Size effects and dislocation patterning in two-dimensional bending

We perform atomistic Monte Carlo simulations of bending a Lennard-Jones single crystal in two dimensions. Dislocations nucleate only at the free surface as there are no sources in the interior of the sample. When dislocations reach sufficient density, they spontaneously coalesce to nucleate grain boundaries, and the resulting microstructure depends strongly on the initial crystal orientation of the sample. In initial yield, we find a reverse size effect, in which larger samples show a higher scaled bending moment than smaller samples for a given strain and strain rate. This effect is associated with source-limited plasticity and high strain rate relative to dislocation mobility, and the size effect in initial yield disappears when we scale the data to account for strain rate effects. Once dislocations coalesce to form grain boundaries, the size effect reverses and we find that smaller crystals support a higher scaled bending moment than larger crystals. This finding is in qualitative agreement with experimental results. Finally, we observe an instability at the compressed crystal surface that suggests a novel mechanism for the formation of a hillock structure. The hillock is formed when a high angle grain boundary, after absorbing additional dislocations, becomes unstable and folds to form a new crystal grain that protrudes from the free surface.Comment: 15 pages, 8 figure

Complete Positivity for Mixed Unitary Categories

In this article we generalize the \CP^\infty-construction of dagger monoidal categories to mixed unitary categories. Mixed unitary categories provide a setting, which generalizes (compact) dagger monoidal categories and in which one may study quantum processes of arbitrary (infinite) dimensions. We show that the existing results for the \CP^\infty-construction hold in this more general setting. In particular, we generalize the notion of environment structures to mixed unitary categories and show that the \CP^\infty-construction on mixed unitary categories is characterized by this generalized environment structure.Comment: Lots of figure

Faint star counts in the near-infrared

We discuss near-infrared star counts at the Galactic pole with a view to guiding the NGST and ground-based NIR cameras. Star counts from deep K-band images from the CFHT are presented, and compared with results from the 2MASS survey and some Galaxy models. With appropriate corrections for detector artifacts and galaxies, the data agree with the models down to K~18, but indicate a larger population of fainter red stars. There is also a significant population of compact galaxies that extend to the observational faint limit of K=20.5. Recent Galaxy models agree well down to K$\sim$19, but diverge at fainter magnitudes.Comment: 14 pages and 4 diagrams; to appear in PAS

Tangent Categories from the Coalgebras of Differential Categories

Following the pattern from linear logic, the coKleisli category of a differential category is a Cartesian differential category. What then is the coEilenberg-Moore category of a differential category? The answer is a tangent category! A key example arises from the opposite of the category of Abelian groups with the free exponential modality. The coEilenberg-Moore category, in this case, is the opposite of the category of commutative rings. That the latter is a tangent category captures a fundamental aspect of both algebraic geometry and Synthetic Differential Geometry. The general result applies when there are no negatives and thus encompasses examples arising from combinatorics and computer science

Using Problem Frames and projections to analyze requirements for distributed systems

Subproblems in a problem frames decomposition frequently make use of projections of the complete problem context. One specific use of projec-tions occurs when an eventual implementation will be distributed, in which case a subproblem must interact with (use) the machine in a projection that represents another subproblem. We refer to subproblems used in this way as services, and propose an extension to projections to represent services as a spe-cial connection domain between subproblems. The extension provides signifi-cant benefits: verification of the symmetry of the interfaces, exposure of the machine-to-machine interactions, and prevention of accidental introduction of shared state. The extension’s usefulness is validated using a case study