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Edited by Tom C. Lubensky, University of Pennsylvania, Philadelphia, PA, and approved June 1, 2017 (received for review February 17, 2017)
Significance
Topological defects play a defining role in systems as extensive as the universe and as minuscule as a microbial colony. Despite significant advances in our understanding of topological defects and their mutual interactions, little is known about the formation and dynamics of defects across different material fields embedded within the same system. Here, using nematic microfluidics as a test bed, we report how topological defects in the flow and the orientational fields emerge and cross-talk with each other. Although discussed in a nematofluidic context, such multifield topological interactions have potential ramifications in a range of systems spanning vastly different length and time scales: from material designing, to exploration of open questions in cosmology and living matter.
Abstract
Topological defects are singularities in material fields that play a vital role across a range of systems: from cosmic microwave background polarization to superconductors and biological materials. Although topological defects and their mutual interactions have been extensively studied, little is known about the interplay between defects in different fields—especially when they coevolve—within the same physical system. Here, using nematic microfluidics, we study the cross-talk of topological defects in two different material fields—the velocity field and the molecular orientational field. Specifically, we generate hydrodynamic stagnation points of different topological charges at the center of star-shaped microfluidic junctions, which then interact with emergent topological defects in the orientational field of the nematic director. We combine experiments and analytical and numerical calculations to show that a hydrodynamic singularity of a given topological charge can nucleate a nematic defect of equal topological charge and corroborate this by creating
Footnotes
↵1Present address: Institute for Environmental Engineering, Eidgenössische Technische Hochschule (ETH) Zurich, 8093 Zurich, Switzerland.
- ↵2To whom correspondence should be addressed. Email: anupams{at}ethz.ch.
Author contributions: L.G., M.R., and A.S. designed research; L.G. developed particle model and performed analytical calculations; Z̆.K. and M.R. performed numerical simulations; A.S. conceptualized research, conducted experiments, analyzed data, and provided advice for all parts of the work; and L.G., Z̆.K., M.R., and A.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1702777114/-/DCSupplemental.
- aInstituut-Lorentz for Theoretical Physics, Leiden University, 2333 CA Leiden, The Netherlands;
- bFaculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia;
- cCondensed Matter Physics Department, Jožef Stefan Institute, 1000 Ljubljana, Slovenia;
- dInstitute for Environmental Engineering, Department of Civil, Environmental, and Geomatic Engineering, Eidgenössische Technische Hochschule (ETH) Zurich, 8093 Zurich, Switzerland;
- eMax-Planck-Institute for Dynamics and Self-Organization, 37077 Goettingen, Germany
Edited by Tom C. Lubensky, University of Pennsylvania, Philadelphia, PA, and approved June 1, 2017 (received for review February 17, 2017)
Significance
Topological defects play a defining role in systems as extensive as the universe and as minuscule as a microbial colony. Despite significant advances in our understanding of topological defects and their mutual interactions, little is known about the formation and dynamics of defects across different material fields embedded within the same system. Here, using nematic microfluidics as a test bed, we report how topological defects in the flow and the orientational fields emerge and cross-talk with each other. Although discussed in a nematofluidic context, such multifield topological interactions have potential ramifications in a range of systems spanning vastly different length and time scales: from material designing, to exploration of open questions in cosmology and living matter.
Abstract
Topological defects are singularities in material fields that play a vital role across a range of systems: from cosmic microwave background polarization to superconductors and biological materials. Although topological defects and their mutual interactions have been extensively studied, little is known about the interplay between defects in different fields—especially when they coevolve—within the same physical system. Here, using nematic microfluidics, we study the cross-talk of topological defects in two different material fields—the velocity field and the molecular orientational field. Specifically, we generate hydrodynamic stagnation points of different topological charges at the center of star-shaped microfluidic junctions, which then interact with emergent topological defects in the orientational field of the nematic director. We combine experiments and analytical and numerical calculations to show that a hydrodynamic singularity of a given topological charge can nucleate a nematic defect of equal topological charge and corroborate this by creating , , and topological defects in four-, six-, and eight-arm junctions. Our work is an attempt toward understanding materials that are governed by distinctly multifield topology, where disparate topology-carrying fields are coupled and concertedly determine the material properties and response.
- multifield topology
- nematic liquid crystals
- topological defects
- microfluidics
- cross-interactions
Footnotes
↵1Present address: Institute for Environmental Engineering, Eidgenössische Technische Hochschule (ETH) Zurich, 8093 Zurich, Switzerland.
- ↵2To whom correspondence should be addressed. Email: anupams{at}ethz.ch.
Author contributions: L.G., M.R., and A.S. designed research; L.G. developed particle model and performed analytical calculations; Z̆.K. and M.R. performed numerical simulations; A.S. conceptualized research, conducted experiments, analyzed data, and provided advice for all parts of the work; and L.G., Z̆.K., M.R., and A.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1702777114/-/DCSupplemental.
Topological cross-talk across material fields
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