74,437 research outputs found
A rheological investigation of vesicular rhyolite
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
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
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
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
We consider diffraction at random point scatterers on general discrete point
sets in , 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
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 . We
derive consistency conditions among the higher G\^ateaux derivatives of
when restricted to the subspace of edge weighted graphs .
Surprisingly, these constraints are rigid enough to imply that the multilinear
functionals satisfying the
constraints are determined by a finite set of constants indexed by isomorphism
classes of multigraphs with 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 where has at
most edges form a basis for the space of smooth graphon parameters whose
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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