The effects of an electric field on the flow patterns and defect dynamics of two-dimensional active nematics are numerically investigated. We found that field-induced director reorientation causes anisotropic active turbulence characterized by enhanced flow perpendicular to the electric field. The average flow speed and its anisotropy are maximized at an intermediate field strength. Topological defects in the anisotropic active turbulence are localized and show characteristic dynamics {with simultaneous creation of} two pairs of defects. A laning state characterized by stripe domains with alternating flow directions is found at a larger field strength near the transition to the uniformly aligned state. We obtained periodic oscillations between the laning state and active turbulence, which resembles an experimental observation of active nematics subject to anisotropic friction.
In two dimensional nematics, topological defects are point like singularities with both a charge and a phase. We study topological defects within curved nematic textures on the surface of a cylinder. This allows us to isolate the effect of extrinsic curvature on the structure of the topological defect. By minimizing the energy associated with distortions in the nematic director around the core of a defect we show that the phase of the topological defect is coupled to the orientation of the cylinder. This coupling depends on the relative energetic cost associated with splay, bend and twist dist…
We study the dynamics of active nematic films on a substrate driven by active flows with or without the incompressible constraint.Through simulations and theoretical analysis, we show that arch patterns are stable in the compressible case, whilst they become unstable under the incompressibility constraint. For compressible flows at high enough activity, stable arches organize themselves into a smectic-like pattern, which induce an associated global polar ordering of $+1/2$ nematic defects. By contrast, divergence-free flows give rise to a local nematic order of the $+1/2$ defects, consisting o…
We adapt the Halperin-Mazenko formalism to analyze two-dimensional active nematics coupled to a generic fluid flow. The governing hydrodynamic equations lead to evolution laws for nematic topological defects and their corresponding density fields. We find that $\pm 1/2$ defects are propelled by the local fluid flow and by the nematic orientation coupled with the flow shear rate. In the overdamped and compressible limit, we recover the previously obtained active self-propulsion of the +1/2 defects. Non-local hydrodynamic effects are primarily significant for incompressible flows, for which it i…
Topological defects are one of the most conspicuous features of liquid crystals. In two dimensional nematics, they have been shown to behave effectively as particles with both, charge and orientation, which dictate their interactions. Here, we study "twisted" defects that have a radially dependent orientation. We find that twist can be partially relaxed through the creation and annihilation of defect pairs. By solving the equations for defect motion and calculating the forces on defects, we identify four distinct elements that govern the relative relaxational motion of interacting topological …
Topological defects in active liquid crystals can be confined by introducing gradients of activity. Here, we examine the dynamical behavior of two defects confined by a sharp gradient of activity that separates an active circular region and a surrounding passive nematic material. Continuum simulations are used to explain how the interplay among energy injection into the system, hydrodynamic interactions, and frictional forces governs the dynamics of topologically required self-propelling $+1/2$ defects. Our findings are rationalized in terms of a phase diagram for the dynamical response of def…
Eppur si muove: Shape of topological defects -- and consequent motion -- in active nematics
CY Cergy Paris Université（塞吉-蓬图瓦兹CY大学）；CEA, CNRS Université Paris-Saclay（法国原子能与替代能源委员会，CNRS巴黎萨克雷大学）；Sorbonne Université（索邦大学）；Laboratoire Jean Perrin, Sorbonne Université and CNRS（让·佩兰实验室，索邦大学和CNRS）
We investigate the emergence of orientational order among +1/2 disclinations in active nematic liquid crystals. Using a combination of theoretical and experimental methods, we show that +1/2 disclinations have short-range antiferromagnetic alignment, as a consequence of the elastic torques originating from their polar structure. The presence of intermediate -1/2 disclinations, however, turns this interaction from anti-aligning to aligning at scales that are smaller than the typical distance between like-sign defects. No long-range orientational order is observed. Strikingly, these effects are …
