Coercivity and stability results for an extended Navier-Stokes system

In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of controlling the nonlinear terms. We address questions of global existence and stability in bounded domains with no-slip boundary conditions. Even in two space dimensions, global existence is open in general, and remains so, primarily due to the lack of a self-contained $L^2$ energy estimate. However, through use of new $H^1$ coercivity estimates for the linear equations, we establish a number of global existence and stability results, including results for small divergence and a time-discrete scheme. We also prove global existence in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure

An experimental investigation of the effects of \u3ci\u3en\u3c/i\u3e-decane on the supercritical pyrolysis of toluene

Future and current high-speed jet aircraft will require their fuels to act as the primary coolants as well as propellants. Fuels will be exposed to severe temperatures and pressures in hypersonic aircraft, up to 700°C and 130 atm, respectively, conditions that are supercritical for most pure hydrocarbons. Under supercritical conditions, hydrocarbon fuels undergo pyrolytic reactions, which may lead to the formation of polycyclic aromatic hydrocarbons (PAH), known precursors to carbonaceous solid deposits. Such deposits may clog fuel lines and injection nozzles, hindering safe engine performance. Hence, it is important to understand the reactions that lead to the formation of PAH. While jet fuels are composed primarily of alkanes, a significant portion of their composition is comprised of aromatics. In our effort to understand PAH formation, we must first understand the interactions of aliphatic and aromatic fuel components. Therefore, the aromatic model fuel toluene (critical temperature, 319°C; critical pressure, 41 atm) has been pyrolyzed both alone and in the presence of the aliphatic model fuel n-decane (critical temperature, 345°C; critical pressure, 20.8 atm) in an isothermal flow reactor at 570°C and 600°C, 94.6 atm, and 133 sec. Analyses of 12 gas-phase and 53 condensed-phase hydrocarbon products were performed with gas chromatography (GC) with flame-ionization detection (FID) and GC/FID coupled with mass spectrometry (MS), respectively. Results indicate that n-decane addition increases toluene conversion and product yields. In n-decane-doped toluene pyrolysis at 570°C, n-decane conversion is inhibited by the smaller radical pool relative to n-decane-only pyrolysis at the same temperature. 1-Alkene formation is generally enhanced compared to n-alkanes at 570°C, a result that contrasts with results obtained from n-decane-only pyrolysis at the same temperature. Additionally, results suggest that interactions of alkenes and benzylic-type radicals are important to the formation of high-ring number aromatics. Increasing the temperature to 600°C increases the conversions of both toluene and n-decane and causes a general rise in product yields. Yields of aliphatics and n-alkylbenzenes with long-carbon chains decrease at 600°C due to decomposition of the alkyl chain. Product yields as functions of n-decane concentration at 570°C and 600°C are presented, and possible product formation pathways are discussed

Energy Efficient Service Delivery in Clouds in Compliance with the Kyoto Protocol

Cloud computing is revolutionizing the ICT landscape by providing scalable and efficient computing resources on demand. The ICT industry - especially data centers, are responsible for considerable amounts of CO2 emissions and will very soon be faced with legislative restrictions, such as the Kyoto protocol, defining caps at different organizational levels (country, industry branch etc.) A lot has been done around energy efficient data centers, yet there is very little work done in defining flexible models considering CO2. In this paper we present a first attempt of modeling data centers in compliance with the Kyoto protocol. We discuss a novel approach for trading credits for emission reductions across data centers to comply with their constraints. CO2 caps can be integrated with Service Level Agreements and juxtaposed to other computing commodities (e.g. computational power, storage), setting a foundation for implementing next-generation schedulers and pricing models that support Kyoto-compliant CO2 trading schemes

Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

Realizations of Differential Operators on Conic Manifolds with Boundary

We study the closed extensions (realizations) of differential operators subject to homogeneous boundary conditions on weighted L_p-Sobolev spaces over a manifold with boundary and conical singularities. Under natural ellipticity conditions we determine the domains of the minimal and the maximal extension. We show that both are Fredholm operators and give a formula for the relative index.Comment: 41 pages, 1 figur

Assessing the role of accuracy-based feedback in value-driven attentional capture

© 2018, The Psychonomic Society, Inc. Despite being physically nonsalient and task-irrelevant, objects rendered in a color that once signaled monetary reward reflexively capture attention during visual search, a phenomenon known as value-driven attentional capture (VDAC). However, it remains a subject of empirical controversy whether learned reward associations are necessary to driving subsequent attentional capture: VDAC-like effects have been observed when accuracy-based feedback alone was used during the VDAC training phase, resulting in attentional capture by objects that were never associated with monetary reward; perplexingly, the presence of these VDAC-like effects in the literature conflicts with those of a number of control studies in which no such capture has been observed, leaving the issue currently unresolved. In this Registered Report, we present new empirical evidence of attentional capture by unrewarded former targets following limited accuracy-based training. We proposed to replicate these results in an independent sample and to test an empirically derived hypothesis concerning a methodological difference between the studies that have shown VDAC-like effects with accuracy-based feedback and those that have not. In short, we found no evidence that this methodological difference accounts for the inconsistencies in the literature, but our replication efforts were overwhelmingly successful, thus reinvigorating debate about the role that selection history may play in value-driven attentional capture

Differentiation and dynamics of competitiveness impacts from the EU ETS

We summarises the main factors that differentiate impacts of the EU ETS on profitability and market share. By examining sampling a range of sectors, we present some simple metrics and indicators to help judge the nature of potential impacts. We also consider briefly the mitigation response to these impacts by sectors, and how they may evolve over time. The broad conclusion confirms the aggregate findings presented in the existing literature - most participating sectors are likely to profit under the current ETS structure out to 2012 at the cost of a modest loss of market share, but this may not hold for individual companies and regions. The period 2008-12 can assist participating sectors to build experience and financial reserves for longer term technology investments and diversification, providing the continuation and basic principles of the EU ETS post-2012 is quickly defined and incentives are in place for sectors to pursue this.Emissions trading, industrial competitiveness, spillovers, allowance allocation, perverse incentives.