Dictionary Learning-based Inpainting on Triangular Meshes

The problem of inpainting consists of filling missing or damaged regions in images and videos in such a way that the filling pattern does not produce artifacts that deviate from the original data. In addition to restoring the missing data, the inpainting technique can also be used to remove undesired objects. In this work, we address the problem of inpainting on surfaces through a new method based on dictionary learning and sparse coding. Our method learns the dictionary through the subdivision of the mesh into patches and rebuilds the mesh via a method of reconstruction inspired by the Non-local Means method on the computed sparse codes. One of the advantages of our method is that it is capable of filling the missing regions and simultaneously removes noise and enhances important features of the mesh. Moreover, the inpainting result is globally coherent as the representation based on the dictionaries captures all the geometric information in the transformed domain. We present two variations of the method: a direct one, in which the model is reconstructed and restored directly from the representation in the transformed domain and a second one, adaptive, in which the missing regions are recreated iteratively through the successive propagation of the sparse code computed in the hole boundaries, which guides the local reconstructions. The second method produces better results for large regions because the sparse codes of the patches are adapted according to the sparse codes of the boundary patches. Finally, we present and analyze experimental results that demonstrate the performance of our method compared to the literature

Analysis of a load application point in spline coupling teeth

The objective of this paper is to investigate the position of the resultant force in involute spline coupling teeth due to the contact pressure distribution for both ideal and misaligned conditions. In general, spline coupling teeth are in contact all along the involute profile and the load is far from uniform along the contact line. Theoretical models available in publications consider the resultant contact force as it is applied at the pitch diameter, and this study aims to evaluate the error introduced within the confines of a common approximation environment. This analysis is carried out through using finite element method (FEM) models, considering spline couplings in both ideal and misaligned conditions. Results show that the differences between the load application diameter and pitch diameter are not very obvious in both ideal and misaligned conditions; however, this approximation becomes more important for the calculation of the tooth stiffness

Generation of an ultrastable 578 nm laser for Yb lattice clock

In this paper we described the development and the characterization of a 578 nm laser source to be the clock laser for an Ytterbium Lattice Optical clock. Two independent laser sources have been realized and the characterization of the stability with a beat note technique is presente

Mesoscale theory of grains and cells: crystal plasticity and coarsening

Solids with spatial variations in the crystalline axes naturally evolve into cells or grains separated by sharp walls. Such variations are mathematically described using the Nye dislocation density tensor. At high temperatures, polycrystalline grains form from the melt and coarsen with time: the dislocations can both climb and glide. At low temperatures under shear the dislocations (which allow only glide) form into cell structures. While both the microscopic laws of dislocation motion and the macroscopic laws of coarsening and plastic deformation are well studied, we hitherto have had no simple, continuum explanation for the evolution of dislocations into sharp walls. We present here a mesoscale theory of dislocation motion. It provides a quantitative description of deformation and rotation, grounded in a microscopic order parameter field exhibiting the topologically conserved quantities. The topological current of the Nye dislocation density tensor is derived from a microscopic theory of glide driven by Peach-Koehler forces between dislocations using a simple closure approximation. The resulting theory is shown to form sharp dislocation walls in finite time, both with and without dislocation climb.Comment: 5 pages, 3 figure

Prospects for Detection of Exoplanet Magnetic Fields Through Bow-Shock Observations During Transits

An asymmetry between the ingress and egress times was observed in the near-UV light curve of the transit planet WASP-12b. Such asymmetry led us to suggest that the early ingress in the UV light curve of WASP-12b, compared to the optical observations, is caused by a shock around the planet, and that shocks should be a common feature in transiting systems. Here, we classify all the transiting systems known to date according to their potential for producing shocks that could cause observable light curve asymmetries. We found that 36/92 of known transiting systems would lie above a reasonable detection threshold and that the most promising candidates to present shocks are: WASP-19b, WASP-4b, WASP-18b, CoRoT-7b, HAT-P-7b, CoRoT-1b, TrES-3, and WASP-5b. For prograde planets orbiting outside the co-rotation radius of fast rotating stars, the shock position, instead of being ahead of the planetary motion as in WASP-12b, trails the planet. In this case, we predict that the light curve of the planet should present a late-egress asymmetry. We show that CoRoT-11b is a potential candidate to host such a behind shock and show a late egress. If observed, these asymmetries can provide constraints on planetary magnetic fields. For instance, for a planet that has a magnetic field intensity similar to Jupiter's field (~ 14 G) orbiting a star whose magnetic field is between 1 and 100G, the stand-off distance between the shock and the planet, which we take to be the size of the planet's magnetosphere, ranges from 1 to 40 planetary radii.Comment: 7 pages (including the complete version of Table 1), 2 Tables, 3 Figures. Accepted by MNRAS Letter

Effective Elastic Moduli in Solids with High Crack Density

We investigate the weakening of elastic materials through randomly distributed circles and cracks numerically and compare the results to predictions from homogenization theories. We find a good agreement for the case of randomly oriented cracks of equal length in an isotropic plane-strain medium for lower crack densities; for higher densities the material is weaker than predicted due to precursors of percolation. For a parallel alignment of cracks, where percolation does not occur, we analytically predict a power law decay of the effective elastic constants for high crack densities, and confirm this result numerically.Comment: 8 page

Two-particle anomalous diffusion: Probability density functions and self-similar stochastic processes

Two-particle dispersion is investigated in the context of anomalous diffusion. Two different modeling approaches related to time subordination are considered and unified in the framework of self-similar stochastic processes. By assuming a single-particle fractional Brownian motion and that the two-particle correlation function decreases in time with a power law, the particle relative separation density is computed for the cases with time subordination directed by a unilateral M-Wright density and by an extremal Lévy stable density. Looking for advisable mathematical properties (for instance, the stationarity of the increments), the corresponding selfsimilar stochastic processes are represented in terms of fractional Brownian motions with stochastic variance, whose profile is modelled by using the M-Wright density or the Lévy stable density

Beyond the fundamental noise limit in coherent optical fiber links

It is well known that temperature variations and acoustic noise affect ultrastable frequency dissemination along optical fiber. Active stabilization techniques are in general adopted to compensate for the fiber-induced phase noise. However, despite this compensation, the ultimate link performances remain limited by the so called delay-unsuppressed fiber noise that is related to the propagation delay of the light in the fiber. In this paper, we demonstrate a data post-processing approach which enables us to overcome this limit. We implement a subtraction algorithm between the optical signal delivered at the remote link end and the round-trip signal. In this way, a 6 dB improvement beyond the fundamental limit imposed by delay-unsuppressed noise is obtained. This result enhances the resolution of possible comparisons between remote optical clocks by a factor of 2. We confirm the theoretical prediction with experimental data obtained on a 47 km metropolitan fiber link, and propose how to extend this method for frequency dissemination purposes as well