74,437 research outputs found

    A rheological investigation of vesicular rhyolite

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    The rheology of vesiculating rhyolitic systems exerts a strong control on the transport of silicic magmas in the subvolcanic to volcanic environments. We present here an investigation of vesiculating and vesiculated rhyolites using dilatometric methods. This study examines the effect of vesicle content on the viscosity of a natural supercooled rhyolitic liquid with 0–70% vesicles. The experimental samples of rhyolitic glass are derived from fusion of a natural obsidian from Little Glass Butte, Oregon. Crystal-free rhyolite glasses of varying porosity were prepared by fusing obsidian powder in a Pt crucible. Differing porosities were obtained by varying the temperature (1300—1650°C) and duration (0.5–6 h) of the fusions. Cylindrical samples of the resulting vesiculated rhyolites were cored from the crucible using diamond tools and their ends were ground flat and parallel for dilatometry. The porosity of each sample was determined from Archimedean buoyancy density determinations and comparison with bubble-free rhyolite (2.331 g/cm3, porosity = 1 - p/po). The density of foamed samples was determined using their mass, volume and regular geometry. Viscosities were determined in the parallel plate mode at stresses of 5 × 103 to 105 Pa. The viscosimeter was calibrated using NBS 711 glass. The bubble contents were microscopically investigated using a video-reflected light system and image analysis software. Distribution functions of the size, orientation, aspect ratio and surface porosity were obtained. The viscosity of rhyolite decreases with increasing bubble content. A general relationship of the form: η(|) = η(0)/(1 + C|), describes the effect of porosity, | (in volume fraction) on the viscosity, η, where C is a dimensionless constant (= 22.4 ± 2.9) and log10η(0) = 10.94 ± 0.04 Pa s at 850°C

    Shape, shear and flexion II - Quantifying the flexion formalism for extended sources with the ray-bundle method

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    Flexion-based weak gravitational lensing analysis is proving to be a useful adjunct to traditional shear-based techniques. As flexion arises from gradients across an image, analytic and numerical techniques are required to investigate flexion predictions for extended image/source pairs. Using the Schwarzschild lens model, we demonstrate that the ray-bundle method for gravitational lensing can be used to accurately recover second flexion, and is consistent with recovery of zero first flexion. Using lens plane to source plane bundle propagation, we find that second flexion can be recovered with an error no worse than 1% for bundle radii smaller than {\Delta}{\theta} = 0.01 {\theta}_E and lens plane impact pararameters greater than {\theta}_E + {\Delta}{\theta}, where {\theta}_E is the angular Einstein radius. Using source plane to lens plane bundle propagation, we demonstrate the existence of a preferred flexion zone. For images at radii closer to the lens than the inner boundary of this zone, indicative of the true strong lensing regime, the flexion formalism should be used with caution (errors greater than 5% for extended image/source pairs). We also define a shear zone boundary, beyond which image shapes are essentially indistinguishable from ellipses (1% error in ellipticity). While suggestive that a traditional weak lensing analysis is satisfactory beyond this boundary, a potentially detectable non-zero flexion signal remains.Comment: 14 pages, 13 figures, accepted for publication in Monthly Notices of the Royal Astronomical Societ

    Quantifying galaxy shapes: Sersiclets and beyond

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    Parametrising galaxy morphologies is a challenging task, e.g., in shear measurements of weak lensing or investigations of galaxy evolution. The huge variety of morphologies requires an approach that is highly flexible, e.g., accounting for azimuthal structure. We revisit the method of sersiclets, where galaxy morphologies are decomposed into basis functions based on the Sersic profile. This approach is justified by the fact that the Sersic profile is the first-order Taylor expansion of any real light profile. We show that sersiclets overcome the modelling failures of shapelets. However, sersiclets implicate an unphysical relation between the steepness of the light profile and the spatial scale of azimuthal structures, which is not obeyed by real galaxy morphologies and can therefore give rise to modelling failures. Moreover, we demonstrate that sersiclets are prone to undersampling, which restricts sersiclet modelling to highly resolved galaxy images. Analysing data from the Great08 challenge, we demonstrate that sersiclets should not be used in weak-lensing studies. We conclude that although the sersiclet approach appears very promising at first glance, it suffers from conceptual and practical problems that severly limit its usefulness. The Sersic profile can be enhanced by higher-order terms in the Taylor expansion, which can drastically improve model reconstructions of galaxy images. If orthonormalised, these higher-order profiles can overcome the problems of sersiclets while preserving their mathematical justification.Comment: 14 pages, 12 figures, 2 tables; accepted by MNRA

    Images and nonlocal vortex pinning in thin superfluid films

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    For thin films of superfluid adsorbed on a disordered substrate, we derive the equation of motion for a vortex in the presence of a random potential within a mean field (Hartree) description of the condensate. The compressible nature of the condensate leads to an effective pinning potential experienced by the vortex which is nonlocal, with a long range tail that smoothes out the random potential coupling the condensate to the substrate. We interpret this nonlocality in terms of images, and relate the effective potential governing the dynamics to the pinning energy arising from the expectation value of the Hamiltonian with respect to the vortex wavefunction.Comment: 19 pages, revtex, to appear Phys. Rev.

    Universal bounds on the selfaveraging of random diffraction measures

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    We consider diffraction at random point scatterers on general discrete point sets in Rν\R^\nu, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence of the random scattering measures applied to an observable towards its mean, when the finite volume tends to infinity. We give an explicit universal large deviation upper bound that is exponential in the number of scatterers. The rate is given in terms of a universal function that depends on the point set only through the minimal distance between points, and on the observable only through a suitable Sobolev-norm. Our proof uses a cluster expansion and also provides a central limit theorem

    Differential Calculus on Graphon Space

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    Recently, the theory of dense graph limits has received attention from multiple disciplines including graph theory, computer science, statistical physics, probability, statistics, and group theory. In this paper we initiate the study of the general structure of differentiable graphon parameters FF. We derive consistency conditions among the higher G\^ateaux derivatives of FF when restricted to the subspace of edge weighted graphs Wp\mathcal{W}_{\bf p}. Surprisingly, these constraints are rigid enough to imply that the multilinear functionals Λ:Wpn→R\Lambda: \mathcal{W}_{\bf p}^n \to \mathbb{R} satisfying the constraints are determined by a finite set of constants indexed by isomorphism classes of multigraphs with nn edges and no isolated vertices. Using this structure theory, we explain the central role that homomorphism densities play in the analysis of graphons, by way of a new combinatorial interpretation of their derivatives. In particular, homomorphism densities serve as the monomials in a polynomial algebra that can be used to approximate differential graphon parameters as Taylor polynomials. These ideas are summarized by our main theorem, which asserts that homomorphism densities t(H,−)t(H,-) where HH has at most NN edges form a basis for the space of smooth graphon parameters whose (N+1)(N+1)st derivatives vanish. As a consequence of this theory, we also extend and derive new proofs of linear independence of multigraph homomorphism densities, and characterize homomorphism densities. In addition, we develop a theory of series expansions, including Taylor's theorem for graph parameters and a uniqueness principle for series. We use this theory to analyze questions raised by Lov\'asz, including studying infinite quantum algebras and the connection between right- and left-homomorphism densities.Comment: Final version (36 pages), accepted for publication in Journal of Combinatorial Theory, Series
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