391 research outputs found

    Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics

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    Finding the eigenvalues of a Sturm-Liouville problem can be a computationally challenging task, especially when a large set of eigenvalues is computed, or just when particularly large eigenvalues are sought. This is a consequence of the highly oscillatory behaviour of the solutions corresponding to high eigenvalues, which forces a naive integrator to take increasingly smaller steps. We will discuss some techniques that yield uniform approximation over the whole eigenvalue spectrum and can take large steps even for high eigenvalues. In particular, we will focus on methods based on coefficient approximation which replace the coefficient functions of the Sturm-Liouville problem by simpler approximations and then solve the approximating problem. The use of (modified) Magnus or Neumann integrators allows to extend the coefficient approximation idea to higher order methods

    An adaptive algorithm for n-body field expansions

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    An expansion of a density field or particle distribution in basis functions which solve the Poisson equation both provides an easily parallelized n-body force algorithm and simplifies perturbation theories. The expansion converges quickly and provides the highest computational advantage if the lowest-order potential-density pair in the basis looks like the unperturbed galaxy or stellar system. Unfortunately, there are only a handful of such basis in the literature which limits this advantage. This paper presents an algorithm for deriving these bases to match a wide variety of galaxy models. The method is based on efficient numerical solution of the Sturm-Liouville equation and can be used for any geometry with a separable Laplacian. Two cases are described in detail. First for the spherical case, the lowest order basis function pair may be chosen to be exactly that of the underlying model. The profile may be cuspy or have a core and truncated or of infinite extent. Secondly, the method yields a three-dimensional cylindrical basis appropriate for studying galaxian disks. In this case, the vertical and radial bases are coupled; the lowest order radial part of the basis function can be chosen to match the underlying profile only in the disk plane. Practically, this basis is still a very good match to the overall disk profile and converges in a small number of terms.Comment: 16 pages, 5 figures, submitted to A

    The precautions of clinical waste: disposable medical sharps in the United Kingdom

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    This article deals with recent changes in UK guidance on clinical waste, in particular a shift to disposable, single-use instruments and sharps. I use interviews conducted with nurses from a GP practice and two clinical waste managers at alternative treatment and incineration sites as a springboard for reflection on the relationship between the legislation on clinical waste management and its implementation. Scrutinizing the UK guidance, European legislation and World Health Organization principles, I draw out interviewees’ concerns that the changed practices lead to an expansion of the hazardous waste category, with an increased volume going to incineration. This raises questions regarding the regulations’ environmental and health effects, and regarding the precautionary approach embedded in the regulations. Tracing the diverse reverberations of the term ‘waste’ in different points along the journeys made by sharps in particular, and locating these questions in relation to existing literature on waste, I emphasize that public health rationales for the new practices are not made clear in the guidance. I suggest that this relative silence on the subject conceals both the uncertainties regarding the necessity for these means of managing the risks of infectious waste, and the tensions between policies of precautionary public health and environmental sustainability

    Interaction between Injection Points during Hydraulic Fracturing

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    We present a model of the hydraulic fracturing of heterogeneous poroelastic media. The formalism is an effective continuum model that captures the coupled dynamics of the fluid pressure and the fractured rock matrix and models both the tensile and shear failure of the rock. As an application of the formalism, we study the geomechanical stress interaction between two injection points during hydraulic fracturing (hydrofracking) and how this interaction influences the fracturing process. For injection points that are separated by less than a critical correlation length, we find that the fracturing process around each point is strongly correlated with the position of the neighboring point. The magnitude of the correlation length depends on the degree of heterogeneity of the rock and is on the order of 30-45 m for rocks with low permeabilities. In the strongly correlated regime, we predict a novel effective fracture-force that attracts the fractures toward the neighboring injection point.Comment: Submitte
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