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Dancing Droplets on a Defect Line [Poster]

Liquid crystalline (LC) phases are made up of molecules or other small units that organize into mesoscale assemblies. Their order resembles that of crystalline solids, but since the molecules have some freedom to move position and direction, these assemblies also behave like liquids. Thus, highly birefringent and responsive phases with many defect (or disclination) lines can emerge. These ever fluctuating lines indicate regions of the LC where the position of the molecules disrupt the local rotational symmetry within the phase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Index-like theorems from line defect vevs

In this paper we investigate the relation between complexified Fenchel-Nielsen coordinates and spectral network coordinates on Seiberg-Witten moduli space. The main technique is the comparison of exact expressions for the expectation value of ’t Hooft defects in certain 4D SU(2) N = 2 gauge theories. We derive an index-like theorem for a class of Dirac operators on singular monopole moduli spaces. Our expression determines the indices of Dirac operators on singular monopole moduli spaces in terms of characteristic numbers for vector bundles over certain Kronheimer-Nakajima quiver varieties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

q-nonabelianization for line defects

We consider the q-nonabelianization map, which maps links L in a 3-manifold M to combinations of links $\tilde{L}$ in a branched N -fold cover $\tilde{M}$. In quantum field theory terms, q-nonabelianization is the UV-IR map relating two different sorts of defect: in the UV we have the six-dimensional (2, 0) superconformal field theory of type gl(N ) on M × R 2,1 , and we consider surface defects placed on L × {x 4 = x 5 = 0}; in the IR we have the (2, 0) theory of type gl (1) on $\tilde{M}$ × R 2,1 , and put the defects on $\tilde{L}$ × {x 4 = x 5 = 0}. In the case M = R 3 , q-nonabelianization computes the Jones polynomial of a link, or its analogue associated to the group U(N ). In the case M = C × R, when the projection of L to C is a simple non-contractible loop, q-nonabelianization computes the protected spin character for framed BPS states in 4d N = 2 theories of class S. In the case N = 2 and M = C × R, we give a concrete construction of the q-nonabelianization map. The construction uses the data of the WKB foliations associated to a holomorphic covering $\tilde{C}$ →C.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Towards deep computer vision for in-line defect detection in polymer electrolyte membrane fuel cell materials

Polymer Electrolyte Membrane (PEM) fuel cells are a promising source of alternative energy. However, their production is limited by a lack of well-established methods for quality control of their constituent materials like the membrane-electrode assembly during roll-to-roll manufacturing. One potential solution is the implementation of deep learning methods to detect unwanted defects through their detection in scanned images. Here we explore the detection of defects like scratches, pinholes, and scuffs in a sample dataset of PEM optical images using two deep learning algorithms: Patch Distribution Modeling (PaDiM) for unsupervised anomaly detection and Faster-RCNN for supervised object detection. Both methods achieve scores on performance metrics (ROC-AUC and PRO-AUC for PaDiM and AP for Faster-RCNN) that are comparable to their scores on benchmark datasets. These methods also have the potential to detect a wider range of defects compared to IR thermography and previous optical inspection methods. Overall, deep learning shows promise at detecting relevant defects of interest and has the potential to achieve real-time defect detection.

30 DIRECT ENERGY CONVERSION↗

A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains

In this study, we present a field formulation for defects that draws from the classical representation of the cores as force dipoles. We write these dipoles as singular distributions. Exploiting the key insight that the variational setting is the only appropriate one for the theory of distributions, we arrive at universally applicable weak forms for defects in nonlinear elasticity. Remarkably, the standard, Galerkin finite element method yields numerical solutions for the elastic fields of defects that, when parameterized suitably, match very well with classical, linearized elasticity solutions. The true potential of our approach, however, lies in its easy extension to generate solutions to elastic fields of defects in the regime of nonlinear elasticity, and even more notably for Toupin's theory of gradient elasticity at finite strains (Toupin Arch. Ration. Mech. Anal., 11 (1962) 385). In computing these solutions we adopt recent numerical work on an isogeometric analytic framework that enabled the first three-dimensional solutions to general boundary value problems of Toupin's theory (Rudraraju et al. Comput. Methods Appl. Mech. Eng., 278 (2014) 705). We first present exhaustive solutions to point defects, edge and screw dislocations, and a study on the energetics of interacting dislocations. Then, to demonstrate the generality and potential of our treatment, we apply it to other complex dislocation configurations, including loops and low-angle grain boundaries.

36 MATERIALS SCIENCE↗