2,022 research outputs found

    On the Γ\Gamma-limit for a non-uniformly bounded sequence of two phase metric functionals

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    In this study we consider the Γ\Gamma-limit of a highly oscillatory Riemannian metric length functional as its period tends to 0. The metric coefficient takes values in either {1,∞}\{1,\infty\} or {1,βε−p}\{1,\beta \varepsilon^{-p}\} where β,ε>0\beta,\varepsilon > 0 and p∈(0,∞)p \in (0,\infty). We find that for a large class of metrics, in particular those metrics whose surface of discontinuity forms a differentiable manifold, the Γ\Gamma-limit exists, as in the uniformly bounded case. However, when one attempts to determine the Γ\Gamma-limit for the corresponding boundary value problem, the existence of the Γ\Gamma-limit depends on the value of pp. Specifically, we show that the power p=1p=1 is critical in that the Γ\Gamma-limit exists for p<1p < 1, whereas it ceases to exist for p≥1p \geq 1. The results here have applications in both nonlinear optics and the effective description of a Hamiltonian particle in a discontinuous potential.Comment: 31 pages, 1 figure. Submitte

    Storyville: Discourses in Southern Musicians\u27 Autobiographies

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    This study utilizes many of the tools of the literary critic to identify and analyze the discursive conventions in autobiographies by American vernacular musicians who came of age in the American South during the era of enforced racial segregation. Through this textual analysis, we can appreciate this seemingly amorphous collection of books as a continuing conversation, where descriptions of the South and its music by turns confirm, contradict, and complicate each other. Ultimately, the dozens of southern musician autobiographies published in the last fifty years engage in a valuable and revealing dialogue, creating a virtual Storyville ; ostensibly disparate works share themes, ideas, and literary approaches, while each narrative is distinguished by unique motifs, idiosyncrasies, and digressions.;From this crosstalk emerges a rich history informed by local knowledge as well as a larger, multifaceted portrait of now-vanished musical communities, such as Storyville-era New Orleans and the Mississippi Delta juke-joint circuit. In collaboration with co-authors, southern musicians typically employ a hybrid discursive style that attempts to balance personal subjectivity with historical authority. This narrative approach encompasses literary devices---such as free indirect discourse and paralepsis---and the thick description common in the social sciences. Through this reportage, musicians establish themselves as uniquely positioned organic intellectuals and citizen-historians of their respective places and times. Read collectively, musicians\u27 published reminiscences provide important and overlooked first-person reflections on life in the Jim Crow South

    Wear modelling of diamond-like carbon coatings against steel in deionised water

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    Diamond-Like Carbon (DLC) coatings are thin protective surface coatings used to reduce friction and minimise wear in a wide range of applications. The focus of this work is the use of DLC coatings within Rolls-Royce’s pressurised water reactors. A strong understanding of material behaviour in this environment is compulsory due to the stringent safety requirements of the nuclear industry. Wear testing of a range of commercial DLC coatings against steel in water, and the dependence of the tribology on normal load, sliding distance, and environmental species, was examined. Wear depth was observed to increase with normal load, and increase non-linearly with sliding distance. Uniquely, it was suggested that the tribology of a DLC coating in water was controlled by the velocity accommodation mode (VAM) of the transfer layer. When interfacial sliding was the dominant VAM, the carbonaceous transfer layer was present at all times, and a low specific wear rate was observed. When shear and recirculation of debris was the dominant VAM, the carbonaceous transfer layer initially present was replaced by iron oxide species, and a high specific wear rate was observed as a result of a three-body mechanism involving hematite.Two individual wear models were developed to predict the wear depth of a DLC coating sliding against steel in water. Each model represents a novel extension to the current literature regarding the modelling of wear. Firstly, an analytical differential equation was derived to predict the wear depth of a ball and a flat surface, in relation to any phenomenological law for wear volume. Secondly, a unique formulation of an incremental wear model for an arbitrary geometry was developed for a DLC coating which included the growth of a transfer layer. An efficient methodology was presented to allow fast integration of the equations whilst damping numerical instabilities. A comparison between the analytic and computational wear models showed a strong agreement in the model predictions, with a comparative error of less than 5%

