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Non-linear partial differential equation encountered in problems of wave propagation
An eikonal equation (from Greek εἰκών, image) is a non-linear first-order partial differential equation that is encountered in problems of wave propagation
Eikonal_equation
Theoretical physics method in wave scattering equations
In theoretical physics, the eikonal approximation (Greek εἰκών for likeness, icon or image) is an approximative method useful in wave scattering equations
Eikonal_approximation
Topics referred to by the same term
Eikonal is the German form of the Greek word εἰκών, meaning likeness, icon or image. It can refer to: Eikonal equation, a non-linear partial differential
Eikonal
United States and German surveillance collaboration
Operation Eikonal is a collaboration between the National Security Agency (NSA) and Bundesnachrichtendienst (BND) for the sharing of telephony and Internet
Operation_Eikonal
Algorithm for solving boundary value problems of the Eikonal equation
method created by James Sethian for solving boundary value problems of the Eikonal equation: | ∇ u ( x ) | = 1 / f ( x ) for x ∈ Ω {\displaystyle |\nabla
Fast_marching_method
Investigation by the German parliamentary committee
ritual intended to create the appearance of an investigation". In Operation Eikonal German BND agents received "Selector Lists" from the NSA − search terms
German Parliamentary Committee investigation of the NSA spying scandal
German_Parliamentary_Committee_investigation_of_the_NSA_spying_scandal
Model of optics describing light as geometric rays
^{2}S=-\nabla ^{2}A_{m-1}.} The first equation is known as the eikonal equation, which determines the eikonal S ( r ) {\displaystyle S(\mathbf {r} )} is a Hamilton–Jacobi
Geometrical_optics
method is a numerical method for solving boundary value problems of the Eikonal equation. | ∇ u ( x ) | = 1 f ( x ) for x ∈ Ω {\displaystyle |\nabla
Fast_sweeping_method
Distance from a point to the boundary of a set
function is differentiable almost everywhere, and its gradient satisfies the eikonal equation | ∇ f | = 1. {\displaystyle |\nabla f|=1.} If the boundary of
Signed_distance_function
cones is the Monge cone. The simplest fully nonlinear equation is the eikonal equation. This has the form | ∇ u | 2 = 1 , {\displaystyle |\nabla u|^{2}=1
Monge_equation
U.S. signals intelligence organization
Technical Research Organisation (NTRO) – India Operation Ivy Bells Operation Eikonal Special Communications Service of Russia (Spetssvyaz) – Russia Unit 8200—Israel's
National_Security_Agency
Straight path on a curved surface or a Riemannian manifold
combinatorial wavefront propagation, direct numerical solution of the eikonal equation, and methods based on heat diffusion; the three methods below
Geodesic
constant. The function ψ {\displaystyle \psi } is called the eikonal. We expect the eikonal to vary slowly with coordinates and time consistent with the
Geometrical_acoustics
Formulation of classical mechanics
equation is to quantum mechanics what the eikonal equation is to the wave equation of optics. Both the eikonal equation and the Hamilton-Jacobi equation
Hamilton–Jacobi_equation
Theory of gravitation as curved spacetime
fact that the important "quasi-optical" singularities of the so-called eikonal approximations of many wave equations, namely the "caustics", are resolved
General_relativity
Calculation technique
engineering physics, the term also encompasses numerical solutions to the Eikonal equation. For example, ray-marching involves repeatedly advancing idealized
Ray_tracing_(physics)
Foreign intelligence agency of Germany
Constitutional Court of Germany List of intelligence agencies of Germany Operation Eikonal "Bundeshaushalt". bundeshaushalt.de. Retrieved 25 January 2020. "President
Federal_Intelligence_Service
Idealized model of light
engineering physics, the term also encompasses numerical solutions to the Eikonal equation. For example, ray-marching involves repeatedly advancing idealized
