Tag Archives: Chaotic Dynamics

Structure of the center manifold of the L1 and L2 collinear libration points in the restricted three-body problem [CL]

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http://arxiv.org/abs/1909.03299


We present a global analysis of the center manifold of the collinear points in the circular restricted three-body problem. The phase-space structure is provided by a family of resonant 2-DOF Hamiltonian normal forms. The near 1:1 commensurability leads to the construction of a detuned Birkhoff-Gustavson normal form. The bifurcation sequences of the main orbit families are investigated by a geometric theory based on the reduction of the symmetries of the normal form, invariant under spatial mirror symmetries and time reversion. This global picture applies to any values of the mass parameter.

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G. Pucacco
Tue, 10 Sep 19
76/80

Comments: Paper included in the Topical Collection for the 50th birthday of CM&DA, 19 pages, 7 figures

Massive evaluation and analysis of Poincaré recurrences on grids of initial data: a tool to map chaotic diffusion [CL]

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http://arxiv.org/abs/1908.09683


We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar\’e recurrence statistics on massive grids of initial data or values of parameters. We concentrate on Hamiltonian systems, featuring the method separately for the cases of bounded and non-bounded phase spaces. The embodiments of the method in each of the cases are specific. We compare the performances of the proposed Poincar\’e recurrence method (PRM) and the custom Lyapunov exponent (LE) methods and show that they expose the global dynamics almost identically. However, a major advantage of the new method over the known global numerical tools, such as LE, FLI, MEGNO, and FA, is that it allows one to construct, in some approximation, charts of local diffusion timescales. Moreover, it is algorithmically simple and straightforward to apply.

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I. Shevchenko, G. Rollin, A. Melnikov, et. al.
Tue, 27 Aug 19
52/85

Comments: 26 pages, 4 figures. Accepted for publication in Computer Physics Communications

Recurrence Network Analysis of Exoplanetary Observables [EPA]

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http://arxiv.org/abs/1908.02158


Recent advancements of complex network representation among several disciplines motivated the investigation of exoplanetary dynamics by means of recurrence networks. We are able to recover different dynamical regimes by means of various network measures obtained from synthetic time series of a model planetary system. The framework of complex networks is also applied to real astronomical observations acquired by recent state-of-the-art surveys. The outcome of the analysis is consistent with earlier studies opening new directions to investigate planetary dynamics.

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T. Kovacs
Wed, 7 Aug 19
60/61

Comments: 8 pages, 9 figures, published in CHAOS

nsCouette — A high-performance code for direct numerical simulations of turbulent Taylor-Couette flow [CL]

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http://arxiv.org/abs/1908.00587


We present nsCouette, a highly scalable software tool to solve the Navier-Stokes equations for incompressible fluid flow between differentially heated and independently rotating, concentric cylinders. It is based on a pseudospectral spatial discretization and dynamic time-stepping. It is implemented in modern Fortran with a hybrid MPI-OpenMP parallelization scheme and thus designed to compute turbulent flows at high Reynolds and Rayleigh numbers. An additional GPU implementation (C-CUDA) for intermediate problem sizes and a basic version for turbulent pipe flow (nsPipe) are also provided.

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J. Lopez, D. Feldmann, M. Rampp, et. al.
Mon, 5 Aug 19
53/53

Comments: ~3000 words, 3 figures (in colour)

Orbital stability of ensembles of particles in regions of magnetic reconnection in Earth's magneto-tail [CL]

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http://arxiv.org/abs/1907.13478


We investigate the collective behaviour of particle orbits in the vicinity of magnetic reconnection in Earth’s magneto-tail. Various regions of different kinds of orbital stability of particle motions are found. We locate regimes of temporary capture of particle orbits in configuration space as well as locations, where strong particle accelerations take place. With this study we are able to provide a detailed map, i.e. the topology, of high and low acceleration centers close to the reconnection site. Quasi-regular and chaotic kinds of motions of elementary particles can be determined as well. The orbital stability of particle orbits is obtained by a statistical analysis of the outcome of the system of variational equations of particle orbits within the framework of particle-in-cell simulations. Using the concept of Lyapunov Characteristic Numbers to ensembles of particle orbits we introduce Lyapunov Ensemble Averages to describe the response of particle orbits to local perturbations induced by the electro-magnetic field.

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C. Lhotka, P. Bourdin and E. Pilat-Lohinger
Thu, 1 Aug 19
40/66

Comments: 21 pages, 10 figures, this https URL

Orbital dynamics in realistic galaxy models: NGC 3726, NGC 3877 and NGC 4010 [GA]

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http://arxiv.org/abs/1907.09573


In the present paper, using a generalization of the Miyamoto and Nagai potential we adjusted the observed rotation curves of three specific spiral galaxies to the analytical circular velocities. The observational data have been taken from a 21 cm-line synthesis imaging survey using the Westerbork Synthesis Radio Telescope, for three particular galaxies in the Ursa Major cluster: NGC 3726, NGC 3877 and NGC 4010. Accordingly, the dynamics of the system is analyzed in terms of the Poincar\’e sections method, finding that for larger values of the angular momentum of the test particle or lower values its total energy the dynamics is mainly regular, while on the opposite cases, the dynamics is mainly chaotic. Our toy model opens the possibility to find chaotic bounded orbits for stars in those particular galaxies.

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F. Dubeibe, S. Martínez-Sicacha and G. González
Wed, 24 Jul 19
53/60

Comments: 7 pages, 9 figures

Orbital and escape dynamics in barred galaxies — IV. Heteroclinic connections [GA]

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http://arxiv.org/abs/1907.09202


Continuing the series of papers on a new model for a barred galaxy, we investigate the heteroclinic connections between the two normally hyperbolic invariant manifolds sitting over the two index-1 saddle points of the effective potential. The heteroclinic trajectories and the nearby periodic orbits of similar shape populate the bar region of the galaxy and a neighbourhood of its nucleus. Thereby we see a direct relation between the important structures of the interior region of the galaxy and the projection of the heteroclinic tangle into the position space. As a side result, we obtain a detailed picture of the primary heteroclinic intersection surface in the phase space.

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E. Zotos and C. Jung
Tue, 23 Jul 19
29/72

Comments: Published in Monthly Notices of the Royal Astronomical Society (MNRAS) journal

Comparative terrestrial atmospheric circulation regimes in simplified global circulation models: II. energy budgets and spectral transfers [EPA]

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http://arxiv.org/abs/1906.07595


The energetics of possible global atmospheric circulation patterns in an Earth-like atmosphere are explored using a simplified GCM based on the University of Hamburg’s Portable University Model for the Atmosphere. Results from a series of simulations, obtained by varying planetary rotation rate {\Omega} with an imposed equator-to-pole temperature difference, were analysed to determine the heat transport and other contributions to the energy budget for the time-averaged, equilibrated flow. These show clear trends with {\Omega}, with the most intense Lorenz energy cycle for an Earth-sized planet occurring with a rotation rate around half that of the present day Earth. KE and APE spectra, E_K(n) and E_A(n) (where n is total spherical wavenumber), also show clear trends with \Omega, with n^{-3} enstrophy-dominated spectra around \Omega* = \Omega/\Omega_E = 1, where \Omega_E is the rotation rate of the Earth) and steeper (\sim n^{-5}) slopes in the zonal mean flow with little evidence for the n^{-5/3} spectrum anticipated for an inverse KE cascade. Instead, both KE and APE spectra become almost flat at scales larger than the internal Rossby radius, L_d, and exhibit near-equipartition at high wavenumbers. At \Omega* << 1, the spectrum becomes dominated by KE with E_K(n) \sim 2-3 E_A(n) at most wavenumbers and a slope \sim n^{-5/3} across most of the spectrum. Spectral flux calculations show that enstrophy and APE are almost always cascaded downscale, regardless of {\Omega}. KE cascades are more complicated, however, with downscale transfers across almost all wavenumbers, dominated by horizontally divergent modes, for \Omega* \lesssim 1/4. At higher rotation rates, transfers of KE become increasingly dominated by rotational components with strong upscale transfers (dominated by eddy-zonal flow interactions) for scales larger than L_d and weaker downscale transfers for scales smaller than L_d.

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P. Read, F. Tabataba-Vakili, Y. Wang, et. al.
Wed, 19 Jun 19
13/60

Comments: 16 pages (19 as published), 9 figures

Comparative terrestrial atmospheric circulation regimes in simplified global circulation models: I. from cyclostrophic super-rotation to geostrophic turbulence [EPA]

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http://arxiv.org/abs/1906.07561


The regimes of possible global atmospheric circulation patterns in an Earth-like atmosphere are explored using a simplified GCM based on the University of Hamburg’s Portable University Model for the Atmosphere with simplified (linear) boundary layer friction, a Newtonian cooling scheme and dry convective adjustment. A series of controlled experiments are conducted by varying planetary rotation rate and imposed equator-to-pole temperature difference. These defining parameters are cast into dimensionless forms to establish a parameter space, in which different circulation regimes are mapped and classified. Clear trends are found when varying planetary rotation rate and frictional and thermal relaxation timescales. The sequence of circulation regimes as a function of planetary rotation rate strongly resembles that obtained in laboratory experiments on rotating, stratified flows, especially if a topographic $\beta$-effect is included in those experiments to emulate the planetary vorticity gradients induced by the spherical curvature of the planet. A regular baroclinic wave regime is also obtained at intermediate values of thermal Rossby number and its characteristics and dominant zonal wavenumber depend strongly on the strength of radiative and frictional damping. These regular waves exhibit some strong similarities to baroclinic storms observed on Mars under some conditions. Multiple jets are found at the highest rotation rates, when the Rossby deformation radius and other eddy-related length scales are much smaller than the radius of the planet. These exhibit some similarity to the multiple zonal jets observed on gas giant planets. Jets form on a scale comparable to the most energetic eddies and the Rhines scale poleward of the supercritical latitude. The balance of heat transport varies strongly with {\Omega}* between eddies and zonally symmetric flows, becoming weak with fast rotation.

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Y. Wang, P. Read, F. Tabataba-Vakili, et. al.
Wed, 19 Jun 19
31/60

Comments: 18 pages (21 pages as published), 11 figures

Normalization of Hamiltonian and nonlinear stability of triangular equilibrium points in the photogravitational restricted three body problem with P-R drag in non-resonance case [CL]

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http://arxiv.org/abs/1906.04482


Normal forms of Hamiltonian are very important to analyze the nonlinear stability of a dynamical system in the vicinity of invariant objects. This paper presents the normalization of Hamiltonian and the analysis of nonlinear stability of triangular equilibrium points in non-resonance case, in the photogravitational restricted three body problem under the influence of radiation pressures and P-R drags of the radiating primaries. The Hamiltonian of the system is normalized up to fourth order through Lie transform method and then to apply the Arnold-Moser theorem, Birkhoff normal form of the Hamiltonian is computed followed by nonlinear stability of the equilibrium points is examined. Similar to the case of classical problem, we have found that in the presence of assumed perturbations, there always exists one value of mass parameter within the stability range at which the discriminant $D_4$ vanish, consequently, Arnold-Moser theorem fails, which infer that triangular equilibrium points are unstable in nonlinear sense within the stability range. Present analysis is limited up to linear effect of the perturbations, which will be helpful to study the more generalized problem.

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R. Kishor, M. Raj and B. Ishwar
Wed, 12 Jun 19
9/59

Comments: 21 Pages

Normalization of Hamiltonian and Nonlinear Stability of the Triangular Equilibrium Points in Non-resonance Case with Perturbations [EPA]

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http://arxiv.org/abs/1906.04495


For the study of nonlinear stability of a dynamical system, normalized Hamiltonian of the system is very important to discuss the dynamics in the vicinity of invariant objects. In general, it represents a nonlinear approximation to the dynamics, which is very helpful to obtain the information about realistic solution of the problem. Present paper reflects about normalization of the Hamiltonian and analysis of nonlinear stability in non-resonance case, in the Chermnykh-like problem under the influence of perturbations in the form of radiation pressure, oblateness, and a disc. To describe nonlinear stability, initially, quadratic part of the Hamiltonian is normalized in the neighborhood of triangular equilibrium point and then higher order normalization is performed. Due to the presence of perturbations and a tedious huge algebraic computation for intermediate terms, we have computed only up to the fourth order normalized Hamiltonian using Lie transforms. In non-resonance case, nonlinear stability of the system is discussed with the help of Arnold-Moser theorem. Again, the effects of radiation pressure, oblateness and presence of the disc are analyzed, separately and it is observed that in the absence as well as presence of perturbation parameters, triangular equilibrium point is unstable in nonlinear sense within the stability range $0<\mu<\mu_1=\bar{\mu_c}$ due to failure of Arnold-Moser theorem. However, perturbation parameters affect the values of $\mu$ at which $D_4=0$, significantly. This study may help to analyze more generalized cases of the problem in the presence of some other types of perturbations such as P-R drag and solar wind drag. The results are limited to the regular symmetric disc but in future it can be extended.

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R. Kishor and B. Kushvah
Wed, 12 Jun 19
34/59

Comments: 25 Pages

Prediction of System Evolution by Learning Machine [CL]

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http://arxiv.org/abs/1905.08313


The orthodox approach for understanding a dynamical system is to establish its equation of motion, by which one can unveil its dynamical behavior at a given system parameter set, and reveal how the dynamic behavior evolves as the system parameters change. Here we show that this task can be fulfilled with a learning machine in a model-free way. We find that, based only on a segmental time series of a state variable recorded at present stage, the dynamics exhibited by the learning machine at different training stages can be mapped to the dynamics of the target system along a particular path in its parameter space following an appropriate training strategy that monotonously decreases the cost. This path is important, because along which the primary dynamical properties of the target system will emerge subsequently, in the simple-to-complex order, matching closely to the evolution of a natural system. A theoretical framework is proposed to explain the underlying mechanism. This revealed function of the learning machine opens up a novel way to probe the global dynamical properties of a black-box system without the equation of motion established artificially, and as such it might have huge potential applications. As an application example, this method is applied to infer what dynamical stages a variable star has experienced and how it will evolve in future by using the light curve observed presently.

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H. Zhao
Wed, 22 May 19
48/59

Comments: 16 pages, 10 figures

On the perturbed photogravitational restricted five-body problem: the analysis of fractal basins of convergence [CL]

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http://arxiv.org/abs/1905.08298


In the framework of photogravitational version of the restricted five-body problem, the existence and stability of the in-plane equilibrium points, the possible regions for motion are explored and analysed numerically, under the combined effect of small perturbations in the Coriolis and centrifugal forces. Moreover, the multivariate version of the Newton-Raphson iterative scheme is applied in an attempt to unveil the topology of the basins of convergence linked with the libration points as function of radiation parameters, and the parameters corresponding to Coriolis and centrifugal forces.

