The Experts below are selected from a list of 177 Experts worldwide ranked by ideXlab platform
Abdur Rahim Choudhary - One of the best experts on this subject based on the ideXlab platform.
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Unified treatment: analyticity, Regge trajectories, Veneziano amplitude, fundamental regions and Moebius transformations
The European Physical Journal C, 2003Co-Authors: Abdur Rahim ChoudharyAbstract:In this paper we present a unified treatment that combines the analyticity properties of the scattering amplitudes, the threshold and asymptotic behaviors, the Invariance Group of Moebius transformations, the automorphic functions defined over this Invariance Group, the fundamental region in (Poincare) geometry, and the generators of the Invariance Group as they relate to the fundamental region. Using these concepts and techniques, we provide a theoretical basis for Veneziano type amplitudes with the ghost elimination condition built in, related the Regge trajectory functions to the generators of the Invariance Group, constrained the values of the Regge trajectories to take only inverse integer values at the threshold, used the threshold behavior in the forward direction to deduce the Pomeranchuk trajectory as well as other relations. The enabling tool for this unified treatment came from the multi-sheet conformal mapping techniques that map the physical sheet to a fundamental region which in turn defines a Riemann surface on which a global uniformization variable for the scattering amplitude is calculated via an automorphic function, which in turn can be constructed as a quotient of two automorphic forms of the same dimension.
V. V. Sreedhar - One of the best experts on this subject based on the ideXlab platform.
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the maximal kinematical Invariance Group of fluid dynamics and explosion implosion duality
Annals of Physics, 2001Co-Authors: L Oraifeartaigh, V. V. SreedharAbstract:Abstract It has recently been found that supernova explosions can be simulated in the laboratory by implosions induced in a plasma by intense lasers. A theoretical explanation is that the inversion transformation, (Σ:t→−1/t, x→x/t), leaves the Euler equations of fluid dynamics, with standard polytropic exponent, invariant. This implies that the kinematical Invariance Group of the Euler equations is larger than the Galilei Group. In this paper we determine, in a systematic manner, the maximal Invariance Group G of general fluid dynamics and show that it is a semi-direct product G =SL(2, R)⋌G, where the SL(2, R) Group contains the time-translations, dilations, and the inversion Σ, and G is the static (nine-parameter) Galilei Group. A subtle aspect of the inclusion of viscosity fields is discussed and it is shown that the Navier–Stokes assumption of constant viscosity breaks the SL(2, R) Group to a two-parameter Group of time translations and dilations in a tensorial way. The 12-parameter Group G is also known to be the maximal Invariance Group of the free Schrodinger equation. It originates in the free Hamilton–Jacobi equation which is central to both fluid dynamics and the Schrodinger equation.
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The maximal Invariance Group of Newton’s equations for a free point particle
American Journal of Physics, 2001Co-Authors: Oliver Jahn, V. V. SreedharAbstract:The maximal Invariance Group of Newton’s equations for a free nonrelativistic point particle is shown to be larger than the Galilei Group. It is a semidirect product of the static (nine-parameter) Galilei Group and an SL(2,R) Group containing time translations, dilations, and a one-parameter Group of time-dependent scalings called expansions. This Group was first discovered by Niederer in the context of the free Schrodinger equation. We also provide a road map from the free nonrelativistic point particle to the equations of fluid mechanics to which the symmetry carries over. The hitherto unnoticed SL(2,R) part of the symmetry Group for fluid mechanics gives a theoretical explanation for an observed similarity between numerical simulations of supernova explosions and numerical simulations of experiments involving laser-induced implosions in inertial confinement plasmas. We also give examples of interacting many-body systems of point particles which have this symmetry Group.
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The Maximal Invariance Group of Newtons's Equations for a Free Point Particle
American Journal of Physics, 2001Co-Authors: Oliver Jahn, V. V. SreedharAbstract:The maximal Invariance Group of Newton's equations for a free nonrelativistic point particle is shown to be larger than the Galilei Group. It is a semi-direct product of the static (nine-parameter) Galilei Group and an $SL(2,R)$ Group containing time-translations, dilations and a one-parameter Group of time-dependent scalings called {\it expansions}. This Group was first discovered by Niederer in the context of the free Schr\"odinger equation. We also provide a road map from the free nonrelativistic point particle to the equations of fluid mechanics to which the symmetry carries over. The hitherto unnoticed $SL(2, R)$ part of the symmetry Group for fluid mechanics gives a theoretical explanation for an observed similarity between numerical simulations of supernova explosions and numerical simulations of experiments involving laser-induced implosions in inertial confinement plasmas. We also give examples of interacting many body systems of point particles which have this symmetry Group.