Ray_(optics)
American theoretical physicist
description of production processes by unitarity. The relevance of the eikonal model by John Francis Gunion, 1970 Ph.D. dissertation". UC San Diego Library
John_F._Gunion
Phenomenon in high-energy physics
turn as it moves in a straight line through the target. This assumes the eikonal approximation, viz that the projectile's trajectory is nearly straight-line
Glauber multiple scattering theory
Glauber_multiple_scattering_theory
Anomalous diffraction theory (also van de Hulst approximation, eikonal approximation, high energy approximation, soft particle approximation) is an approximation
Anomalous_diffraction_theory
Conceptual framework used in numerical analysis of surfaces and shapes
This is due to this being effectively the temporal integration of the Eikonal equation with a fixed front velocity. In mathematical modeling of combustion
Level-set_method
Use of both classical and quantum physics to analyze a system
constant. Physics portal Bohr model Correspondence principle Classical limit Eikonal approximation Einstein–Brillouin–Keller method Old quantum theory Liboff
Semiclassical_physics
Applied mathematician
problems in computational fluid dynamics including Maxwell's equations and Eikonal equations. Educated in China and the US, she works in the US as a professor
Fengyan_Li
equation to model flame propagation D'Alembert's wave equation Eikonal equation in wave propagation Euler–Poisson–Darboux equation in wave theory
List of named differential equations
List_of_named_differential_equations
American mathematician
methods for solving static Hamilton–Jacobi equations. In the case of an Eikonal equation, the first method to do so was developed by Jon N. Tsitsiklis
James_Sethian
German mathematician and astronomer (1848–1919)
(On the integrals of the many-body problem). (Leipzig 1887) Das Eikonal (The Eikonal). (Leipzig 1895) Ernst Zinner (1955). "Bruns, Ernst Heinrich". Neue
Heinrich_Bruns
Theft of corporate information
the equivalent of 30,000 jobs to economic espionage yearly. In Operation Eikonal, German BND agents received "selector lists" from the NSA – search terms
Industrial_espionage
Light rays follow quickest paths
Adequality Augustin-Jean Fresnel Birefringence Calculus of variations Eikonal equation Fermat's and energy variation principles in field theory Geodesic
Fermat's_principle
Form of surveillance, such as wiretapping
web for 'suspicious stuff', were suggested as selectors. In Operation Eikonal, German BND agents received "Selector Lists" − search terms for their dragnet
Targeted_surveillance
Chinese mathematician
science and engineering". Zhao, Hongkai (2005). "A fast sweeping method for Eikonal equations". Mathematics of Computation. 74 (250): 603–627. doi:10
Hongkai_Zhao
Physics phenomenon and formula
θ {\displaystyle \theta } , a scalar field. The second equation is the eikonal equation. It shows the effects of diffraction on the effective wavenumber:
Mild-slope_equation
Solution method for linear differential equations
^{0}:\quad {S_{0}^{\prime }}^{2}=Q(x),} which can be recognized as the eikonal equation, with solution S 0 ( x ) = ± ∫ x 0 x Q ( x ′ ) d x ′ . {\displaystyle
WKB_approximation
Conceptual parallel between optics and classical mechanics
slowly varying amplitude variation and the equations obtained are the Eikonal equation of optics and oceanology and the Hamilton-Jacobi equation. The
Hamilton's optical-mechanical analogy
Hamilton's_optical-mechanical_analogy
Important subject of signal processing and engineering
{\displaystyle L^{2}} in the Hilbert space sense; for instance, one could use the eikonal e k ( t ) := e 2 π i k t {\displaystyle e_{k}(t):=e^{2\pi ikt}\,} , although
Signal_reconstruction
Process of calculating the causal factors that produced a set of observations
