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Stannarius R, Harth K. The structure of disintegrating defect clusters in smectic C freely suspended films. SOFT MATTER 2023; 19:6108-6115. [PMID: 37534765 DOI: 10.1039/d3sm00808h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/04/2023]
Abstract
Disclinations or disclination clusters in smectic C freely suspended films with topological charges larger than one are unstable. They disintegrate, preferably in a spatially symmetric fashion, into single defects with individual charges of +1, which is the smallest positive topological charge allowed in polar vector fields. While the opposite process of defect annihilation is well-defined by the initial defect positions, disintegration starts from a singular state and the following scenario including the emerging regular defect patterns must be selected by specific mechanisms. We analyze experimental data and compare them with a simple model where the defect clusters adiabatically pass quasi-equilibrium solutions in one-constant approximation. It is found that the defects arrange in geometrical patterns that correspond very closely to superimposed singular defect solutions, without additional director distortions. The patterns expand by affine transformations where all distances between individual defects scale with the same time-dependent scaling factor proportional to the square-root of time.
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Affiliation(s)
- Ralf Stannarius
- Institute of Physics, Otto von Guericke University Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany.
| | - Kirsten Harth
- Department of Engineering, Brandenburg University of Applied Sciences, Magdeburger Straße 50, D-14770 Brandenburg an der Havel, Germany.
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Abstract
The magnetic field hz of a moving Pearl vortex in a superconducting thin-film in (x,y) plane is studied with the help of the time-dependent London equation. It is found that for a vortex at the origin moving in +x direction, hz(x,y) is suppressed in front of the vortex, x>0, and enhanced behind (x<0). The distribution asymmetry is proportional to the velocity and to the conductivity of normal quasiparticles. The vortex self-energy and the interaction of two moving vortices are evaluated.
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Zhang YH, Deserno M, Tu ZC. Dynamics of active nematic defects on the surface of a sphere. Phys Rev E 2020; 102:012607. [PMID: 32795046 DOI: 10.1103/physreve.102.012607] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/29/2020] [Accepted: 06/22/2020] [Indexed: 12/12/2022]
Abstract
A nematic liquid crystal confined to the surface of a sphere exhibits topological defects of total charge +2 due to the topological constraint. In equilibrium, the nematic field forms four +1/2 defects, located at the corners of a regular tetrahedron inscribed within the sphere, since this minimizes the Frank elastic energy. If additionally the individual nematogens exhibit self-driven directional motion, the resulting active system creates large-scale flow that drives it out of equilibrium. In particular, the defects now follow complex dynamic trajectories which, depending on the strength of the active forcing, can be periodic (for weak forcing) or chaotic (for strong forcing). In this paper we derive an effective particle theory for this system, in which the topological defects are the degrees of freedom, whose exact equations of motion we subsequently determine. Numerical solutions of these equations confirm previously observed characteristics of their dynamics and clarify the role played by the time dependence of their global rotation. We also show that Onsager's variational principle offers an exceptionally transparent way to derive these dynamical equations, and we explain the defect mobility at the hydrodynamics level.
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Affiliation(s)
- Yi-Heng Zhang
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Markus Deserno
- Department of Physics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, USA
| | - Zhan-Chun Tu
- Department of Physics, Beijing Normal University, Beijing 100875, China
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Minor EN, Howard SD, Green AAS, Glaser MA, Park CS, Clark NA. End-to-end machine learning for experimental physics: using simulated data to train a neural network for object detection in video microscopy. SOFT MATTER 2020; 16:1751-1759. [PMID: 31907505 DOI: 10.1039/c9sm01979k] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We demonstrate a method for training a convolutional neural network with simulated images for usage on real-world experimental data. Modern machine learning methods require large, robust training data sets to generate accurate predictions. Generating these large training sets requires a significant up-front time investment that is often impractical for small-scale applications. Here we demonstrate a 'full-stack' computational solution, where the training data set is generated on-the-fly using a noise injection process to produce simulated data characteristic of the experimental system. We demonstrate the power of this full-stack approach by applying it to the study of topological defect annihilation in systems of liquid crystal freely-suspended films. This specific experimental system requires accurate observations of both the spatial distribution of the defects and the total number of defects, making it an ideal system for testing the robustness of the trained network. The fully trained network was found to be comparable in accuracy to human hand-annotation, with four-orders of magnitude improvement in time efficiency.
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Affiliation(s)
- Eric N Minor
- Department of Physics and Soft Materials Research Center, University of Colorado, Boulder, Colorado, 80309, USA.
