Line defect Schur indices, Verlinde algebras and U(1)rU(1)_r fixed points

Given an $\mathcal{N}=2$ superconformal field theory, we reconsider the Schur index $\mathcal{I}_L(q)$ in the presence of a half line defect $L$. Recently Cordova-Gaiotto-Shao found that $\mathcal{I}_L(q)$ admits an expansion in terms of characters of the chiral algebra $\mathcal{A}$ introduced by Beem et al., with simple coefficients $v_{L,\beta}(q)$. We report a puzzling new feature of this expansion: the $q \to 1$ limit of the coefficients $v_{L_,\beta}(q)$ is linearly related to the vacuum expectation values $\langle L \rangle$ in $U(1)_r$-invariant vacua of the theory compactified on $S^1$. This relation can be expressed algebraically as a commutative diagram involving three algebras: the algebra generated by line defects, the algebra of functions on $U(1)_r$-invariant vacua, and a Verlinde-like algebra associated to $\mathcal{A}$. Our evidence is experimental, by direct computation in the Argyres-Douglas theories of type $(A_1,A_2)$, $(A_1,A_4)$, $(A_1, A_6)$, $(A_1, D_3)$ and $(A_1, D_5)$. In the latter two theories, which have flavor symmetries, the Verlinde-like algebra which appears is a new deformation of algebras previously considered.Comment: 64 pages, 21 figures. v2 published version, references update

Meso-scale modelling of 3D woven composite T-joints with weave variations

A meso-scale modelling framework is proposed to simulate the 3D woven fibre architectures and the mechanical performance of the composite T-joints, subjected to quasi-static tensile pull-off loading. The proposed method starts with building the realistic reinforcement geometries of the 3D woven T-joints at the mesoscale, of which the modelling strategy is applicable for other types of geometries with weave variations at the T-joint junction. Damage modelling incorporates both interface and constituent material damage, in conjunction with a continuum damage mechanics approach to account for the progressive failure behaviour. With a voxel based cohesive zone model, the proposed method is able to model mode I delamination based on the voxel mesh technique, which has advantages in meshing. Predicted results are in good agreement with experimental data beyond initial failure, in terms of load-displacement responses, failure events, damage initiation and propagation. The significant effect of fibre architecture variations on mechanical behaviour is successfully predicted through this modelling method without any further correlation of input parameters in damage model. This predictive method will facilitate the design and optimisation of 3D woven T-joint preforms

Experimental assessment of the mechanical behaviour of 3D woven composite T-joints

To understand the influence of the fibre architecture of 3D woven composite T-joints on mechanical performance, as well as the benefits that 3D woven T-joints can offer over the equivalent 2D laminates, experimental testing is performed on two types of 3D woven T-joint with only weave variation at the junction, and one type of 2D woven laminate T-joint. A quasi-static tensile pull-off loading is selected in this work as this out-of-plane load case is one of the typical loading conditions for such T-joint structures. The significant advantages of 3D woven composite T-joints in terms of ultimate strength and damage tolerance over the 2D alternative were identified in the testing. More importantly, this work showed that variation in the fibre architecture can considerably enhance properties such as delamination resistance and total energy absorption to failure, as well as increasing slightly the stiffness and initial failure load. This experimental assessment has demonstrated that using 3D woven reinforcements is an effective way to improve the load-bearing capability of composite T-joints over laminates, and also that this improvement could be optimised with regard to fibre architecture

Modelling the impacts of pasture contamination and stocking rate for the development of targeted selective treatment strategies for Ostertagia ostertagi infection in calves

A simulation study was carried out to assess whether variation in pasture contamination or stocking rate impact upon the optimal design of targeted selective treatment (TST) strategies. Two methods of TST implementation were considered: 1) treatment of a fixed percentage of a herd according to a given phenotypic trait, or 2) treatment of individuals that exceeded a threshold value for a given phenotypic trait. Four phenotypic traits, on which to base treatment were considered: 1) average daily bodyweight gain, 2) faecal egg count, 3) plasma pepsinogen, or 4) random selection. Each implementation method (fixed percentage or threshold treatment) and determinant criteria (phenotypic trait) was assessed in terms of benefit per R (BPR), the ratio of average benefit in weight gain to change in frequency of resistance alleles R (relative to an untreated population). The impact of pasture contamination on optimal TST strategy design was investigated by setting the initial pasture contamination to 100, 200 or 500 O. ostertagi L3/kg DM herbage; stocking rate was investigated at a low (3calves/ha), conventional (5 calves/ha) or high (7 calves/ha) stocking rates. When treating a fixed percentage of the herd, treatments according to plasma pepsinogen or random selection were identified as the most beneficial (i.e. resulted in the greatest BPR) for all levels of initial pasture contamination and all stocking rates. Conversely when treatments were administered according to threshold values ADG was most beneficial, and was identified as the best TST strategy (i.e. resulted in the greatest overall BPR) for all levels of initial pasture contamination and all stocking rates