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M. Suraj, R. Aggarwal, A. Mittal, et. al.
Wed, 22 May 19
52/59

Comments: 12 Figure

On the dynamics of Comet 1P/Halley: Lyapunov and power spectra [EPA]

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http://arxiv.org/abs/1904.09342


Using a purely Newtonian model for the Solar System, we investigate the dynamics of comet 1P/Halley considering in particular the Lyapunov and power spectra of its orbit, using the nominal initial conditions of JPL’s Horizons system. We carry out precise numerical integrations of the $(N+1)$-restricted problem and the first variational equations, considering a time span of $2\times10^5$~yr. The power spectra are dominated by a broadband component, with peaks located at the current planetary frequencies, including contributions from Jupiter, Venus, the Earth and Saturn, as well as the $1:6$ resonance among Halley and Jupiter and higher harmonics. From the average value of the maximum Lyapunov exponent we estimate the Lyapunov time of the comet’s nominal orbit, obtaining $\tau_L \simeq 562$~yr; the remaining independent Lyapunov exponents (not related by time-reversal symmetry) tend asymptotically to zero as $t^{-1/2}$. Yet, our results do not display convergence of the maximum Lyapunov exponent. We argue that the lack of convergence of the maximum Lyapunov exponent is a signature of transient chaos which will lead to an eventual ejection of the comet from the Solar System.

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J. Pérez-Hernández and L. Benet
Tue, 23 Apr 19
7/58

Comments: Accepted in MNRAS

Chaotic behavior of Eulerian MHD turbulence [CL]

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http://arxiv.org/abs/1808.03632


We study the chaotic properties of a turbulent conducting fluid using direct numerical simulation in the Eulerian frame. The maximal Lyapunov exponent is measured for simulations with varying Reynolds number and magnetic Prandtl number. We extend the Ruelle theory of hydrodynamic turbulence to magnetohydrodynamic turbulence as a working hypothesis and find broad agreement with results. In other simulations we introduce magnetic helicity and these simulations show a diminution of chaos, which is expected to be eliminated at maximum helicity. We also find that the difference between two initially close fields grows linearly at late times, which was also recently found in hydrodynamics. This linear growth rate is found to be dependent on the dissipation rate of the relevant field. We discuss the important consequences this linear growth has on predictability. We infer that the chaos in the system is totally dominated by the velocity field and connect this work to real magnetic systems such as solar weather and confined plasmas.

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R. Ho, A. Berera and D. Clark
Wed, 10 Apr 19
38/54

Comments: 11 pages, 7 figures. In Press Physics of Plasmas, 2019

Global Stability Properties of the Climate: Melancholia States, Invariant Measures, and Phase Transitions [CL]

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http://arxiv.org/abs/1903.08348


For a wide range of values of the incoming solar radiation, the Earth features at least two attracting states, which correspond to competing climates. The warm climate is analogous to the present one; the snowball climate features global glaciation and conditions that can hardly support life forms. Paleoclimatic evidences suggest that in past our planet flipped between these two states. The main physical mechanism responsible for such instability is the ice-albedo feedback. In a previous work, we defined the Melancholia states that sit between the two climates. Such states are embedded in the boundaries between the two basins of attraction and feature extensive glaciation down to relatively low latitudes. Here, we explore the global stability properties of the system by introducing random perturbations as modulations to the intensity of the incoming solar radiation. We observe noise-induced transitions between the competing basins of attractions. In the weak noise limit, large deviation laws define the invariant measure and the statistics of escape times. By empirically constructing the instantons, we show that the Melancholia states are the gateways for the noise-induced transitions. In the region of multistability, in the zero-noise limit, the measure is supported only on one of the competing attractors. For low (high) values of the solar irradiance, the limit measure is the snowball (warm) climate. The changeover between the two regimes corresponds to a first order phase transition in the system. The framework we propose seems of general relevance for the study of complex multistable systems. At this regard, we relate our results to the debate around the prominence of contigency vs. convergence in biological evolution. Finally, we propose a new method for constructing Melancholia states from direct numerical simulations, thus bypassing the need to use the edge-tracking algorithm.

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V. Lucarini and T. Bodai
Thu, 21 Mar 19
36/66

Comments: 37 Pages, 10 Figures

$N$-body chaos and the continuum limit in numerical simulations of self-gravitating systems, revisited [GA]

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http://arxiv.org/abs/1901.08981


We revise the r\^{o}le of discreteness and chaos in the dynamics of self-gravitating systems by means of $N$-body simulations with active and frozen potentials, starting from spherically symmetric stationary states and considering the orbits of single particles as well as the orbits of the system in the full $2N$-dimensional phase space. We investigate the dependence on $N$ of the largest Lyapunov exponent both of single particle orbits and of the full $N$-body system. We also show that the use of frozen $N$-body potentials may be misleading in certain cases.

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P. Cintio and L. Casetti
Mon, 28 Jan 19
16/55

Comments: 9 pages 10 figures. Submitted to MNRAS, Comments welcome

On the predictability of Galileo disposal orbits [EPA]

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http://arxiv.org/abs/1901.06947


The end-of-life disposal of Galileo satellites is needed to avoid collisions with operational spacecraft and to prevent the generation of space debris. Either disposal in stable graveyard orbits or disposal into the atmosphere exploiting eccentricity growth caused by lunisolar resonances are possible. However, there is a concern about the predictability of MEO orbits because of possible chaotic behaviour caused by the overlap of resonances. In this work, we investigate if Galileo disposal orbits are predictable and if safe disposal is possible under initial uncertainties. For this, we employ finite-time Lyapunov exponents (FTLE) and sensitivity analysis and compare these two methods regarding their practicality for analysing the predictability of disposal orbits. The results show that FTLE are not suitable for determining if an orbit behaves chaotically or not on the time scale of interest. Sensitivity analysis, on the other hand, can be used to quantify the effect of uncertainties on the orbital evolution and to determine if safe disposal is possible. In addition, we show that reliable re-entry disposal is feasible with a limited \Delta V budget. However, safe disposal into a graveyard orbit is not always feasible considering uncertainties in the disposal manoeuvre and dynamical model when the available \Delta V for disposal is low.

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D. Gondelach, R. Armellin and A. Wittig
Wed, 23 Jan 19
97/111

Comments: 29 pages, 20 figures

Constraints on ion vs. electron heating by plasma turbulence at low beta [CL]

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http://arxiv.org/abs/1812.09792


It is shown that in low-beta plasmas, such as the solar corona, some instances of the solar wind, the aurora, inner regions of accretion discs, their coronae, and some laboratory plasmas, Alfvenic fluctuations produce no ion heating within the gyrokinetic approximation, i.e., as long as their amplitudes (at the Larmor scale) are small and their frequencies stay below the ion Larmor frequency. Thus, all low-frequency ion heating in such plasmas is due to compressive fluctuations: density perturbations and non-Maxwellian perturbations of the ion distribution function. Because these fluctuations energetically decouple from the Alfvenic ones already in the inertial range, the above conclusion means that the energy partition between ions and electrons in low-beta plasmas is decided at the outer scale, where turbulence is launched, and can in principle be determined from MHD models of the relevant astrophysical systems. Any additional ion heating must come from non-gyrokinetic mechanisms such as cyclotron heating or the stochastic heating owing to distortions of ions’ Larmor orbits. An exception to these conclusions occurs in the Hall limit, i.e., when the ratio of the ion to electron temperatures is as low as the ion beta (equivalently, the electron beta is order unity). In this regime, compressive fluctuations (slow waves) couple to Alfvenic ones above the Larmor scale (viz., at the ion inertial or ion sound scale), the Alfvenic and compressive cascades join and then separate again into cascades of fluctuations that linearly resemble kinetic Alfven and (oblique) ion cyclotron waves, with the former heating electrons and the latter ions. The two cascades are shown to decouple, scalings for them are derived, and it is argued physically that the two species will be heated by them at approximately equal rates.

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A. Schekochihin, Y. Kawazura and M. Barnes
Mon, 31 Dec 18
41/57

Comments: latex, 34 pages, submitted to JPP

Equilibrium points and basins of convergence in the triangular restricted four-body problem with a radiating body [CL]

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http://arxiv.org/abs/1812.08641


The dynamics of the four-body problem have attracted increasing attention in recent years. In this paper, we extend the basic equilateral four-body problem by introducing the effect of radiation pressure, Poynting-Robertson drag, and solar wind drag. In our setup, three primaries lay at the vertices of an equilateral triangle and move in circular orbits around their common center of mass. Here, one of the primaries is a radiating body and the fourth body (whose mass is negligible) does not affect the motion of the primaries. We show that the existence and the number of equilibrium points of the problem depend on the mass parameters and radiation factor. Consequently, the allowed regions of motion, the regions of the basins of convergence for the equilibrium points, and the basin entropy will also depend on these parameters. The present dynamical model is analyzed for three combinations of mass for the primaries: equal masses, two equal masses, different masses. As the main results, we find that in all cases the libration points are unstable if the radiation factor is larger than 0.01 and hence able to destroy the stability of the libration points in the restricted four-body problem composed by Sun, Jupiter, Trojan asteroid and a test (dust) particle. Also, we conclude that the number of fixed points decreases with the increase of the radiation factor.

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J. Osorio-Vargas, G. González and F. Dubeibe
Fri, 21 Dec 18
6/72

Comments: 15 pages, 10 figures, Preprint submitted to Elsevier

Correlations in the chaotic spectrum of pressure modes in rapidly rotating stars [SSA]

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http://arxiv.org/abs/1811.04673


The oscillation spectrum of pressure waves in stars can be determined by monitoring their luminosity. For rapidly rotating stars, the corresponding ray dynamics is mixed, with chaotic and regular zones in phase space. Our numerical simulations show that the chaotic spectra of these systems exhibit strong peaks in the autocorrelation which are at odd with Random Matrix Theory predictions. We explain these peaks through a semiclassical theory based on the peculiar distribution of the actions of classical periodic orbits. Indeed this distribution is strongly bunched around the average action between two consecutive rebounds and its multiples. In stars this phenomenon is a direct consequence of the strong decrease of the sound speed towards the star surface, but it would arise in any other physical system with a similar bunching of orbit actions. The peaks discussed could be observed by space missions and give insight on the star interiors.

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B. Evano, B. Georgeot and F. Lignières
Tue, 13 Nov 18
21/74

Comments: 6 pages, 6 figures

Kazantsev dynamo in turbulent compressible flows [CL]

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http://arxiv.org/abs/1809.01677


We consider the kinematic fluctuation dynamo problem in a flow that is random, white-in-time, with both solenoidal and potential components. This model is a generalization of the well-studied Kazantsev model. If both the solenoidal and potential parts have the same scaling exponent, then, as the compressibility of the flow increases, the growth rate decreases but remains positive. If the scaling exponents for the solenoidal and potential parts differ, in particular if they correspond to typical Kolmogorov and Burgers values, we again find that an increase in compressibility slows down the growth rate but does not turn it off. The slow down is, however, weaker and the critical magnetic Reynolds number is lower than when both the solenoidal and potential components display the Kolmogorov scaling. Intriguingly, we find that there exist cases, when the potential part is smoother than the solenoidal part, for which an increase in compressibility increases the growth rate. We also find that the critical value of the scaling exponent above which a dynamo is seen is unity irrespective of the compressibility. Finally, we realize that the dimension $d = 3$ is special, since for all other values of $d$ the critical exponent is higher and depends on the compressibility.

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M. Afonso, D. Mitra and D. Vincenzi
Mon, 10 Sep 18
8/58

Comments: 11 pages, 5 figures

Observations of Turbulent Magnetic Reconnection Within a Solar Current Sheet [SSA]

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http://arxiv.org/abs/1808.06071


Magnetic reconnection is a fundamental physical process in various astrophysical, space, and laboratory environments. Many pieces of evidence for magnetic reconnection have been uncovered. However, its specific processes that could be fragmented and turbulent have been short of direct observational evidence. Here, we present observations of a super-hot current sheet during SOL2017-09-10T X8.2-class solar flare that display the fragmented and turbulent nature of magnetic reconnection. As bilateral plasmas converge toward the current sheet, significant plasma heating and non-thermal motions are detected therein. Two oppositely directed outflow jets are intermittently expelled out of the fragmenting current sheet, whose intensity shows a power-law distribution in spatial frequency domain. The intensity and velocity of the sunward outflow jets also display a power-law distribution in temporal frequency domain. The length-to-width ratio of the current sheet is estimated to be larger than theoretical threshold of and thus ensures occurrence of tearing mode instability. The observations therefore suggest fragmented and turbulent magnetic reconnection occurring in the long stretching current sheet.

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X. Cheng, Y. Li, L. Wan, et. al.
Tue, 21 Aug 18
46/71

Comments: 15 pages, accepted for publication in ApJ, any comments are welcome!

Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View [CL]

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http://arxiv.org/abs/1808.05098


The Earth is well-known to be, in the current astronomical configuration, in a regime where two asymptotic states can be realised. The warm state we live in is in competition with the ice-covered snowball state. The bistability exists as a result of the positive ice-albedo feedback. In a previous investigation performed on a intermediate complexity climate model we have identified the edge states (Melancholia states) separating the co-existing climates, and studied their dynamic and geometrical properties. The Melancholia states are ice-covered up to the mid-latitudes, are unstable, but attract trajectories initialised on the basins boundary. In this paper, we study the effect of the natural variability of a solar irradiance on the stability of the climate by stochastically perturbing the parameter controlling the intensity of the incoming solar radiation. We detect transitions between the warm and the snowball state and analyse in detail the properties of the noise-induced escapes from the corresponding basins of attraction. We construct the most probable paths for the transitions and find evidence that the Melancholia states act as gateways, similarly to saddle points in an energy landscape.

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V. Lucarini and T. Bodai
Thu, 16 Aug 18
7/46

Comments: 5 pages, 4 figures

Element history of the Laplace resonance: a dynamical approach [EPA]

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http://arxiv.org/abs/1807.02516


We consider the three-body mean motion resonance defined by the Jovian moons Io, Europa, and Ganymede, which is commonly known as the Laplace resonance. In particular, we construct approximate models for the evolution of the librating argument over the period of 100 years, focusing on its principal amplitude and frequency, and on the observed mean motion combinations associated with the quasi-resonant interactions. First, we numerically propagated the Cartesian equations of motion of the Jovian system for the period under examination, and by comparing the results with a suitable set of ephemerides, we derived the main dynamical effects on the target quantities. Using these effects, we built an alternative Hamiltonian formulation and used the normal forms theory to locate the resonance and to compute its main amplitude and frequency. From the Cartesian model we observe that on the timescale considered and with ephemerides as initial conditions, both the librating argument and the diagnostics are well approximated by considering the mutual gravitational interactions of Jupiter and the Galilean moons (including Callisto), and the effect of Jupiter’s J2 harmonic. Under the same initial conditions, the Hamiltonian formulation in which Callisto and J2 are reduced to their secular contributions achieves larger errors for the quantities above, particularly for the librating argument. By introducing appropriate resonant variables, we show that these errors can be reduced by moving in a certain action-angle phase plane, which in turn implies the necessity of a tradeoff in the selection of the initial conditions. In addition to being a good starting point for a deeper understanding of the Laplace resonance, the models and methods described are easily generalizable to different types of multi-body mean motion resonances. They are also prime tools for studying the dynamics of extrasolar systems.

