Interacting Particles and Strings in Path and Surface Representations

Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a Kalb-Ramond field in four dimensions, the topological interaction of two particles due to a BF term in 2+1 dimensions, and the string-particle interaction mediated by a BF term in 3+1 dimensions. In the first case one finds that a consistent "surface-representation" can be built provided that the coupling constant is quantized. The geometrical setting that arises corresponds to a generalized version of the Faraday's lines picture: quantum states are labeled by the shape of the string, from which emanate "Faraday`s surfaces". In the other models, the topological interaction can also be described by geometrical means. It is shown that the open-path (or open-surface) dependence carried by the wave functional in these models can be eliminated through an unitary transformation, except by a remaining dependence on the boundary of the path (or surface). These feature is closely related to the presence of anomalous statistics in the 2+1 model, and to a generalized "anyonic behavior" of the string in the other case.Comment: RevTeX 4, 28 page

Parametric model for the simulation of the railway catenary system static equilibrium problem

Dynamic simulations of pantograph catenary interaction are nowadays essential for improving the performance of railway locomotives, by achieving better current collection at higher speeds and lower wear of thecollecting parts.The first step in performing these simulations is to compute the static equilibrium of the overhead line.The initial dropper lengths play an important role in hanging the contact wire at an appropriate height. From a classical point of view, if one wants to obtain the static equilibrium configuration of the system for different combinations of dropper lengths, one static pro- blem must be solved for each combination of lengths, which involves a prohibitive computational cost. In this paper we propose a parametric model of the catenary, including the undeformed dropper lengths as extra-coordinates of the problem. This multidimensional problem is efficiently solved by means of the Proper Generalized Decomposition (PGD) technique, avoiding the curse of dimensionality issue. The capabilities and performance of the proposed method are shown by numerical examples.The authors would like to acknowledge the financial support of the FPU program offered by the Ministerio de Educacion, Cultura y Deporte under Grant number FPU13/04191. The funding from Universitat Politecnica de Valencia and Generalitat Valenciana (PROMETEO/2012/023) are also acknowledged.Gregori Verdú, S.; Tur Valiente, M.; Nadal, E.; Fuenmayor Fernández, FJ.; Chinesta, F. (2016). Parametric model for the simulation of the railway catenary system static equilibrium problem. Finite Elements in Analysis and Design. 115:21-32. https://doi.org/10.1016/j.finel.2016.02.007S213211