Defect Kinematics in 2D Nematics: Contributions from Surface Topology, Intrinsic and Extrinsic Geometry, Solitons, Defect Orientations, and Elastic Anisotropy
School of Physics, UNSW（新南威尔士大学物理学院）；EMBL Australia Node in Single Molecule Science, School of Medical Sciences, UNSW（UNSW医学院单分子科学澳大利亚EMBL节点）；ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems, UNSW Node（UNSW节点，ARC细胞系统数学分析卓越中心）
Non-equilibrium dynamics of topological defects can be used as a fundamental propulsion mechanism in microscopic active matter. Here, we demonstrate swimming of topological defect-propelled colloidal particles in (passive) nematic fluids through experiments and numerical simulations. Dynamic swim strokes of the topological defects are driven by colloidal rotation in an external magnetic field, causing periodic defect rearrangement which propels the particles. The swimming velocity is determined by the colloid's angular velocity, sense of rotation and defect polarity. By controlling them we can…
We numerically investigate how spatial variations of extensile or contractile active stress affect bulk active nematic systems in two and three dimensions. In the absence of defects, activity gradients drive flows which re-orient the nematic director field and thus act as an effective anchoring force. At high activity, defects are created and the system transitions into active turbulence, a chaotic flow state characterized by strong vorticity. We find that in two-dimensional (2D) systems active torques robustly align $+1/2$ defects parallel to activity gradients, with defect heads pointing tow…
Nontrivial shape of colloidal particles create complex elastic distortions and topological defects in liquid crystals and play a key role in governing their electrophoretic propulsion through the medium. Here, we report experimental results on defects and electrophoretic transport of anisometric (snowman-shaped) dielectric particles subjected to an alternating electric field perpendicular to the director in a nematic liquid crystal. We demonstrate that the shape asymmetry gives rise to defect-polymorphism by nucleating point or ring defects at multiple locations on the particle and controls th…
We describe the geometry of bend distortions in twist-bend nematic liquid crystals in terms of their fundamental degeneracies, which we call $β$ lines. These represent a new class of line-like topological defect. We use them to construct and characterise novel structures, including grain boundary and focal conic smectic-like defects, Skyrmions, and knotted merons. We analyse their local geometry and global structure, showing that their intersection with any surface is twice the Skyrmion number. Finally, we demonstrate how arbitrary knots and links can be created and describe them in terms of m…
We develop a description of defect loops in three-dimensional active nematics based on a multipole expansion of the far-field director and show how this leads to a self-dynamics dependent on the loop's geometric type. The dipole term leads to active stresses that generate a global self-propulsion for splay and bend loops. The quadrupole moment is non-zero only for non-planar loops and generates a net `active torque', such that defect loops are both self-motile and self-orienting. Our analysis identifies right- and left-handed twist loops as the only force and torque free geometries, suggesting…
Flatiron Institute（平顿研究所）；Center for Computational Biology, Flatiron Institute（平顿研究所计算生物学中心）；Departament de Física de la Matèria Condensada, Universitat de Barcelona（巴塞罗那大学凝聚态物理系）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Cluster of Excellence Physics of Life, TU Dresden（德累斯顿工业大学生命物理学卓越集群）；Collège de France（法兰西公学院）；Laboratoire PhysicoChimie Curie, Institut Curie, Université Paris Sciences & Lettres (PSL), Sorbonne Universités, Université Pierre et Marie Curie (UPMC)（居里研究所物理化学实验室，巴黎文理研究大学，索邦大学，皮埃尔和玛丽·居里大学）；Universitat de Barcelona Institute of Complex Systems (UBICS)（巴塞罗那大学复杂系统研究所）
In a sharp contrast to the response of silica particles we show that the metal-dielectric Janus particles with boojum defects in a nematic liquid crystal are self-propelled under the action of an electric field applied perpendicular to the director. The particles can be transported along any direction in the plane of the sample by selecting the appropriate orientation of the Janus vector with respect to the director. The direction of motion of the particles is controllable by varying the field amplitude and frequency. The command demonstrated on the motility of the particles is promising for t…