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F. Paita, A. Celletti and G. Pucacco
Tue, 10 Jul 18
74/79

Comments: 13 pages, 11 Figures, to appear on Astronomy and Astrophysics

Looking for the gluon condensation signature in proton using the Earth limb gamma-ray spectra [CL]

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http://arxiv.org/abs/1805.10618


A new type of gamma ray spectrum is predicted in a general hadronic framework if considering the gluon condensation effects in proton. The result presents the power-law with a sharp break in the gamma ray spectra at the TeV-band. We suggest to probe this GC-signature in the Earth limb gamma-ray spectra using the DArk Matter Particle Explorer and the CALorimetric Electron Telescope on orbit.

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L. Feng, J. Ruan, F. Wang, et. al.
Tue, 29 May 18
63/73

Comments: N/A

Fractal Measures and Nonlinear Dynamics of Over-contact Binaries [CL]

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http://arxiv.org/abs/1805.08351


Over-contact binaries are a subclass of eclipsing binaries whose component stars share a common envelope apart from filling their Roche lobes. We conduct a detailed analysis of the underlying nonlinear dynamics of about 463 over contact binary stars, classified as such in the second revision of the eclipsing binary catalog, in the Kepler Field of view (\cite{prvsa2011kepler}). We use two main techniques, namely the correlation dimension($D_2$), calculated from the reconstructed dynamics and the main peak bicoherence function from Fourier transforms of the light curves of these star systems. Our results indicate that almost all the light curves show signatures of deterministic chaos. This will be a helpful addition in understanding the origin of variable maxima and eclipse time variations in eclipsing binaries. We also check for correlations of the bicoherence of the light curves and the fractal properties of the reconstructed phase space of the stars with the inherent properties of the binary, and find that significant correlations exist between many of these properties, the most significant among which is the correlation between the fill-out factor with correlation dimension, $D_2$ and main peak bicoherence, $b_F(f)$. These results indicate that the nonlinear properties of the stars change as the system evolves. These correlations seem to be the first of its kind made between the nonlinear properties of the underlying dynamics of a class of astrophysical objects, and its inherent physical properties.

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S. George, R. Misra and G. Ambika
Thu, 24 May 18
45/58

Comments: 9 pages, 11 figures, submitted to MNRAS

Satellite capture mechanism in a sun-planet-binary four-body system [CL]

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http://arxiv.org/abs/1804.10415


This paper studies the binary disruption problem and asteroid capture mechanism in a sun-planet-binary four-body system. Firstly, the binary disruption condition is studied and the result shows that the binary is always disrupted at the perigee of their orbit instantaneously. Secondly, an analytic expression to describe the energy exchange between the binary is derived based on the instantaneous disruption hypothesis. The analytic result is validated through numerical integration. We obtain the energy exchange in encounters simultaneously by the analytic expression and numerical integration. The maximum deviation of this two results is always less than 25% and the mean deviation is about 8.69%. The analytic expression can give us an intuitive description of the energy exchange between the binary. It indicates that the energy change depends on the hyperbolic shape of the binary orbit with respect to the planet, the masses of planet and the primary member of the binary, the binary phase at perigee. We can illustrate the capture/escape processes and give the capture/escape region of the binary clearly by numerical simulation. We analyse the influence of some critical factors to the capture region finally.

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S. Gong and M. Li
Mon, 30 Apr 18
54/63

Comments: N/A

Presence of horizon makes particle motion chaotic [CL]

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http://arxiv.org/abs/1803.06527


We analyze the motion of a massless particle very near to the event horizon. It reveals that the radial motion has exponential growing nature which is the signature of the presence of chaos in the particle motion. This is being confirmed by investigating the Poincar$\acute{e}$ section of the trajectories with the introduction of a harmonic trap to confine the particle’s motion. Two situations are investigated: (a) the black hole is {\it any} static, spherically metric and, (b) spacetime represents a stationary, axisymetric black hole (e.g., Kerr metric). In both cases, the largest Lyapunov exponent has upper bound which is the surface gravity of the horizon. We find that the inclusion of rotation in the spacetime introduces more chaotic fluctuations in the system. The possible implications are finally discussed.

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S. Dalui, B. Majhi and P. Mishra
Thu, 22 Mar 18
9/58

Comments: 5 pages + supplementary material, 6 figures

Drift and its mediation in terrestrial orbits [CL]

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http://arxiv.org/abs/1803.00153


The slow deformation of terrestrial orbits in the medium range, subject to lunisolar resonances, is well approximated by a family of Hamiltonian flow with $2.5$ degree-of-freedom. The action variables of the system may experience chaotic variations and large drift that we may quantify. Using variational chaos indicators, we compute high-resolution portraits of the action space. Such refined meshes allow to reveal the existence of tori and structures filling chaotic regions. Our elaborate computations allow us to isolate precise initial conditions near specific zones of interest and study their asymptotic behaviour in time. Borrowing classical techniques of phase- space visualisation, we highlight how the drift is mediated by the complement of the numerically detected KAM tori.

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J. Daquin, I. Gkolias and A. Rosengren
Fri, 2 Mar 18
54/61

Comments: 20 pages, 10 figures, 1 table, 45 references. Comments and feedbacks greatly appreciated

Numerical verification of the microscopic time reversibility of Newton's equations of motion: Fighting exponential divergence [IMA]

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http://arxiv.org/abs/1802.00970


Numerical solutions to Newton’s equations of motion for chaotic self gravitating systems of more than 2 bodies are often regarded to be irreversible. This is due to the exponential growth of errors introduced by the integration scheme and the numerical round-off in the least significant figure. This secular growth of error is sometimes attributed to the increase in entropy of the system even though Newton’s equations of motion are strictly time reversible. We demonstrate that when numerical errors are reduced to below the physical perturbation and its exponential growth during integration the microscopic reversibility is retrieved. Time reversibility itself is not a guarantee for a definitive solution to the chaotic N-body problem. However, time reversible algorithms may be used to find initial conditions for which perturbed trajectories converge rather than diverge. The ability to calculate such a converging pair of solutions is a striking illustration which shows that it is possible to compute a definitive solution to a highly unstable problem. This works as follows: If you (i) use a code which is capable of producing a definitive solution (and which will therefore handle converging pairs of solutions correctly), (ii) use it to study the statistical result of some other problem, and then (iii) find that some other code produces a solution S with statistical properties which are indistinguishable from those of the definitive solution, then solution S may be deemed veracious.

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S. Zwart and T. Boekholt
Tue, 6 Feb 18
28/62

Comments: Accepted for publication in Communications in Nonlinear Science and Numerical Simulation. Calculations are performed with Brutus as part of the AMUSE framework. Simultion data will become available online

Stability and self-organization of planetary systems [EPA]

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http://arxiv.org/abs/1801.08575


We show that stability of planetary systems is intimately connected with their internal order. An arbitrary initial distribution of planets is susceptible to catastrophic events in which planets either collide or are ejected from the planetary system. These instabilities are a fundamental consequence of chaotic dynamics and of Arnold diffusion characteristic of many body gravitational interactions. To ensure stability over astronomical time scale of a realistic planetary system — in which planets have masses comparable or those of planets in the solar system — the motion must be quasi-periodic. A dynamical mechanism is proposed which naturally evolves a planetary system to a periodic state from an arbitrary initial condition. A planetary self-organization predicted by the theory is similar to the one found in our solar system.

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R. Pakter and Y. Levin
Mon, 29 Jan 18
6/54

Comments: N/A

Turbulent superstructures in Rayleigh-Bénard convection [CL]

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http://arxiv.org/abs/1801.04478


Turbulent Rayleigh-B\’enard convection displays a large-scale order in the form of rolls and cells on lengths larger than the layer height once the fluctuations of temperature and velocity are removed. These turbulent superstructures are reminiscent of the patterns close to the onset of convection. They are analyzed by numerical simulations of turbulent convection in fluids at different Prandtl number ranging from 0.005 to 70 and for Rayleigh numbers up to $10^7$. For each case, we identify characteristic scales and times that separate the fast, small-scale turbulent fluctuations from the gradually changing large-scale superstructures. The characteristic scales of the large-scale patterns, which change with Prandtl and Rayleigh number, are also found to be correlated with the boundary layer dynamics, and in particular the clustering of thermal plumes at the top and bottom plates. Our analysis suggests a scale separation and thus the existence of a simplified description of the turbulent superstructures in geo- and astrophysical settings.

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A. Pandey, J. Scheel and J. Schumacher
Tue, 16 Jan 18
43/79

Comments: 16 pages (incl. Supplementary Material), 12 figures (all with downsized figure size)

Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations [EPA]

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http://arxiv.org/abs/1801.02458


The discovery of Pluto’s small moons in the last decade brought attention to the dynamics of the dwarf planet’s satellites. Recent work has considered resonant interactions in the orbits of Pluto’s small moons, with the Pluto-Charon system apparently inducing rotational chaos in non-spherical moons without the need of resonance. However, New Horizons observations suggest that despinning due to tidal dissipation has not taken place. Still, a tidally evolving Styx does appear to exhibit intermittent obliquity variations and episodes of tumbling, suggesting some form of chaos in the rotational dynamics. With these systems in mind, we study a planar $N$-body system in which all the bodies are point masses, except for a single rigid body. We then present a reduced model consisting of a planar $N$-body problem with the rigid body treated as a 1D continuum (i.e. the body is treated as a rod with an arbitrary mass distribution). Such a model provides a good approximation to highly asymmetric geometries, such as the recently observed interstellar asteroid ‘Oumuamua, but is also amenable to analysis. We analytically demonstrate the existence of homoclinic chaos in the case where one of the orbits is nearly circular by way of the Melnikov method, and give numerical evidence for chaos when the orbits are more complicated. We show that the extent of chaos in parameter space is strongly tied to the deviations from a purely circular orbit. These results suggest that chaos is ubiquitous in many-body problems when one or more of the rigid bodies exhibits non-spherical and highly asymmetric geometries. The excitation of chaotic rotations does not appear to require tidal dissipation, obliquity variation, or orbital resonance. Such dynamics give a possible explanation for routes to chaotic dynamics observed in $N$-body systems such as the Pluto system where some of the bodies are highly non-spherical.

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J. Kwiecinski, A. Kovacs, A. Krause, et. al.
Tue, 9 Jan 18
94/94

Comments: 27 pages, 7 figures. arXiv admin note: text overlap with arXiv:1701.05594 by other authors

Dynamical analysis of bounded and unbounded orbits in a generalized Hénon-Heiles system [CL]

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http://arxiv.org/abs/1712.01873


The H\’enon-Heiles potential was first proposed as a simplified version of the gravitational potential experimented by a star in the presence of a galactic center. Currently, this system is considered a paradigm in dynamical systems because despite its simplicity exhibits a very complex dynamical behavior. In the present paper, we perform a series expansion up to the fifth-order of a potential with axial and reflection symmetries, which after some transformations, leads to a generalized H\’enon-Heiles potential. Such new system is analyzed qualitatively in both regimes of bounded and unbounded motion via the Poincar\’e sections method and plotting the exit basins. On the other hand, the quantitative analysis is performed through the Lyapunov exponents and the basin entropy, respectively. We find that in both regimes the chaoticity of the system decreases as long as the test particle energy gets far from the critical energy. Additionally, we may conclude that despite the inclusion of higher order terms in the series expansion, the new system shows wider zones of regularity (islands) than the ones present in the H\’enon-Heiles system.

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F. Dubeibe, A. Riano-Doncel and E. Zotos
Thu, 7 Dec 17
10/72

Comments: 8 pages, 5 figures

Quantum chaos of dark matter in the Solar System [CL]

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http://arxiv.org/abs/1711.07815


We perform time-dependent analysis of quantum dynamics of dark matter particles in the Solar System. It is shown that this problem has similarities with a microwave ionization of Rydberg atoms studied previously experimentally and analytically. On this basis it is shown that the quantum effects for chaotic dark matter dynamics become significant for dark matter mass ratio to electron mass being smaller than $2 \times 10^{-15}$. Below this border multiphoton diffusion over Rydberg states of dark matter atom becomes exponentially localized in analogy with the Anderson localization in disordered solids. The life time of dark matter in the Solar System is determined in dependence on mass ratio in the localized phase and a few photon ionization regime. Various implications of these quantum results are discussed for the capture of dark matter from Galaxy and its steady-state density distribution.

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D. Shepelyansky
Thu, 23 Nov 17
48/52

Comments: 5 pages, 2 figures

Quantum chaos of dark matter in the Solar System [CL]

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http://arxiv.org/abs/1711.07815


We perform time-dependent analysis of quantum dynamics of dark matter particles in the Solar System. It is shown that this problem has similarities with a microwave ionization of Rydberg atoms studied previously experimentally and analytically. On this basis it is shown that the quantum effects for chaotic dark matter dynamics become significant for dark matter mass ratio to electron mass being smaller than $2 \times 10^{-15}$. Below this border multiphoton diffusion over Rydberg states of dark matter atom becomes exponentially localized in analogy with the Anderson localization in disordered solids. The life time of dark matter in the Solar System is determined in dependence on mass ratio in the localized phase and a few photon ionization regime. Various implications of these quantum results are discussed for the capture of dark matter from Galaxy and its steady-state density distribution.

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D. Shepelyansky
Thu, 23 Nov 17
25/52

Comments: 5 pages, 2 figures

Negative magnetic eddy diffusivity due to oscillatory $α$-effect [CL]

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http://arxiv.org/abs/1711.02390


We study large-scale kinematic dynamo action of steady mirror-antisymmetric flows of incompressible fluid, that involve small spatial scales only, by asymptotic methods of the multiscale stability theory. It turns out that, due to the magnetic $\alpha$-effect in such flows, mean field experiences harmonic oscillations in time on the scale $T_1=\varepsilon t$ without growth or decay. Here $\varepsilon$ is the spatial scale ratio and $t$ is the fast time of the order of the flow turnover time. The interaction of the accompanying fluctuating magnetic field with the flow gives rise to an anisotropic magnetic eddy diffusivity, whose dependence on the direction of the large-scale wave vector generically exhibits a singular behaviour, and thus to negative eddy diffusivity for whichever molecular magnetic diffusivity. Consequently, such flows always act as kinematic dynamos on the time scale $T_2=\varepsilon^2t$. We investigate numerically this dynamo mechanism for two sample flows.

