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Frank Morgan - One of the best experts on this subject based on the ideXlab platform.
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geometric measure theory
2009Co-Authors: Frank MorganAbstract:Geometric measure theory could be described as differential geometry, generalized through measure theory to deal with maps and surfaces that are not necessarily smooth and applied to the calculus of variations. It dates from the 1960 foundational paper of Herbert Federer and Wendell Fleming on Normal and Integral Currents , recognized by the 1986 AMS Steele Prize for a paper of fundamental or lasting importance. This chapter presents an outline of the purpose and basic concepts of geometric measure theory. Along with its successes and advantages, the definition of a surface as a mapping has certain drawbacks: (1) there is an inevitable a Priori Restriction on the types of singularities that can occur; (2) there is an a Priori Restriction on the topological complexity; and (3) the natural topology lacks compactness properties. The importance of compactness properties appears in the direct method. The direct method for finding a surface of least area with a given boundary has three steps: (1) take a sequence of surfaces with areas decreasing to the infimum, (2) extract a convergent subsequence, and (3) show that the limit surface is the desired surface of least area. An alternative to surfaces as mappings is provided by rectifiable currents, the m -dimensional, oriented surfaces of geometric measure theory.
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chapter 1 geometric measure theory
Geometric Measure Theory (Second Edition)#R##N#A Beginner's Guide, 1995Co-Authors: Frank MorganAbstract:Publisher Summary Geometric measure theory could be described as differential geometry, generalized through measure theory to deal with maps and surfaces that are not necessarily smooth and applied to the calculus of variations. It dates from the 1960 foundational paper of Herbert Federer and Wendell Fleming on Normal and Integral Currents, recognized by the 1986 AMS Steele Prize for a paper of fundamental or lasting importance. This chapter presents an outline of the purpose and basic concepts of geometric measure theory. Along with its successes and advantages, the definition of a surface as a mapping has certain drawbacks: (1) there is an inevitable a Priori Restriction on the types of singularities that can occur; (2) there is an a Priori Restriction on the topological complexity; and (3) the natural topology lacks compactness properties. The importance of compactness properties appears in the direct method. The direct method for finding a surface of least area with a given boundary has three steps: (1) take a sequence of surfaces with areas decreasing to the infimum, (2) extract a convergent subsequence, and (3) show that the limit surface is the desired surface of least area. An alternative to surfaces as mappings is provided by rectifiable currents, the m-dimensional, oriented surfaces of geometric measure theory.
Boissier Mathilde - One of the best experts on this subject based on the ideXlab platform.
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Couplage de méthodes d’optimisation de formes et d’optimisation de trajectoires en fabrication additive
HAL CCSD, 2020Co-Authors: Boissier MathildeAbstract:This work investigates path planning optimization for powder bed fusion additive manufacturing processes, and relates them to the design of the built part. The state of the art mainly studies trajectories based on existing patterns and, besides their mechanical evaluation, their relevance has not been related to the object’s shape. We propose in this work a systematic approach to optimize the path without any a Priori Restriction. The typical optimization problem is to melt the desired structure, without over-heating (to avoid thermally induced residual stresses) and possibly with a minimal path length. The state equation is the heat equation with a source term depending on the scanning path. Two physical 2-d models are proposed, involving temperature constraint: a transient and a steady state one (in which time dependence is removed). Based on shape optimization for the steady state model and control for the transient model, path optimization algorithms are developed. Numerical results are then performed allowing a critical assessment of the choices we made. To increase the path design freedom, we modify the steady state algorithm to introduce path splits. Two methods are compared. In the first one, the source power is added to the optimization variables and an algorithm mixing relaxation-penalization techniques and the control of the total variation is set. In a second