A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework

[EN] Today industries do not only require fast simulation techniques but also verification techniques for the simulations. The proper generalized decomposition (PGD) has been situated as a suitable tool for fast simulation for many physical phenomena. However, so far, verification tools for the PGD are under development. The PGD approximation error mainly comes from two different sources. The first one is related with the truncation of the PGD approximation and the second one is related with the discretization error of the underlying numerical technique. In this work we propose a fast error indicator technique based on recovery techniques, for the discretization error of the numerical technique used by the PGD technique, for refinement purposes.Authors 5 and 6 thank the financial support of the research Project DPI2013-46317-R of the Ministerio de Economia y Competitividad (Spain). The funding from Universitat Politecnica de Valencia and Generalitat Valenciana (PROMETEO/2012/023) are also acknowledged. These authors also thank the support of the Framework Programme 7 Initial Training Network Funding under Grant number 289361 "Integrating Numerical Simulation and Geometric Design Technology".Nadal, E.; Leygue, A.; Chinesta, F.; Beringhier, M.; Ródenas, J.; Fuenmayor Fernández, FJ. (2015). A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework. Computational Mechanics. 55(2):251-266. https://doi.org/10.1007/s00466-014-1097-yS251266552Ammar A, Mokdad B, Chinesta F, Keunings R (2006) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J Non-Newton Fluid Mech 139:153–176Ammar A, Mokdad B, Chinesta F, Keunings R (2007) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. J Non-Newton Fluid Mech 144:98–121Chinesta F, Ladeveze P, Cueto E (2011) A short review on model order reduction based on proper generalized decomposition. Arch Comput Methods Eng 18:395–404Giner E, Bognet B, Ródenas JJ, Leygue A, Fuenmayor FJ, Chinesta F (2013) The proper generalized decomposition (PGD) as a numerical procedure to solve 3D cracked plates in linear elastic fracture mechanics. Int J Solids Struct 50:1710–1720Chinesta F, Ammar A, Leygue A, Keunings R (2011) An overview of the proper generalized decomposition with applications in computational rheology. J Non-Newton Fluid Mech 166(11):578–592Ammar A, Chinesta F, Diez P, Huerta A (2010) An error estimator for separated representations of highly multidimensional models. Comput Methods Appl Mech Eng 199(25–28):1872–1880Moitinho de Almeida JP (2013) A basis for bounding the errors of proper generalised decomposition solutions in solid mechanics. Int J Numer Methods Eng 94:961–984Ladevèze P, Chamoin L (2011) On the verification of model reduction methods based on the proper generalized decomposition. Comput Methods Appl Mech Eng 200:2032–2047Ladevèze P, Leguillon D (1983) Error estimate procedure in the finite element method and applications. SIAM J Numer Anal 20(3):485–509Babuška I, Rheinboldt WC (1978) A-posteriori error estimates for the finite element method. Int J Numer Methods Eng 12(10):1597–1615Ródenas JJ, Tur M, Fuenmayor FJ, Vercher A (2007) Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique. Int J Numer Methods Eng 70(6):705–727Díez P, Parés N, Huerta A (2003) Recovering lower bounds of the error by postprocessing implicit residual a posteriori error estimates. Int J Numer Methods Eng 56(10):1465–1488Bognet B, Bordeu F, Chinesta F, Leygue A, Poitou A (2012) Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity. Comput Methods Appl Mech Eng 201–204:1–12Bognet B, Leygue A, Chinesta F (2014) Separated representations of 3D elastic solutions in shell geometries. Adv Model Simul Eng Sci 1(1):1–4Ghnatios C, Chinesta F, Binetruy C (2013) 3D modeling of squeeze flows occurring in composite laminates. Int J Mater Form 9(1):1–11Zienkiewicz OC, Zhu JZ (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Numer Methods Eng 24(2):337–357Chinesta F, Keunings R, Leygue A (2013) The proper generalized decomposition for advanced numerical simulations: a primer. Springer Publishing Company, New York IncorporatedDonea J, Huerta A (2002) Finite element methods for flow problems. Wiley, New YorkGonzalez D, Cueto E, Chinesta F, Diez P, Huerta A (2013) SUPG-based stabilization of proper generalized decompositions for high-dimensional advection-diffusion equations. Int J Numer Methods Eng 94(13):1216–1232Chinesta F, Ammar A, Cueto E (2010) Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models. Arch Comput Methods Eng 17(4):327–350Chinesta F, Leygue A, Bordeu F, Aguado JV, Cueto E, Gonzalez D, Alfaro I, Ammar A, Huerta A (2013) PGD-based computational vademecum for efficient design, optimization and control. Arch Comput Methods Eng 20:31–59Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int J Numer Methods Eng 33(7):1331–1364Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity. Int J Numer Methods Eng 33(7):1365–1382Kvamsdal T, Okstad KM (1998) Error estimation based on superconvergent patch recovery using statically admissible stress fields. Int J Numer Methods Eng 42(3):443–472Wiberg NE, Abdulwahab F (1993) Patch recovery based on superconvergent derivatives and equilibrium. Int J Numer Methods Eng 36(16):2703–2724Wiberg NE, Abdulwahab F, Ziukas S (1994) Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions. Int J Numer Methods Eng 37(20):3417–3440Blacker T, Belytschko T (1994) Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. Int J Numer Methods Eng 37(3):517–536Ródenas JJ, González-Estrada OA, Tarancón JE, Fuenmayor FJ (2008) A recovery-type error estimator for the extended finite element method based on singular+smooth stress field splitting. Int J Numer Methods Eng 76(4):545–571Ródenas JJ, González-Estrada OA, Díez P, Fuenmayor FJ (2010) Accurate recovery-based upper error bounds for the extended finite element framework. Comput Methods Appl Mech Eng 199(37–40):2607–2621Nadal E, (2014) Cartesian grid FEM (cgFEM): high performance h-adaptive FE analysis with efficient error control. Application to structural shape optimization. PhD thesis, Universitat Politècnica de ValènciaKarihaloo BL, Xiao QZ (2003) Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Comput Struct 81(3):119–129González-Estrada OA, Ródenas JJ, Chinesta F, Fuenmayor FJ (2013) Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM. Comput Mech 52:321–344Fuenmayor FJ, Oliver JL (1996) Criteria to achieve nearly optimal meshes in the h-adaptive finite element mehod. 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Fast simulation of the pantograph-catenary dynamic interaction

