Papers by C. Efthymiopoulos
Toward the design of a novel hybrid parallel N-body method in scope of modern cloud architectures
The Journal of Supercomputing
A parallel Self Mesh-Adaptive N-body method based on approximate inverses
The Journal of Supercomputing
Monthly Notices of the Royal Astronomical Society, 2016
Using N-body simulations we study the structures induced on a galactic disc by repeated flybys of... more Using N-body simulations we study the structures induced on a galactic disc by repeated flybys of a companion in decaying eccentric orbit around the disc. Our system is composed by a stellar disc, bulge and live dark matter halo, and we study the system's dynamical response to a sequence of a companion's flybys, when we vary i) the disc's temperature (parameterized by Toomre's Q-parameter) and ii) the companion's mass and initial orbit. We use a new 3D Cartesian grid code: MAIN (Mesh-adaptive Approximate Inverse N-body solver). The main features of MAIN are reviewed, with emphasis on the use of a new Symmetric Factored Approximate Sparse Inverse (SFASI) matrix in conjunction with the multigrid method that allows the efficient solution of Poisson's equation in three space variables. We find that: i) companions need to be assigned initial masses in a rather narrow window of values in order to produce significant and more long-standing non-axisymmetric structures (bars and spirals) in the main galaxy's disc by the repeated flyby mechanism. ii) a crucial phenomenon is the antagonism between companion-excited and self-excited modes on the disc. Values of Q > 1.5 are needed in order to allow for the growth of the companion-excited modes to prevail over the the growth of the disc's self-excited modes. iii) We give evidence that the companion-induced spiral structure is best represented by a density wave with pattern speed nearly constant in a region extending from the ILR to a radius close to, but inside, corotation.
The Average Power-Law growth of deviation vector and Tsallis entropy
Astrophysics and Space Science Proceedings, 2008
Bohmian Trajectories in the Scattering Problem
The Legacy of John S Nicolis, 2014
Parallel N-body Particle Mesh Type Methods Based on Domain Decomposition and the Multigrid Method
Techniques for Parallel, Distributed and Cloud Computing in Engineering, 2015
Monthly Notices of the Royal Astronomical Society, 2015
Using both numerical and analytical approaches, we demonstrate the existence of an effective powe... more Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L ∝ m p between the mean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole in the center of a galaxy and the mass parameter m, i.e. ratio of the mass of the black hole over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p ≈ 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the black hole's sphere of influence. We thus predict p = 2/3 − q with q ≈ 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the black hole affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x 1 family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the Inner Lindbland resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.
Charged particles’ acceleration through Reconnecting Current Sheets in Solar Flares
Astrophysics and Space Science Proceedings, 2008
The coalescence of invariant manifolds in barred-spiral galaxies
Astrophysics and Space Science Proceedings, 2008
Invariant manifolds and the spiral arms of barred galaxies
Astrophysics and Space Science Proceedings, 2008
Stickiness, Cantori and lobe dynamics
We study the phase space structure of the sticky region around an island of stability. We locate ... more We study the phase space structure of the sticky region around an island of stability. We locate the most important cantori with noble rotation numbers, by approaching them with the periodic orbits with rotation numbers rational approximations of the noble numbers. Two different sticky domains are distinguished. The first domain corresponds to stickiness time 10^5 - 10^7 periods. Its boundary
Nonlinearity, 2015
We consider normal forms in 'magnetic bottle' type Hamiltonians of the form H = 1 2 (ρ 2 ρ + ω 2 ... more We consider normal forms in 'magnetic bottle' type Hamiltonians of the form H = 1 2 (ρ 2 ρ + ω 2 1 ρ 2) + 1 2 p 2 z + hot (second frequency ω 2 equal to zero in the lowest order). Our main results are: i) a novel method to construct the normal form in cases of resonance, and ii) a study of the asymptotic behavior of both the non-resonant and the resonant series. We find that, if we truncate the normal form series at order r, the series remainder in both constructions decreases with increasing r down to a minimum, and then it increases with r. The computed minimum remainder turns to be exponentially small in 1 ∆E , where ∆E is the mirror oscillation energy, while the optimal order scales as an inverse power of ∆E. We estimate numerically the exponents associated with the optimal order and the remainder's exponential asymptotic behavior. In the resonant case, our novel method allows to compute a 'quasi-integral' (i.e. truncated formal integral) valid both for each particular resonance as well as away from all resonances. We applied these results to a specific magnetic bottle Hamiltonian. The non resonant normal form yields theorerical invariant curves on a surface of section which fit well the empirical curves away from resonances. On the other hand the resonant normal form fits very well both the invariant curves inside the islands of a particular resonance as well as the non-resonant invariant curves. Finally, we discuss how normal forms allow to compute a critical threshold for the onset of global chaos in the magnetic bottle.