    Investigation of Outlife Time on the Environmental Durability of P2-Etched, Adhesively-Bonded Aluminum Alloys Using the ASTM Wedge Test

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    P2 etchant is an environmentally-friendly aluminum etchant which has the potential to replace the Forest Products Laboratory (FPL) etchant as the industry standard. Environmental durability of adhesively-bonded aluminum surfaces etched using a paste version of the P2 etchant were tested using the Boeing-developed wedge test (ASTM D3762 - 03(2010)). This project specifically aimed to examine the relationship between outlife time (the time between etching and adhering) and the ability of bonded aluminum samples to pass the wedge test. Two aluminum alloys, 2024-T3 and 7075-T6, were wedge tested and the etched surfaces examined with an atomic force microscope (AFM) and a scanning electron microscope (SEM). The etchant improved durability of the bonded specimens and helped produce passing 2024 specimens for times ranging up to one week. Results of the 2024 testing demonstrated slightly decreased bond durability on average with increased outlife times, while the results of the 7075 testing were less conclusive and require more investigation to make meaningful conclusions. With more 2024 testing, the data could ideally be used to find a consistent critical outlife time near where bond durability decreases below the minimally-acceptable value. The results of this study may help Raytheon Company to improve their manufacturing procedures by defining a broader range of acceptable outlife times

    Deductions from the Export Basket: Capabilities, Wealth and Trade

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    This paper re-explores the relation between a country's level of wealth and the mix of products it exports. We argue that both are simultaneously determined by countries' capabilities i.e. by countries' productivity and quality levels for each good. Our theoretical setup has two features. (1) Some goods have fewer high-quality producers/countries than others i.e. there is Ricardian comparative advantage. (2) Imperfect competition allows high- and low-quality producers to coexist, which we refer to as 'product ranges'. These two features generate a very particular non-monotonic, general equilibrium relationship between a country's export mix and its wage (GDP per capita). We show that this non-monotonicity permeates the 1980-2005 international data on trade and GDP per capita. Our setup also explains two other facets of the data: (1) Product ranges are huge and (2) for the poorest third of countries, changes in export mix substantially over-predict growth in GDP per capita. This suggests that the main challenge for low-income countries is to raise quality and productivity in their existing product lines.

    Tomographic reconstruction of neopterous Carboniferous insect nymphs

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    Two new polyneopteran insect nymphs from the Montceau-les-Mines Lagerstätte of France are presented. Both are preserved in three dimensions, and are imaged with the aid of X-ray micro-tomography, allowing their morphology to be recovered in unprecedented detail. One–Anebos phrixos gen. et sp. nov.–is of uncertain affinities, and preserves portions of the antennae and eyes, coupled with a heavily spined habitus. The other is a roachoid with long antennae and chewing mouthparts very similar in form to the most generalized mandibulate mouthparts of extant orthopteroid insects. Computer reconstructions reveal limbs in both specimens, allowing identification of the segments and annulation in the tarsus, while poorly developed thoracic wing pads suggest both are young instars. This work describes the morphologically best-known Palaeozoic insect nymphs, allowing a better understanding of the juveniles’ palaeobiology and palaeoecology. We also consider the validity of evidence from Palaeozoic juvenile insects in wing origin theories. The study of juvenile Palaeozoic insects is currently a neglected field, yet these fossils provide direct evidence on the evolution of insect development. It is hoped this study will stimulate a renewed interest in such work

    SL2 tilting modules in the mixed case

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    Using the non-semisimple Temperley-Lieb calculus, we study the additive and monoidal structure of the category of tilting modules for SL2\mathrm{SL}_{2} in the mixed case. This simultaneously generalizes the semisimple situation, the case of the complex quantum group at a root of unity, and the algebraic group case in positive characteristic. We describe character formulas and give a presentation of the category of tilting modules as an additive category via a quiver with relations. Turning to the monoidal structure, we describe fusion rules and obtain an explicit recursive description of the appropriate analog of Jones-Wenzl projectors. We also discuss certain theta values, the tensor ideals, mixed Verlinde quotients and the non-degeneracy of the braiding.Comment: 53 pages, many figures, comments welcom
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