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Shankar S, Scharrer LVD, Bowick MJ, Marchetti MC. Design rules for controlling active topological defects. Proc Natl Acad Sci U S A 2024; 121:e2400933121. [PMID: 38748571 PMCID: PMC11127047 DOI: 10.1073/pnas.2400933121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2024] [Accepted: 04/12/2024] [Indexed: 05/27/2024] Open
Abstract
Topological defects play a central role in the physics of many materials, including magnets, superconductors, and liquid crystals. In active fluids, defects become autonomous particles that spontaneously propel from internal active stresses and drive chaotic flows stirring the fluid. The intimate connection between defect textures and active flow suggests that properties of active materials can be engineered by controlling defects, but design principles for their spatiotemporal control remain elusive. Here, we propose a symmetry-based additive strategy for using elementary activity patterns, as active topological tweezers, to create, move, and braid such defects. By combining theory and simulations, we demonstrate how, at the collective level, spatial activity gradients act like electric fields which, when strong enough, induce an inverted topological polarization of defects, akin to a negative susceptibility dielectric. We harness this feature in a dynamic setting to collectively pattern and transport interacting active defects. Our work establishes an additive framework to sculpt flows and manipulate active defects in both space and time, paving the way to design programmable active and living materials for transport, memory, and logic.
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Affiliation(s)
- Suraj Shankar
- Department of Physics, Harvard University, Cambridge, MA02138
- Department of Physics, University of Michigan, Ann Arbor, MI48109
| | - Luca V. D. Scharrer
- Department of Physics, University of California, Santa Barbara, CA93106
- Department of Physics, The University of Chicago, Chicago, IL60637
| | - Mark J. Bowick
- Department of Physics, University of California, Santa Barbara, CA93106
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA93106
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Partovifard A, Grawitter J, Stark H. Controlling active turbulence by activity patterns. SOFT MATTER 2024; 20:1800-1814. [PMID: 38305449 DOI: 10.1039/d3sm01050c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/03/2024]
Abstract
By patterning activity in space, one can control active turbulence. To show this, we use Doi's hydrodynamic equations of a semidilute solution of active rods. A linear stability analysis reveals the resting isotropic fluid to be unstable above an absolute pusher activity. The emergent activity-induced paranematic state displays active turbulence, which we characterize by different quantities including the energy spectrum, which shows the typical power-law decay with exponent -4. Then, we control the active turbulence by a square lattice of circular spots where activity is switched off. In the parameter space lattice constant versus surface-to-surface distance of the spots, we identify different flow states. Most interestingly, for lattice constants below the vorticity correlation length and for spot distances smaller than the nematic coherence length, we observe a multi-lane flow state, where flow lanes with alternating flow directions are separated by a street of vortices. The flow pattern displays pronounced multistability and also appears transiently at the transition to the isotropic active-turbulence state. At larger lattice constants a trapped vortex state is identified with a non-Gaussian vorticity distribution due to the low flow vorticity at the spots. It transitions to conventional active turbulence for increasing spot distance.
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Affiliation(s)
- Arghavan Partovifard
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany.
| | - Josua Grawitter
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany.
| | - Holger Stark
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany.
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Rønning J, Marchetti MC, Angheluta L. Defect self-propulsion in active nematic films with spatially varying activity. ROYAL SOCIETY OPEN SCIENCE 2023; 10:221229. [PMID: 36816847 PMCID: PMC9929493 DOI: 10.1098/rsos.221229] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/21/2022] [Accepted: 01/24/2023] [Indexed: 06/18/2023]
Abstract
We study the dynamics of topological defects in active nematic films with spatially varying activity and consider two set-ups: (i) a constant activity gradient and (ii) a sharp jump in activity. A constant gradient of extensile (contractile) activity endows the comet-like +1/2 defect with a finite vorticity that drives the defect to align its nose in the direction of decreasing (increasing) gradient. A constant gradient does not, however, affect the known self-propulsion of the +1/2 defect and has no effect on the -1/2 that remains a non-motile particle. A sharp jump in activity acts like a wall that traps the defects, affecting the translational and rotational motion of both charges. The +1/2 defect slows down as it approaches the interface and the net vorticity tends to reorient the defect polarization so that it becomes perpendicular to the interface. The -1/2 defect acquires a self-propulsion towards the activity interface, while the vorticity-induced active torque tends to align the defect to a preferred orientation. This effective attraction of the negative defects to the wall is consistent with the observation of an accumulation of negative topological charge at both active/passive interfaces and physical boundaries.
