Phys. B, 2014, 23(11): 118701-118701.

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Near equilibrium dynamics and one-dimensional spatial-temporal structures of polar active liquid crystals

Near equilibrium dynamics and one-dimensional spatial-temporal structures of polar active liquid crystals

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