Tag Archives: Chaotic Dynamics

On mean elements in artificial satellite theory [CL]

Posted on by

http://arxiv.org/abs/2305.09303


The merits of a perturbation theory based on a mean to osculating transformation that is pure periodic in the fast angle are investigated. The exact separation of the purely short-period effects of the perturbed Keplerian dynamics from the long-period mean frequencies is achieved by a non-canonical transformation, which, therefore, cannot be computed by Hamiltonian methods. For this case, the evolution of the mean elements strictly adheres to the average behavior of the osculating orbit. However, due to the inescapable truncation of perturbation solutions, the fact that this theory confines the long-period variations of the semimajor axis into the mean variation equations, how tiny they may be, can have adverse effects in the accuracy of long-term semi-analytic propagations based on it

Read this paper on arXiv…

M. Lara
Wed, 17 May 23
64/67

Comments: 26 pages, 6 figures, 2 Tables, submitted to Celestial Mechanics and Dynamical Astronomy

Extreme-mass-ratio inspirals into rotating boson stars: nonintegrability, chaos, and transient resonances [CL]

Posted on by

http://arxiv.org/abs/2305.05691


General relativity predicts that black holes are described by the Kerr metric, which has integrable geodesics. This property is crucial to produce accurate waveforms from extreme-mass-ratio inspirals. Astrophysical environments, modifications of gravity and new fundamental fields may lead to nonintegrable geodesics, inducing chaotic effects. We study geodesics around self-interacting rotating boson stars and find robust evidence of nonintegrability and chaos. We identify islands of stability around resonant orbits, where the orbital radial and polar oscillation frequency ratios, known as rotation numbers, remain constant throughout the island. These islands are generically present both in the exterior and the interior of compact boson stars. A monotonicity change of rotation curves takes place as orbits travel from the exterior to the interior of the star. Therefore, configurations with neutron-star-like compactness can support degenerate resonant islands. This anomaly is reported here for the first time and it is not present in black holes. Such configurations can also support extremely prolonged resonant islands that span from the exterior to the interior of the star and are shielded by thick chaotic layers. We adiabatically evolve inspirals using approximated post-Newtonian fluxes and find time-dependent plateaus in the rotation curves which are associated with island-crossing orbits. Crossings of external islands give rise to typical gravitational-wave glitches found in non-Kerr objects. Furthermore, when an inspiral is traversing an internal island that is surrounded by a thick chaotic layer, a new type of simultaneous multifrequency glitch occurs that may be detectable with space interferometers such as LISA, and can serve as evidence of an extreme-mass-ratio inspiral around a supermassive boson star.

Read this paper on arXiv…

K. Destounis, F. Angeloni, M. Vaglio, et. al.
Thu, 11 May 23
28/55

Comments: 22 pages, 17 figures, higher resolution plots available upon request

Timescales of Chaos in the Inner Solar System: Lyapunov Spectrum and Quasi-integrals of Motion [EPA]

Posted on by

http://arxiv.org/abs/2305.01683


Numerical integrations of the Solar System reveal a remarkable stability of the orbits of the inner planets over billions of years, in spite of their chaotic variations characterized by a Lyapunov time of only 5 million years and the lack of integrals of motion able to constrain their dynamics. To open a window on such long-term behavior, we compute the entire Lyapunov spectrum of a forced secular model of the inner planets. We uncover a hierarchy of characteristic exponents that spans two orders of magnitude, manifesting a slow-fast dynamics with a broad separation of timescales. A systematic analysis of the Fourier harmonics of the Hamiltonian, based on computer algebra, reveals three symmetries that characterize the strongest resonances responsible for the orbital chaos. These symmetries are broken only by weak resonances, leading to the existence of quasi-integrals of motion that are shown to relate to the smallest Lyapunov exponents. A principal component analysis of the orbital solutions independently confirms that the quasi-integrals are among the slowest degrees of freedom of the dynamics. Strong evidence emerges that they effectively constrain the chaotic diffusion of the orbits, playing a crucial role in the statistical stability over the Solar System lifetime.

