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Relevant bibliographies by topics / Système eikonale

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Academic literature on the topic 'Système eikonale'

Author: Grafiati

Published: 7 August 2022

Last updated: 8 August 2022

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Journal articles on the topic "Système eikonale"

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Soravia, Pierpaolo. "Degenerate Eikonal equations with discontinuous refraction index." ESAIM: Control, Optimisation and Calculus of Variations 12, no. 2 (March 22, 2006): 216–30. http://dx.doi.org/10.1051/cocv:2005033.

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Waheed, Umair bin, Ehsan Haghighat, Tariq Alkhalifah, Chao Song, and Qi Hao. "PINNeik: Eikonal solution using physics-informed neural networks." Computers & Geosciences 155 (October 2021): 104833. http://dx.doi.org/10.1016/j.cageo.2021.104833.

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Maragos, Petros, and Muhammad Akmal Butt. "Curve Evolution, Differential Morphology, and Distance Transforms Applied to Multiscale and Eikonal Problems." Fundamenta Informaticae 41, no. 1,2 (2000): 91–129. http://dx.doi.org/10.3233/fi-2000-411204.

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Vázquez, Luis, M. Pilar Velasco, Dumitru Baleanu, J. Luis Vázquez-Poletti, and Salvador Jiménez. "From Eikonal to Antieikonal Approximations: Competition of Scales in the Framework of Schrödinger and Classical Wave Equation." Journal of Computational and Nonlinear Dynamics 17, no. 8 (April 1, 2022). http://dx.doi.org/10.1115/1.4054153.

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Abstract We present a description of certain limits associated with the Schrödinger equation, the classical wave equation, and Maxwell equations. Such limits are mainly characterized by the competition of two fundamental scales. More precisely: (1) The competition of an exploratory wavelength and the scale of fluctuations is associated with the media where the propagation takes place. From that, the universal behaviors arise eikonal and anti-eikonal. (2) In the context above, it is specially relevant and promising the study of propagation of electromagnetic waves in a media with a self-similar structure, like a fractal one. These systems offer the suggestive scenario where the eikonal and anti-eikonal behaviors are simultaneous. This kind of study requires large and massive computations that are mainly possible in the framework of the cloud computing. Recently, we started to carry out this task. (3) Finally and as a collateral aspect, we analyze the Planck constant in the interval 0≤h≤∞.

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Andreeva, T. A., W. W. Durgin, and S. E. Wojcik. "Influence of Imperfect Internal Waves on Long-Range Underwater Acoustic Propagation." Journal of Computational and Nonlinear Dynamics 5, no. 1 (November 12, 2009). http://dx.doi.org/10.1115/1.4000322.

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This work presents a numerical analysis of the effect of random fluctuations of internal waves on the chaotic dynamics of ray trajectories in ocean acoustics. The Eikonal equation is considered in a form of the second order, nonlinear ordinary differential equation. Random phase modulations in the form of zero mean Gaussian white noise are considered for modeling an imperfectly periodic single mode internal wave. It is shown that in the presence of random fluctuations the intersection of acoustic rays with the ocean surface occurs sooner and becomes more frequent than predicted by deterministic ocean models.

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Bonnans, Frédéric, Guillaume Bonnet, and Jean-Marie Mirebeau. "A linear finite-difference scheme for approximating Randers distances on Cartesian grids." ESAIM: Control, Optimisation and Calculus of Variations, June 2, 2022. http://dx.doi.org/10.1051/cocv/2022043.

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Randers distances are an asymmetric generalization of Riemannian distances, and arise in optimal control problems subject to a drift term, among other applications. We show that Randers eikonal equation can be approximated by a logarithmic transformation of an anisotropic second order linear equation, generalizing Varadhan's formula for Riemannian manifolds. Based on this observation, we establish the convergence of a numerical method for computing Randers distances, from point sources or from a domain's boundary, on Cartesian grids of dimension two and three, which is consistent at order two thirds, and uses tools from low-dimensional algorithmic geometry for best efficiency. We also propose a numerical method for optimal transport problems whose cost is a Randers distance, exploiting the linear structure of our discretization and generalizing previous works in the Riemannian case. Numerical experiments illustrate our results.

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Kumar, Jitendra, and Ashish Dutta. "Energy optimal motion planning of a 14-DOF biped robot on 3D terrain using a new speed function incorporating biped dynamics and terrain geometry." Robotica, May 14, 2021, 1–29. http://dx.doi.org/10.1017/s0263574721000515.