Lecture Notes in Physics, 2007
Angular Dynamical Spectra and their Applications
The Dynamics of Small Bodies in the Solar System, 1999
Title: Angular Dynamical Spectra and their Applications. Authors: Efthymiopoulos, C.; Voglis, N.;... more Title: Angular Dynamical Spectra and their Applications. Authors: Efthymiopoulos, C.; Voglis, N.; Contopoulos, G. Publication: The Dynamics of Small Bodies in the Solar System, A Major Key to Solar System Studies, edited by Bonnie A. Steves and Archie E. Roy. ...
New Developments in the Dynamics of Planetary Systems, 2001
We apply the theory of the third integral to a self-consistent galactic model, generated by the c... more We apply the theory of the third integral to a self-consistent galactic model, generated by the collapse of a N-body system. The final configuration after the collapse is a stationary triaxial system, that represents an almost prolate non-rotating elliptical galaxy with its longest axis in the zdirection. This system is represented by an axisymmetric potential V plus a small triaxial perturbation V 1. The orbits in the potential V are of three types: box orbits, tube orbits (corresponding to various resonances), and chaotic orbits. The intersections of the box and tube orbits by a Poincaré surface of section z = 0 are closed invariant curves. The main tube orbits are like ellipses and form an island of stability on the (R,Ṙ) plane. We calculated the third integral I in the potential V for the general non-resonant case and for various resonant cases. The agreement between the invariant curves of the orbits and the level curves of the third integral is good for the box and tube orbits, if we truncate the third integral at an appropriate level. As expected the third integral fails in the case of chaotic orbits. The most important result is the form of the number density F on the Poincaré surface of section. This function decreases exponentially outwards for the box orbits, like F ∝ exp(−bI), while it is constant, as expected, for the chaotic orbits. In the case of the island of the main tube orbits it has a minimum at the center of the island. This can be explained by the form of the near elliptical orbits that are elongated along R, thus they fail to support a self-consistent galaxy, which is elongated along the z-axis.
Counterrotating Galaxies and Memory of Cosmological Initial Conditions
New Developments in the Dynamics of Planetary Systems, 2001
ABSTRACT As it is known, a good number of galaxies are observed to have counterrotating cores. A ... more ABSTRACT As it is known, a good number of galaxies are observed to have counterrotating cores. A popular scenario to explain the formation of such galaxies is based on a secondary process of merging of galaxies with their satellites, or gas infall, or merger events between galaxies. An alternative mechanism, proposed by Voglis et al., 1991, and by Harsoula and Voglis 1998, could also be responsible for the formation of these galaxies directly from cosmological initial conditions (direct scenario). The novel mechanism was demonstrated by using quiet cosmological initial conditions in N-body simulations. In the present paper we extend our N-body simulations using clumpy initial conditions and show that this mechanism still works to create counterrotating galaxies. Counterrotation is a result of the considerable amount of memory of initial conditions surviving for times comparable to the Hubble time, despite the large degree of instability of individual orbits and the dramatic redistribution and mixing of the particles in phase space. We show, for example, that the particles remember, in a statistical sense, not only their distance from the center of mass (memory of energy), but also the initial orientation of their position relative to the direction of an external tidal field, which determines the sign and the amount of angular momentum that is transferred to the particles of the system.
Impact of Modern Dynamics in Astronomy, 1999
Two simple and efficient numerical methods to explore the phase space structure are presented, ba... more Two simple and efficient numerical methods to explore the phase space structure are presented, based on the properties of the "dynamical spectra". 1) We calculate a "spectral distance" D of the dynamical spectra for two different initial deviation vectors. D-• 0 in the case of chaotic orbits, while D-• const ^ 0 in the case of ordered orbits. This method is by orders of magnitude faster than the method of the Lyapunov Characteristic Number (LCN). 2) We define a sensitive indicator called ROTOR (ROtational TOri Recongnizer) for 2D maps. The ROTOR remains zero in time on a rotational torus, while it tends to infinity at a rate oc N = number of iterations, in any case other than a rotational torus. We use this method to locate the last KAM torus of an island of stability, as well as the most important cantori causing stickiness near it.
Invariant Spectra of Orbits in Multidimensional Symplectic Maps
Hamiltonian Systems with Three or More Degrees of Freedom, 1999
... SPECTRA OF ORBITS IN MULTIDIMENSIONAL SYMPLECTIC MAPS N. VOGLIS, C.EFTHYMIOPOULOS AND G ... C... more ... SPECTRA OF ORBITS IN MULTIDIMENSIONAL SYMPLECTIC MAPS N. VOGLIS, C.EFTHYMIOPOULOS AND G ... CONTOPOULOS Department of Astronomy, University of Athens, GR-15784, Athens, Greece 1. Introduction ... m~,-oo< a< am,(3) [2 (am-a0rJ with parameters ao, ...
Orbits in barred galaxies
Lecture Notes in Physics, 1996
Impact of Modern Dynamics in Astronomy, 1999
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Papers by C. Efthymiopoulos