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A. Andrievsky, R. Chertovskih and V. Zheligovsky
Fri, 10 Nov 17
3/55

Comments: N/A

Chaotic dynamics in the (47171) Lempo triple system [EPA]

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http://arxiv.org/abs/1710.08401


We investigate the dynamics of the (47171) Lempo triple system, also known by 1999TC$_{36}$. We derive a full 3D $N$-body model that takes into account the orbital and spin evolution of all bodies, which are assumed triaxial ellipsoids. We show that, for reasonable values of the shapes and rotational periods, the present best fitted orbital solution is chaotic and unstable in short time-scales. The formation mechanism of this system is unknown, but the orbits can be stabilised when tidal dissipation is taken into account. The dynamics of this system is very rich, but depends on many parameters that are presently unknown. A better understanding of this systems thus requires more observations, which also need to be fitted with a complete model like the one presented here.

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A. Correia
Tue, 24 Oct 17
55/68

Comments: 43 pages, 8 figures

On multiplicative Lie invariants and two-fluid plasma Cauchy invariants equation [CL]

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http://arxiv.org/abs/1709.03356


To understand and model non-ideal flows, we use the simple result $(\partial_t + L_v) (\omega_1 \wedge \omega_2) = S_1 \wedge \omega_2 + \omega_1 \wedge S_2$ from the Lie-varying forms $(\partial_t + L_v) \omega_i = S_i: \ i = 1, 2$. If the (Lie-)sources/sinks satisfy $S_1 \wedge \omega_2 + \omega_1 \wedge S_2 = 0$, a multiplicative' Lie invariant follows, extending the classical approaches offinding new invariants from known ones of ideal flows’ and of modeling non-ideal flows constrained by invariant(s), beyond the traditional ones, the Gauss method, say. Precise relations, such as the generalised Cauchy invariants equation, as found here for two-fluid plasma dynamics, also extend to wider application space.

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J. Zhu
Tue, 12 Sep 17
65/71

Comments: N/A

How vortices and shocks provide for a flux loop in two-dimensional compressible turbulence [CL]

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http://arxiv.org/abs/1709.00814


Large-scale turbulence in fluid layers and other quasi two-dimensional compressible systems consists of planar vortices and waves. Separately, wave turbulence usually produces direct energy cascade, while solenoidal planar turbulence transports energy to large scales by an inverse cascade. Here we consider turbulence at finite Mach numbers when interaction between acoustic waves and vortices is substantial. We employ solenoidal pumping at intermediate scales and show how both direct and inverse energy cascades are formed starting from the pumping scale. We show that there is an inverse cascade of kinetic energy up to a scale, $\ell$, where typical velocity reaches the speed of sound; that creates shock waves which provide for a compensating direct cascade. When the system size is less than $\ell$, the steady state contains a system-size pair of long-living condensate vortices connected by a system of shocks. Thus turbulence in fluid layers processes energy via a loop: most energy first goes to large scales via vortices and is then transported by waves to small-scale dissipation.

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G. Falkovich and A. Kritsuk
Tue, 5 Sep 17
21/76

Comments: 11 pages, 7 figures; Accepted to Phys. Rev. Fluids as Rapid Communication

Partially chaotic orbits in a perturbed cubic force model [GA]

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http://arxiv.org/abs/1707.08156


Three types of orbits are theoretically possible in autonomous Hamiltonian systems with three degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides energy) and regular (they obey two isolating integrals besides energy). The existence of partially chaotic orbits has been denied by several authors, however, arguing either that there is a sudden transition from regularity to full chaoticity, or that a long enough follow up of a supposedly partially chaotic orbit would reveal a fully chaotic nature. This situation needs clarification, because partially chaotic orbits might play a significant role in the process of chaotic diffusion. Here we use numerically computed Lyapunov exponents to explore the phase space of a perturbed three dimensional cubic force toy model, and a generalization of the Poincar\’e maps to show that partially chaotic orbits are actually present in that model. They turn out to be double orbits joined by a bifurcation zone, which is the most likely source of their chaos, and they are encapsulated in regions of phase space bounded by regular orbits similar to each one of the components of the double orbit.

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J. Muzzio
Thu, 27 Jul 17
40/49

Comments: Accepted for publication by the Monthly Notices of the Royal Astronomical Society, July 23, 2017

Long-term influence of asteroids on planet longitudes and chaotic dynamics of the solar system [EPA]

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http://arxiv.org/abs/1707.03577


The aim of this paper is to compare different sources of stochasticity in the solar system. More precisely we study the importance of the long term influence of asteroids on the chaotic dynamics of the solar system. We show that the effects of asteroids on planets is similar to a white noise process, when those effects are considered on a time scale much larger than the correlation time $\tau_{\varphi}\simeq10^{4}$ yr of asteroid trajectories. We compute the time scale $\tau_{e}$ after which the effects of the stochastic evolution of the asteroids lead to a loss of information for the initial conditions of the perturbed Laplace\textendash Lagrange secular dynamics. The order of magnitude of this time scale is precisely determined by theoretical argument. This time scale should be compared with the Lyapunov time $\tau_{i}$ of the solar system without asteroids (intrinsic chaos). We conclude that $\tau_{i}\simeq10\, \text{Myr} \ll \tau_{e} \simeq10^{4}\, \text{Myr}$, showing that the external sources of chaoticity arise as a small perturbation in the stochastic secular behavior of the solar system, rather due to intrinsic chaos.

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F. Bouchet and E. Woillez
Thu, 13 Jul 17
59/60

Comments: Astronomy and Astrophysics – A&A, EDP Sciences, 2017

Escape dynamics through a continuously growing leak [EPA]

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http://arxiv.org/abs/1706.01759


We formulate a model that describes the escape dynamics in a leaky chaotic system in which the size of the leak depends on the number of the in-falling particles. The basic motivation of this work is the astrophysical process which describes the planetary accretion. In order to study the dynamics generally, the standard map is investigated in two cases when the dynamics is fully hyperbolic and in the presence of KAM islands. In addition to the numerical calculations, an analytic solution to the temporal behavior of the model is also derived. We show that in the early phase of the leak expansion, as long as there are enough particles in the system, the number of survivors deviates from the well-known exponential decay. Furthermore, the analytic solution returns the classical result in the limiting case when the number of particles does not affect the leak size.

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T. Kovacs and J. Vanyo
Wed, 7 Jun 17
16/52

Comments: 11 pages, 11 figures

Chaotic zones around rotating small bodies [EPA]

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http://arxiv.org/abs/1705.02845


Small bodies of the Solar system, like asteroids, trans-Neptunian objects, cometary nuclei, planetary satellites, with diameters smaller than one thousand kilometers usually have irregular shapes, often resembling dumb-bells, or contact binaries. The spinning of such a gravitating dumb-bell creates around it a zone of chaotic orbits. We determine its extent analytically and numerically. We find that the chaotic zone swells significantly if the rotation rate is decreased, in particular, the zone swells more than twice if the rotation rate is decreased ten times with respect to the “centrifugal breakup” threshold. We illustrate the properties of the chaotic orbital zones in examples of the global orbital dynamics about asteroid 243 Ida (which has a moon, Dactyl, orbiting near the edge of the chaotic zone) and asteroid 25143 Itokawa.

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J. Lages, D. Shepelyansky and I. Shevchenko
Tue, 9 May 17
61/82

Comments: 14 pages, 7 figures, accepted for publication in The Astronomical Journal

One hundred and fifty-two new families of Newtonian periodic planar three-body orbits [CL]

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http://arxiv.org/abs/1705.00527


The famous three-body problem can be traced back to Isaac Newton in 1680s. In the 300 years since this “three-body problem” was first recognized, just three families of solutions had been found, until 2013 when \v{S}uvakov and Dmitra\v{s}inovi\’c [Phys. Rev. Lett. 110, 114301 (2013)] made a breakthrough to find 13 new distinct periodic orbits, which belong to 11 new families of Newtonian planar three-body problem with equal mass and zero angular momentum. In this letter, we numerically obtained 164 families of Newtonian planar periodic three-body orbits with equal mass and zero angular momentum, including the well-known Figure-eight family found by Moore in 1993, the 11 families found by \v{S}uvakov and Dmitra\v{s}inovi\’c in 2013, and 152 completely new families that have been never reported. With the definition of the average period $\bar{T} = T/k$, where $k$ is the length of the so-called free group element, these 164 families of the periodic three-body orbits suggest that there should exist the quasi Kepler’s third law $\bar{R}\propto |E|^{-1}= 0.56 \, \bar{T}^{2/3}$, where $\bar{R}$ is the mean of hyper-radius of the three-body system and $E$ is its total kinetic and potential energy, respectively. The movies and pictures of the periodic three-body orbits in the real space and the corresponding close curves in the “shape sphere” can be found via the website: this http URL

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X. Li and S. Liao
Mon, 8 May 17
38/54

Comments: 16 pages, 11 tables, 2 figures

Recurrence network measures for hypothesis testing using surrogate data: application to black hole light curves [CL]

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http://arxiv.org/abs/1704.08606


Recurrence networks and the associated statistical measures have become important tools in the analysis of time series data. In this work, we test how effective the recurrence network measures are in analyzing real world data involving two main types of noise, white noise and colored noise. We use two prominent network measures as discriminating statistic for hypothesis testing using surrogate data for a specific null hypothesis that the data is derived from a linear stochastic process. We show that the characteristic path length is especially efficient as a discriminating measure with the conclusions reasonably accurate even with limited number of data points in the time series. We also highlight an additional advantage of the network approach in identifying the dimensionality of the system underlying the time series through a convergence measure derived from the probability distribution of the local clustering coefficients. As examples of real world data, we use the light curves from a prominent black hole system and show that a combined analysis using three primary network measures can provide vital information regarding the nature of temporal variability of light curves from different spectroscopic classes.

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R. Jacob, K. Harikrishnan, R. Misra, et. al.
Fri, 28 Apr 17
29/55

Comments: 29 pages, 15 figures, submitted to . Communications in Nonlinear Science and Numerical Simulation

Rotation of an oblate satellite – dependence on the true anomaly [EPA]

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http://arxiv.org/abs/1704.02015


[abridged] A model of planar oscillations of an oblate satellite is investigated in terms of the dependence of its dynamics on the true anomaly $f$. The model is represented in a three-dimensional phase space. Maximal Lyapunov exponent (mLE) is computed in a two-dimensional space of the angular initial conditions for various initial conditions $f_0$. It is showed that the phase flow in the full three-dimensional space is twisted with a period of $2\pi$, i.e. one orbital period, but the distribution and strength of chaos is unchanged, meaning that the character of motion does not change, but simply migrates through the phase space. The twist is in good agreement with bifurcation diagrams constructed against $f_0$, which reveal a complicated mixture of chaotic and quasiperiodic trajectories. The onset of chaos, usually attributed to overlapping of the major spin-orbit resonances, for a sufficiently high value of the satellite’s oblateness, $\omega^2$, is easily visible with a so called generalized bifurcation diagram, i.e. an mLE map in a mixed space of $\omega^2$ and the initial condition.
The equation of motion is transformed to a two-dimensional model in which $f$ is the independent variable. This allows to utilize the Hamiltonian formalism to its extent, first to examine the diffusion of a dense set of initial conditions in the (now two-dimensional) phase space, and second, to employ a control method of suppressing chaos. The latter allows to construct a control term an order of magnitude smaller than the potential to which it is added. The diffusion of the trajectory in the phase space is not only diminished, but turns the motion into strictly periodic.

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M. Tarnopolski
Mon, 10 Apr 17
15/36

Comments: 27 pages, 15 figures

Unraveling the escape dynamics and the nature of the normally hyperbolic invariant manifolds in tidally limited star clusters [GA]

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http://arxiv.org/abs/1702.07287


The escape mechanism of orbits in a star cluster rotating around its parent galaxy in a circular orbit is investigated. A three degrees of freedom model is used for describing the dynamical properties of the Hamiltonian system. The gravitational field of the star cluster is represented by a smooth and spherically symmetric Plummer potential. We distinguish between ordered and chaotic orbits as well as between trapped and escaping orbits, considering only unbounded motion for several energy levels. The Smaller Alignment Index (SALI) method is used for determining the regular or chaotic nature of the orbits. The basins of escape are located and they are also correlated with the corresponding escape time of the orbits. Areas of bounded regular or chaotic motion and basins of escape were found to coexist in the $(x,z)$ plane. The properties of the normally hyperbolic invariant manifolds (NHIMs), located in the vicinity of the index-1 Lagrange points $L_1$ and $L_2$, are also explored. These manifolds are of paramount importance as they control the flow of stars over the saddle points, while they also trigger the formation of tidal tails observed in star clusters. Bifurcation diagrams of the Lyapunov periodic orbits as well as restrictions of the Poincar\’e map to the NHIMs are deployed for elucidating the dynamics in the neighbourhood of the saddle points. The extended tidal tails, or tidal arms, formed by stars with low velocity which escape through the Lagrange points are monitored. The numerical results of this work are also compared with previous related work.

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E. Zotos and C. Jung
Fri, 24 Feb 17
6/50

Comments: Published in Monthly Notices of the Royal Astronomical Society (MNRAS) journal

Chaos Control with Ion Propulsion [CL]

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http://arxiv.org/abs/1702.06581


The escape dynamics around the triangular Lagrangian point L5 in the real Sun-Earth-Moon-Spacecraft system is investigated. Appearance of the finite time chaotic behaviour suggests that widely used methods and concepts of dynamical system theory can be useful in constructing a desired mission design. Existing chaos control methods are modified in such a way that we are able to protect a test particle from escape. We introduce initial condition maps in order to have a suitable numerical method to describe the motion in high dimensional phase space. Results show that the structure of initial condition maps can be split into two well-defined domains. One of these two parts has a regular contiguous shape and is responsible for long time escape; it is a long-lived island. The other one shows a filamentary fractal structure in initial condition maps. The short time escape is governed by this object. This study focuses on a low-cost method which successfully transfers a reference trajectory between these two regions using an appropriate continuous control force. A comparison of the Earth-Moon transfer is also presented to show the efficiency of our method.