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Affiliation(s)
- Jonas Rønning
- Njord Centre, Department of Physics, University of Oslo, PO Box 1048, Oslo 0316, Norway
| | - M. Cristina Marchetti
- Department of Physics and Biomolecular Science and Engineering Program, University of California Santa Barbara, Santa Barbara, CA 93106, USA
| | - Luiza Angheluta
- Njord Centre, Department of Physics, University of Oslo, PO Box 1048, Oslo 0316, Norway
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Coelho RCV, Araújo NAM, Telo da Gama MM. Dispersion of activity at an active-passive nematic interface. SOFT MATTER 2022; 18:7642-7653. [PMID: 36169262 DOI: 10.1039/d2sm00988a] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Efficient nutrient mixing is crucial for the survival of bacterial colonies and other living systems known as active nematics. However, the dynamics of this mixing is non-trivial as there is a coupling between nutrients concentration and velocity field. To address this question, we solve the hydrodynamic equation for active nematics to model the bacterial swarms coupled to an advection-diffusion equation for the activity field, which is proportional to the concentration of nutrients. At the interface between active and passive nematics the activity field is transported by the interfacial flows and in turn it modifies them through the generation of active stresses. We find that the dispersion of this conserved activity field is subdiffusive due to the emergence of a barrier of negative defects at the active-passive interface, which hinders the propagation of the motile positive defects.
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Affiliation(s)
- Rodrigo C V Coelho
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
| | - Nuno A M Araújo
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
| | - Margarida M Telo da Gama
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
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Ruske LJ, Yeomans JM. Activity gradients in two- and three-dimensional active nematics. SOFT MATTER 2022; 18:5654-5661. [PMID: 35861255 DOI: 10.1039/d2sm00228k] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
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 towards contractile regions. In three-dimensional (3D) active nematics disclination lines preferentially lie in the plane perpendicular to activity gradients due to active torques acting on line segments. The average orientation of the defect structures in the plane perpendicular to the line tangent depends on the defect type, where wedge-like +1/2 defects align parallel to activity gradients, while twist defects are aligned anti-parallel. Understanding the response of active nematic fluids to activity gradients is an important step towards applying physical theories to biology, where spatial variations of active stress impact morphogenetic processes in developing embryos and affect flows and deformations in growing cell aggregates, such as tumours.
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Affiliation(s)
- Liam J Ruske
- Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
| | - Julia M Yeomans
- Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
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Zhang R, Mozaffari A, de Pablo JJ. Logic operations with active topological defects. SCIENCE ADVANCES 2022; 8:eabg9060. [PMID: 35196084 PMCID: PMC8865799 DOI: 10.1126/sciadv.abg9060] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Accepted: 12/30/2021] [Indexed: 05/31/2023]
Abstract
Logic operations performed by semiconductor-based transistors are the basis of modern computing. There is considerable interest in creating autonomous materials systems endowed with the capability to make decisions. In this work, we introduce the concept of using topological defects in active matter to perform logic operations. When an extensile active stress in a nematic liquid crystal is turned on, +1/2 defects can self-propel, in analogy to electron transport under a voltage gradient. By relying on hydrodynamic simulations of active nematics, we demonstrate that patterns of activity, when combined with surfaces imparting certain orientations, can be used to control the formation and transport of +1/2 defects. We further show that asymmetric high- and low-activity patterns can be used to create effective defect gates, tunnels, and amplifiers. The proposed active systems offer the potential to perform computations and transmit information in active soft materials, including actin-, tubulin-, and cell-based systems.