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Tang X, Selinger JV. Theory of defect motion in 2D passive and active nematic liquid crystals. SOFT MATTER 2019; 15:587-601. [PMID: 30608104 DOI: 10.1039/c8sm01901k] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The motion of topological defects is an important feature of the dynamics of all liquid crystals, and is especially conspicuous in active liquid crystals. Understanding defect motion is a challenging theoretical problem, because the dynamics of orientational order is coupled with backflow of the fluid, and because a liquid crystal has several distinct viscosity coefficients. Here, we suggest a coarse-grained, variational approach, which describes the motion of defects as effective "particles". For passive liquid crystals, the theory shows how the drag depends on defect orientation, and shows the coupling between translational and rotational motion. For active liquid crystals, the theory provides an alternative way to describe motion induced by the activity coefficient.
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Affiliation(s)
- Xingzhou Tang
- Department of Physics and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | - Jonathan V Selinger
- Department of Physics and Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
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Fowler N, Dierking DI. Kibble-Zurek Scaling during Defect Formation in a Nematic Liquid Crystal. Chemphyschem 2017; 18:812-816. [PMID: 28185393 DOI: 10.1002/cphc.201700023] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2017] [Revised: 02/01/2017] [Indexed: 11/10/2022]
Abstract
Symmetry-breaking phase transitions are often accompanied by the formation of topological defects, as in cosmological theories of the early universe, superfluids, liquid crystals or solid-state systems. This scenario is described by the Kibble-Zurek mechanism, which predicts corresponding scaling laws for the defect density ρ. One such scaling law suggests a relation ρ≈τQ-1/2 with τQ the change of rate of a control parameter. In contrast to the scaling of the defect density during annihilation with ρ≈t-1 , which is governed by the attraction of defects of the same strength but opposite sign, the defect formation process, which depends on the rate of change of a physical quantity initiating the transition, has only rarely been investigated. Herein, we use nematic liquid crystals as a different system to demonstrate the validity of the predicted scaling relation for defect formation. It is found that the scaling exponent is independent of temperature and material employed, thus universal, as predicted.
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Affiliation(s)
- Nicholas Fowler
- School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
| | - Dr Ingo Dierking
- School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
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Klein A, Agam O, Aleiner IL. Instability of the Abrikosov Lattice due to Nonanalytic Core Reconstruction of Vortices in Bosonic Superfluids. PHYSICAL REVIEW LETTERS 2017; 118:085303. [PMID: 28282165 DOI: 10.1103/physrevlett.118.085303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2016] [Indexed: 06/06/2023]
Abstract
We study the impact of the nonanalytic reconstruction of vortex cores on static vortex structures in weakly coupled superfluids. We show that, in rotating two-dimensional systems, the Abrikosov vortex lattice is unstable to vortex core deformation: Each zero of the wave function becomes a cut of finite length. The directors characterizing the orientations of the cuts are themselves ordered in superstructures due either to surface effects or to interaction with shear deformations of the lattice (spiral structure). Similar instability may also be observable in clean superconducting films.
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Affiliation(s)
- Avraham Klein
- The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Oded Agam
- The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Igor L Aleiner
- Physics Department, Columbia University, New York, New York 10027, USA
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Stannarius R, Harth K. Defect Interactions in Anisotropic Two-Dimensional Fluids. PHYSICAL REVIEW LETTERS 2016; 117:157801. [PMID: 27768347 DOI: 10.1103/physrevlett.117.157801] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2016] [Indexed: 06/06/2023]
Abstract
Disclinations in liquid crystals bear striking analogies to defect structures in a wide variety of physical systems, and their straightforward optical observability makes them excellent models to study fundamental properties of defect interactions. We employ freely suspended smectic-C films, which behave as quasi-two-dimensional polar nematics. A procedure to capture high-strength disclinations in localized spots is introduced. These disclinations are released in a controlled way, and the motion of the mutually repelling topological charges with strength +1 is studied quantitatively. We demonstrate that the classical models, which employ elastic one-constant approximation, fail to describe their dynamics correctly. In realistic liquid crystals, even small differences between splay and bend constants lead to the selection of pure splay or pure bend +1 defects. For those, the models work only in very special configurations. In general, additional director walls are involved which reinforce the repulsive interactions substantially.
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Affiliation(s)
- R Stannarius
- Institute for Experimental Physics, Otto von Guericke University, D-39106 Magdeburg, Germany
| | - K Harth
- Institute for Experimental Physics, Otto von Guericke University, D-39106 Magdeburg, Germany
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