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J. Sliz, T. Kovacs and A. Suli
Thu, 23 Feb 17
20/48

Comments: 14 pages, 11 figures, accepted for publication in Astronomische Nachrichten

The gluon condensation at high energy hadron collisions [CL]

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http://arxiv.org/abs/1702.02249


We report that the saturation/CGC model of gluon distribution is unstable under action of the chaotic solution in a nonlinear QCD evolution equation, and it evolves to the distribution with a sharp peak at the critical momentum. We find that this gluon condensation is caused by a new kind of shadowing-antishadowing effects, and it leads to a series of unexpected effects in high energy hadron collisions including astrophysical events. For example, the extremely intense fluctuations in the transverse-momentum and rapidity distributions of the gluon jets present the gluon-jet bursts; a sudden increase of the proton-proton cross sections may fill the GZK suppression; the blocking QCD evolution will restrict the maximum available energy of the hadron-hadron colliders.

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W. Zhu and J. Lan
Thu, 9 Feb 17
58/67

Comments: 45 pages, 19 figures, to be published in Nucl. Phys. B

The structure of invariant tori in a 3D galactic potential [CL]

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http://arxiv.org/abs/1009.1993


We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type. We have used the color and rotation method to investigate the properties of the invariant tori in the 4D spaces of section. We compare our results with those of previous works and we describe the morphology of the rotational, as well as of the tube tori in the 4D space. We find sticky chaotic orbits in the immediate neighborhood of sets of invariant tori surrounding 3D stable periodic orbits. Particularly useful for galactic dynamics is the behavior of chaotic orbits trapped for long time between 4D invariant tori. We find that they support during this time the same structure as the quasi-periodic orbits around the stable periodic orbits, contributing however to a local increase of the dispersion of velocities. Finally we find that the tube tori do not appear in the 3D projections of the spaces of section in the axisymmetric Hamiltonian we examined.

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M. Katsanikas and P. Patsis
Mon, 9 Jan 17
21/52

Comments: 26 pages, 34 figures, accepted for publication in the International Journal of Bifurcation and Chaos

Chains of rotational tori and filamentary structures close to high multiplicity periodic orbits in a 3D galactic potential [CL]

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http://arxiv.org/abs/1103.3981


This paper discusses phase space structures encountered in the neighborhood of periodic orbits with high order multiplicity in a 3D autonomous Hamiltonian system with a potential of galactic type. We consider 4D spaces of section and we use the method of color and rotation [Patsis and Zachilas 1994] in order to visualize them. As examples we use the case of two orbits, one 2-periodic and one 7-periodic. We investigate the structure of multiple tori around them in the 4D surface of section and in addition we study the orbital behavior in the neighborhood of the corresponding simple unstable periodic orbits. By considering initially a few consequents in the neighborhood of the orbits in both cases we find a structure in the space of section, which is in direct correspondence with what is observed in a resonance zone of a 2D autonomous Hamiltonian system. However, in our 3D case we have instead of stability islands rotational tori, while the chaotic zone connecting the points of the unstable periodic orbit is replaced by filaments extending in 4D following a smooth color variation. For more intersections, the consequents of the orbit which started in the neighborhood of the unstable periodic orbit, diffuse in phase space and form a cloud that occupies a large volume surrounding the region containing the rotational tori. In this cloud the colors of the points are mixed. The same structures have been observed in the neighborhood of all m-periodic orbits we have examined in the system. This indicates a generic behavior.

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M. Katsanikas, P. Patsis and A. Pinotsis
Mon, 9 Jan 17
26/52

Comments: 12 pages,22 figures, Accepted for publication in the International Journal of Bifurcation and Chaos

The structure and evolution of confined tori near a Hamiltonian Hopf Bifurcation [CL]

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http://arxiv.org/abs/1012.2463


We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits from stability to complex instability (also known as Hamiltonian Hopf Bifurcation) the four eigenvalues of the stable periodic orbits move out of the unit circle. Then the periodic orbits become complex unstable. In this paper we first integrate initial conditions close to the ones of a complex unstable periodic orbit, which is close to the transition point. Then, we plot the consequents of the corresponding orbit in a 4D surface of section. To visualize this surface of section we use the method of color and rotation [Patsis and Zachilas 1994]. We find that the consequents are contained in 2D “confined tori”. Then, we investigate the structure of the phase space in the neighborhood of complex unstable periodic orbits, which are further away from the transition point. In these cases we observe clouds of points in the 4D surfaces of section. The transition between the two types of orbital behavior is abrupt.

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M. Katsanikas, P. Patsis and G. Contopoulos
Mon, 9 Jan 17
42/52

Comments: 10 pages, 14 figures, accepted for publication in the International Journal of Bifurcation and Chaos

Instabilities and stickiness in a 3D rotating galactic potential [CL]

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http://arxiv.org/abs/1201.2108


We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the four dimensional spaces of section we use the method of color and rotation. We investigate the structure of the invariant manifolds that we found in the neighborhood of simple and double unstable periodic orbits in the 4D spaces of section. We consider orbits in the neighborhood of the families x1v2, belonging to the x1 tree, and the z-axis (the rotational axis of our system). Close to the transition points from stability to simple instability, in the neighborhood of the bifurcated simple unstable x1v2 periodic orbits we encounter the phenomenon of stickiness as the asymptotic curves of the unstable manifold surround regions of the phase space occupied by rotational tori existing in the region. For larger energies, away from the bifurcating point, the consequents of the chaotic orbits form clouds of points with mixing of color in their 4D representations. In the case of double instability, close to x1v2 orbits, we find clouds of points in the four dimensional spaces of section. However, in some cases of double unstable periodic orbits belonging to the z-axis family we can visualize the associated unstable eigensurface. Chaotic orbits close to the periodic orbit remain sticky to this surface for long times (of the order of a Hubble time or more). Among the orbits we studied we found those close to the double unstable orbits of the x1v2 family having the largest diffusion speed.

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M. Katsanikas, P. Patsis and G. Contopoulos
Mon, 9 Jan 17
44/52

Comments: 29pages, 25 figures, accepted for publication in the International Journal of Bifurcation and Chaos

Theoretical foundations of the Schrödinger method for LSS formation [CL]

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http://arxiv.org/abs/1612.04572


It has been shown that the formation of large scale structures (LSS) in the universe can be described in terms of a Schr$\ddot{o}$dinger-Poisson system. This procedure, known as Schr$\ddot{o}$dinger method, has no theoretical basis, but it is intended as a mere tool to model the N-body dynamics of dark matter halos which form LSS. Furthermore, in this approach the “Planck constant” $\hbar$ in the Schr$\ddot{o}$dinger equation is just a free parameter. In this paper we give a theoretical foundation of the Schr$\ddot{o}$dinger method based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. The order of magnitude of the effective Planck constant is estimated as $\hbar \sim m^{5/3} G^{1/2} (N/<\rho>)^{1/6}$, where $N$ and $m$ are the number and the mass of the dark matter halos, $<\rho_0>$ is their average density, and $G$ the gravitational constant. The relevance of this finding for the study of LSS is discussed.

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F. Briscese
Thu, 15 Dec 16
30/59

Comments: N/A

Constraints on Bounded Motion and Mutual Escape for the Full 3-Body Problem [EPA]

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http://arxiv.org/abs/1611.09997


When gravitational aggregates are spun to fission they can undergo complex dynamical evolution, including escape and reconfiguration. Previous work has shown that a simple analysis of the full 2-body problem provides physically relevant insights for whether a fissioned system can lead to escape of the components and the creation of asteroid pairs. In this paper we extend the analysis to the full 3-body problem, utilizing recent advances in the understanding of fission mechanics of these systems. Specifically, we find that the full 3-body problem can eject a body with as much as 0.31 of the total system mass, significantly larger than the 0.17 mass limit previously calculated for the full 2-body problem. This paper derives rigorous limits on a fissioned 3-body system with regards to whether fissioned system components can physically escape from each other and what other stable relative equilibria they could settle in. We explore this question with a narrow focus on the Spherical Full Three Body Problem studied in detail earlier.

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D. Scheeres
Thu, 1 Dec 16
4/75

Comments: Accepted for publication in Celestial Mechanics and Dynamical Astronomy

On the complexity and the information content of cosmic structures [CEA]

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http://arxiv.org/abs/1611.09348


The emergence of cosmic structure is commonly considered one of the most complex phenomena in Nature. However, this complexity has never been defined nor measured in a quantitative and objective way. In this work we propose a method to measure the information content of cosmic structure and to quantify the complexity that emerges from it, based on Information Theory. The emergence of complex evolutionary patterns is studied with a statistical symbolic analysis of the datastream produced by state-of-the-art cosmological simulations of forming galaxy clusters. This powerful approach allows us to measure how many bits of information are necessary to predict the evolution of energy fields in a statistical way, and it offers a simple way to quantify when, where and how the cosmic gas behaves in complex ways. The most complex behaviors are found in the peripheral regions of galaxy clusters, where supersonic flows drive shocks and large energy fluctuations over a few tens of million years. Describing the evolution of magnetic energy requires at least a twice as large amount of bits than for the other energy fields. When radiative cooling and feedback from galaxy formation are considered, the cosmic gas is overall found to double its degree of complexity. In the future, Cosmic Information Theory can significantly increase our understanding of the emergence of cosmic structure as it represents an innovative framework to design and analyze complex simulations of the Universe in a simple, yet powerful way.

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F. Vazza
Tue, 29 Nov 16
21/77

Comments: 15 pages, 14 figures. MNRAS accepted, in press

Revisiting Evidence of Chaos in X-ray Light Curves: The Case of GRS 1915+105 [HEAP]

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http://arxiv.org/abs/1611.02264


Nonlinear time series analysis has been widely used to search for signatures of low-dimensional chaos in light curves emanating from astrophysical bodies. A particularly popular example is the microquasar GRS 1915+105, whose irregular but systematic X-ray variability has been well studied using data acquired by the Rossi X-ray Timing Explorer (RXTE). With a view to building simpler models of X-ray variability, attempts have been made to classify the light curves of GRS 1915+105 as chaotic or stochastic. Contrary to some of the earlier suggestions, after careful analysis, we find no evidence for chaos or determinism in any of the GRS 1915+105 classes. The dearth of long and stationary data sets representing all the different variability classes of GRS 1915+105 make it a poor candidate for analysis using nonlinear time series techniques. We conclude that either very exhaustive data analysis with sufficiently long and stationary light curves should be performed keeping all the pitfalls of nonlinear time series analysis in mind, or alternative schemes of classifying the light curves should be adopted. The generic limitations of the techniques that we point out in the context of GRS 1915+105 affect all similar investigations of light curves from other astrophysical sources.

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M. Mannattil, H. Gupta and S. Chakraborty
Tue, 8 Nov 16
8/75

Comments: Accepted in The Astrophysical Journal

Distributed chaos and Rayleigh-Benard turbulence at very high Ra [CL]

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http://arxiv.org/abs/1608.04657


It is shown, by the means of distributed chaos approach and using the experimental data, that at very large Rayleigh number $Ra > 10^{14}$ and Prandtl number $Pr \sim 1$ the Rayleigh-B\'{e}nard turbulence can undergo a transition related to spontaneous breaking of the fundamental Lagrangian relabeling symmetry. Due to the Noether’s theorem helicity plays central role in this process. After the transition the temperature spectrum has a stretched exponential form $E (k) \propto \exp(-k/k_{\beta})^{\beta}$ with $\beta =2/5$ both at the cell midplain and at the near-wall (low boundary) regions. There is a similarity between this phenomenon and the effects of polymer additives.

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A. Bershadskii
Wed, 2 Nov 16
13/55

Comments: N/A

Strong turbulent convection: distributed chaos and large-scale circulation [CL]

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http://arxiv.org/abs/1604.07762


Two types of spontaneous breaking of the space translational symmetry in distributed chaos have been considered for turbulent thermal convection at large values of Rayleigh number. First type is related to boundaries and second type is related to appearance of inertial range of scales. The first type is dominated by vorticity correlation integral: $\int_{V} \langle {\boldsymbol \omega} ({\bf x},t) \cdot {\boldsymbol \omega} ({\bf x} + {\bf r},t) \rangle_{V} d{\bf r}$ and is characterized by stretched exponential spectrum $\exp-(k/k_{\beta})^{\beta }$ with $\beta =1/2$. The second type is dominated by energy correlation integral: $\int_{V} \langle {\bf u}^2 ({\bf x},t) ~ {\bf u}^2({\bf x} + {\bf r},t) \rangle_{V} d{\bf r}$ and is characterized by $\beta =3/5$. Good agreement has been established with laboratory experimental data obtained at large values of Rayleigh number $Ra \sim 10^{11}-10^{14}$ (the range relevant to solar photosphere) in upright cylinder cells. Taylor hypothesis transforms the wavenumber spectrum into frequency spectrum $\exp-(f/f_{\beta})^{1/2}$. It is shown that turnover frequency of large-scale circulation (wind): $f_w = f_{\beta}/2$. Results of an experiment in horizontal cylinder are also briefly discussed. The analysis suggests that in this case the large-scale circulation can be considered as a natural (harmonic) part of the distributed chaos.

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A. Bershadskii
Wed, 19 Oct 16
27/87

Comments: extended version (a discussion and some data have been added)

Vertical stability of circular orbits in relativistic razor-thin disks [CL]

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http://arxiv.org/abs/1610.02369


During the last few decades, there has been a growing interest in exact solutions of Einstein equations describing razor-thin disks. Despite the progress in the area, the analytical study of geodesic motion crossing the disk plane in these systems is not yet so developed. In the present work, we propose a definite vertical stability criterion for circular equatorial timelike geodesics in static, axially symmetric thin disks, possibly surrounded by other structures preserving axial symmetry. It turns out that the strong energy condition for the disk stress-energy content is sufficient for vertical stability of these orbits. Moreover, adiabatic invariance of the vertical action variable gives us an approximate third integral of motion for oblique orbits which deviate slightly from the equatorial plane. Such new approximate third integral certainly points to a better understanding of the analytical properties of these orbits. The results presented here, derived for static spacetimes, may be a starting point to study the motion around rotating, stationary razor-thin disks. Our results also allow us to conjecture that the strong energy condition should be sufficient to assure transversal stability of periodic orbits for any singular timelike hypersurface, provided it is invariant by the geodesic flow.

