Robustness of topological defects in discrete domains

Hoffmann, Karl B.; Sbalzarini, Ivo F.

doi:10.1103/physreve.103.012602

Cited by 4 publications

(9 citation statements)

References 31 publications

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“…3(a), we identify AE1/2 defects via discrete contour integral of the director field. 32,33 By tracking their trajectories (marked by light green and purple lines) and symmetry axes (marked by dark green and purple lines), we obtain the distributions of the magnitude of defects' translational (V) and rotational (O) velocities as shown in panel (b). We find that, in contrast to the fast streaming behaviors in wet systems, here the +1/2-order defect moves as slowly as the À1/2order defect, with the most probable speed only about 0.3 (the single rod moving speed is 1).…”

Section: Bd Particle Simulationmentioning

confidence: 99%

Understanding topological defects in fluidized dry active nematics

et al. 2022

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Section: Bd Particle Simulationmentioning

confidence: 99%

Understanding topological defects in fluidized dry active nematics

et al. 2022

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“…For each detected cluster, we determine the center of mass (x clust , y clust ) of all defect locations (unit weights) in that cluster. We use discretized circular paths around the center point to compute the total topological charge, robustness [3,4], and the total number of microscopic defects enclosed by increasing path radii r ∈ (0, ∞). We find that paths smaller than the inner core radius R 1 lead to erratically fluctuating index estimates of low robustness (Fig.…”

Section: Defect Cores and Their Sizementioning

confidence: 99%

“…While we find the core radius estimator to work reliably in our benchmarks, other heuristics are possible as well. For example, one could alternatively fit a piecewise constant function to identify the onset of the robustness plateau at the core size radius, or employ a magnitude-aware version of the robustness measure [3]. One could also include information about the total number of enclosed microscopic defects, which also plateaus beyond the core radius (Fig.…”

Section: Defect Cores and Their Sizementioning

confidence: 99%

“…Finally, one can generalize to path shapes other than circles, e.g. by "expansion over the critical edge" [3], and use the same heuristics to quantify core size in terms of area rather than radius.…”

Section: Defect Cores and Their Sizementioning

confidence: 99%

“…Due to the discrete nature of a defect, its existence cannot depend continuously on a discretized orientation field, rendering defect identification challenging in applications with noisy or otherwise imperfect orientation measurements. Based on this observation, we have previously introduced a robustness measure for topological defects, which quantifies the largest admissible change in any single orientation value along the path that does not alter the defect estimator [3]. It therefore measures the sensitivity of a defect estimate to noise or temporal dynamics of the orientation field in a discrete domain.…”

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Estimation of unordered core size using a robustness measure for topological defects in discretized orientation and vector fields

Hoffmann

Sbalzarini

2021

Proc Appl Math & Mech

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We show how the finite sizes of unordered defect cores in discretized orientation and vector fields can reliably be estimated using a robustness measure for topological defects. Topological defects, or singular points, in vector and orientation fields are considered in applications from material science to life sciences to fingerprint recognition. Their identification from discretized two‐dimensional fields must deal with discontinuities, since the estimated topological charge jumps in (half‐)integer steps upon orientation changes above a certain threshold. We use a recently proposed robustness measure [Hoffmann & Sbalzarini, Phys. Rev. E 103(1), 012602 (2021)] that exploits this effect to quantify the influence of noise in a vector field, and of the path chosen for defect estimation, on the detection reliability in two‐dimensional discrete domains. Here, we show how this robustness measure can be used to quantify the sizes of unordered regions surrounding a defect, which are known as unordered cores. We suggest that the size of an unordered core can be identified as the smallest path radius of sufficient robustness. The resulting robust core‐size estimation complements singular point and index estimation and may serve as uncertainty quantification of defect localization, or as an additional feature for defect characterization.

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Phase Separation in a Binary Mixture of Semiflexible Polymers Confined in a Repulsive Sphere

2021

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Lyotropic solutions containing two types of semiflexible macromolecules in spherical confinement are studied by molecular dynamics simulations and density functional theory, using a coarse-grained model. The case of strong stiffness disparity between both types of polymers is treated, and for simplicity, we take the contour lengths of both types of polymers to be equal. Only sphere radii larger than this contour length are considered, so that many chains can be packed inside the sphere, even when the chains are stretched out in a nematic state. For the chosen polymer solution, in the bulk one finds with increasing monomer concentration a transition from an isotropic phase through an isotropic–nematic two-phase region to a homogeneous nematic phase to which both constituents contribute. In the corresponding confined systems, there is an interplay between these phase transitions and surface enrichment of one component (typically, but not always, the stiffer one). In rather dilute confined solutions, the main effect of the surfaces is that the random orientation of the end-to-end vectors of the stiff chains is perturbed in a surface shell whose thickness is roughly the contour length. In more concentrated systems, a thin layer of wall-attached stiff chains is observed in addition, while (for equal mole fractions of both constituents) the stiffer component can also form an almost cylindrical domain with a bipolar orientational order, surrounded in the remainder of the sphere by the less stiff component. Topological defects in the nematic order can be identified, similar to the case where a single type of semiflexible polymer is confined in a sphere. The radial profiles of monomer concentrations and of various order parameters are compared to analogous data near planar and cylindrical repulsive walls, to provide a comprehensive picture of confinement effects on such polymer solutions.

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Robustness of topological defects in discrete domains

Cited by 4 publications

References 31 publications

Understanding topological defects in fluidized dry active nematics

Understanding topological defects in fluidized dry active nematics

Estimation of unordered core size using a robustness measure for topological defects in discretized orientation and vector fields

Phase Separation in a Binary Mixture of Semiflexible Polymers Confined in a Repulsive Sphere

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