Long-term Test Arrangement for Externally Strengthened Reinforced Concrete Elements

Methods for external strengthening of concrete use elements of very high tensional strength glued on to its tensioned surface. These elements may be of metal, carbon fibers (CFRP), glass fibers or others, usually having very good mechanical properties. However, these high-strength elements are normally attached to concrete by epoxy resins. Epoxy resins have a low Young`s modulus and therefore a higher rate of creep may have an influence on the long-term behavior of such external strengthening. In order to verify this idea experimentally a special space-saving arrangement of tests is described in this paper. Panels act as loaded beams but simultaneously as a load for the other panels in a stand. The different load magnitude acting on a different layer of panels should make it possible to study the long-term influence of the degree of shear force on the glue creep. Certainly, the glue creep may be dependent on the type of epoxy resin; therefore several epoxy resin types are included in the tests

The fundamental pro-groupoid of an affine 2-scheme

A natural question in the theory of Tannakian categories is: What if you don't remember \Forget? Working over an arbitrary commutative ring $R$, we prove that an answer to this question is given by the functor represented by the \'etale fundamental groupoid \pi_1(\spec(R)), i.e.\ the separable absolute Galois group of $R$ when it is a field. This gives a new definition for \'etale \pi_1(\spec(R)) in terms of the category of $R$-modules rather than the category of \'etale covers. More generally, we introduce a new notion of "commutative 2-ring" that includes both Grothendieck topoi and symmetric monoidal categories of modules, and define a notion of $\pi_1$ for the corresponding "affine 2-schemes." These results help to simplify and clarify some of the peculiarities of the \'etale fundamental group. For example, \'etale fundamental groups are not "true" groups but only profinite groups, and one cannot hope to recover more: the "Tannakian" functor represented by the \'etale fundamental group of a scheme preserves finite products but not all products.Comment: 46 pages + bibliography. Diagrams drawn in Tik

Brown representability for space-valued functors

In this paper we prove two theorems which resemble the classical cohomological and homological Brown representability theorems. The main difference is that our results classify small contravariant functors from spaces to spaces up to weak equivalence of functors. In more detail, we show that every small contravariant functor from spaces to spaces which takes coproducts to products up to homotopy and takes homotopy pushouts to homotopy pullbacks is naturally weekly equivalent to a representable functor. The second representability theorem states: every contravariant continuous functor from the category of finite simplicial sets to simplicial sets taking homotopy pushouts to homotopy pullbacks is equivalent to the restriction of a representable functor. This theorem may be considered as a contravariant analog of Goodwillie's classification of linear functors.Comment: 19 pages, final version, accepted by the Israel Journal of Mathematic

Hierarchical Graph Transformation

If systems are specified by graph transformation, large graphs should be structured in order to be comprehensible. In this paper, we present an approach for the rule-based transformation of hierarchically structured (hyper)graphs. In these graphs, distinguished hyperedges contain graphs that can be hierarchical again. Our framework extends the well-known double-pushout approach from at to hierarchical graphs. In particular, we show how pushouts and pushout complements of hierarchical graphs and graph morphisms can be constructed recursively. Moreover, we make rules more expressive by introducing variables which allow to copy and to remove hierarchical subgraphs in a single rule application

Effects of Age and Loading Velocity on the Delamination Strength of the Human Aorta

Delamination strength is the mechanical property which plays a key role in the pathological process referred to as Arterial Dissection. This dissection, known especially for its occurrence in the thoracic aorta, is manifested by a separation of the layers of an artery wall, and may end with total rupture and internal haemorrhaging. Although its incidence is relatively rare, from 3 to 6 cases per 100 000 per year, it is a life-threating disease with a significant lethality [1-3]. The exact conditions under which the dissection is initiated, and as a crack propagates through the arterial wall, remain an open topic in computational as well as experimental mechanics. The aim of our study is to contribute to the deepening of our knowledge of Arterial Dissection, by collecting experimental data which is suitable for the purpose of showing how the delamination strength measured in the peeling experiments depends on age and anatomical location. In addition to the effects of age and location, our study also focuses on the effect of loading rate. The experimental branch of our research is complemented by a computational modelling of the delamination interface, in which we are looking for a numerical characterization of the material parameters describing discontinuity propagation. An XFEM model of the peeling experiment is built in Abaqus, which in our approach plays the role of the regression analysis, incorporating the cohesive zone (CZ) in order to model the delaminating arterial layers. The main objective is to obtain a detailed description of a set of constitutive parameters, which would be age- and location-specific. Our present data suggest that delamination strength strongly depends on age, and furthermore, the anatomical site also seems to be a significant factor. On the other hand, the loading velocity does not cause significant changes in results

Companions, codensity and causality

In the context of abstract coinduction in complete lattices, the notion of compatible function makes it possible to introduce enhancements of the coinduction proof principle. The largest compatible function, called the companion, subsumes most enhancements and has been proved to enjoy many good properties. Here we move to universal coalgebra, where the corresponding notion is that of a final distributive law. We show that when it exists the final distributive law is a monad, and that it coincides with the codensity monad of the final sequence of the given functor. On sets, we moreover characterise this codensity monad using a new abstract notion of causality. In particular, we recover the fact that on streams, the functions definable by a distributive law or GSOS specification are precisely the causal functions. Going back to enhancements of the coinductive proof principle, we finally obtain that any causal function gives rise to a valid up-to-context technique

Bousfield localisations along Quillen bifunctors

Consider a Quillen adjunction of two variables between combinatorial model categories from C x D to E, and a set S of morphisms in C. We prove that there is a localised model structure L_S E on E, where the local objects are the S-local objects in E described via the right adjoint. These localised model structures generalise Bousfield localisations of simplicial model categories, Barnes and Roitzheim's familiar model structures, and Barwick's enriched Bousfield localisations. In particular, we can use these model structures to define Postnikov sections in more general left proper combinatorial model categories