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R. Vieira, J. Ramos-Caro and A. Saa
Mon, 10 Oct 16
27/51

Comments: 13 pages, 4 figures; Accepted for publication in Physical Review D

Effects of magnetic and kinetic helicities on the growth of magnetic fields in laminar and turbulent flows by helical-Fourier decomposition [CL]

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http://arxiv.org/abs/1609.01781


We present a numerical and analytical study of incompressible homogeneous conducting fluids using a Fourier-helical representation. We analytically study both small- and large-scale dynamo properties, as well as the inverse cascade of magnetic helicity, in the most general minimal subset of interacting velocity and magnetic fields on a closed Fourier triad. We mainly focus on the dependency of magnetic field growth as a function of the distribution of kinetic and magnetic helicities among the three interacting wavenumbers. By combining direct numerical simulations of the full magnetohydrodynamics (MHD) equations with the Fourier-helical decomposition we numerically confirm that in the kinematic dynamo regime the system develops a large-scale magnetic helicity with opposite sign compared to the small-scale kinetic helicity, a sort of triad-by-triad $\alpha$-effect in Fourier space. Concerning the small-scale perturbations, we predict theoretically and confirm numerically that the largest instability is achived for the magnetic component with the same helicity of the flow, in agreement with the Stretch-Twist-Fold mechanism. Viceversa, in presence of a Lorentz feedback on the velocity, we find that the inverse cascade of magnetic helicity is mostly local if magnetic and kinetic helicities have opposite sign, while it is more non-local and more intense if they have the same sign, as predicted by the analytical approach. Our analytical and numerical results further demonstrate the potential of the helical-Fourier decomposition to elucidate the entangled dynamics of magnetic and kinetic helicities both in fully developed turbulence and in laminar flows.

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M. Linkmann, G. Sahoo, M. McKay, et. al.
Thu, 8 Sep 16
1/60

Comments: N/A

Modelling resonances and orbital chaos in disk galaxies. Application to a Milky Way spiral model [GA]

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http://arxiv.org/abs/1608.08991


Context: Resonances in the stellar orbital motion under perturbations from spiral arms structure play an important role in the evolution of the disks of spiral galaxies. The epicyclic approximation allows the determination of the corresponding resonant radii on the equatorial plane (for nearly circular orbits), but is not suitable in general.
Aims: To expand the study of resonant orbits by analysing stellar motions perturbed by spiral arms with Gaussian-shaped profiles, without any restriction on the stellar orbital configurations, and expand the concept of Lindblad (epicyclic) resonances for orbits with large radial excursions.
Methods: We define a representative plane of initial conditions, which covers the whole phase space of the system. Dynamical maps on representative planes are constructed numerically, in order to characterize the phase-space structure and identify the precise location of the resonances. The study is complemented by the construction of dynamical power spectra, which provide the identification of fundamental oscillatory patterns in the stellar motion.
Results: Our approach allows a precise description of the resonance chains in the whole phase space, giving a broader view of the dynamics of the system when compared to the classical epicyclic approach, even for objects in retrograde motion. The analysis of the solar neighbourhood shows that, depending on the current azimuthal phase of the Sun with respect to the spiral arms, a star with solar kinematic parameters may evolve either inside the stable co-rotation resonance or in a chaotic zone.
Conclusions: Our approach contributes in quantifying the domains of resonant orbits and the degree of chaos in the whole Galactic phase-space structure. It may serve as a starting point to apply these techniques to the investigation of clumps in the distribution of stars in the Galaxy, such as kinematic moving groups.

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T. Michtchenko, R. Vieira, D. Barros, et. al.
Thu, 1 Sep 16
55/74

Comments: 17 pages, 14 figures. Submitted to A&A

Does the Planetary Dynamo Go Cycling On? Re-examining the Evidence for Cycles in Magnetic Reversal Rate [EPA]

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http://arxiv.org/abs/1608.07303


The record of reversals of the geomagnetic field has played an integral role in the development of plate tectonic theory. Statistical analyses of the reversal record are aimed at detailing patterns and linking those patterns to core-mantle processes. The geomagnetic polarity timescale is a dynamic record and new paleomagnetic and geochronologic data provide additional detail. In this paper, we examine the periodicity revealed in the reversal record back to 375 Ma using Fourier analysis. Four significant peaks were found in the reversal power spectra within the 16-40-million-year range. Plotting the function constructed from the sum of the frequencies of the proximal peaks yield a transient 26 Myr periodicity, suggesting chaotic motion with a periodic attractor. The possible 16 Myr periodicity, a previously recognized result, may be correlated with “pulsation” of mantle plumes.

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A. Melott, A. Pivarunas, J. Meert, et. al.
Mon, 29 Aug 16
20/41

Comments: 4 figures. Submitted to Earth and Planetary Science Letters

Detecting Dynamical States from Noisy Time Series using Bicoherence [CL]

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http://arxiv.org/abs/1608.05206


Deriving meaningful information from observational data is often restricted by many limiting factors, the most important of which is the presence of noise. In this work, we present the use of the bicoherence function to extract information about the underlying nonlinearity from noisy time series. We show that a system evolving in the presence of noise which has its dynamical state concealed from quantifiers like the power spectrum and correlation dimension D2, can be revealed using the bicoherence function. We define an index called main peak bicoherence function as the bicoherence associated with the maximal power spectral peak. We show that this index is extremely useful while dealing with quasi-periodic data as it can distinguish strange non chaos from quasi periodicity even with added noise. We demonstrate this in a real world scenario, by taking the bicoherence of variable stars showing period doubling and strange non-chaotic behavior. Our results indicate that bicoherence analysis can also bypass the method of surrogate analysis using Fourier phase randomization, used to differentiate linear stochastic processes from non linear ones, in conventional methods involving measures like D2.

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S. George, G. Ambika and R. Misra
Fri, 19 Aug 16
28/45

Comments: 16 pages, 15 figures, submitted to Nonlinear Dynamics

Jets or vortices – what flows are generated by an inverse turbulent cascade? [CL]

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http://arxiv.org/abs/1608.04628


An inverse cascade – energy transfer to progressively larger scales – is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent flow expected to have the largest available scale and conform with the symmetries of the domain. In a doubly periodic rectangle, the mean flow with zero total momentum was therefore believed to be unidirectional, with two jets along the short side; while for an aspect ratio close to unity, a vortex dipole was expected. Using direct numerical simulations, we show that in fact neither the box symmetry is respected nor the largest scale is realized: the flow is never purely unidirectional since the inverse cascade produces coherent vortices, whose number and relative motion are determined by the aspect ratio. This spontaneous symmetry breaking is closely related to the hierarchy of averaging times. Long-time averaging restores translational invariance due to vortex wandering along one direction, and gives jets whose profile, however, can be deduced neither from the largest-available-scale argument, nor from the often employed maximum-entropy principle or quasi-linear approximation.

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A. Frishman, J. Laurie and G. Falkovich
Wed, 17 Aug 16
6/48

Comments: N/A

Influence of a second satellite on the rotational dynamics of an oblate moon [EPA]

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http://arxiv.org/abs/1607.07333


The gravitational influence of a second satellite on the rotation of an oblate moon is numerically examined. A simplified model, assuming the axis of rotation perpendicular to the (Keplerian) orbit plane, is derived. The differences between the two models, i.e. in the absence and presence of the second satellite, are investigated via bifurcation diagrams and by evolving compact sets of initial conditions in the phase space. It turns out that the presence of another satellite causes some trajectories, that were regular in its absence, to become chaotic. Moreover, the highly structured picture revealed by the bifurcation diagrams in dependence on the eccentricity of the oblate body’s orbit is destroyed when the gravitational influence is included, and the periodicities and critical curves are destroyed as well. For demonstrative purposes, focus is laid on parameters of the Saturn-Titan-Hyperion system, and on oblate satellites on low-eccentric orbits, i.e. $e\approx 0.005$.

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M. Tarnopolski
Tue, 26 Jul 16
39/75

Comments: 19 pages, 9 figures; accepted for publication in Celestial Mechanics and Dynamical Astronomy

Integrability of motion around galactic razor-thin disks [GA]

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http://arxiv.org/abs/1606.06349


We consider the three-dimensional bounded motion of a test particle around razor-thin disk configurations, by focusing on the adiabatic invariance of the vertical action associated with disk-crossing orbits. We find that it leads to an approximate third integral of motion predicting envelopes of the form $Z(R)\propto[\Sigma(R)]^{-1/3}$, where $R$ is the radial galactocentric coordinate, $Z$ is the z-amplitude (vertical amplitude) of the orbit and $\Sigma$ represents the surface mass density of the thin disk. This third integral, which was previously formulated for the case of flattened 3D configurations, is tested for a variety of trajectories in different thin-disk models.

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R. Vieira and J. Ramos-Caro
Wed, 22 Jun 16
1/50

Comments: Version accepted for publication at Celestial Mechanics and Dynamical Astronomy. Replaces arxiv version arxiv:1206.6501. The final publication is available at Springer via this http URL

From order to chaos in Earth satellite orbits [EPA]

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http://arxiv.org/abs/1606.04180


We consider Earth satellite orbits in the range of semi-major axes where the perturbing effects of Earth’s oblateness and lunisolar gravity are of comparable order. This range covers the medium-Earth orbits (MEO) of the Global Navigation Satellite Systems and the geosynchronous orbits (GEO) of the communication satellites. We recall a secular and quadrupolar model, based on the Milankovitch vector formulation of perturbation theory, which governs the long-term orbital evolution subject to the predominant gravitational interactions. We study the global dynamics of this two-and-a-half degrees of freedom Hamiltonian system by means of the fast Lyapunov indicator (FLI), used in a statistical sense. Specifically, we characterize the degree of chaoticity of the action space using angles-averaged normalized FLI maps, thereby overcoming the angle dependencies of the conventional stability maps. Emphasis is placed upon the phase-space structures near secular resonances which are of first importance to the space debris community. We confirm and quantify the transition from order to chaos in MEO, stemming from the critical inclinations, and find that highly inclined GEO orbits are particularly unstable. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors, and, from a mathematical perspective, have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.

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I. Gkolias, J. Daquin, F. Gachet, et. al.
Wed, 15 Jun 16
19/54

Comments: 28 pages, 8 figures. Submitted to AJ. Comments are greatly appreciated

Diffusive chaos in navigation satellites orbits [EPA]

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http://arxiv.org/abs/1606.00106


The navigation satellite constellations in medium-Earth orbit exist in a background of third-body secular resonances stemming from the perturbing gravitational effects of the Moon and the Sun. The resulting chaotic motions, emanating from the overlapping of neighboring resonant harmonics, induce especially strong perturbations on the orbital eccentricity, which can be transported to large values, thereby increasing the collision risk to the constellations and possibly leading to a proliferation of space debris. We show here that this transport is of a diffusive nature and we present representative diffusion maps that are useful in obtaining a global comprehension of the dynamical structure of the navigation satellite orbits.

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J. Daquin, A. Rosengren and K. Tsiganis
Thu, 2 Jun 16
41/60

Comments: 8 pages, 5 figures, conference Chaos, complexity and transport (Marseille, France)

Marginal resonances and intermittent behaviour in the motion in the vicinity of a separatrix [CL]

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http://arxiv.org/abs/1605.08986


A condition upon which sporadic bursts (intermittent behaviour) of the relative energy become possible is derived for the motion in the chaotic layer around the separatrix of non-linear resonance. This is a condition for the existence of a marginal resonance, i.e. a resonance located at the border of the layer. A separatrix map in Chirikov’s form [Chirikov, B. V., Phys. Reports 52, 263 (1979)] is used to describe the motion. In order to provide a straightforward comparison with numeric integrations, the separatrix map is synchronized to the surface of the section farthest from the saddle point. The condition of intermittency is applied to clear out the nature of the phenomenon of bursts of the eccentricity of chaotic asteroidal trajectories in the 3/1 mean motion commensurability with Jupiter. On the basis of the condition, a new intermittent regime of resonant asteroidal motion is predicted and then identified in numeric simulations.

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I. Shevchenko
Tue, 31 May 16
21/70

Comments: 19 pages, 6 figures

On the recurrence and Lyapunov time scales of the motion near the chaos border [CL]

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http://arxiv.org/abs/1605.08765


Conditions for the emergence of a statistical relationship between $T_r$, the chaotic transport (recurrence) time, and $T_L$, the local Lyapunov time (the inverse of the numerically measured largest Lyapunov characteristic exponent), are considered for the motion inside the chaotic layer around the separatrix of a nonlinear resonance. When numerical values of the Lyapunov exponents are measured on a time interval not greater than $T_r$, the relationship is shown to resemble the quadratic one. This tentatively explains numerical results presented in the literature.

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I. Shevchenko
Mon, 30 May 16
32/36

Comments: 16 pages, 2 figures

Supersymmetric Theory of Stochastic ABC Model: A Numerical Study [CL]

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http://arxiv.org/abs/1604.08609


In this paper, we investigate numerically the stochastic ABC model, a toy model in the theory of astrophysical kinematic dynamos, within the recently proposed supersymmetric theory of stochastics (STS). STS characterises stochastic differential equations (SDEs) by the spectrum of the stochastic evolution operator (SEO) on elements of the exterior algebra or differentials forms over the system’s phase space, X. STS can thereby classify SDEs as chaotic or non-chaotic by identifying the phenomenon of stochastic chaos with the spontaneously broken topological supersymmetry that all SDEs possess. We demonstrate the following three properties of the SEO, deduced previously analytically and from physical arguments: the SEO spectra for zeroth and top degree forms never break topological supersymmetry, all SDEs possesses pseudo-time-reversal symmetry, and each de Rahm cohomology class provides one supersymmetric eigenstate. Our results also suggests that the SEO spectra for forms of complementary degrees, i.e., k and dim X -k, may be isospectral.

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I. Ovchinnikov, Y. Sun, T. Ensslin, et. al.
Mon, 2 May 16
39/49

Comments: Revtex 4-1, 9 pages, 3 figures

Multiple Bifurcations in the Periodic Orbit around Eros [EPA]

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http://arxiv.org/abs/1604.07226


We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are studied. Multiple bifurcations in periodic orbit families consist of four kinds of basic bifurcations. We found both binary period-doubling bifurcations and binary tangent bifurcations in periodic orbit families around asteroid 433 Eros. The periodic orbit family with binary period-doubling bifurcations is nearly circular, with almost zero inclination, and is reversed relative to the body of the asteroid 433 Eros. This implies that there are two stable regions separated by one unstable region for the motion around this asteroid. In addition, we found triple bifurcations which consist of two real saddle bifurcations and one period-doubling bifurcation. A periodic orbit family generated from an equilibrium point of asteroid 433 Eros has five bifurcations, which are one real saddle bifurcation, two tangent bifurcations, and two period-doubling bifurcations.

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Y. Ni, Y. Jiang and H. Baoyin
Tue, 26 Apr 16
47/61

Comments: 36pages, 12 figures

Escape dynamics and fractal basins boundaries in the three-dimensional Earth-Moon system [EPA]

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http://arxiv.org/abs/1604.03403


The orbital dynamics of a spacecraft, or a comet, or an asteroid in the Earth-Moon system in a scattering region around the Moon using the three dimensional version of the circular restricted three-body problem is numerically investigated. The test particle can move in bounded orbits around the Moon or escape through the openings around the Lagrange points $L_1$ and $L_2$ or even collide with the surface of the Moon. We explore in detail the first four of the five possible Hill’s regions configurations depending on the value of the Jacobi constant which is of course related with the total orbital energy. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of orbits in several two-dimensional types of planes and distinguishing between four types of motion: (i) ordered bounded, (ii) trapped chaotic, (iii) escaping and (iv) collisional. In particular, we locate the different basins and we relate them with the corresponding spatial distributions of the escape and collision times. Our outcomes reveal the high complexity of this planetary system. Furthermore, the numerical analysis suggests a strong dependence of the properties of the considered basins with both the total orbital energy and the initial value of the $z$ coordinate, with a remarkable presence of fractal basin boundaries along all the regimes. Our results are compared with earlier ones regarding the planar version of the Earth-Moon system.

