Relevant bibliographies by topics / Eikonal system

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Eikonal system'

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Published: 7 August 2022

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Journal articles on the topic "Eikonal system"

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Meher, Mehrollah, and Davood Rostamy. "Hybrid of differential quadrature and sub-gradients methods for solving the system of Eikonal equations." Nonlinear Engineering 10, no. 1 (January 1, 2021): 436–49. http://dx.doi.org/10.1515/nleng-2021-0035.

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Abstract Many important natural phenomena of wave propagations are modeled by Eikonal equations and a variety of new methods are needed to solve them. The differential quadrature method (DQM) is an effective numerical method for solving the system of differential equations that can achieve accurate numerical results using fewer grid points and therefore requires relatively little computational effort. In this paper, we focus on the implementation of the non-smooth Eikonal optimization by using a hybrid of polynomial differential quadrature (PDQ) or Fourier differential quadrature (FDQ) method and sub-gradients idea. Our goal is to develop a new Eikonal equation system design for wave propagation equations, as well as the efficiency and accuracy of new grid points to reduce errors and compare errors in various physical equation problems, especially wave propagation equations, and achieve their convergence. We explore the accuracy and stability of the Eikonal equation system by two-dimensional and three-dimensional numerical examples and the use of three types of grid points in a comprehensive manner. This article aims to create a new and innovative solution to the non-smooth Eikonal equation system. This new method is much more efficient and effective than traditional numerical solution methods same as DQ.
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Sava, Paul, and Sergey Fomel. "3-D traveltime computation using Huygens wavefront tracing." GEOPHYSICS 66, no. 3 (May 2001): 883–89. http://dx.doi.org/10.1190/1.1444977.

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Traveltime computation is widely used in seismic modeling, imaging, and velocity analysis. The two most commonly used methods are ray tracing and numerical solutions to the eikonal equation. Eikonal solvers are fast and robust but are limited to computing only the first‐arrival traveltimes. Ray tracing can compute multiple arrivals but lacks the robustness of eikonal solvers. We propose a robust and complete method of traveltime computation. It is based on a system of partial differential equations, which is equivalent to the eikonal equation but formulated in the ray‐coordinates system. We use a first‐order discretization scheme that is interpreted very simply in terms of the Huygens’s principle. Our explicit finite‐difference solution to the eikonal equation solved in the ray‐coordinates system delivers both computational speed and stability since we use more than one point on the current wavefront at every time step. The finite‐difference method has proven to be a robust alternative to conventional ray tracing, while being faster and having a better ability to handle rough velocity media and penetrate shadow zones.
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Penttinen, M. "Small-Angle Scattering on a System of Magnetic and Electric Charges." International Journal of Modern Physics A 12, no. 18 (July 20, 1997): 3193–204. http://dx.doi.org/10.1142/s0217751x97001687.

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The generalization of the conformal scattering method for small-angle scattering processes involving magnetic monopoles and ordinary charges is constructed. Using this generalization we show that the introduction of magnetic charges corresponds to analytical continuation of the eikonal amplitude in the complex charge plane (the imaginary part is proportional to the magnetic charge). We calculate explicitly the eikonal amplitude for scattering on a dyon and two monopoles in terms of confluent hypergeometric functions. The singularities of the corresponding amplitudes (focal points) are studied in detail.
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KIM, YONG JOO, and MOON HOE CHA. "NON-EIKONAL PHASE SHIFT ANALYSIS FOR 12C + 12C ELASTIC SCATTERING." International Journal of Modern Physics E 09, no. 01 (February 2000): 67–76. http://dx.doi.org/10.1142/s0218301300000052.

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We present first-order non-eikonal correction to the eikonal phase shifts for heavy ion elastic scattering based on Coulomb trajectories of colliding nuclei. It has been applied satisfactorily to elastic angular distributions of the 12 C + 12 C system at E lab = 240, 360 and 1016 MeV. The refractive oscillations observed in the elastic scattering angular distributions could be explained due to interference between the near- and far-side amplitudes. The presence of a nuclear rainbow is evidenced through classical deflection function. We have found that the first-order non-eikonal effect on the imaginary potential is important when the absorptive potential is weak and the real potential is strong.
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Filpo, Eduardo, Jessé Costa, and Jörg Schleicher. "Image-guided ray tracing and its applications." GEOPHYSICS 86, no. 3 (April 21, 2021): U39—U47. http://dx.doi.org/10.1190/geo2020-0642.1.

