1,721,859 research outputs found
Robust Algorithms for Digital Image Correlation in the Presence of Displacement Discontinuities
Full text linkDigital Image Correlation (DIC) is a well-known non-contact experimental technique. Its most common implementation is the subset-based approach, which performs a local least-squares fitting of a simple displacement model — usually an affine transform — to identify the displacement components at the center of the small area under investigation (the subset). Because of the statistical approach, DIC is usually able to provide reliable results even when theoretical prerequisites are not fully satisfied or in the presence of noise. However, the least-squares algorithm is not robust when the data set contains multiple statistical distributions. Indeed, the algorithm does not discriminate between them and process all the input data; thus, the resulting solution is usually unsatisfactory. A typical example implying the described context is the presence of cracks or shear bands inside the subset: as different sections of the inspected area move in different directions, the algorithm is unable to select a solution and the correlation between the reference and the test image is usually poor. This work proposes using RANSAC, a well-known robust algorithm, to select the largest domain of the subset. Because a similar problem has to be faced when computing strain components by the polynomial-fitting method, a simple modification of the main algorithm is suggested to handle also this problem
A non-existence problem for degenerate elliptic PDE's
No full textWe consider a non-linear subelliptic problem in a bounded open set of Rn. We give a very weak notion of solution and we prove a non-existence result for the problem. This result generalizes the analogous elliptic case already considered by H. Brezis and X. Cabré
Full Field Methods and Residual Stress Analysis in Orthotropic Material: a Simplified Approach
No full textThis work analyzes the problem of residual stress determination in an orthotropic material using the hole drilling technique combined with non-contact, full field optical methods. Due to the complex behavior of the material, two theoretical approaches were proposed: Smith’s real values formulation and a general solution by Lekhnitskii. In principle the latter suffices,
but its usage is not easy due to the complex value solution and the nonlinear fit required to estimate the residual stress values; on the contrary, Smith’s formulation is much simpler, but cannot be used on a certain class of materials. In this work the twopproaches are combined to obtain a general, simpler formulation
Weighted BV functions
No full textWe provide a definition of weighted function of bounded variation when the weight function ω belongs to a certain subclass of Muckenhoupt's A1 weight class. We obtain Poincaré and isoperimetric inequalities in this space and, as an application, we prove existence of minimal surfaces
On the Implementation of the Integral Method for Residual Stress Measurement by Integrated Digital Image Correlation
Full text linkThe Integrated Digital Image Correlation method (iDIC) is a simple and effective approach for residual stress measurement. iDIC differs from Digital Image Correlation because it replaces the “generic” displacement functions used to describe the displacement field around the measurement point with problem-specific ones. By this simple modification, stress components become the unknowns of the problem, thus allowing a single-pass analysis. Advantages are significant in terms of accuracy, robustness and ease of implementation. However, the implementation of the Integral Method for estimation of depth-dependent residual stress components is difficult. This work suggests two alternative approaches to solve this problem; in the former, the direct solution of the triangular linear system is employed to incrementally identify the stress distribution. In the latter, a global spatio-temporal minimization involving all the acquired images is suggested
A Γ-convergence result for doubling metric measures and associated perimeters
No full textIn this paper we study the notion of perimeter associated with doubling metric measures or strongly A∞ weights. We prove that the metric perimeter in the sense of L. Ambrosio and M. Miranda jr. coincides with the metric Minkowski content and can be obtained also as a Γ-limit of Modica-Mortola type degenerate integral functionals
Neuroprotective effects of polyphenols through their activity against oxidative stress and inflammation.
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The distributional divergence of horizontal vector fields vanishing at infinity on Carnot groups
Full text linkWe define a BV -type space in the setting of Carnot groups (i.e., simply
connected Lie groups with stratified nilpotent Lie algebra) that allows one to
characterize all distributions F for which there exists a continuous horizontal
vector field {\Phi}, vanishing at infinity, that solves the equation divH{\Phi}
= F. This generalize to the setting of Carnot groups some results by De Pauw
and Pfeffer, [12], and by De Pauw and Torres, [13], for the Euclidean setting.Comment: 24 page
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