The Experts below are selected from a list of 162 Experts worldwide ranked by ideXlab platform
O A Godin - One of the best experts on this subject based on the ideXlab platform.
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Fermat Principle for a nonstationary medium
Physical Review Letters, 2003Co-Authors: A G Voronovich, O A GodinAbstract:: One possible formulation of a variational Principle of the Fermat type for systems with time-dependent parameters is suggested. In a stationary case, it reduces to the Mopertui-Lagrange least-action Principle. A class of Hamiltonians (dispersion relations) is indicated, for which the variational Principle reduces to the Fermat Principle in a general nonstationary case. Hamiltonians that are homogeneous functions of momenta are in this category. For the important case of nondispersive waves (corresponding to Hamiltonians being homogeneous function of momenta order 1) the Fermat Principle fully determines the geometry of the rays. Equations relating the variation of signal frequency with the rate of change of propagation time are established.
Thomas F. Eibert - One of the best experts on this subject based on the ideXlab platform.
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A Ray-Tracing Algorithm Based on the Computation of (Exact) Ray Paths With Bidirectional Ray-Tracing
IEEE Transactions on Antennas and Propagation, 2020Co-Authors: Mehmet Mert Taygur, Thomas F. EibertAbstract:A novel ray-tracing algorithm to cope with the phase errors due to incorrect ray path computations in ray-launching approaches is presented. The algorithm utilizes bidirectional ray-tracing to collect information about wavefronts incident on an interaction surface and yields considerable improvements in accuracy compared to conventional unidirectional ray-tracing. The points, where exact ray paths intersect with the surface, are obtained according to the Fermat Principle of least time. If the interaction surface is aligned with diffraction edges, the corresponding critical points of the second kind can also be retrieved and complicated diffraction treatments by shooting diffracted rays on Keller cones can be avoided. Thus, a substantial reduction in the number of rays can be achieved. Furthermore, a typical problem encountered in traditional ray-tracing due to the reception sphere mechanism, i.e., incorrect ray contributions, can mostly be evaded. Numerical results demonstrate the capabilities of the new algorithm and its advantages against traditional techniques.
Paolo Piccione - One of the best experts on this subject based on the ideXlab platform.
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Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes
Communications in Mathematical Physics, 2009Co-Authors: Roberto Giambò, Fabio Giannoni, Paolo PiccioneAbstract:Given a Lorentzian manifold ( M , g ), an event p and an observer U in M , then p and U are light conjugate if there exists a lightlike geodesic γ : [0, 1] → M joining p and U whose endpoints are conjugate along γ . Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M , then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat Principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.
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the Fermat Principle in general relativity and applications
Journal of Mathematical Physics, 2002Co-Authors: Fabio Giannoni, Antonio Masiello, Paolo PiccioneAbstract:In this paper we use a general version of Fermat’s Principle for light rays in general relativity and a curve shortening method to write the Morse relations for light rays joining an event with a smooth timelike curve in a Lorentzian manifold with boundary. The Morse relations are obtained under the most general assumptions and one can apply them to have a mathematical description of the gravitational lens effect in a very general context. Moreover, Morse relations can be used to check if existing models are corrected.
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the Fermat Principle in general relativity and applications
arXiv: Mathematical Physics, 1999Co-Authors: Fabio Giannoni, Antonio Masiello, Paolo PiccioneAbstract:In this paper we use a general version of Fermat's Principle for light rays in General Relativity and a curve shortening method to write the Morse relations for light rays joining an event with a smooth timelike curve in a Lorentzian manifold with boundary. As a physical meaning, one can apply the Morse relations to have a mathematical description of the "gravitational lens effect" in a very general context.
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A General-Relativistic Fermat Principle for Extended Light Sources and Extended Receivers
General Relativity and Gravitation, 1998Co-Authors: Volker Perlick, Paolo PiccioneAbstract:In an arbitrary Lorentzian manifold, we fix a spacelike submanifold P and a timelike submanifold Γ. We interpret P as (the surface of) a light source at a particular instant of time, and we interpret Γ as the history of (the surface of) a receiver. We prove the following version of Fermat's Principle. Among all lightlike curves from P to Γ, the lightlike geodesics which are perpendicular to P and spatially perpendicular to Γ are characterized by stationary arrival time. Here, the arrival time is defined with the help of an arbitrary time function on Γ. Moreover, we show that the second variation of the arrival time at a stationary point is characterized by a Morse index theorem.
