Implicit Density Functional Theory

A fermion ground state energy functional is set up in terms of particle density, relative pair density, and kinetic energy tensor density. It satisfies a minimum principle if constrained by a complete set of compatibility conditions. A partial set, which thereby results in a lower bound energy under minimization, is obtained from the solution of model systems, as well as a small number of exact sum rules. Prototypical application is made to several one-dimensional spinless non-interacting models. The effectiveness of "atomic" constraints on model "molecules" is observed, as well as the structure of systems with only finitely many bound states.Comment: 9 pages, 4 figure

The Influence of Quadrature Errors on Isogeometric Mortar Methods

Mortar methods have recently been shown to be well suited for isogeometric analysis. We review the recent mathematical analysis and then investigate the variational crime introduced by quadrature formulas for the coupling integrals. Motivated by finite element observations, we consider a quadrature rule purely based on the slave mesh as well as a method using quadrature rules based on the slave mesh and on the master mesh, resulting in a non-symmetric saddle point problem. While in the first case reduced convergence rates can be observed, in the second case the influence of the variational crime is less significant

Geometric characteristics of conics in Bézier form

In this paper, we address the calculation of geometric characteristics of conic sections (axes, asymptotes, centres, eccentricity, foci) given in Bézier form in terms of their control polygons and weights, making use of real and complex projective and affine geometry and avoiding the use of coordinates

TVL₁ Planarity Regularization for 3D Shape Approximation

The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within. This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy

Comparing faceted and smoothed tool surface descriptions in sheet metal forming simulation

This study deals with different tool surface description methods used in the finite element analysis of sheet metal forming processes. The description of arbitrarily-shaped tool surfaces using the traditional linear finite elements is compared with two distinct smooth surface description approaches: (i) Bézier patches obtained from the ComputerAided Design model and (ii) smoothing the finite element mesh using Nagata patches. The contact search algorithm is presented for each approach, exploiting its special features in order to ensure an accurate and efficient contact detection. The influence of the tool modelling accuracy on the numerical results is analysed using two sheet forming examples, the unconstrained cylindrical bending and the reverse deep drawing of a cylindrical cup. Smoothing the contact surfaces with Nagata patches allows creating more accurate tool models, both in terms of shape and normal vectors, when compared with the conventional linear finite element mesh. The computational efficiency is evaluated in this study through the total number of increments and the required CPU time. The mesh refinement in the faceted description approach is not effective in terms of computational efficiency due to large discontinuities in the normal vector field across facets, even when adopting fine meshes.The authors gratefully acknowledge the financial support of the Portuguese Foundation for Science and Technology (FCT) via the projects PTDC/EME-TME/118420/2010 and PEst-C/EME/ UI0285/2013 and by FEDER funds through the program COMPETE – Programa Operacional Factores de Competitividade, under the project CENTRO-07-0224-FEDER-002001 (MT4MOBI). The first author is also grateful to the FCT for the PhD grant SFRH/BD/69140/2010.info:eu-repo/semantics/publishedVersio

Scene Segmentation Driven by Deep Learning and Surface Fitting

This paper proposes a joint color and depth segmentation scheme exploiting together geometrical clues and a learning stage. The approach starts from an initial over-segmentation based on spectral clustering. The input data is also fed to a Convolutional Neural Network (CNN) thus producing a per-pixel descriptor vector for each scene sample. An iterative merging procedure is then used to recombine the segments into the regions corresponding to the various objects and surfaces. The proposed algorithm starts by considering all the adjacent segments and computing a similarity metric according to the CNN features. The couples of segments with higher similarity are considered for merging. Finally the algorithm uses a NURBS surface fitting scheme on the segments in order to understand if the selected couples correspond to a single surface. The comparison with state-of-the-art methods shows how the proposed method provides an accurate and reliable scene segmentation

CAD-based shape optimisation of the NASA CRM wing-body intersection using differentiated CAD-kernel

In industrial design existence of a master CAD geometry of a product enables simultaneous multi-disciplinary collaboration. Adjoint CFD methods have become increasingly accepted for aerodynamic shape optimisations due to their low computational cost. However, use of CAD-based parametrisations for aerodynamic gradient-based shape optimisation is not widely used, one reason being that current CAD systems to do not compute derivatives. In this work, we present the automatically differentiated (AD) version of Open Cascade Technology (OCCT) CAD kernel which can provide derivatives with respect to CAD parameters. OCCT is differentiated in block-vector AD mode which significantly reduces the cost for computing the derivatives. This work contains further OCCT extension for NURBS-based optimisation with intersecting patches and a description of the surface mesh movement linked to the change of the intersection line. These techniques are applied to the drag reduction of the NASA Common Research Model via the modification of the intersection between the root fairing and the wing

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

International audienceWe formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter‐grains elongation/compression energy from inter‐grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model

Memetic electromagnetism algorithm for surface reconstruction with rational bivariate Bernstein basis functions

Surface reconstruction is a very important issue with outstanding applications in fields such as medical imaging (computer tomography, magnetic resonance), biomedical engineering (customized prosthesis and medical implants), computer-aided design and manufacturing (reverse engineering for the automotive, aerospace and shipbuilding industries), rapid prototyping (scale models of physical parts from CAD data), computer animation and film industry (motion capture, character modeling), archaeology (digital representation and storage of archaeological sites and assets), virtual/augmented reality, and many others. In this paper we address the surface reconstruction problem by using rational Bézier surfaces. This problem is by far more complex than the case for curves we solved in a previous paper. In addition, we deal with data points subjected to measurement noise and irregular sampling, replicating the usual conditions of real-world applications. Our method is based on a memetic approach combining a powerful metaheuristic method for global optimization (the electromagnetism algorithm) with a local search method. This method is applied to a benchmark of five illustrative examples exhibiting challenging features. Our experimental results show that the method performs very well, and it can recover the underlying shape of surfaces with very good accuracy.This research is kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project #TIN2012-30768, Toho University, and the University of Cantabria. The authors are particularly grateful to the Department of Information Science of Toho University for all the facilities given to carry out this work. We also thank the Editor and the two anonymous reviewers who helped us to improve our paper with several constructive comments and suggestions