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Abstract In this paper, a new method is proposed to find a feasible energy-efficient path between an initial point and goal point on uneven terrain and then to optimally traverse the path. The path is planned by integrating the geometric features of the uneven terrain and the biped robot dynamics. This integrated information of biped dynamics and associated cost (energy) for moving toward the goal point is used to define the value of a new speed function at each point on the discretized surface of the terrain. The value is stored as a matrix called the dynamic transport cost (DTC). The path is obtained by solving the Eikonal equation numerically by fast marching method (FMM) on an orthogonal grid, by using the information stored in the DTC matrix. One step of walk on uneven terrain is characterized by 10 footstep parameters (FSPs); these FSPs represent the position of swinging foot at the starting and ending time of the walk, orientation, and state (left or right) of support foot. A walking dataset was created for different walking conditions (FSPs), which the biped robot is likely to encounter when it has to walk on the uneven terrain. The corresponding energy optimal hip and foot trajectory parameters (HFTPs) are obtained by optimization using a genetic algorithm (GA). The created walk dataset is generalized by training a feedforward neural network (NN) using the scaled conjugate gradient (SCG) algorithm. The Foot placement planner gives a sequence of foot positions and orientations along the obtained path, which is followed by the biped robot by generating real-time optimal foot and hip trajectories using the learned NN. Simulation results on different types of uneven terrains validate the proposed method.

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Dissertations / Theses on the topic "Système eikonale"

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Oussaily, Aya. "Étude théorique et numérique des systèmes modélisant la dynamique des densités des dislocations." Thesis, Compiègne, 2021. https://bibliotheque.utc.fr/Default/doc/SYRACUSE/2021COMP2634.

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Dans cette thèse, nous nous intéressons à l’analyse théorique et numérique de la dynamique des densités des dislocations. Les dislocations sont des défauts linéaires qui se déplacent dans les cristaux lorsque ceux-ci sont soumis à des contraintes extérieures. D’une manière générale, la dynamique des densités des dislocations est décrite par un système d’équations de transport, où les champs de vitesse dépendent de manière non-locale des densités des dislocations. Au départ, notre travail se focalise sur l’étude d’un système unidimensionnel (2 × 2) de type Hamilton-Jacobi dérivé d’un système bidimensionnel proposé par Groma et Balogh en 1999. Pour ce modèle, nous montrons un résultat d’existence globale et d’unicité. En addition, nous nous intéressons à l’étude numérique de ce problème, complété par des conditions initiales croissantes, en proposant un schéma aux différences finies implicite dont on prouve la convergence. Ensuite, en s’inspirant du travail effectué pour la résolution de la dynamique des densités des dislocations, nous mettons en œuvre une théorie plus générale permettant d’obtenir un résultat similaire d’existence et d’unicité d’une solution dans le cas des systèmes de type eikonal unidimensionnels. En considérant des conditions initiales croissantes, nous faisons une étude numérique pour ce système. Sous certaines conditions de monotonies sur la vitesse, nous proposons un schéma aux différences finies implicite permettant de calculer la solution discrète et simuler ainsi la dynamique des dislocations à travers ce modèle
In this thesis, we are interested in the theoretical and numerical studies of dislocations densities. Dislocations are linear defects that move in crystals when those are subjected to exterior stress. More generally, the dynamics of dislocations densities are described by a system of transport equations where the velocity field depends non locally on the dislocations densities. First, we are interested in the study of a one dimensional submodel of a (2 × 2) Hamilton-Jacobi system introduced by Groma and Balogh in 1999, proposed in the two dimensional case. For this system, we prove global existence and uniqueness results. Adding to that, considering nondecreasing initial data, we study this problem numerically by proposing a finite difference implicit scheme for which we show the convergence. Then, inspired by the first work, we show a more general theory which allows us to get similar results of existence and uniqueness of solution in the case of one dimensional eikonal systems. By considering nondecreasing initial data, we study this problem numerically. Under certain conditions on the velocity, we propose a finite difference implicit scheme allowing us to calculate the discrete solution and simulate then the dislocations dynamics via this model

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Ley, Olivier. "Evolution de fronts avec vitesse non-locale et équations de Hamilton-Jacobi." Habilitation à diriger des recherches, Université François Rabelais - Tours, 2008. http://tel.archives-ouvertes.fr/tel-00362409.