Read this paper on arXiv…

F. Mogavero, N. Hoang and J. Laskar
Thu, 4 May 23
34/60

Comments: 24 pages, 11 figures. Published in Physical Review X

Performance of chaos diagnostics based on Lagrangian descriptors. Application to the 4D standard map [EPA]

Posted on by

http://arxiv.org/abs/2305.00978


We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD) computations of initially nearby orbits to detect chaos in conservative dynamical systems with phase space dimensionality higher than two. In particular, we consider the recently introduced methods of the difference ($D_L^n$) and the ratio ($R_L^n$) of the LDs of neighboring orbits, as well as a quantity ($S_L^n$) related to the finite-difference second spatial derivative of the LDs, and use them to determine the chaotic or regular nature of ensembles of orbits of a prototypical area-preserving map model, the 4-dimensional (4D) symplectic standard map. Using the distributions of the indices’ values we determine appropriate thresholds to discriminate between regular and chaotic orbits, and compare the obtained characterization against that achieved by the Smaller Alignment Index (SALI) method of chaos detection, by recording the percentage agreement $P_A$ between the two classifications. We study the influence of various factors on the performance of these indices, and show that the increase of the final number of orbit iterations T and the order n of the indices (i.e. the dimensionality of the space where the considered nearby orbits lie), as well as the decrease of the distance $\sigma$ of neighboring orbits, increase the $P_A$ values along with the required computational effort. Balancing between these two factors we find appropriate T, n and $\sigma$ values, which allow the efficient use of the $D_L^n$, $R_L^n$ and $S_L^n$ indices as short time and computationally cheap chaos diagnostics achieving $P_A \gtrsim 90 \%$, with $D_L^n$ and $S_L^n$ having larger $P_A$ values than $R_L^n$. Our results show that the three LDs-based indices perform better for systems with large percentages of chaotic orbits.

Read this paper on arXiv…

S. Zimper, A. Ngapasare, M. Hillebrand, et. al.
Wed, 3 May 23
27/67

Comments: N/A

Reliable and Repeatable Transit Through Cislunar Space Using the 2:1 Resonant Spatial Orbit Family [EPA]

Posted on by

http://arxiv.org/abs/2304.13584


This work focuses on the identification of reliable and repeatable spatial (three-dimensional) trajectories that link the Earth and the Moon. For this purpose, this paper aims to extend the 2:1 resonant prograde family and 2:1 resonant retrograde family to three dimensions and to introduce spatial orbits that are not currently present in the literature. These orbits, named the 2:1 resonant spatial family, bifurcate from the two-dimensional families and smoothly transition between them in phase space. The stability properties of this new family of resonant orbits are discussed, and, interestingly, this family includes marginally stable members. Furthermore, this new family of orbits is applied to several engineering problems in the Earth-Moon system. First, this paper selects an appropriate member of 2:1 resonant spatial family on the basis of its stability properties and relationships with other multibody orbits in the regime. Next, this work combines this trajectory with momentum exchange tethers to transit payloads throughout the system in a reliable and repeatable fashion. Finally, this paper studies the process of aborting a catch and related recovery opportunities.

Read this paper on arXiv…

A. Binder and D. Arnas
Thu, 27 Apr 23
42/78

Comments: 33 pages, 31 figures

Chaotic dynamics of off-equatorial orbits around Pseudo-Newtonian Schwarzschild and Kerr-like compact objects surrounded by dipolar halo [CL]

Posted on by

http://arxiv.org/abs/2303.14740


In this paper, we implement a generalized pseudo-Newtonian potential and prescribe a numerical fitting formalism, to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around both Schwarzschild and Kerr-like compact object primaries surrounded by a dipolar halo of matter. The chaotic dynamics of the orbits are detailed for both non-relativistic and special-relativistic test particles. The dependence of the degree of chaos on the rotation parameter $a$ and the inclination angle $i$ is established individually using widely used indicators, such as the Poincar\’e Map and the Lyapunov Characteristic Number. We find that although the chaoticity of the orbits has a positive correlation with $i$, the growth in the chaotic behaviour is not systematic. There exists a threshold value of the inclination angle $i_{\text{c}}$, after which the degree of chaos shows a sharp increase. On the other hand, the chaoticity of the inclined orbits anti-correlates with $a$ at the lower inclination angles. At higher values of $i$, the degree of chaos is maximum for the maximally counter-rotating compact objects, though it has a weak negative, sometimes positive, correlation with $a$ at its higher values. The studies performed with several initial conditions and orbital parameters reveal the intricate nature of the system.