physical space) of a wave-front issued from a point source, satisfies the Eikonal equation: ‖ ∇ τ ( x ) ‖ = s ( x ) , {\displaystyle \|\nabla \tau (x)\|=s(x)
Inverse_problem
government surveillance projects Mass surveillance XKeyscore Operation Eikonal ECHELON PRISM "Special Source Operations (SSO) slides with details on RAMPART-A
RAMPART-A
American mathematician and physicist
Fluids 22.7 (1979): 1355–1358. Weitzner, Harold, and D. B. Batchelor. "An eikonal expansion of the Vlasov–Maxwell equations valid near cyclotron resonance
Harold_Weitzner
Solution to partial differential equation
involves a more refined argument. The previous boundary value problem is an eikonal equation in a single spatial dimension with f = 1 {\displaystyle f=1}
Viscosity_solution
American seismologist (born 1959)
of ray tracing which relied on a finite-difference approximation of the eikonal equation and which has been used widely in both earthquake and reflection
John_Vidale
Data structure for integer priorities
of the fast marching method for solving boundary value problems of the Eikonal equation, used to model wave propagation. This method finds the times at
Bucket_queue
Reformulation of general relativity
"unify" quantum mechanics and general relativity, because the semiclassical Eikonal approximation in the context of quantum theory and general relativity has
Hamilton–Jacobi–Einstein equation
Hamilton–Jacobi–Einstein_equation
Italian mathematician (born 1979)
1007/s00220-017-2900-3 A. Siconolfi and A. Sorrentino, Global results for Eikonal Hamilton-Jacobi equations on networks, Analysis & PDE 11 (1): 171–211,
Alfonso Sorrentino (mathematician)
Alfonso_Sorrentino_(mathematician)
Type of discrete calculus
S2CID 9687337. Desquesnes, Xavier; Elmoataz, Abderrahim; Lézoray, Olivier (2013). "Eikonal Equation Adaptation on Weighted Graphs: Fast Geometric Diffusion Process
Calculus on finite weighted graphs
Calculus_on_finite_weighted_graphs
British physicist and computer scientist
an approximation that is often called geometric. It formulates as the Eikonal equation and is only applicable under certain conditions including that
Jenifer_Haselgrove
condition in symplectic topology and Floer theory. In geometric optics, the eikonal equation determines a Lagrangian submanifold Λ ⊂ T ∗ X {\displaystyle \Lambda
Maslov_index
{\displaystyle iu_{t}+u_{xx}+2|u|_{x}^{2}u+|u|^{4}u=0} Integrable systems Eikonal equation any | ∇ u ( x ) | = F ( x ) , x ∈ Ω {\displaystyle \displaystyle
List of nonlinear partial differential equations
List_of_nonlinear_partial_differential_equations
Echolocation (animal) Echolocation (human) Eddy (fluid dynamics) Edge wave Eikonal equation Ekman layer Ekman spiral Ekman transport El Niño–Southern Oscillation
Index_of_wave_articles
Russian-French mathematical physicist (1948–2024)
l'Institut Henri Poincaré A. 44 (2): 195–210. Yafaev, D. R. (1986). "The eikonal approximation and the asymptotics of the total scattering cross-section
Dmitri_Yafaev
German theoretical physicist
Glauber as semiclassical approximation and is also known under the name eikonal approximation. Hans Bethe confirmed Molière's results on multiple scattering
Gert_Molière
material is examined by the BKM; in the BKM is also used to solve nonlinear Eikonal equation. Method of fundamental solutions Regularized meshfree method Boundary
Boundary_knot_method
EIKONAL
EIKONAL
EIKONAL
EIKONAL
Male
English
Variant spelling of English Korey, possibly KORI means "deep hollow, ravine."
Boy/Male
Hindu, Indian
Spirit of Happiness; Spirit of Joy; God of Ganesha and Vignesh
Boy/Male
Arabic, Muslim
Kindness of the Creator
Surname or Lastname
English
English : patronymic from the medieval personal name Sim, a short form of Simon.
Girl/Female
Greek
Pure.
Girl/Female
Indian
The Flower Jasmine
Boy/Male
Tamil
Joy, Happiness
Boy/Male
Hindu, Indian, Telugu
Son
Female
Greek
(ΤεÏψιχόÏη) Greek myth name of a muse of dance, TERPSIKHORE means "enjoying the dance."
Boy/Male
Indian
Brilliant
EIKONAL
EIKONAL
EIKONAL
EIKONAL
EIKONAL