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Ce mémoire présente mes travaux de recherche effectués après ma thèse, entre 2002 et 2008. Les thèmes principaux sont les équations aux dérivées partielles non-linéaires et des problèmes d'évolutions de fronts ou d'interfaces. Il est organisé en trois chapitres.

Le premier chapitre concerne l'évolution de fronts avec une vitesse normale prescrite. Pour étudier ce genre de problème, une première approche, dite par lignes de niveaux, consiste àreprésenter le front comme une ligne de niveau d'une fonction auxiliaire u. Cette approche ramène l'étude du problème d'évolution géométrique à un problème d'EDP puisque u vérifie une équation de Hamilton-Jacobi. Quelques résultats dans le cas de vitesses locales comme la courbure moyenne sont présentés mais la majorité des résultats concerne le cas de vitesses non-locales décrivant la dynamique des dislocations dans un cristal ou modélisant l'asymptotique d'un système de FitzHugh-Nagumo apparaissant en biologie. Une approche différente, basée sur des solutions de viscosité géométriques, est utilisée pour étudier des problèmes de propagation de fronts apparaissant en optimisation de formes. Le but est de trouver un ensemble optimal minimisant une énergie du type capacité à volume ou périmètre constant. L'idée est de déformer le bord d'un ensemble donné avec une vitesse normale adéquate de manière à diminuer au plus son énergie. La mise en oeuvre de cette idée nécessite la construction rigoureuse d'une telle évolution pour tout temps et la preuve de la convergence vers une solution du problème initial. De plus, la décroissance de l'énergie est obtenue le long du flot.

Le deuxième chapitre décrit des résultats d'unicité, d'existence et d'homogénéisation pour des équations de Hamilton-Jacobi-Bellman. La majeure partie du travail effectué concerne des équations provenant de problèmes de contrôle stochastique avec des contrôles non-bornés. Les équations comportent alors des termes quadratiques par rapport au gradient et les solutions étudiées sont elles-mêmes à croissance quadratique. Des liens entre ces solutions et les fonctions valeurs des problèmes de contrôle correspondants sont établis. La seconde partie est consacrée à un théorème d'homogénéisation pour un système d'équations de Hamilton-Jacobi du premier ordre.

Le troisième et dernier chapitre traite d'un sujet un peu à part, à savoir le lien entre les flots de gradient et l'inégalité de Lojasiewicz. La principale originalité de ce travail est de placer l'étude dans un cadre hilbertien pour des fonctions semiconvexes, ce qui sort du cadre de l'inégalité de Lojasiewicz classique. Le principal théorème produit des caractérisations de cette inégalité. Les résultats peuvent être précisés dans le cas des fonctions convexes ; en particulier, un contre-exemple de fonction convexe ne vérifiant pas l'inégalité de Lojasiewicz est construit. Cette dernière inégalité est reliée à la longueur des trajectoires de gradient. Une borne de cette longueur est obtenue pour les fonctions convexes coercives en dimension deux même lorsque cette inégalité n'est pas vérifiée.

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Petrášová, Tereza. "Dijkstrův algoritmus v problému proudění chodců." Master's thesis, 2018. http://www.nusl.cz/ntk/nusl-387371.

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Title: On the Dijkstra's algorithm in the Pedestrian Flow Problem Author: Tereza Petrášová Department: Department of Numerical Mathematics Supervisor: doc. RNDr. Jiří Felcman, CSc., Department of Numerical Mathe- matics Abstract: The pedestrian flow problem is described by a coupled system of the first order hyperbolic partial differential equations with the source term and by the functional minimization problem for the desired direction of motion. The functional minimization is based on the modified Dijkstra's algorithm used to find the minimal path to the exit. The original modification of the Dijkstra's algorithm is proposed to increase its efficiency in the pedestrian flow problem. This approach is compared with the algorithm of Bornemann and Rasch for determination of the desired direction of motion based on the solution of the so- called Eikonal equation. Both approaches are numerically tested in the framework of two splitting algorithms for solution of the coupled problem. The former splitting algorithm is based on the finite volume method yielding for the given time instant the piecewise constant approximation of the solution. The latter one uses the implicit discretization by a space-time discontinuous Galerkin method based on the discontinuous piecewise polynomial approximation. The numerical examples...

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Book chapters on the topic "Système eikonale"

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Jung, Young-Dae, and Jung-Sik Yoon. "Eikonal Cross Section for Elastic Electron-Ion Scattering in Strongly Coupled Plasma." In Strongly Coupled Coulomb Systems, 633–38. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/0-306-47086-1_118.