Read this paper on arXiv…

S. Das and S. Roychowdhury
Tue, 28 Mar 23
49/81

Comments: 17 pages, 14 figures

First total recovery of Sun global Alfven resonance: least-squares spectra of decade-scale dynamics of N-S-separated fast solar wind reveal solar-type stars act as revolving-field magnetoalternators [SSA]

Posted on by

http://arxiv.org/abs/2301.07219


The Sun reveals itself in the 385.8-2.439-nHz band of polar ({\phi}Sun>|70{\deg}|) fast (>700 km s^-1) solar wind’s decade-scale dynamics as a globally completely vibrating, revolving-field magnetoalternator rather than a proverbial engine. Thus North-South separation of 1994-2008 Ulysses <10 nT wind polar samplings spanning ~1.6 10^7-2.5 10^9-erg base energies reveals Gauss-Vanicek spectral signatures of an entirely >99%-significant Sun-borne global sharp Alfven resonance (AR), Pi=PS/i, imprinted into the winds to the order n=100+ and co-triggered by the PS=~11-yr Schwabe global mode northside, its ~10-yr degeneration equatorially, and ~9-yr degeneration southside. The Sun is a typical ~3-dB-attenuated ring-system of differentially rotating and contrarily (out-of-phase) vibrating conveyor belts and layers with a continuous spectrum and resolution (<81.3 nHz (S), <55.6 nHz (N)) in lowermost frequencies (<2 {\mu}Hz in most modes). AR is accompanied by an also sharp symmetrical antiresonance P(-) whose both N/S tailing harmonics P(-17) are the well-known PR=~154-day Rieger period dominating planetary dynamics and space weather. Unlike a resonating motor restrained from separating its casing, the freely resonating Sun exhausts the wind in an axial shake-off beyond L1 at highly coherent discrete wave modes generated in the Sun, so to understand solar-type stars, only global decadal scales matter. The result verified against remote data and the experiment, so it instantly replaces dynamo with magnetoalternator and advances Standard Stellar Models, improving fundamental understanding of billions of trillions of solar-type stars. Gauss-Vanicek spectral analysis revolutionizes planetary & space sciences by rigorously simulating multiple spacecraft or fleet formations from a single spacecraft and physics by directly computing nonlinear global dynamics (rendering spherical approximation obsolete).

Read this paper on arXiv…

M. Omerbashich
Thu, 19 Jan 23
51/100

Comments: 31 pages, 7 figures, 3 tables

Earth as a time crystal: macroscopic nature of a quantum-scale phenomenon from transformative moderation of geomagnetic polarity, topography, and climate by precession resonance due to many-body entrainment [CL]

Posted on by

http://arxiv.org/abs/2301.02578


Claims of paleodata periodicity are many and so controversial that superimposing Phanerozoic (0-541 My) mass-extinction periods renders life on Earth impossible. This period hunt coincided with geochronology modernization tying geological timescales to orbital frequencies, enabling separation of astronomical signals from harmonics. I thus show on diverse data (geomagnetic polarity, cratering, extinction episodes) as a proxy of planetary paleodynamics that many-body subharmonic entrainment induces Earth’s resonant response to astronomical forcing so that $2\pi$-phase-shifted axial precession p=26 ky and its Pi=$2\pi$p/i; i=1,…n harmonics get resonantly responsible for paleodata periodicity. This quasiperiodic nature of strata is co-triggered by a p’/4-lockstep to p’=41-ky obliquity. For verification, residuals analysis after suppressing $2\pi$p (and so Pi) in GPTS-95 reversals timescale’s calibration at the South Atlantic Anomaly, extending to end-Campanian (0-83 My), successfully detected weak signals of Earth-Mars planetary resonances reported previously from older epochs. The only residual signal is 26.5-My Rampino period — carrier wave of crushing deflections and transformative polarity reversals. While the ($2\pi$p, Pi) resonant response of the Earth to orbital forcing is the long-sought energy transfer mechanism of the Milankovitch theory, fundamental system properties — $2\pi$-phase-shift, 1/4 lockstep to a forcer, and discrete time translation symmetry (multiplied/halved periods) — typical of a quantum time crystal, here appear macroscopic, making time crystal concept unremarkable. The surprising cross-scale outcome confirms planetary precession is a cataclysmic geodynamic phenomenon as claimed previously, e.g., as the Earth expansion mechanism; then a time crystal in quantum dynamics could be due to particle entrainment, such as the collisions resulting in Feshbach resonances.