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a Fermat Principle on lorentzian manifolds and applications
Applied Mathematics Letters, 1996Co-Authors: F Antonacci, Paolo PiccioneAbstract:Abstract We present a version of the Fermat Principle to Lorentzian manifolds endowed with a time function. The Principle is used to obtain some results concerning the existence and multiplicity of light rays, generalizing part of the work in [1–3]. At this time, the results are announced and discussed, while the details of their proofs are left to a forthcoming paper [4].
A G Voronovich - One of the best experts on this subject based on the ideXlab platform.
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Fermat Principle for a nonstationary medium
Physical Review Letters, 2003Co-Authors: A G Voronovich, O A GodinAbstract:: One possible formulation of a variational Principle of the Fermat type for systems with time-dependent parameters is suggested. In a stationary case, it reduces to the Mopertui-Lagrange least-action Principle. A class of Hamiltonians (dispersion relations) is indicated, for which the variational Principle reduces to the Fermat Principle in a general nonstationary case. Hamiltonians that are homogeneous functions of momenta are in this category. For the important case of nondispersive waves (corresponding to Hamiltonians being homogeneous function of momenta order 1) the Fermat Principle fully determines the geometry of the rays. Equations relating the variation of signal frequency with the rate of change of propagation time are established.
Antonio Masiello - One of the best experts on this subject based on the ideXlab platform.
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On the energy functional on Finsler manifolds and applications to stationary spacetimes
Mathematische Annalen, 2011Co-Authors: Erasmo Caponio, Miguel Ángel Javaloyes, Antonio MasielloAbstract:In this paper we first study some global properties of the energy functional on a non-reversible Finsler manifold. In particular we present a fully detailed proof of the Palais–Smale condition under the completeness of the Finsler metric. Moreover, we define a Finsler metric of Randers type, which we call Fermat metric, associated to a conformally standard stationary spacetime. We shall study the influence of the Fermat metric on the causal properties of the spacetime, mainly the global hyperbolicity. Moreover, we study the relations between the energy functional of the Fermat metric and the Fermat Principle for the light rays in the spacetime. This allows one to obtain existence and multiplicity results for light rays, using the Finsler theory. Finally the case of timelike geodesics with fixed energy is considered.
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the Fermat Principle in general relativity and applications
Journal of Mathematical Physics, 2002Co-Authors: Fabio Giannoni, Antonio Masiello, Paolo PiccioneAbstract:In this paper we use a general version of Fermat’s Principle for light rays in general relativity and a curve shortening method to write the Morse relations for light rays joining an event with a smooth timelike curve in a Lorentzian manifold with boundary. The Morse relations are obtained under the most general assumptions and one can apply them to have a mathematical description of the gravitational lens effect in a very general context. Moreover, Morse relations can be used to check if existing models are corrected.
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the Fermat Principle in general relativity and applications
arXiv: Mathematical Physics, 1999Co-Authors: Fabio Giannoni, Antonio Masiello, Paolo PiccioneAbstract:In this paper we use a general version of Fermat's Principle for light rays in General Relativity and a curve shortening method to write the Morse relations for light rays joining an event with a smooth timelike curve in a Lorentzian manifold with boundary. As a physical meaning, one can apply the Morse relations to have a mathematical description of the "gravitational lens effect" in a very general context.
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On a Fermat Principle in general relativity. A Ljusternik-Schnirelmann theory for light rays
Annali di Matematica Pura ed Applicata, 1998Co-Authors: Fabio Giannoni, Antonio MasielloAbstract:In this paper existence and multiplicity results for lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds are proved under intrinsic assumptions. Such results are obtained using an extension to Lorentzian Geometry of the classical Fermat Principle in optics. The results are proved using critical point theory on infinite dimensional manifolds. An application to the gravitational lens effect is presented .
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On a Fermat Principle in general relativity. A Morse theory for light rays
General Relativity and Gravitation, 1996Co-Authors: Fabio Giannoni, Antonio MasielloAbstract:In this paper an infinite dimensional Morse theory for lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds is developed under intrinsic assumptions. It yields applications to the gravitational lens effect. In particular we show that the number of images in the gravitational lens effect is infinite or odd.