3,363 research outputs found
3D discrete rotations using hinge angles
International audienceIn this paper, we study 3D rotations on grid points computed by using only integers. For that purpose, we investigate the intersection between the 3D half-grid and the rotation plane. From this intersection, we define 3D hinge angles which determine a transit of a grid point from a voxel to its adjacent voxel during the rotation. Then, we give a method to sort all 3D hinge angles with integer computations. The study of 3D hinge angles allows us to design a 3D discrete rotation and to estimate the rotation between a pair of digital images in correspondence
Common Arc Method for Diffraction Pattern Orientation
Very short pulses of x-ray free-electron lasers opened the way to obtain
diffraction signal from single particles beyond the radiation dose limit. For
3D structure reconstruction many patterns are recorded in the object's unknown
orientation. We describe a method for orientation of continuous diffraction
patterns of non-periodic objects, utilizing intensity correlations in the
curved intersections of the corresponding Ewald spheres, hence named Common Arc
orientation. Present implementation of the algorithm optionally takes into
account the Friedel law, handles missing data and is capable to determine the
point group of symmetric objects. Its performance is demonstrated on simulated
diffraction datasets and verification of the results indicates high orientation
accuracy even at low signal levels. The Common Arc method fills a gap in the
wide palette of the orientation methods.Comment: 16 pages, 10 figure
Curvatures and discrete Gauss-Codazzi equation in (2+1)-dimensional loop quantum gravity
We derive the Gauss-Codazzi equation in the holonomy and plane-angle
representations and we use the result to write a Gauss-Codazzi equation for a
discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This
allows us to write operators acting on spin network states in (2+1)-dimensional
loop quantum gravity, representing the 3-dimensional intrinsic, 2-dimensional
intrinsic, and 2-dimensional extrinsic curvatures.Comment: 16 pages, 10 figure
Polarization Drift Channel Model for Coherent Fibre-Optic Systems
A theoretical framework is introduced to model the dynamical changes of the
state of polarization during transmission in coherent fibre-optic systems. The
model generalizes the one-dimensional phase noise random walk to higher
dimensions, accounting for random polarization drifts, emulating a random walk
on the Poincar\'e sphere, which has been successfully verified using
experimental data. The model is described in the Jones, Stokes and real
four-dimensional formalisms, and the mapping between them is derived. Such a
model will be increasingly important in simulating and optimizing future
systems, where polarization-multiplexed transmission and sophisticated digital
signal processing will be natural parts. The proposed polarization drift model
is the first of its kind as prior work either models polarization drift as a
deterministic process or focuses on polarization-mode dispersion in systems
where the state of polarization does not affect the receiver performance. We
expect the model to be useful in a wide-range of photonics applications where
stochastic polarization fluctuation is an issue.Comment: 15 pages, 4 figure
Wrinkling in engineering fabrics: a comparison between two different comprehensive modelling approaches
We consider two ‘comprehensive’ modelling approaches for engineering fabrics. We distinguish the two approaches using the terms ‘semi-discrete’ and ‘continuum’, reflecting their natures. We demonstrate a fitting procedure, used to identify the constitutive parameters of the continuum model from predictions of the semi-discrete model, the parameters of which are in turn fitted to experimental data. We, then, check the effectiveness of the continuum model by verifying the correspondence between semi-discrete and continuum model predictions using test cases not previously used in the identification process. Predictions of both modelling approaches are compared against full-field experimental kinematic data, obtained using stereoscopic digital image correlation techniques, and also with measured force data. Being a reduced order model and being implemented in an implicit rather than an explicit finite-element code, the continuum model requires significantly less computational power than the semi-discrete model and could therefore be used to more efficiently explore the mechanical response of engineering fabrics
Critically Twisted Kinematic Chains
Els caleidocicles de Möbius són una famÃlia nova de mecanismes amb un grau de llibertat. Presentem cadenes quinemà tiques noves amb propietats similars i busquem casos especials. Donem un argument de plausibilitat per la mobilitat de les cadenes basat en un teorema nou sobre la transposició d'elements adjacents. Finalment, discutim la relació entre els nostres sistemes i el camp emergent de la geometria diferencial discreta.Los caleidociclos de Möbius son una familia nueva de mecanismos con un grado de libertad. Presentamos cadenas quinemáticas nuevas con propiedades similares y buscamos casos especiales. Damos un argumento de plausibilidad para la mobilidad de las cadenas basado en un teorema nuevo sobre la transposición de elementos adyacentes. Finalmente, discutimos la relación entre nuestros sistemas y el campo emergente de la geometrÃa diferencial discreta.Möbius kaleidocycles are a newly discovered family of underconstrained linkages with one degree of freedom. We present many new kinematic chains with similar properties and look for special cases. We give a plausibility argument for the mobility of our chains based on a new theorem on the transposition of adjacent links. Finally, we discuss the relationship between our systems and the emerging field of discrete differential geometry.Outgoin
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