Two-dimensional Time-dependent Point Interactions

We study the time-evolution of a quantum particle subjected to time-dependent zero-range forces in two dimensions. After establishing a conceivable ansatz for the solution to the Schr\"{o}dinger equation, we prove that the wave packet time-evolution is completely specified by the solutions of a system of Volterra-type equations -- the {\it charge equations} -- involving the coefficients of the singular part of the wave function, thus extending to the two-dimensional case known results in one and three dimensions.Comment: 17 pages, AMS-LaTex; presentation of the model changed, small changes to Lemma 2.1 and Proposition 2.

A Note on the Dirac Operator with Kirchoff-Type Vertex Conditions on Metric Graphs

In this note we present some properties of the Dirac operator on noncompact metric graphs with Kirchoff-type vertex conditions. In particular, we discuss its spectral features and describe the associated quadratic form

Multiple crack propagation in friction stir welded aluminium joints

This paper is concerned with the simulation of crack propagation in friction stir welded butt joints, in order to assess the influence of process induced microstructural alterations and residual stresses on the fatigue behaviour of the assembly. The approach employed is based on the coupled use of the finite element method and the dual boundary element method in order to take advantage of the main capabilities of the two methods. The distribution of the process induced residual stresses has been mapped by means of the contour method. Then, the computed residual stresses field has been superimposed, in a dual boundary element environment, to the stress field as a result of a remote fatigue traction load and the crack growth is simulated. A two-parameter crack growth law, based on the evaluation of two thresholds, for the material being analysed, is used for the crack propagation rate assessment. The stress intensity factors are evaluated using the J-integral technique. Computational results have been compared with experimental data, provided from constant amplitude crack propagation tests on welded samples, showing the subdivision of the overall fatigue life in the two periods of crack initiation and crack propagation

A Quantum Model of Feshbach Resonances

We consider a quantum model of two-channel scattering to describe the mechanism of a Feshbach resonance. We perform a rigorous analysis in order to count and localize the energy resonances in the perturbative regime, i.e., for small inter-channel coupling, and in the non-perturbative one. We provide an expansion of the effective scattering length near the resonances, via a detailed study of an effective Lippmann-Schwinger equation with energy-dependent potential.Comment: 29 pages, pdfLaTe

The Production of Epistemic Culture and Agency during a First-Grade Engineering Design Unit in an Urban Emergent School

Primary school practices are often bound by traditions that perpetuate compliance and skills-based, decontextualized, rote memorization activities. These histories of practice, prevalent in schools serving mostly Black and Brown children, make it inordinately difficult for students to author themselves as knowledge builders (i.e., with epistemic agency), which is a form of injustice. Engineering is a potentially fertile context to support the creation of epistemic culture, whereby young students’ assets are recognized, named, and leveraged as they create and shape the group’s disciplinary knowledge. The authors investigated this potential. The primary research question was: How do first-grade students in an urban emergent school author themselves as epistemic agents during an engineering design unit? Using a social practice theory lens and ethnographic methods, the authors studied 29 days of a materials engineering unit focusing on the teacher’s epistemic commitments, implicit meanings of knowledge in classroom discourse, and practices that opened space for students’ epistemic agency. Data collection included fieldnotes and video of class activities and teacher and student interviews. Class discussions about the properties and uses of materials yielded a rich context for studying epistemic culture. The teacher’s epistemic commitments included an eschewing of disciplinary silos, recognizing the nonlinear nature of knowledge-building about engineering, and acknowledging children’s thinking as an asset for engineering knowledge production. Examples of students’ discursive moves demonstrating epistemic agency included: reminding others about the relevance of previous lessons to the current topic, mirroring the teacher’s instructional moves, claiming voice, space, time, and material resources for knowledge-building, translating one another’s ideas, and making unsolicited connections to their lives. Young children’s intellectual assets can too easily be overlooked in traditional learning contexts. This study demonstrates the affordances of responsive engineering instruction in recognizing and building on youths’ intellectual curiosity and enthusiasm for substantively contributing to the classroom’s knowledge-generating practices

Modelling of friction stir welding and its influence on the structural behaviour of aluminium stiffened panels

This work deals with the modelling and numerical simulation of aluminium stiffened panels, assembled by means of friction stir welding (FSW) operations, and subjected to compressive loads that can catastrophically induce buckling (global or local) unstable modes and, subsequently, overall failure. Due to their geometrical complexity, added to localized thermo-mechanical effects that typically come from joining by welding, approximation methods such as the Finite Element Method are typically used in such nonlinear analyses, having proved to be useful to designers focused on the prediction of the behaviour (before and post buckling) of such structures. Being grounded on previous contributions from the authors, the present paper aims to bring a number of innovative aspects to the current state of the art by considering in the developed models the simultaneous influence of residual stress fields, material softening effects and geometrical imperfections. Doing so, it is possible to infer about the singular and combined influence of these effects in the overall structural performance of stiffened panels, building up a useful and comprehensive methodology for design stages

Numerical simulation of the buckling behaviour of stiffened panels: Benchmarks for assessment of distinct modelling strategies

This work deals with the effective modelling and simulation of the behavior of stiffened panels, when subjected to compressive (buckling) loads. Within the Finite Element Method, two numerical strategies are compared, namely the Riks method and the displacement incremental control method, including damping effects. The capabilities and limitations of both approaches are explored for two distinct benchmarks: a panel with a blade stiffener, and a panel with a T shaped stiffener. In both cases, material (plasticity) and geometrical (large displacements) nonlinearities are considered, together with a modelling strategy based on shell elements. Following previous works of the authors, each panel accounts for initial geometric imperfections coming from friction stir welding joining operations. The paper shows a number of considerations that must be undertaken when choosing between one of the two modelling strategies. Both benchmarks involve a number of challenges from the point of view of modelling unstable structural behaviors, and therefore the proposed benchmarks can represent a valid set of case studies in the understanding of the capabilities of current numerical simulation codes

Prediction of Friction Stir Welding effects on AA2024-T3 plates and stiffened panels using a shell-based finite element model

Manufacturing-induced effects significantly affect in-service behaviour of welded structures, such as integrally stiffened panels for aeronautic applications. Being a complex phenomenon with several variables involved, the assessment of the effects coming from welding usually relies on numerical simulations. Here, a novel shell-based finite element model is proposed to accurately simulate the transient thermal fields and stress-strain distributions resulting from friction stir welding (FSW) processes. The capability of the model to predict (i) residual stresses, (ii) material softening and (iii) geometric distortion of the welded parts is assessed by the modelling and simulation of FSW applied on aluminium integrally stiffened panels