Simulation of the pantograph-catenary dynamic interaction has now become a useful tool for designing and optimizing the system. In order to perform accurate simulations, including system non-linearities, the Finite Element Method is commonly employed combined with a time integration scheme, even though the computational time required may be longer than with the use of other simpler approaches. In this paper we propose a two-stage methodology (Offline/Online) which notably reduces the computational cost without any loss in accuracy and makes it possible to successfully carry out very efficient optimizations or even Hardware in the Loop simulations with real-time requirements.The authors would like to acknowledge the financial support received from the FPU program offered by the Ministerio de Educacion, Cultura y Deporte under grant number (FPU13/04191), and also funding from the Universitat Politecnica de Valencia and the Generalitat Valenciana (PROMETEO/2016/007).Gregori Verdú, S.; Tur Valiente, M.; Nadal Soriano, E.; Aguado, J.; Fuenmayor Fernández, FJ.; Chinesta, F. (2017). Fast simulation of the pantograph-catenary dynamic interaction. Finite Elements in Analysis and Design. 129:1-13. https://doi.org/10.1016/j.finel.2017.01.007S11312

Absentismo laboral en trabajadores públicos de Mallorca

Objetivo. Valorar los procesos de absentismo en una empresa pública en el periodo 1991-2008 y la influencia de algunas variables socio demográficas. Material y método. Estudio descriptivo transversal un total de 10154 procesos de absentismo (incapacidad temporal, accidente de trabajo e indisposición) en trabajadores públicos. Se analiza la influencia de la edad y el sexo. Resultados. Se estudian un total de 6542 episodios de incapacidad temporal, 2297 indisposiciones y 615 accidentes laborales. El número total de días perdidos es de 302147. Las mujeres y los trabajadores mayores de 45 años son los grupos que presentan mayor número de procesos de absentismo y los que pierden mayor número de días. Conclusiones. El presente trabajo es uno de los primeros que presenta datos de indisposiciones, un aspecto del absentismo que muy pocas veces se ha analizado.Objective. Assess the processes of absenteeism in a public company between 1991-2008 and the influence of some socio demographic variables. Methods. Cross-sectional study of 10154 absences processes (temporary disability, industrial accident and mild ailments) in public workers. The influence of age and sex is analyzed. Results. 6542 episodes of temporary disability, 2297 mild ailments and 615 industrial accidents were studied. The total number of “lost days” is 302147. Women and workers over 45 are the groups with the highest number of absenteeism processes and more “lost days”. Conclusions. This work is one of the first to present data of mild ailments, one aspect of absenteeism rarely been analyzed

Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM

In this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent patch recovery (SPR). Boundary equilibrium is enforced using a nearest point approach that modifies the MLS functional. Lagrange multipliers are used to impose a nearly exact satisfaction of the internal equilibrium equation. The numerical results show the high accuracy of the proposed error estimator

Domain integral formulation for 3-D curved and non-planar cracks with the extended finite element method

The computation of stress intensity factors (SIFS) in curved and non-planar cracks using domain integrals introduces some difficulties related to the use of curvilinear gradients. Several approaches exist in the literature that consider curvilinear corrections within a finite element framework, but these depend on each particular crack configuration and they are not general. In this work, we introduce the curvilinear gradient correction within the extended finite element method framework (XFEM), based only on the level set information used for the crack description and the local coordinate system definition. Our formulation depends only on the level set coordinates and, therefore, an explicit analytical description of the crack is not needed. It is shown that this curvilinear correction improves the results and enables the study of generic cracks. In addition, we have introduced a simple error indicator for improving the SIF computed via the interaction integral, thanks to the better behavior of the J-integral as it does not need auxiliary extraction fields.This work has been carried out within the framework of the research projects DPI2007-66995-C03-02 and DPI2010-20990 financed by the Ministerio de Economia y Competitividad. The support of the Generalitat Valenciana, Programme PROMETEO 2012/023 is also acknowledged.González Albuixech, VF.; Giner Maravilla, E.; Tarancón Caro, JE.; Fuenmayor Fernández, FJ.; Gravouil, A. (2013). Domain integral formulation for 3-D curved and non-planar cracks with the extended finite element method. Computer Methods in Applied Mechanics and Engineering. 264:129-144. https://doi.org/10.1016/j.cma.2013.05.016S12914426