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Gomatam, J., and P. Grindrod. "Three-Dimensional Waves in Excitable Reaction-Diffusion Systems: the Eikonal Approximation." In Nonlinear Wave Processes in Excitable Media, 201–11. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4899-3683-7_20.

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Camara, Oscar, Ali Pashaei, Rafael Sebastian, and Alejandro F. Frangi. "Personalization of Fast Conduction Purkinje System in Eikonal-Based Electrophysiological Models with Optical Mapping Data." In Statistical Atlases and Computational Models of the Heart, 281–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15835-3_29.

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Dacorogna, Bernard, Roland Glowinski, Yuri Kuznetsov, and Tsorng-Whay Pan. "On a Conjugate Gradient/Newton/Penalty Method for the Solution of Obstacle Problems. Application to the Solution of an Eikonal System with Dirichlet Boundary Conditions." In Scientific Computation, 263–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-18560-1_17.

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Sage, Sandrine, Gilles Grandjean, and Jacques Verly. "Java Tomography System (JaTS), a Seismic Tomography Software Using Fresnel Volumes, a Fast Marching Eikonal Solver and a Probabilistic Reconstruction Method: Conclusive Synthetic Test Cases." In Engineering Geology for Infrastructure Planning in Europe, 226–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-39918-6_27.

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Zinn-Justin, Jean. "Quantum evolution: From particles to non-relativistic fields." In Quantum Field Theory and Critical Phenomena, 90–104. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0005.

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Chapter 4 has introduced the functional integral representation of the quantum statistical operators and thus, formally, evolution in imaginary or Euclidean time. By contrast, to calculate the evolution operator and the scattering S-matrix elements, quantities relevant to particle physics, it is necessary to make a continuation from imaginary to real time. However, the representation of the S-matrix follows from additional considerations. To illustrate the power of the formalism, we show how to recover the perturbative expansion of the scattering amplitude, some semi-classical approximations, and the eikonal approximation. When the asymptotic states at large time are eigenstates of the harmonic oscillator, instead of free particles, the holomorphic formalism becomes useful. A simple generalization of the path integral of Chapter 4 leads to the corresponding path integral representation of the S-matrix. In the case of the Bose gas, the evolution operator is then given by a holomorphic field integral. A parallel formalism leads to an analogous representation for the evolution operator of a system of non-relativistic fermions.

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Conference papers on the topic "Système eikonale"

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Zysk, Adam M., John C. Schotland, and P. Scott Carney. "Eikonal Representation of Partially Coherent Fields in Geometrical Optical Systems." In Frontiers in Optics. Washington, D.C.: OSA, 2005. http://dx.doi.org/10.1364/fio.2005.fthk4.

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Rapoport, Diego L., and Daniel M. Dubois. "Torsion Fields, Propagating Singularities, Nilpotence, Quantum Jumps and the Eikonal Equations." In COMPUTING ANTICIPATORY SYSTEMS: CASYS ‘09: Ninth International Conference on Computing Anticipatory Systems. AIP, 2010. http://dx.doi.org/10.1063/1.3527144.

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Krautter, Martin. "The Eikonal function: the common concept in ray optics and particle mechanics." In Lens and Optical Systems Design. SPIE, 1993. http://dx.doi.org/10.1117/12.142826.

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Hoffnagle, John A., and David L. Shealy. "Extending Stavroudis’s solution of the eikonal equation to multi-element optical systems." In Frontiers in Optics. Washington, D.C.: OSA, 2009. http://dx.doi.org/10.1364/fio.2009.fthh2.

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de Meijere, J. L. F., J. A. Schuurman, and C. H. F. Velzel. "The Use Of The Pseudo-Eikonal In The Optimization Of Optical Systems." In 1988 International Congress on Optical Science and Engineering, edited by Andre Masson, Joachim J. Schulte-in-den-Baeumen, and Hannfried Zuegge. SPIE, 1989. http://dx.doi.org/10.1117/12.949355.

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Bhatt, Santosh, Lawrence Townsend, Sirikul Sriprisan, and Mahmoud PourArsalan. "Analytical Derivation of Abrasion-Ablation Model With Corrections to the First Order Eikonal Expansions." In 41st International Conference on Environmental Systems. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2011. http://dx.doi.org/10.2514/6.2011-5251.

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