2,619 research outputs found
Advances in the numerical treatment of grain-boundary migration: Coupling with mass transport and mechanics
This work is based upon a coupled, lattice-based continuum formulation that
was previously applied to problems involving strong coupling between mechanics
and mass transport; e.g. diffusional creep and electromigration. Here we
discuss an enhancement of this formulation to account for migrating grain
boundaries. The level set method is used to model grain-boundary migration in
an Eulerian framework where a grain boundary is represented as the zero level
set of an evolving higher-dimensional function. This approach can easily be
generalized to model other problems involving migrating interfaces; e.g. void
evolution and free-surface morphology evolution. The level-set equation is
recast in a remarkably simple form which obviates the need for spatial
stabilization techniques. This simplified level-set formulation makes use of
velocity extension and field re-initialization techniques. In addition, a
least-squares smoothing technique is used to compute the local curvature of a
grain boundary directly from the level-set field without resorting to
higher-order interpolation. A notable feature is that the coupling between mass
transport, mechanics and grain-boundary migration is fully accounted for. The
complexities associated with this coupling are highlighted and the
operator-split algorithm used to solve the coupled equations is described.Comment: 28 pages, 9 figures, LaTeX; Accepted for publication in Computer
Methods in Applied Mechanics and Engineering. [Style and formatting
modifications made, references added.
Model adaptivity for finite element analysis of thin or thick plates based on equilibrated boundary stress resultants
Purpose – The purpose of this paper is to address error-controlled adaptive finite element (FE) method for thin and thick plates. A procedure is presented for determining the most suitable plate model (among available hierarchical plate models) for each particular FE of the selected mesh, that is provided as the final output of the mesh adaptivity procedure. \ud
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Design/methodology/approach – The model adaptivity procedure can be seen as an appropriate extension to model adaptivity for linear elastic plates of so-called equilibrated boundary traction approach error estimates, previously proposed for 2D/3D linear elasticity. Model error indicator is based on a posteriori element-wise computation of improved (continuous) equilibrated boundary stress resultants, and on a set of hierarchical plate models. The paper illustrates the details of proposed model adaptivity procedure for choosing between two most frequently used plate models: the one of Kirchhoff and the other of Reissner-Mindlin. The implementation details are provided for a particular case of the discrete Kirchhoff quadrilateral four-node plate FE and the corresponding Reissner-Mindlin quadrilateral with the same number of nodes. The key feature for those elements that they both provide the same quality of the discretization space (and thus the same discretization error) is the one which justifies uncoupling of the proposed model adaptivity from the mesh adaptivity. \ud
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Findings – Several numerical examples are presented in order to illustrate a very satisfying performance of the proposed methodology in guiding the final choice of the optimal model and mesh in analysis of complex plate structures. \ud
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Originality/value – The paper confirms that one can make an automatic selection of the most appropriate plate model for thin and thick plates on the basis of proposed model adaptivity procedure.\u
Primes from sums of two squares and missing digits
Let be the set of integers missing any three fixed digits from
their decimal expansion. We produce primes in a thin sequence by proving an
asymptotic formula for counting primes of the form , with
.
The proof draws on ideas from the work of Friedlander-Iwaniec on primes of
the form , as well as ideas from the work of Maynard on primes
with restricted digits.Comment: 60 page
Correlation testing in time series, spatial and cross-sectional data
We provide a general class of tests for correlation in time series, spatial, spatio-temporal and cross-sectional data. We motivate our focus by reviewing how computational and theoretical difficulties of point estimation mount as one moves from regularly-spaced time series data, through forms of irregular spacing, and to spatial data of various kinds. A broad class of computationally simple tests is justiied. These specialize Lagrange multiplier tests against parametric departures of various kinds. Their forms are illustrated in case of several models for describing correlation in various kinds of data. The initial focus assumes homoscedasticity, but we also robustify the tests to nonparametric heteroscedasticity.Correlation; heteroscedasticity; Lagrange multiplier tests.