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E. Zotos
Wed, 13 Apr 16
7/60

Comments: Published in Astrophysics and Space Science (A&SS) journal. arXiv admin note: text overlap with arXiv:1512.08683, arXiv:1508.05201

Orbital and escape dynamics in barred galaxies – I. The 2D system [GA]

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http://arxiv.org/abs/1604.03412


In this paper we use the two-dimensional (2D) version of a new analytical gravitational model in order to explore the orbital as well as the escape dynamics of the stars in a barred galaxy composed of a spherically symmetric central nucleus, a bar, a flat disk and a dark matter halo component. A thorough numerical investigation is conducted for distinguishing between bounded and escaping motion. Furthermore bounded orbits are further classified into non-escaping regular and trapped chaotic using the Smaller ALingment Index (SALI) method. Our aim is to determine the basins of escape through the two symmetrical escape channels around the Lagrange points $L_2$ and $L_3$ and also to relate them with the corresponding distribution of the escape rates of the orbits. We integrate initial conditions of orbits in several types of planes so as to obtain a more complete view of the overall orbital properties of the dynamical system. We also present evidence that the unstable manifolds which guide the orbits in and out the interior region are directly related with the formation of spiral and ring stellar structures observed in barred galaxies. In particular, we examine how the bar’s semi-major axis determines the resulting morphologies. Our numerical simulations indicate that weak barred structures favour the formation of $R_1$ rings or $R_1’$ pseudo-rings, while strong bars on the other hand, give rise to $R_1R_2$ and open spiral morphologies. Our results are compared with earlier related work. The escape dynamics and the properties of the manifolds of the full three-dimensional (3D) galactic system will be given in an accompanying paper.

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C. Jung and E. Zotos
Wed, 13 Apr 16
19/60

Comments: Published in Monthly Notices of the Royal Astronomical Society (MNRAS) journal

Binary black hole shadows, chaotic scattering and the Cantor set [CL]

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http://arxiv.org/abs/1603.04469


We investigate the qualitative features of binary black hole shadows using the model of two extremally charged black holes in static equilibrium (a Majumdar–Papapetrou solution). Our perspective is that binary spacetimes are natural exemplars of chaotic scattering, because they admit more than one fundamental null orbit, and thus an uncountably-infinite set of perpetual null orbits which generate scattering singularities in initial data. Inspired by the three-disc model, we develop an appropriate symbolic dynamics to describe planar null geodesics on the double black hole spacetime. We show that a one-dimensional (1D) black hole shadow may constructed through an iterative procedure akin to the construction of the Cantor set; thus the 1D shadow is self-similar. Next, we study non-planar rays, to understand how angular momentum affects the existence and properties of the fundamental null orbits. Taking slices through 2D shadows, we observe three types of 1D shadow: regular, Cantor-like, and highly chaotic. The switch from Cantor-like to regular occurs where outer fundamental orbits are forbidden by angular momentum. The highly chaotic part is associated with an unexpected feature: stable and bounded null orbits, which exist around two black holes of equal mass $M$ separated by $a_1 < a < \sqrt{2} a_1$, where $a_1 = 4M/\sqrt{27}$. To show how this possibility arises, we define a certain potential function and classify its stationary points. We conjecture that the highly chaotic parts of the 2D shadow possess the Wada property. Finally, we consider the possibility of following null geodesics through event horizons, and chaos in the maximally-extended spacetime.

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J. Shipley and S. Dolan
Mon, 4 Apr 16
21/61

Comments: 35 pages, 20 figures

Chaotic Emission from Electromagnetic Systems Considering Self-Interaction [CL]

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http://arxiv.org/abs/0604204


The emission of electromagnetic waves from a system described by the H\’enon-Heiles potential is studied in this work. The main aim being to analyze the behavior of the system when the damping term is included explicitly into the equations of motion. Energy losses at the chaotic regime and at the regular regime are compared. The results obtained here are similar to the case of gravitational waves emission, as long we consider only the energy loss. The main difference being that in the present work the energy emitted is explicitly calculated solving the equation of motion without further approximations. It is expected that the present analysis may be useful when studying the analogous problem of dissipation in gravitational systems.

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F. Kokubun and V. Zanchin
Thu, 31 Mar 16
28/53

Comments: Typos in Refs. corrected. Other minor changes

Key Issues Review: Numerical studies of turbulence in stars [SSA]

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http://arxiv.org/abs/1603.05569


The numerical simulation of turbulence in stars has led to a rich set of possibilities regarding stellar pulsations, asteroseismology, thermonuclear yields, and formation of neutron stars and black holes. The breaking of symmetry by turbulent flow grows in amplitude as collapse is approached, which insures that the conditions at the onset of collapse are not spherical. This lack of spherical symmetry has important implications for the mechanism of explosion and ejected nucleosynthesis products. Numerical resolution of several different types of three–dimensional (3D) stellar simulations are compared; it is suggested that core collapse simulations may be under-resolved.
New physical effects which appear in 3D are summarized.
Connections between simulations of progenitor explosion and observations of supernova remnants (SNR) are discussed.
Present treatment of boundaries, for mixing regions during He–burning, requires revision.

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W. Arnett and C. Meakin
Fri, 18 Mar 16
53/53

Comments: 8 pages, 1 figure, 1 table, submitted to Reports on Progress in Physics

Chaotic motion and the evolution of morphological components in a time-dependent model of a barred galaxy within a dark matter halo [GA]

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http://arxiv.org/abs/1603.02294


Studies of dynamical stability (chaotic versus regular motion) in galactic dynamics often rely on static analytical models of the total gravitational potential. Potentials based upon self-consistent N-body simulations offer more realistic models, fully incorporating the time-dependent nature of the systems. Here we aim at analysing the fractions of chaotic motion within different morphological components of the galaxy. We wish to investigate how the presence of chaotic orbits evolves with time, and how their spatial distribution is associated with morphological features of the galaxy. We employ a time-dependent analytical potential model that was derived from an N-body simulation of a strongly barred galaxy. With this analytical potential we may follow the dynamical evolution of ensembles of orbits. Using the Generalized Alignment Index (GALI) chaos detection method, we study the fraction of chaotic orbits, sampling the dynamics of both the stellar disc and of the dark matter halo. Within the stellar disc, the global trend is for chaotic motion to decrease in time, specially in the region of the bar. We scrutinized the different changes of regime during the evolution (orbits that are permanently chaotic, permanently regular, those that begin regular and end chaotic, and those that begin chaotic and end regular), tracing the types of orbits back to their common origins. Within the dark matter halo, chaotic motion also decreases globally in time. The inner halo (r < 5 kpc) is where most chaotic orbits are found and it is the only region where chaotic orbits outnumber regular orbits, in the early evolution.

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R. Machado and T. Manos
Wed, 9 Mar 16
44/71

Comments: 15 pages, 10 figures, accepted for publication in MNRAS

Electromagnetic radiation of charged particles in stochastic motion [HEAP]

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http://arxiv.org/abs/1603.01750


The study of the Brownian motion of a charged particle in electric and magnetic fields fields has many important applications in plasma and heavy ions physics, as well as in astrophysics. In the present paper we consider the electromagnetic radiation properties of a charged non-relativistic particle in the presence of electric and magnetic fields, of an exterior non-electromagnetic potential, and of a friction and stochastic force, respectively. We describe the motion of the charged particle by a Langevin and generalized Langevin type stochastic differential equation. We investigate in detail the cases of the Brownian motion with or without memory in a constant electric field, in the presence of an external harmonic potential, and of a constant magnetic field. In all cases the corresponding Langevin equations are solved numerically, and a full description of the spectrum of the emitted radiation and of the physical properties of the motion is obtained. The Power Spectral Density (PSD) of the emitted power is also obtained for each case, and, for all considered oscillating systems, it shows the presence of peaks, corresponding to certain intervals of the frequency.

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T. Harko and G. Mocanu
Tue, 8 Mar 16
8/83

Comments: 24 pages, 22 figures, accepted for publication in EPJC

Turbulence and distributed chaos with spontaneously broken symmetry [CL]

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http://arxiv.org/abs/1601.07364


It is shown that in turbulent flows the distributed chaos with spontaneously broken translational space symmetry (homogeneity) has a stretch exponential spectrum $\exp-(k/k_{\beta})^{\beta }$ with $\beta =1/2$. Good agreement has been established between the theory and the data of direct numerical simulation of a channel flow. An astrophysical application to the large-scale galaxies distribution has been briefly discussed and good agreement with the data of recent Sloan Digital Sky Survey SDSS-III has been established.

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A. Bershadskii
Mon, 1 Feb 16
42/42

Comments: N/A

Pressure-anisotropy-driven microturbulence and magnetic-field evolution in shearing, collisionless plasma [HEAP]

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http://arxiv.org/abs/1512.08131


The nonlinear state of a high-beta collisionless plasma is investigated when an imposed linear shear amplifies or diminishes a uniform magnetic field, driving pressure anisotropies and hence firehose/mirror instabilities. The evolution of the resulting microscale turbulence is considered when the shear is switched off or reversed after one shear time (mimicking local behaviour of a macroscopic flow), so a new macroscale configuration is superimposed on the microscale state left behind by the previous one. There is a threshold value of plasma beta: when $\beta\ll\Omega/S$ (ion cyclotron frequency/shear rate), the emergence of firehose/mirror fluctuations driven unstable by shear and their disappearance when the shear is removed/reversed are quasi-instantaneous compared to the shear time, viz., the decay time of these fluctuations is $\sim\beta/\Omega \ll 1/S$ (this result follows from the free decay of the fluctuations being constrained by the same marginal-stability thresholds as their growth). In contrast, when $\beta\gtrsim\Omega/S$ (“ultra-high” beta), the old microscale state can only be removed on the shear timescale. In this regime, driven firehose fluctuations grow secularly to order-unity amplitudes, compensating for the decay of the mean field and so pinning pressure anisotropy at marginal stability with no appreciable scattering of particles—which is unlike what happens at moderate $\beta$. When the shear reverses, the shearing away of this firehose turbulence compensates for the increase in the mean field and thus prevents growth of the pressure anisotropy, stopping the system from going mirror-unstable. Therefore, at ultra-high beta, the system stays close to the firehose threshold, the mirror instability is largely suppressed, while the mean magnetic energy barely changes at all. Implications for plasma dynamo and thus the origin of cosmic magnetism are discussed.

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S. Melville, A. Schekochihin and M. Kunz
Tue, 29 Dec 15
32/54

Comments: MNRAS-style latex, 21 pages, 37 figures, submitted to MNRAS

Kinematic Dynamo, Supersymmetry Breaking, and Chaos [GA]

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http://arxiv.org/abs/1512.01651


The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an important model system for understanding astrophysical magnetism. Here, the mathematical correspondence between the KD and a specific stochastic differential equation (SDE) viewed from the perspective of the supersymmetric theory of stochastics (STS) is discussed. The STS is a novel, approximation-free framework to investigate SDEs. The correspondence reported here permits insights from the STS to be applied to the theory of KD and vice versa. It was previously known that the fast KD in the idealistic limit of no magnetic diffusion requires chaotic flows. The KD-STS correspondence shows that this is also true for the diffusive KD. From the STS perspective, the KD possesses a topological supersymmetry and the dynamo effect can be viewed as its spontaneous breakdown. This supersymmetry breaking can be regarded as the stochastic generalization of the concept of dynamical chaos. As this supersymmetry breaking happens in both the diffusive and the non-diffusive case, the necessity of the underlying SDE being chaotic is given in either case. The observed exponentially growing and oscillating KD modes prove physically that dynamical spectra of the STS evolution operator that break the topological supersymmetry exist with both, real and complex ground state eigenvalues. Finally, we comment on the non-existence of dynamos for scalar quantities.

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I. Ovchinnikov and T. Ensslin
Tue, 8 Dec 15
25/71

Comments: 10 pages, 1 figure, submitted

Bifurcation sequences in the symmetric 1:1 Hamiltonian resonance [CL]

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http://arxiv.org/abs/1512.00707


We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under $Z_2 \times Z_2$ symmetry. The rich structure of these classical systems is investigated with geometric methods and the relation with the singularity theory approach is also highlighted. The geometric approach is the most straightforward way to obtain a general picture of the phase-space dynamics of the family as is defined by a complete subset in the space of control parameters complying with the symmetry constraint. It is shown how to find an energy-momentum map describing the phase space structure of each member of the family, a catastrophe map that captures its global features and formal expressions for action-angle variables. Several examples, mainly taken from astrodynamics, are used as applications.

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A. Marchesiello and G. Pucacco
Thu, 3 Dec 15
65/65

Comments: 36 pages, 10 figures, accepted on International Journal of Bifurcation and Chaos. arXiv admin note: substantial text overlap with arXiv:1401.2855

Passive scalar mixing at finite correlation times and the Batchelor spectrum [CL]

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http://arxiv.org/abs/1511.08206


An elegant model for passive scalar mixing was given by Kraichnan (1968) assuming the velocity to be delta-correlated in time. For realistic random flows this assumption becomes invalid. We generalize the Kraichnan model to include the effects of a finite correlation time, $\tau$, using renewing flows. The generalized evolution equation for the 3-D passive scalar spectrum $\hat{M}(k,t)$ or its correlation function $M(r,t)$, gives the Kraichnan equation when $\tau \to 0$, and extends it to the next order in $\tau$. It involves third and fourth order derivatives of $M$ or $\hat{M}$ (in the high $k$ limit). For small-$\tau$ (or small Strouhl number), it can be recast using the Landau-Lifshitz approach, to one with at most second derivatives of $\hat{M}$. We present both a scaling solution to this equation neglecting diffusion and a more exact solution including diffusive effects. Interestingly, to leading order in $\tau$, we show that the steady state 1-D passive scalar spectrum, preserves the Batchelor (1959) form, $E_\theta(k) \propto k^{-1}$, in the viscous-convective limit, independent of $\tau$. When passive scalar fluctuations decay, we show that the decay rate is reduced for finite $\tau$, but the spectrum $E_\theta(k) \propto k^{1/2}$ independent of $\tau$ . We also present results from high resolution ($1024^3$) direct numerical simulations of passive scalar mixing. We find reasonable agreement with predictions of the Batchelor spectrum, during steady state. The scalar spectrum during decay is however shallower than what theory predicts, a feature which remains intriguing.

