2,270 research outputs found

    Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains

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    We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enable one to efficiently tackle the integral fractional Laplacian. In particular, we develop techniques for the treatment of the dense stiffness matrix including the computation of the entries, the efficient assembly and storage of a sparse approximation and the efficient solution of the resulting equations. The main idea consists of generalising proven techniques for the treatment of boundary integral equations to general fractional orders. Importantly, the approximation does not make any strong assumptions on the shape of the underlying domain and does not rely on any special structure of the matrix that could be exploited by fast transforms. We demonstrate the flexibility and performance of this approach in a couple of two-dimensional numerical examples

    A theory for the impact of a wave breaking onto a permeable barrier with jet generation

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    We model a water wave impact onto a porous breakwater. The breakwater surface is modelled as a thin barrier composed of solid matter pierced by channels through which water can flow freely. The water in the wave is modelled as a finite-length volume of inviscid, incompressible fluid in quasi-one-dimensional flow during its impact and flow through a typical hole in the barrier. The fluid volume moves at normal incidence to the barrier. After the initial impact the wave water starts to slow down as it passes through holes in the barrier. Each hole is the source of a free jet along whose length the fluid velocity and width vary in such a way as to conserve volume and momentum at zero pressure. We find there are two types of flow, depending on the porosity, ß , of the barrier. If ß : 0 = ß < 0.5774 then the barrier is a strong impediment to the flow, in that the fluid velocity tends to zero as time tends to infinity. But if ß : 0.5774 = ß = 1 then the barrier only temporarily holds up the flow, and the decelerating wave water passes through in a finite time. We report results for the velocity and impact pressure due to the incident wave water, and for the evolving shape of the jet, with examples from both types of impact. We account for the impulse on the barrier and the conserved kinetic energy of the flow. Consideration of small ß gives insight into the sudden changes in flow and the high pressures that occur when a wave impacts a nearly impermeable seawall

    Salford postgraduate annual research conference (SPARC) 2012 proceedings

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    These proceedings bring together a selection of papers from the 2012 Salford Postgraduate Annual Research Conference (SPARC). They reflect the breadth and diversity of research interests showcased at the conference, at which over 130 researchers from Salford, the North West and other UK universities presented their work. 21 papers are collated here from the humanities, arts, social sciences, health, engineering, environment and life sciences, built environment and business

    Investigating changes in blood-cerebrospinal fluid barrier function in a rat model of chronic hypertension using non-invasive magnetic resonance imaging

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    Chronic hypertension is a major risk factor for the development of neurodegenerative disease, yet the etiology of hypertension-driven neurodegeneration remains poorly understood. Forming a unique interface between the systemic circulation and the brain, the blood-cerebrospinal fluid barrier (BCSFB) at the choroid plexus (CP) has been proposed as a key site of vulnerability to hypertension that may initiate downstream neurodegenerative processes. However, our ability to understand BCSFB’s role in pathological processes has, to date, been restricted by a lack of non-invasive functional measurement techniques. In this work, we apply a novel Blood-Cerebrospinal Fluid Barrier Arterial Spin Labeling (BCSFB-ASL) Magnetic resonance imaging (MRI) approach with the aim of detecting possible derangement of BCSFB function in the Spontaneous Hypertensive Rat (SHR) model using a non-invasive, translational technique. SHRs displayed a 36% reduction in BCSFB-mediated labeled arterial water delivery into ventricular cerebrospinal fluid (CSF), relative to normotensive controls, indicative of down-regulated choroid plexus function. This was concomitant with additional changes in brain fluid biomarkers, namely ventriculomegaly and changes in CSF composition, as measured by T1 lengthening. However, cortical cerebral blood flow (CBF) measurements, an imaging biomarker of cerebrovascular health, revealed no measurable change between the groups. Here, we provide the first demonstration of BCSFB-ASL in the rat brain, enabling non-invasive assessment of BCSFB function in healthy and hypertensive rats. Our data highlights the potential for BCSFB-ASL to serve as a sensitive early biomarker for hypertension-driven neurodegeneration, in addition to investigating the mechanisms relating hypertension to neurodegenerative outcomes

    Arsenic distribution and speciation in the fronds of the hyperaccumulator Pteris vittata

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    Pteris vittata is the first plant reported to be a hyperaccumulator of arsenic (As), and little is known about the mechanisms of As hyperaccumulation in this plant. Arsenic distribution at the whole plant (fronds) and cellular level was investigated using chemical analyses and energy dispersive X-ray microanalyses (EDXA). Speciation of As in the fronds was determined using X-ray absorption near edge spectroscopy (XANES) analyses. The majority of As was found in the pinnae (96% of total As). The concentration of As in pinnae decreased from the base to the apex of the fronds. Arsenic concentrations in spores and midribs were much lower than in the pinnae. EDXA analyses revealed that As was compartmentalized mainly in the upper and lower epidermal cells, probably in the vacuoles. The distribution pattern of potassium was similar to As, whereas other elements (Ca, Cl, K, Mg, P and S) were distributed differently. XANES analyses showed that approximately 75% of the As in fronds was present in the As(III) oxidation state and the remaining as As(V)

    On Inflation with Non-minimal Coupling

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    A simple realization of inflation consists of adding the following operators to the Einstein-Hilbert action: (partial phi)^2, lambda phi^4, and xi phi^2 R, with xi a large non-minimal coupling. Recently there has been much discussion as to whether such theories make sense quantum mechanically and if the inflaton phi can also be the Standard Model Higgs. In this note we answer these questions. Firstly, for a single scalar phi, we show that the quantum field theory is well behaved in the pure gravity and kinetic sectors, since the quantum generated corrections are small. However, the theory likely breaks down at ~ m_pl / xi due to scattering provided by the self-interacting potential lambda phi^4. Secondly, we show that the theory changes for multiple scalars phi with non-minimal coupling xi phi dot phi R, since this introduces qualitatively new interactions which manifestly generate large quantum corrections even in the gravity and kinetic sectors, spoiling the theory for energies > m_pl / xi. Since the Higgs doublet of the Standard Model includes the Higgs boson and 3 Goldstone bosons, it falls into the latter category and therefore its validity is manifestly spoiled. We show that these conclusions hold in both the Jordan and Einstein frames and describe an intuitive analogy in the form of the pion Lagrangian. We also examine the recent claim that curvature-squared inflation models fail quantum mechanically. Our work appears to go beyond the recent discussions.Comment: 14 pages, 2 figures. Version 2: Clarified findings and improved wording. Elaborated important sections and removed an unnecessary section. Added references. Version 3: Updated towards JHEP version. Version 4: Final JHEP versio
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