Some results on -ary bent functions
Kumar et al.(1985) have extended the
notion of classical bent Boolean functions in the generalized setup
on \BBZ_q^n. They have provided an analogue of classical
Maiorana-McFarland type bent functions. In this paper, we study the
crosscorrelation of a subclass of such generalized
Maiorana-McFarland (\mbox{GMMF}) type bent functions. We provide a
construction of quaternary () bent functions on
variables in terms of their subfunctions on -variables. Analogues
of sum-of-squares indicator and absolute indicator of
crosscorrelation of Boolean functions are defined in the generalized
setup. Further, -ary functions are studied in terms of these
indictors and some upper bounds of these indicators are obtained.
Finally, we provide some constructions of balanced quaternary
functions with high nonlinearity under Lee metric
Some results concerning global avalanche characteristics of two -ary functions
The global avalanche characteristics criteria was first introduced by
Zhou et al. (Inform. Sci. 180(2) (2010) 256-265).
This article is concerned with some new bounds on global avalanche characteristics of two -ary functions. Based on the above result we obtain a bound on of f \in \cB_{n, q} in terms of s of the restricted functions on \BBZ_{n-1}^q, and construct a class of -ary bent functions from -plateaued functions having dijoint Walsh spectra
VLT multi-object spectroscopy of 33 eclipsing binaries in the Small Magellanic Cloud. New distance and depth of the SMC, and a record-breaking apsidal motion
Aim: Our purpose is to provide reliable stellar parameters for a significant
sample of eclipsing binaries, which are representative of a whole dwarf and
metal-poor galaxy. We also aim at providing a new estimate of the mean distance
to the SMC and of its depth along the line of sight for the observed field of
view. Method: We use radial velocity curves obtained with the ESO FLAMES
facility at the VLT and light curves from the OGLE-II photometric survey. The
radial velocities were obtained by least-squares fits of the observed spectra
to synthetic ones, excluding the hydrogen Balmer lines. Results: Our sample
contains 23 detached, 9 semi-detached and 1 overcontact systems. Most detached
systems have properties consistent with stellar evolution calculations from
single-star models at the standard SMC metallicity Z = 0.004, though they tend
to be slightly overluminous. The few exceptions are probably due to third light
contribution or insufficient signal-to-noise ratio. The mass ratios are
consistent with a flat distribution, both for detached and
semi-detached/contact binaries. A mass-luminosity relation valid from ~4 to ~18
Msol is derived. The uncertainties are in the +-2 to +-11% range for the
masses, in the +-2 to +-5% range for the radii and in the +-1 to +-6% range for
the effective temperatures. The average distance modulus is 19.11+-0.03
(66.4+-0.9 kpc). The moduli derived from the V and from the I data are
consistent within 0.01 mag. The 2-sigma depth of the SMC is, for our field, of
0.25 mag or 7.6 kpc under the assumption of a gaussian distribution of stars
along the line of sight. Three systems show significant apsidal motion, one of
them with an apsidal period of 7.6 years, the shortest known to date for a
detached system with main sequence stars.Comment: 61 pages, 41 figures; accepted for publication in Astronomy &
Astrophysic
Shearlets and Optimally Sparse Approximations
Multivariate functions are typically governed by anisotropic features such as
edges in images or shock fronts in solutions of transport-dominated equations.
One major goal both for the purpose of compression as well as for an efficient
analysis is the provision of optimally sparse approximations of such functions.
Recently, cartoon-like images were introduced in 2D and 3D as a suitable model
class, and approximation properties were measured by considering the decay rate
of the error of the best -term approximation. Shearlet systems are to
date the only representation system, which provide optimally sparse
approximations of this model class in 2D as well as 3D. Even more, in contrast
to all other directional representation systems, a theory for compactly
supported shearlet frames was derived which moreover also satisfy this
optimality benchmark. This chapter shall serve as an introduction to and a
survey about sparse approximations of cartoon-like images by band-limited and
also compactly supported shearlet frames as well as a reference for the
state-of-the-art of this research field.Comment: in "Shearlets: Multiscale Analysis for Multivariate Data",
Birkh\"auser-Springe
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