method, notion of topological derivative are applied to the path to cleverly remove and add pieces. eventually, in the steady state, we conduct a concurrent optimization of the part’s shape and of the scanning path. This multiphysics optimization problem raises perspectives gathering direct applications and future generalizations.Cette thèse porte sur l’optimisation des trajectoires de lasage pour la fabrication additive sur lit de poudre, ainsi que leur lien avec la géométrie de la pièce à construire. L’état de l’art est principalement constitué par des trajectoires basées sur des motifs, dont l’impact sur les propriétés mécaniques des objets finaux est quantifié. Cependant, peu d’analyses permettent de relier leur pertinence à la forme de la pièce elle-même. Nous proposons dans ce travail une approche systématique visant à optimiser la trajectoire sans Restriction a Priori. Le problème d’optimisation consiste à fusionner la structure en évitant de surchauffer (ce qui induirait des contraintes résiduelles) tout en minimisant le temps de fabrication. L’équation d’état est donc l’équation de la chaleur, dont le terme source dépend de la trajectoire. Deux modèles 2-d sont proposés pour contrôler la température : l’un transitoire et le second stationnaire (pas de dépendance en temps). Basés sur des techniques d’optimisation de forme pour le stationnaire et sur des outils de contrôle pour le transitoire, des algorithmes d’optimisation sont développés. Les applications numériques qui en découlent permettent une analyse critique des différents choix effectués. Afin de laisser plus de liberté dans la conception, l’algorithme stationnaire est adapté à la modification du nombre de composantes connexes de la trajectoire lors de l’optimisation. Deux méthodes sont comparées. Dans la première, la puissance de la source est ajoutée aux variables d’optimisation et un algorithme impliquant une relaxation-pénalisation et un contrôle de la variation totale est proposé. Dans la seconde, la notion de dérivation topologique est adaptée à la source. Enfin, dans le cadre stationnaire, nous détaillons le couplage de l’optimisation de la forme de la pièce, pour améliorer ses performances mécaniques, et de la trajectoire de lasage. Ce problème multiphysique ouvre des perspectives d'applications et de généralisations futures
J. Hughes - One of the best experts on this subject based on the ideXlab platform.
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Grass-Root Coaches Knowledge, Understanding, Attitude And Confidence to Deliver Injury Prevention Training in Youth Soccer: a Comparison of Coaches in Three EU Countries
Journal of Science in Sport and Exercise, 2020Co-Authors: Mark De Ste Croix, F. Ayala, S. Hernandez Sanchez, M. Lehnert, J. HughesAbstract:Purpose It is well recognised that injury prevention training can reduce injury incidence, however current coach education pathways do not provide grass-root coaches with the knowledge and confidence to deliver such training to youth players. The aim of this study was to explore differences in knowledge, understanding, attitude and confidence to deliver such injury prevention training in three European countries. Methods A total of 269 grass-root soccer coaches from 3 European countries (Czech Republic, UK, Spain) were recruited for this study. A validated questionnaire exploring knowledge, understanding, attitude towards and confidence to deliver youth injury prevention training was completed prior to a 2 h workshop on injury prevention training. Differences between countries was examined using Bayesian factors to quantify the evidence for and against the hypothesis of independence (H_0) by assuming a Poisson sampling scheme (as there was no a Priori Restriction on any cell count, nor on the grand total) (BF_10 Poisson). Results Current knowledge, attitude and confidence to deliver injury prevention training to youth players was poor across all three European countries. Relatively few coaches were currently using injury prevention training in their coaching sessions (23%). There were some country specific differences for attitude towards injury prevention training and confidence to deliver injury training, with Spanish coaches reporting a more positive attitude and confidence to deliver such training. Significantly fewer coaches in the UK were using injury prevention training compared to coaches in Spain and the Czech Republic. Conclusion As coaches identified a need for coach education and few were delivering injury prevention training, there is a clear need to embed and implement this programme into the grassroots coaching framework of sports governing bodies to improve adoption, implementation and maintenance.
Li Hao - One of the best experts on this subject based on the ideXlab platform.