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Affiliation(s)
- Rui Zhang
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
| | - Ali Mozaffari
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA
- OpenEye Scientific Software, Inc., 9 Bisbee Court Suite D, Santa Fe, New Mexico 87508, USA
| | - Juan J. de Pablo
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA
- Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA
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Jones R, Melnyk O, Macêdo R, Camley RE. Vertically Stacked Soliton‐Like Domain Walls in Nematic Liquid Crystals. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202100252] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Reed Jones
- UCCS BioFrontiers Center and Department of Physics and Energy Science University of Colorado Colorado Springs Colorado Springs CO 80918 USA
| | - Olha Melnyk
- UCCS BioFrontiers Center and Department of Physics and Energy Science University of Colorado Colorado Springs Colorado Springs CO 80918 USA
- Herman B Wells Center for Pediatric Research Department of Pediatrics Indiana University School of Medicine Indianapolis IN 46202 USA
| | - Rair Macêdo
- James Watt School of Engineering Electronics & Nanoscale Engineering Division University of Glasgow Glasgow G12 8QQ UK
| | - Robert E. Camley
- UCCS BioFrontiers Center and Department of Physics and Energy Science University of Colorado Colorado Springs Colorado Springs CO 80918 USA
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Submersed micropatterned structures control active nematic flow, topology, and concentration. Proc Natl Acad Sci U S A 2021; 118:2106038118. [PMID: 34535551 DOI: 10.1073/pnas.2106038118] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/24/2021] [Indexed: 01/10/2023] Open
Abstract
Coupling between flows and material properties imbues rheological matter with its wide-ranging applicability, hence the excitement for harnessing the rheology of active fluids for which internal structure and continuous energy injection lead to spontaneous flows and complex, out-of-equilibrium dynamics. We propose and demonstrate a convenient, highly tunable method for controlling flow, topology, and composition within active films. Our approach establishes rheological coupling via the indirect presence of fully submersed micropatterned structures within a thin, underlying oil layer. Simulations reveal that micropatterned structures produce effective virtual boundaries within the superjacent active nematic film due to differences in viscous dissipation as a function of depth. This accessible method of applying position-dependent, effective dissipation to the active films presents a nonintrusive pathway for engineering active microfluidic systems.
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Mozaffari A, Zhang R, Atzin N, de Pablo JJ. Defect Spirograph: Dynamical Behavior of Defects in Spatially Patterned Active Nematics. PHYSICAL REVIEW LETTERS 2021; 126:227801. [PMID: 34152186 DOI: 10.1103/physrevlett.126.227801] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Revised: 01/06/2021] [Accepted: 05/03/2021] [Indexed: 06/13/2023]
Abstract
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 defects in terms of activity and frictional damping strength. Different regions of the underlying phase diagram correspond to distinct dynamical modes, namely immobile defects, steady rotation of defects, bouncing defects, bouncing-cruising defects, dancing defects, and multiple defects with irregular dynamics. These dynamic states raise the prospect of generating synchronized defect arrays for microfluidic applications.
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Affiliation(s)
- Ali Mozaffari
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Rui Zhang
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Noe Atzin
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Juan J de Pablo
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
- Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, USA
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Lavrentovich OD. Design of nematic liquid crystals to control microscale dynamics. LIQUID CRYSTALS REVIEWS 2021; 8:59-129. [PMID: 34956738 PMCID: PMC8698256 DOI: 10.1080/21680396.2021.1919576] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2020] [Accepted: 04/11/2021] [Indexed: 05/25/2023]
Abstract
The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.
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Affiliation(s)
- Oleg D Lavrentovich
- Advanced Materials and Liquid Crystal Institute, Department of Physics, Materials Science Graduate Program, Kent State University, Kent, OH 44242, USA
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