16,282 research outputs found
Splinets 1.5.0 -- Periodic Splinets
Periodic splines are a special kind of splines that are defined over a set of
knots over a circle and are adequate for solving interpolation problems related
to closed curves. This paper presents a method of implementing the objects
representing such splines and describes how an efficient orthogonal basis can
be obtained. The proposed orthonormalized basis is called a periodic splinet in
the reference to earlier work where analogous concepts and tools have been
introduced for splines on an interval. Based on this methodology, the periodic
splines and splinets are added to the earlier version of the R package
"Splinets". Moreover, the developed computational tools have been applied to
functionally analyze a standard example of functional circular data of wind
directions and speeds.Comment: 16 page
Radial spline assembly for antifriction bearings
An outer race carrier is constructed for receiving an outer race of an antifriction bearing assembly. The carrier in turn is slidably fitted in an opening of a support wall to accommodate slight axial movements of a shaft. A plurality of longitudinal splines on the carrier are disposed to be fitted into matching slots in the opening. A deadband gap is provided between sides of the splines and slots, with a radial gap at ends of the splines and slots and a gap between the splines and slots sized larger than the deadband gap. With this construction, operational distortions (slope) of the support wall are accommodated by the larger radial gaps while the deadband gaps maintain a relatively high springrate of the housing. Additionally, side loads applied to the shaft are distributed between sides of the splines and slots, distributing such loads over a larger surface area than a race carrier of the prior art
Powell-Sabin B-splines and unstructured standard T-splines for the solution of the Kirchhoff-Love plate theory exploiting BĂ©zier extraction
The equations that govern Kirchhoff–Love plate theory are solved using quadratic Powell–Sabin B-splines and unstructured standard T-splines. Bézier extraction is exploited to make the formulation computationally efficient. Because quadratic Powell–Sabin B-splines result in inline image-continuous shape functions, they are of sufficiently high continuity to capture Kirchhoff–Love plate theory when cast in a weak form. Unlike non-uniform rational B-splines (NURBS), which are commonly used in isogeometric analysis, Powell–Sabin B-splines do not necessarily capture the geometry exactly. However, the fact that they are defined on triangles instead of on quadrilaterals increases their flexibility in meshing and can make them competitive with respect to NURBS, as no bending strip method for joined NURBS patches is needed. This paper further illustrates how unstructured T-splines can be modified such that they are inline image-continuous around extraordinary points, and that the blending functions fulfil the partition of unity property. The performance of quadratic NURBS, unstructured T-splines, Powell–Sabin B-splines and NURBS-to-NURPS (non-uniform rational Powell–Sabin B-splines, which are obtained by a transformation from a NURBS patch) is compared in a study of a circular plat
Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes
In the present work we introduce a complete set of algorithms to efficiently
perform adaptive refinement and coarsening by exploiting truncated hierarchical
B-splines (THB-splines) defined on suitably graded isogeometric meshes, that
are called admissible mesh configurations. We apply the proposed algorithms to
two-dimensional linear heat transfer problems with localized moving heat
source, as simplified models for additive manufacturing applications. We first
verify the accuracy of the admissible adaptive scheme with respect to an
overkilled solution, for then comparing our results with similar schemes which
consider different refinement and coarsening algorithms, with or without taking
into account grading parameters. This study shows that the THB-spline
admissible solution delivers an optimal discretization for what concerns not
only the accuracy of the approximation, but also the (reduced) number of
degrees of freedom per time step. In the last example we investigate the
capability of the algorithms to approximate the thermal history of the problem
for a more complicated source path. The comparison with uniform and
non-admissible hierarchical meshes demonstrates that also in this case our
adaptive scheme returns the desired accuracy while strongly improving the
computational efficiency.Comment: 20 pages, 12 figure
Principled Design and Implementation of Steerable Detectors
We provide a complete pipeline for the detection of patterns of interest in
an image. In our approach, the patterns are assumed to be adequately modeled by
a known template, and are located at unknown position and orientation. We
propose a continuous-domain additive image model, where the analyzed image is
the sum of the template and an isotropic background signal with self-similar
isotropic power-spectrum. The method is able to learn an optimal steerable
filter fulfilling the SNR criterion based on one single template and background
pair, that therefore strongly responds to the template, while optimally
decoupling from the background model. The proposed filter then allows for a
fast detection process, with the unknown orientation estimation through the use
of steerability properties. In practice, the implementation requires to
discretize the continuous-domain formulation on polar grids, which is performed
using radial B-splines. We demonstrate the practical usefulness of our method
on a variety of template approximation and pattern detection experiments
Relativistic polarization analysis of Rayleigh scattering by atomic hydrogen
A relativistic analysis of the polarization properties of light elastically
scattered by atomic hydrogen is performed, based on the Dirac equation and
second order perturbation theory. The relativistic atomic states used for the
calculations are obtained by making use of the finite basis set method and
expressed in terms of splines and polynomials. We introduce two
experimental scenarios in which the light is circularly and linearly polarized,
respectively. For each of these scenarios, the polarization-dependent angular
distribution and the degrees of circular and linear polarization of the
scattered light are investigated as a function of scattering angle and photon
energy. Analytical expressions are derived for the polarization-dependent
angular distribution which can be used for scattering by both hydrogenic as
well as many-electron systems. Detailed computations are performed for Rayleigh
scattering by atomic hydrogen within the incident photon energy range 0.5 to 10
keV. Particular attention is paid to the effects that arise from higher
(nondipole) terms in the expansion of the electron-photon interaction.Comment: 8 pages, 5 figure
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