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Eikonal solvers have important applications in seismic data processing and inversion, the so-called image-guided methods. To this day, in image-guided applications, the solution of the eikonal equation is implemented using partial-differential-equation solvers, such as fast-marching or fast-sweeping methods. We have found that alternatively, one can numerically integrate the dynamic Hamiltonian system defined by the image-guided eikonal equation and reconstruct the solution with image-guided rays. We evaluate interesting applications of image-guided ray tracing to seismic data processing, demonstrating the use of the resulting rays in image-guided interpolation and smoothing, well-log interpolation, image flattening, and residual-moveout picking. Some of these applications make use of properties of the ray-tracing system that are not directly obtained by eikonal solvers, such as ray position, ray density, wavefront curvature, and ray curvature. These ray properties open space for a different set of applications of the image-guided eikonal equation, beyond the original motivation of accelerating the construction of minimum distance tables. We stress that image-guided ray tracing is an embarrassingly parallel problem that makes its implementation highly efficient on massively parallel platforms. Image-guided ray tracing is advantageous for most applications involving the tracking of seismic events and imaging-guided interpolation. Our numerical experiments using synthetic and real data sets indicate the efficiency and robustness of image-guided rays for the selected applications.
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SHUTTLEWORTH, I. G. "ANALYSIS OF THE (3 × 3)-H/Cu(111) SYSTEM USING EIKONAL-LEVEL HELIUM ATOM SCATTERING SIMULATIONS." Surface Review and Letters 14, no. 06 (December 2007): 1089–93. http://dx.doi.org/10.1142/s0218625x07010810.

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The saturated (3 × 3)- H / Cu (111) system has been investigated by Eikonal-level helium atom scattering (HAS) simulations of previously reported HAS diffraction images. Basing the investigation on an unreconstructed single-domain structure with H atoms occupying three-fold hollow adsorption sites, a systematic trial of all possible structures has been performed and a series of structures has been shown to agree with the experimental images. Comparison of this fitting process to diffraction images taken at low (30°) and high (47°) angles of incidence has shown that the Eikonal approximation is a reasonable scattering algorithm for the H / Cu (111) system.
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KIM, YONG JOO, and MOON HOE CHA. "SECOND-ORDER EIKONAL MODEL ANALYSIS OF16O+16OELASTIC SCATTERING." International Journal of Modern Physics E 10, no. 04n05 (August 2001): 373–86. http://dx.doi.org/10.1142/s0218301301000563.

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We analyze the elastic scattering angular distributions of the16O +16O system at Elab=480 MeV and 704 MeV within the framework of the second-order eikonal model based on Coulomb trajectories of colliding nuclei. The diffractive oscillatory structure observed in the elastic angular distribution could be explained due to the interference between the near- and far-side scattering amplitudes. The presence of a nuclear rainbow in this system is evidenced through a classical deflection function. The effective optical potential is developed from the second-order non-eikonal phase shifts.
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Peletier, Mark A., and Marco Veneroni. "Stripe patterns and a projection-valued formulation of the eikonal equation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1965 (April 28, 2012): 1730–39. http://dx.doi.org/10.1098/rsta.2011.0425.

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We describe recent work on striped patterns in a system of block copolymers. A by-product of the characterization of such patterns is a new formulation of the eikonal equation. In this formulation, the unknown is a field of projection matrices of the form P = e ⊗ e , where e is a unit vector field. We describe how this formulation is better adapted to the description of striped patterns than the classical eikonal equation, and illustrate this with examples.
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Ahdid, Rachid, Said Safi, Mohamed Fakir, and Bouzid Manaut. "Geodesic Distance on Riemannian Manifold using Jacobi Iterations in 3D Face Recognition System." International Journal of Informatics and Communication Technology (IJ-ICT) 6, no. 1 (June 22, 2017): 10. http://dx.doi.org/10.11591/ijict.v6i1.pp10-19.

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In this paper, we present an automatic application of 3D face recognition system using geodesic distance in Riemannian geometry. We consider, in this approach, the three dimensional face images as residing in Riemannian manifold and we compute the geodesic distance using the Jacobi iterations as a solution of the Eikonal equation. The problem of solving the Eikonal equation, unstructured simplified meshes of 3D face surface, such as tetrahedral and triangles are important for accurately modeling material interfaces and curved domains, which are approximations to curved surfaces in R<sup>3</sup>. In the classifying steps, we use: Neural Networks (NN), K-Nearest Neighbor (KNN) and Support Vector Machines (SVM). To test this method and evaluate its performance, a simulation series of experiments were performed on 3D Shape REtrieval Contest 2008 database (SHREC2008).<strong></strong>
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KIM, YONG JOO, and MOON HOE CHA. "COULOMB-MODIFIED EIKONAL PHASE SHIFT ANALYSIS BASED ON HYPERBOLIC TRAJECTORY FOR 12C + 12C ELASTIC SCATTERINGS." International Journal of Modern Physics E 13, no. 02 (April 2004): 439–50. http://dx.doi.org/10.1142/s0218301304002296.

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We present a Coulomb-modified eikonal model formalism based on hyperbolic trajectory for heavy-ion elastic scattering. This formalism has been applied satisfactorily to elastic scatterings of the 12 C + 12 C system at E lab =240, 360 and 1016 MeV. The presence of a nuclear rainbow in this system is evidenced through a classical deflection function. The Fraunhöfer oscillations observed in the elastic angular distributions can be explained due to interference between the near- and far-side amplitudes. We have found that the hyperbolic trajectory effect on the eikonal model is important when the absorptive potential is weak and the real potential is strong.
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Dissertations / Theses on the topic "Eikonal system"

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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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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 "Eikonal system"

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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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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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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 "Eikonal system"

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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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