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Sur des stratégies de calcul ondulatoires pour les milieux hétérogènes
2017Co-Authors: Li HaoAbstract:Ce travail de thèse s'intéresse au développement de stratégies de calcul pour résoudre les problèmes de Helmholtz, en moyennes fréquences, dans les milieux hétérogènes. Il s'appuie sur l'utilisation de la Théorie Variationnelle des Rayons Complexes (TVRC), et enrichit l'espace des fonctions qu'elle utilise par des fonctions d'Airy, quand le carré de la longueur d'onde du milieu varie linéairement. Il s'intéresse aussi à une généralisation de la prédiction de la solution pour des milieux dont la longueur d'onde varie d'une quelconque autre manière. Pour cela, des approximations à l'ordre zéro et à l'ordre un sont définies, et vérifient localement les équations d'équilibre selon une certaine moyenne sur les sous domaines de calcul.Plusieurs démonstrations théoriques des performances de la méthodes sont menées, et plusieurs exemples numériques illustrent les résultats. La complexité retenue pour ces exemples montrent que l'approche retenue permet de prédire le comportement vibratoire de problèmes complexes, tel que le régime oscillatoire des vagues dans un port maritime. Ils montrent également qu'il est tout à fait envisageable de mixer les stratégies de calcul développées avec celles classiquement utilisées, telle que la méthode des éléments finis, pour construire des stratégies de calcul utilisables pour les basses et les moyennes fréquences, en même temps.This thesis develops numerical approaches to solve mid-frequency heterogeneous Helmholtz problem. When the square of wave number varies linearly in the media, one considers an extended Variational Theory of Complex Rays(VTCR) with shape functions namely Airy wave functions, which satisfy the governing equation. Then a general way to handle heterogeneous media by the Weak Trefftz Discontinuous Galerkin (WTDG) is proposed. There is no a Priori Restriction for the wave number. One locally develops general approximated solution of the governing equation, the gradient of the wave number being the small parameter. In this way, zero order and first order approximations are defined, namely Zero Order WTDG and First Order WTDG. Their shape functions only satisfy the local governing equation in average sense.Theoretical demonstration and academic examples of approaches are addressed. Then the extended VTCR and the WTDG are both applied to solve a harbor agitation problem. Finally, a FEM/WAVE WTDG is further developed to achieve a mix use of the Finite Element method(FEM) approximation and the wave approximation in the same subdomains, at the same time for frequency bandwidth including LF and MF
Mark De Ste Croix - One of the best experts on this subject based on the ideXlab platform.
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Grass-Root Coaches Knowledge, Understanding, Attitude And Confidence to Deliver Injury Prevention Training in Youth Soccer: a Comparison of Coaches in Three EU Countries
Journal of Science in Sport and Exercise, 2020Co-Authors: Mark De Ste Croix, F. Ayala, S. Hernandez Sanchez, M. Lehnert, J. HughesAbstract:Purpose It is well recognised that injury prevention training can reduce injury incidence, however current coach education pathways do not provide grass-root coaches with the knowledge and confidence to deliver such training to youth players. The aim of this study was to explore differences in knowledge, understanding, attitude and confidence to deliver such injury prevention training in three European countries. Methods A total of 269 grass-root soccer coaches from 3 European countries (Czech Republic, UK, Spain) were recruited for this study. A validated questionnaire exploring knowledge, understanding, attitude towards and confidence to deliver youth injury prevention training was completed prior to a 2 h workshop on injury prevention training. Differences between countries was examined using Bayesian factors to quantify the evidence for and against the hypothesis of independence (H_0) by assuming a Poisson sampling scheme (as there was no a Priori Restriction on any cell count, nor on the grand total) (BF_10 Poisson). Results Current knowledge, attitude and confidence to deliver injury prevention training to youth players was poor across all three European countries. Relatively few coaches were currently using injury prevention training in their coaching sessions (23%). There were some country specific differences for attitude towards injury prevention training and confidence to deliver injury training, with Spanish coaches reporting a more positive attitude and confidence to deliver such training. Significantly fewer coaches in the UK were using injury prevention training compared to coaches in Spain and the Czech Republic. Conclusion As coaches identified a need for coach education and few were delivering injury prevention training, there is a clear need to embed and implement this programme into the grassroots coaching framework of sports governing bodies to improve adoption, implementation and maintenance.