Micro-plasticity and intermittent dislocation activity in a simplified micro structural model

Here we present a model to study the micro-plastic regime of a stress-strain curve. In this model an explicit dislocation population represents the mobile dislocation content and an internal shear-stress field represents a mean-field description of the immobile dislocation content. The mobile dislocations are constrained to a simple dipolar mat geometry and modelled via a dislocation dynamics algorithm, whilst the shear-stress field is chosen to be a sinusoidal function of distance along the mat direction. The latter, defined by a periodic length and a shear-stress amplitude, represents a pre-existing micro-structure. These model parameters, along with the mobile dislocation density, are found to admit a diversity of micro-plastic behaviour involving intermittent plasticity in the form of a scale-free avalanche phenomenon, with an exponent for the strain burst magnitude distribution similar to those seen in experiment and more complex dislocation dynamics simulations.Comment: 30 pages, 12 figures, to appear in "Modelling and Simulation in Materials Science and Engineering

Ground State Electromagnetic Moments of ³⁷Ca

The hyperfine coupling constants of neutron deficient $^{37}$Ca were deduced from the atomic hyperfine spectrum of the $4s~^2S_{1/2}$ $\leftrightarrow$ $4p~^2P_{3/2}$ transition in Ca II, measured using the collinear laser spectroscopy technique. The ground-state magnetic-dipole and spectroscopic electric-quadrupole moments were determined for the first time as $\mu = +0.7453(72) \mu_N$ and $Q = -15(11)$ $e^2$fm$^2$, respectively. The experimental values agree well with nuclear shell model calculations using the universal sd model-space Hamiltonians versions A and B (USDA/B) in the $sd$-model space with a 95\% probability of the canonical nucleon configuration. It is shown that the magnetic moment of $^{39}$Ca requires a larger non-$sd$-shell component than that of $^{37}$Ca for good agreement with the shell-model calculation, indicating a more robust closed sub-shell structure of $^{36}$Ca at the neutron number $N$ = 16 than $^{40}$Ca. The results are also compared to valence-space in-medium similarity renormalization group calculations based on chiral two- and three-nucleon interactions

Generalized Kac-Moody Algebras from CHL dyons

We provide evidence for the existence of a family of generalized Kac-Moody(GKM) superalgebras, G_N, whose Weyl-Kac-Borcherds denominator formula gives rise to a genus-two modular form at level N, Delta_{k/2}(Z), for (N,k)=(1,10), (2,6), (3,4), and possibly (5,2). The square of the automorphic form is the modular transform of the generating function of the degeneracy of CHL dyons in asymmetric Z_N-orbifolds of the heterotic string compactified on T^6. The new generalized Kac-Moody superalgebras all arise as different `automorphic corrections' of the same Lie algebra and are closely related to a generalized Kac-Moody superalgebra constructed by Gritsenko and Nikulin. The automorphic forms, Delta_{k/2}(Z), arise as additive lifts of Jacobi forms of (integral) weight k/2 and index 1/2. We note that the orbifolding acts on the imaginary simple roots of the unorbifolded GKM superalgebra, G_1 leaving the real simple roots untouched. We anticipate that these superalgebras will play a role in understanding the `algebra of BPS states' in CHL compactifications.Comment: LaTeX, 35 pages; v2: improved referencing and discussion; typos corrected; v3 [substantial revision] 44 pages, modularity of additive lift proved, product representation of the forms also given; further references adde

Negotiating different disciplinary discourses: biology students’ ritualized and exploratory participation in mathematical modeling activities

Non-mathematics specialists’ competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students’ mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the theory of commognition to investigate the tensions between ritualized and exploratory participation in the students’ MM activity. We focus particularly on a quintessential routine in MM, assumption building: we trace attempts which start from ritualized engagement in the shape of “guesswork” and evolve into more productively exploratory formulations. We also identify signs of persistent commognitive conflict in the students’ activity, both intra-mathematical (concerning what is meant by a “math task”) and extra-mathematical (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students’ discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary

The Beta-decay Paul Trap Mk IV: Design and commissioning

The Beta-decay Paul Trap is an open-geometry, linear trap used to measure the decays of $^8$Li and $^8$B to search for a tensor contribution to the weak interaction. In the latest $^8$Li measurement of Burkey et al. (2022), $\beta$ scattering was the dominant experimental systematic uncertainty. The Beta-decay Paul Trap Mk IV reduces the prevalence of $\beta$ scattering by a factor of 4 through a redesigned electrode geometry and the use of glassy carbon and graphite as electrode materials. The trap has been constructed and successfully commissioned with $^8$Li in a new data campaign that collected 2.6 million triple coincidence events, an increase in statistics by 30% with 4 times less $\beta$ scattering compared to the previous $^8$Li data set.Comment: 17 pages, 7 figure

Particle tracking for polydisperse sedimenting droplets in phase separation

When a binary fluid demixes under a slow temperature ramp, nucleation, coarsening and sedimentation of droplets lead to an oscillatory evolution of the phase separating system. The advection of the sedimenting droplets is found to be chaotic. The flow is driven by density differences between the two phases. Here, we show how image processing can be combined with particle tracking to resolve droplet size and velocity simultaneously. Droplets are used as tracer particles, and the sedimentation velocity is determined. Taking these effects into account, droplets with radii in the range of 4 -- 40 micrometers are detected and tracked. Based on this data we resolve the oscillations in the droplet size distribution which are coupled to the convective flow.Comment: 13 pages; 16 figures including 3 photographs and 3 false-color plot

Author Correction: Non-local effect of impurity states on the exchange coupling mechanism in magnetic topological insulators

A Correction to this paper has been published: https://doi.org/10.1038/s41535-021-00314-