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A. Aiyer, K. Subramanian and P. Bhat
Mon, 30 Nov 15
44/78

Comments: 20 pages, 2 figures, Submitted to JFM

Order and chaos in a three dimensional galaxy model [GA]

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http://arxiv.org/abs/1511.04872


We explore the orbital dynamics of a realistic three dimensional model describing the properties of a disk galaxy with a spherically symmetric central dense nucleus and a triaxial dark matter halo component. Regions of phase space with regular and chaotic motion are identified depending on the parameter values for triaxiality of the dark matter halo and for breaking the rotational symmetry. The four dimensional Poincar\’e map of the three degrees of freedom system is analyzed by a study of its restriction to various two dimensional invariant subsets of its domain.

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C. Jung and E. Zotos
Tue, 17 Nov 15
33/87

Comments: Published in Mechanics Research Communications (MRC) journal

Simple nonlinear models suggest variable star universality [SSA]

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http://arxiv.org/abs/1510.04719


Dramatically improved data from observatories like the CoRoT and Kepler spacecraft have recently facilitated nonlinear time series analysis and phenomenological modeling of variable stars, including the search for strange (aka fractal) or chaotic dynamics. We recently argued [Lindner et al., Phys. Rev. Lett. 114 (2015) 054101] that the Kepler data includes “golden” stars, whose luminosities vary quasiperiodically with two frequencies nearly in the golden ratio, and whose secondary frequencies exhibit power-law scaling with exponent near -1.5, suggesting strange nonchaotic dynamics and singular spectra. Here we use a series of phenomenological models to make plausible the connection between golden stars and fractal spectra. We thereby suggest that at least some features of variable star dynamics reflect universal nonlinear phenomena common to even simple systems.

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J. Lindner, V. Kohar, B. Kia, et. al.
Mon, 19 Oct 15
17/44

Comments: 9 pages, 9 figures, accepted for publication in Physica D

Effect of data gaps on correlation dimension computed from light curves of variable stars [IMA]

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http://arxiv.org/abs/1410.4454


Observational data, especially astrophysical data, is often limited by gaps in data that arises due to lack of observations for a variety of reasons. Such inadvertent gaps are usually smoothed over using interpolation techniques. However the smoothing techniques can introduce artificial effects, especially when non-linear analysis is undertaken. We investigate how gaps can affect the computed values of correlation dimension of the system, without using any interpolation. For this we introduce gaps artificially in synthetic data derived from standard chaotic systems, like the R{\”o}ssler and Lorenz, with frequency of occurrence and size of missing data drawn from two Gaussian distributions. Then we study the changes in correlation dimension with change in the distributions of position and size of gaps. We find that for a considerable range of mean gap frequency and size, the value of correlation dimension is not significantly affected, indicating that in such specific cases, the calculated values can still be reliable and acceptable. Thus our study introduces a method of checking the reliability of computed correlation dimension values by calculating the distribution of gaps with respect to its size and position. This is illustrated for the data from light curves of three variable stars, R Scuti, U Monocerotis and SU Tauri. We also demonstrate how a cubic spline interpolation can cause a time series of Gaussian noise with missing data to be misinterpreted as being chaotic in origin. This is demonstrated for the non chaotic light curve of variable star SS Cygni, which gives a saturated D$_{2}$ value, when interpolated using a cubic spline. In addition we also find that a careful choice of binning, in addition to reducing noise, can help in shifting the gap distribution to the reliable range for D$_2$ values.

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S. George, G. Ambika and R. Misra
Tue, 13 Oct 15
63/64

Comments: 13 pages, 15 figures

Chaotic features of the last scattering in CMB spectrum [CL]

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http://arxiv.org/abs/1510.01909


It is shown, using the data obtained by the Planck space telescope (2009-2013), that the angular CMB Doppler spectrum: $C_l \sim \exp-(l/l_c)$, with $l_c \simeq 300$ in the interval $370 < l < 2500$. The waviness observed along the exponential decay has period (distance between peaks) equal to the same $l_c \simeq 300$. It means that the waviness is generated by the same, presumably chaotic, mechanism that generates the exponential decay. Comparison with deterministic chaos simulations has been briefly discussed.

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A. Bershadskii
Fri, 9 Oct 15
7/61

Comments: N/A

On geodesic dynamics in deformed black-hole fields [CL]

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http://arxiv.org/abs/1509.08536


“Almost all” seems to be known about isolated stationary black holes in asymptotically flat space-times and about the behaviour of {\em test} matter and fields in their backgrounds. The black holes likely present in galactic nuclei and in some X-ray binaries are commonly being represented by the Kerr metric, but actually they are not isolated (they are detected only thanks to a strong interaction with the surroundings), they are not stationary (black-hole sources are rather strongly variable) and they also probably do not live in an asymptotically flat universe. Such “perturbations” may query the classical black-hole theorems (how robust are the latter against them?) and certainly affect particles and fields around, which can have observational consequences. In the present contribution we examine how the geodesic structure of the static and axially symmetric black-hole space-time responds to the presence of an additional matter in the form of a thin disc or ring. We use several different methods to show that geodesic motion may become chaotic, to reveal the strength and type of this irregularity and its dependence on parameters. The relevance of such an analysis for galactic nuclei is briefly commented on.

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O. Semerak and P. Sukova
Wed, 30 Sep 15
61/71

Comments: 32 pages, 9 figures

Fractal structures for the Jacobi Hamiltonian of restricted three-body problem [EPA]

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http://arxiv.org/abs/1509.07638


We study the dynamical chaos and integrable motion in the planar circular restricted three-body problem and determine the fractal dimension of the spiral strange repeller set of non-escaping orbits at different values of mass ratio of binary bodies and of Jacobi integral of motion. We find that the spiral fractal structure of the Poincar\’e section leads to a spiral density distribution of particles remaining in the system. We also show that the initial exponential drop of survival probability with time is followed by the algebraic decay related to the universal algebraic statistics of Poincar\’e recurrences in generic symplectic maps.

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G. Rollin, J. Lages and D. Shepelyansky
Mon, 28 Sep 15
40/67

Comments: 9 pages, 12 figures

Time Series with Tailored Nonlinearities [CL]

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http://arxiv.org/abs/1509.00223


It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncor- related Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for e.g. turbulence and financial data can thus be explained in terms of phase correlations.

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C. Raeth and I. Laut
Wed, 2 Sep 15
72/87

Comments: 5 pages, 5 figures, Phys. Rev. E, Rapid Communication, accepted

Practical application of KAM theory to galactic dynamics: II. Application to weakly chaotic orbits in barred galaxies [GA]

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http://arxiv.org/abs/1508.05959


Owing to the pioneering work of Contopoulos, a strongly barred galaxy is known to have irregular orbits in the vicinity of the bar. By definition, irregular orbits can not be represented by action-angle tori everywhere in phase space. This thwarts perturbation theory and complicates our understanding of their role in galaxy structure and evolution. This paper provides a qualitative introduction to a new method based on KAM theory for investigating the morphology of regular and irregular orbits based on direct computation of tori described in Paper 1 and applies it to a galaxy disc bar. Using this method, we find that much of the phase space inside of the bar radius becomes chaotic for strong bars, excepting a small region in phase space between the ILR and corotation resonances for orbits of moderate ellipticity. This helps explain the preponderance of moderately eccentric bar-supporting orbits as the bar strength increases. This also suggests that bar strength may be limited by chaos! The chaos results from stochastic layers that form around primary resonances owing to separatrix splitting. Most investigations of orbit regularity are performed using numerical computation of Lyapunov exponents or related indices. We show that Lyapunov exponents poorly diagnose the degree of stochasticity in this problem; the island structure in the stochastic sheaths allow orbit to change morphology while presenting anomalously small Lyapunov exponent values (i.e. weak chaos). For example, a weakly chaotic orbit may appear to change its morphology spontaneously, while appearing regular except during the change itself. The numerical KAM approach sensitively detects these dynamics and provides a model Hamiltonian for further investigation. It may underpredict the number of broken tori for strong perturbations.

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M. Weinberg
Wed, 26 Aug 15
2/62

Comments: 17 pages, 12 figures

Helical mode interactions and spectral transfer processes in magnetohydrodynamic turbulence [CL]

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http://arxiv.org/abs/1508.05528


Spectral transfer processes in magnetohydrodynamic (MHD) turbulence are investigated analytically by decomposition of the velocity and magnetic fields in Fourier space into helical modes. Steady solutions of the dynamical system which governs the evolution of the helical modes are determined, and a stability analysis of these solutions is carried out. The interpretation of the analysis is that unstable solutions lead to energy transfer between the interacting modes while stable solutions do not. From this, a dependence of possible interscale energy and helicity transfers on the helicities of the interacting modes is derived. As expected from the inverse cascade of magnetic helicity in 3D MHD turbulence, mode interactions with like helicities lead to transfer of energy and magnetic helicity to smaller wavenumbers. However, some interactions of modes with unlike helicities also contribute to an inverse energy transfer. As such, an inverse energy cascade for nonhelical magnetic fields is shown to be possible. Furthermore, it is found that high values of the cross-helicity may have an asymmetric effect on forward and reverse transfer of energy, where forward transfer is more quenched in regions of high cross-helicity than reverse transfer. This conforms with recent observations of solar wind turbulence. For specific helical interactions the relation to dynamo action is established.

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M. Linkmann, A. Berera, M. McKay, et. al.
Tue, 25 Aug 15
66/69

Comments: 34 pages including references, 4 figures

Comparing the escape dynamics in tidally limited star cluster models [GA]

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http://arxiv.org/abs/1508.05198


The aim of this work is to compare the orbital dynamics in three different models describing the properties of a star cluster rotating around its parent galaxy in a circular orbit. In particular, we use the isochrone and the Hernquist potentials to model the spherically symmetric star cluster and we compare our results with the corresponding ones of a previous work in which the Plummer model was applied for the same purpose. Our analysis takes place both in the configuration $(x,y)$ and in the phase $(x,\dot{x})$ space in order to elucidate the escape process as well as the overall orbital properties of the tidally limited star cluster. We restrict our investigation into two dimensions and we conduct a thorough numerical analysis distinguishing between ordered and chaotic orbits as well as between trapped and escaping orbits, considering only unbounded motion for several energy levels above the critical escape energy. It is of particular interest to determine the escape basins towards the two exit channels (near the Lagrangian points $L_1$ and $L_2$) and relate them with the corresponding escape times of the orbits.

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E. Zotos
Mon, 24 Aug 15
39/43

Comments: Published in MNRAS journal. arXiv admin note: substantial text overlap with arXiv:1411.4864, arXiv:1505.03968, arXiv:1505.03847

Chaos in Terrestrial Planet Formation [EPA]

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http://arxiv.org/abs/1508.00917


Terrestrial planets are thought to be the result of a vast number of gravitational interactions and collisions between smaller bodies. We use numerical simulations to show that practically identical initial conditions result in a wide array of final planetary configurations. This highly chaotic behaviour questions the predictability of different scenarios for the formation and evolution of our solar system and planetary systems in general. However, multiple realisations of the same initial conditions can be used to predict certain global statistics. We present two sets of numerical experiments that quantify this behaviour. Firstly, we demonstrate that simulations with slightly displaced particles are completely divergent after ~500 years, irrespective of initial displacement, particle number, and code accuracy. If a single planetesimal is moved by less than one millimetre, then a different set of planets results — this timescale for chaotic divergence decreases with increasing particle number. Secondly, we show final planetary configurations of initially similar simulations with and without giant planets after evolving them for ~148 Myr. We find that the same simulations including giant planets tend to generate higher mass planets at lower semi-major axes than simulations without gas giants. This prediction can be tested with forthcoming observational programs. By extracting outliers in the observations, we cautiously predict that Kepler-10, Kepler-9, 61 Vir, HD 134060, and HD 51608 may host as yet undetected giant planets.

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V. Hoffmann, S. Grimm, B. Moore, et. al.
Thu, 6 Aug 15
48/48

Comments: 17 pages, 15 figures, submitted to MNRAS, simulation outputs available at this https URL

On the relevance of chaos for halo stars in the Solar Neighbourhood [GA]

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http://arxiv.org/abs/1508.00579


We show that diffusion due to chaotic mixing in the Neighbourhood of the Sun may not be as relevant as previously suggested in erasing phase space signatures of past Galactic accretion events. For this purpose, we analyse Solar Neighbourhood-like volumes extracted from cosmological simulations that naturally account for chaotic orbital behaviour induced by the strongly triaxial and cuspy shape of the resulting dark matter haloes, among other factors. In the approximation of an analytical static triaxial model, our results show that a large fraction of stellar halo particles in such local volumes have chaos onset times (i.e., the timescale at which stars commonly associated with chaotic orbits will exhibit their chaotic behaviour) significantly larger than a Hubble time. Furthermore, particles that do present a chaotic behaviour within a Hubble time do not exhibit significant diffusion in phase space.

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N. Maffione, F. Gomez, P. Cincotta, et. al.
Wed, 5 Aug 15
46/46

Comments: 20 pages, 16 figures. Accepted for publication in MNRAS

Anomalous scaling in magnetohydrodynamic turbulence: Effects of anisotropy and compressibility in the kinematic approximation [CL]

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http://arxiv.org/abs/1507.08516


The field theoretic renormalization group and the operator product expansion are applied to the model of passive vector (magnetic) field advected by a random turbulent velocity field. The latter is governed by the Navier–Stokes equation for compressible fluid, subject to external random force with the covariance $\propto \delta(t-t’) k^{4-d-y}$, where $d$ is the dimension of space and $y$ is an arbitrary exponent. From physics viewpoints, the model describes magnetohydrodynamic turbulence in the so-called kinematic approximation, where the effects of the magnetic field on the dynamics of the fluid are neglected. The original stochastic problem is reformulated as a multiplicatively renormalizable field theoretic model; the corresponding renormalization group equations possess an infrared attractive fixed point. It is shown that various correlation functions of the magnetic field and its powers demonstrate anomalous scaling behavior in the inertial-convective range already for small values of~$y$. The corresponding anomalous exponents, identified with scaling (critical) dimensions of certain composite fields (“operators” in the quantum-field terminology), can be systematically calculated as series in $y$. The practical calculation is performed in the leading one-loop approximation, including exponents in anisotropic contributions. It should be emphasized that, in contrast to Gaussian ensembles with finite correlation time, the model and the perturbation theory presented here are manifestly Galilean covariant.

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N. Antonov and M. Kostenko
Fri, 31 Jul 15
14/59

Comments: 14 pages, LaTeX source, two EPS figures. arXiv admin note: text overlap with arXiv:1410.1262