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The Maximal Kinematical Invariance Group of Fluid Dynamics and Explosion–Implosion Duality
Annals of Physics, 2001Co-Authors: Lochlainn O'raifeartaigh, V. V. SreedharAbstract:Abstract It has recently been found that supernova explosions can be simulated in the laboratory by implosions induced in a plasma by intense lasers. A theoretical explanation is that the inversion transformation, (Σ:t→−1/t, x→x/t), leaves the Euler equations of fluid dynamics, with standard polytropic exponent, invariant. This implies that the kinematical Invariance Group of the Euler equations is larger than the Galilei Group. In this paper we determine, in a systematic manner, the maximal Invariance Group G of general fluid dynamics and show that it is a semi-direct product G =SL(2, R)⋌G, where the SL(2, R) Group contains the time-translations, dilations, and the inversion Σ, and G is the static (nine-parameter) Galilei Group. A subtle aspect of the inclusion of viscosity fields is discussed and it is shown that the Navier–Stokes assumption of constant viscosity breaks the SL(2, R) Group to a two-parameter Group of time translations and dilations in a tensorial way. The 12-parameter Group G is also known to be the maximal Invariance Group of the free Schrodinger equation. It originates in the free Hamilton–Jacobi equation which is central to both fluid dynamics and the Schrodinger equation.
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The maximal Invariance Group of Newton's equations for a free point particle
American Journal of Physics, 2001Co-Authors: Oliver Jahn, V. V. SreedharAbstract:The maximal Invariance Group of Newton’s equations for a free nonrelativistic point particle is shown to be larger than the Galilei Group. It is a semidirect product of the static (nine-parameter) Galilei Group and an SL(2,R) Group containing time translations, dilations, and a one-parameter Group of time-dependent scalings called expansions. This Group was first discovered by Niederer in the context of the free Schrodinger equation. We also provide a road map from the free nonrelativistic point particle to the equations of fluid mechanics to which the symmetry carries over. The hitherto unnoticed SL(2,R) part of the symmetry Group for fluid mechanics gives a theoretical explanation for an observed similarity between numerical simulations of supernova explosions and numerical simulations of experiments involving laser-induced implosions in inertial confinement plasmas. We also give examples of interacting many-body systems of point particles which have this symmetry Group.
Simona Rota Nodari - One of the best experts on this subject based on the ideXlab platform.
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Orbital stability via the energy-momentum method: the case of higher dimensional symmetry Groups
Archive for Rational Mechanics and Analysis, 2019Co-Authors: Stephan De Bièvre, Simona Rota NodariAbstract:We consider the orbital stability of relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional Invariance Group for the dynamics. We prove a persistence result for such relative equilibria, present a generalization of the Vakhitov-Kolokolov slope condition to this higher dimensional setting, and show how it allows to prove the local coercivity of the Lyapunov function, which in turn implies orbital stability. The method is applied to study the orbital stability of relative equilibria of nonlinear Schrödinger and Manakov equations. We provide a comparison of our approach to the one by Grillakis-Shatah-Strauss.
Carl E. Wulfman - One of the best experts on this subject based on the ideXlab platform.
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Group-theoretic intrepetation of the bound states of Morse oscillators.
Physical review. A Atomic molecular and optical physics, 1996Co-Authors: Carl E. WulfmanAbstract:Using operators of the Invariance Group of their time-dependent Schr\"odinger equations it is shown that the bound states of Morse oscillators are bases for discrete nonunitary irreducible representations (non-UIRs) of the Groups $\mathrm{Sp}(2, R)$, SU(1,1), and SO(2,1). Hermiticity requirements and the dependence of the Group generators on the dynamical variables determine the operator of an isometry which connects these non-UIRs of the noncompact Invariance Groups to UIRs of the compact Groups SU(2) and SO(3) that have been used as spectrum-generating Groups for Morse systems.
Stephan De Bièvre - One of the best experts on this subject based on the ideXlab platform.
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Orbital stability via the energy-momentum method: the case of higher dimensional symmetry Groups
Archive for Rational Mechanics and Analysis, 2019Co-Authors: Stephan De Bièvre, Simona Rota NodariAbstract:We consider the orbital stability of relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional Invariance Group for the dynamics. We prove a persistence result for such relative equilibria, present a generalization of the Vakhitov-Kolokolov slope condition to this higher dimensional setting, and show how it allows to prove the local coercivity of the Lyapunov function, which in turn implies orbital stability. The method is applied to study the orbital stability of relative equilibria of nonlinear Schrödinger and Manakov equations. We provide a comparison of our approach to the one by Grillakis-Shatah-Strauss.
