3,926 research outputs found
Multilevel Solvers for Unstructured Surface Meshes
Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner
Rheology of magmas with bimodal crystal size and shape distributions: insights from analog experiments
Magmas in volcanic conduits commonly contain microlites in association with preexisting phenocrysts, as often indicated by volcanic rock textures. In this study, we present two different experiments that inves- tigate the flow behavior of these bidisperse systems. In the first experiments, rotational rheometric methods are used to determine the rheology of monodisperse and polydisperse suspensions consisting of smaller, prolate particles (microlites) and larger, equant particles (phenocrysts) in a bubble‐free Newtonian liquid (silicate melt). Our data show that increasing the relative proportion of prolate microlites to equant pheno- crysts in a magma at constant total particle content can increase the relative viscosity by up to three orders of magnitude. Consequently, the rheological effect of particles in magmas cannot be modeled by assuming a monodisperse population of particles. We propose a new model that uses interpolated parameters based on the relative proportions of small and large particles and produces a considerably improved fit to the data than earlier models. In a second series of experiments we investigate the textures produced by shearing bimodal suspensions in gradually solidifying epoxy resin in a concentric cylinder setup. The resulting textures show the prolate particles are aligned with the flow lines and spherical particles are found in well‐organized strings, with sphere‐depleted shear bands in high‐shear regions. These observations may explain the measured variation in the shear thinning and yield stress behavior with increasing solid fraction and particle aspect ratio. The implications for magma flow are discussed, and rheological results and tex- tural observations are compared with observations on natural samples
On the distortions in calculated GW parameters during slanted atmospheric soundings
The significant distortions introduced in the measured atmospheric gravity wavelengths by soundings other than those in vertical and horizontal directions, are discussed as a function of the elevation angle of the sounding path and the gravity wave aspect ratio. Under- or overestimation of real vertical wavelengths during the measurement process depends on the value of these two parameters. The consequences of these distortions on the calculation of the energy and the vertical flux of horizontal momentum are analyzed and discussed in the context of two experimental limb satellite setups: GPS-LEO radio occultations and TIMED/SABER ((Atmosphere using Broadband Emission Radiometry/Thermosphere-Ionosphere-Mesosphere-Energetics and Dynamics)) measurements. Possible discrepancies previously found between the momentum flux calculated from satellite temperature profiles, on site and from model simulations, may to a certain degree be attributed to these distortions. A recalculation of previous momentum flux climatologies based on these considerations seems to be a difficult goal.Fil: de la Torre, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Ingeniería; ArgentinaFil: Alexander, Pedro Manfredo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Schmidt, Torsten. German Research Centre for Geosciences; AlemaniaFil: Llamedo Soria, Pablo Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Ingeniería; ArgentinaFil: Hierro, Rodrigo Federico. Universidad Austral. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
A Novel Generic Framework for Track Fitting in Complex Detector Systems
This paper presents a novel framework for track fitting which is usable in a
wide range of experiments, independent of the specific event topology, detector
setup, or magnetic field arrangement. This goal is achieved through a
completely modular design. Fitting algorithms are implemented as
interchangeable modules. At present, the framework contains a validated Kalman
filter. Track parameterizations and the routines required to extrapolate the
track parameters and their covariance matrices through the experiment are also
implemented as interchangeable modules. Different track parameterizations and
extrapolation routines can be used simultaneously for fitting of the same
physical track. Representations of detector hits are the third modular
ingredient to the framework. The hit dimensionality and orientation of planar
tracking detectors are not restricted. Tracking information from detectors
which do not measure the passage of particles in a fixed physical detector
plane, e.g. drift chambers or TPCs, is used without any simplifications. The
concept is implemented in a light-weight C++ library called GENFIT, which is
available as free software
A continuous analogue of the tensor-train decomposition
We develop new approximation algorithms and data structures for representing
and computing with multivariate functions using the functional tensor-train
(FT), a continuous extension of the tensor-train (TT) decomposition. The FT
represents functions using a tensor-train ansatz by replacing the
three-dimensional TT cores with univariate matrix-valued functions. The main
contribution of this paper is a framework to compute the FT that employs
adaptive approximations of univariate fibers, and that is not tied to any
tensorized discretization. The algorithm can be coupled with any univariate
linear or nonlinear approximation procedure. We demonstrate that this approach
can generate multivariate function approximations that are several orders of
magnitude more accurate, for the same cost, than those based on the
conventional approach of compressing the coefficient tensor of a tensor-product
basis. Our approach is in the spirit of other continuous computation packages
such as Chebfun, and yields an algorithm which requires the computation of
"continuous" matrix factorizations such as the LU and QR decompositions of
vector-valued functions. To support these developments, we describe continuous
versions of an approximate maximum-volume cross approximation algorithm and of
a rounding algorithm that re-approximates an FT by one of lower ranks. We
demonstrate that our technique improves accuracy and robustness, compared to TT
and quantics-TT approaches with fixed parameterizations, of high-dimensional
integration, differentiation, and approximation of functions with local
features such as discontinuities and other nonlinearities
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