Read this paper on arXiv…

M. Omerbashich
Mon, 9 Jan 23
38/59

Comments: N/A

Direct driving of simulated planetary jets by upscale energy transfer [EPA]

Posted on by

http://arxiv.org/abs/2212.09401


The precise mechanism that forms jets and large-scale vortices on the giant planets is unknown. An inverse cascade has been suggested. Alternatively, energy may be directly injected by small-scale convection. Our aim is to clarify whether an inverse cascade feeds zonal jets and large-scale eddies in a system of rapidly rotating, deep, geostrophic spherical-shell convection. We analyze the nonlinear scale-to-scale transfer of kinetic energy in such simulations as a function of the azimuthal wave number, m. We find that the main driving of the jets is associated with upscale transfer directly from the small convective scales to the jets. This transfer is very nonlocal in spectral space, bypassing large-scale structures. The jet formation is thus not driven by an inverse cascade. Instead, it is due to a direct driving by Reynolds stresses from small-scale convective flows. Initial correlations are caused by the effect of uniform background rotation and shell geometry on the flows. While the jet growth suppresses convection, it increases the correlation of the convective flows, which further amplifies the jet growth until it is balanced by viscous dissipation. To a much smaller extent, energy is transferred upscale to large-scale vortices directly from the convective scales, mostly outside the tangent cylinder. There, large-scale vortices are not driven by an inverse cascade either. Inside the tangent cylinder, the transfer to large-scale vortices is weaker, but more local in spectral space, leaving open the possibility of an inverse cascade as a driver of large-scale vortices. In addition, large-scale vortices receive kinetic energy from the jets via forward transfer. We therefore suggest a jet instability as an alternative formation mechanism of largescale vortices. Finally, we find that the jet kinetic energy scales as $\ell^{-5}$, the same as for the zonostrophic regime.

Read this paper on arXiv…

V. Böning, P. Wulff, W. Dietrich, et. al.
Tue, 20 Dec 22
81/97

Comments: 15 pages, 14 figures, accepted for publication in A&A

Detection of separatrices and chaotic seas based on orbit amplitudes [EPA]

Posted on by

http://arxiv.org/abs/2212.02200


The Maximum Eccentricity Method (MEM) is a standard tool for the analysis of planetary systems and their stability. The method amounts to estimating the maximal stretch of orbits over sampled domains of initial conditions. The present paper leverages on the MEM to introduce a sharp detector of separatrices and chaotic seas. After introducing the MEM analogue for nearly-integrable action-angle Hamiltonians, i.e., diameters, we use low-dimensional dynamical systems with multi-resonant modes and junctions, supporting chaotic motions, to recognise the drivers of the diameter metric. Once this is appreciated, we present a second-derivative based index measuring the regularity of this application. This quantity turns to be a sensitive and robust indicator to detect separatrices, resonant webs and chaotic seas. We discuss practical applications of this framework in the context of $N$-body simulations for the planetary case affected by mean-motion resonances, and demonstrate the ability of the index to distinguish minute structures of the phase space, otherwise undetected with the original MEM.

Read this paper on arXiv…

J. Daquin and C. Charalambous
Tue, 6 Dec 22
59/87

Comments: Under review at Celestial Mechanics and Dynamical Astronomy. 8 Figures, 59 references, 17 pages. Comments and feedback welcome

Regimes of charged particle dynamics in current sheets: the machine learning approach [CL]

Posted on by

http://arxiv.org/abs/2211.03787


Current sheets are spatially localized almost-1D structures with intense plasma currents. They play a key role in storing the magnetic field energy and they separate different plasma populations in planetary magnetospheres, the solar wind, and the solar corona. Current sheets are primary regions for the magnetic field line reconnection responsible for plasma heating and charged particle acceleration. One of the most interesting and widely observed type of 1D current sheets is the rotational discontinuity, that can be force-free or include plasma compression. Theoretical models of such 1D current sheets are based on the assumption of adiabatic motion of ions, i.e. ion adiabatic invariants are conserved. We focus on three current sheet configurations, widely observed in the Earth magnetopause and magnetotail and in the near-Earth solar wind. Magnetic field in such current sheets is supported by currents carried by transient ions, which exist only when there is a sufficient number of invariants. In this paper, we apply a novel machine learning approach, AI Poincar’e, to determine parametrical domains where adiabatic invariants are conserved. For all three current sheet configurations, these domains are quite narrow and do not cover the entire parametrical range of observed current sheets. We discuss possible interpretation of obtained results indicating that 1D current sheets are dynamical rather than static plasma equilibria.

Read this paper on arXiv…

A. Lukin, A. Artemyev, D. Vainchtein, et. al.
Wed, 9 Nov 22
71/76

Comments: N/A

Chaos in multiplanetary extrasolar systems [EPA]

Posted on by

http://arxiv.org/abs/2211.01721


Here we present an initial look at the dynamics and stability of 178 multiplanetary systems which are already confirmed and listed in the NASA Exoplanet Archive. To distinguish between the chaotic and regular nature of a system, the value of the MEGNO indicator for each system was determined. Almost three-quarters of them could be labelled as long-term stable. Only 45 studied systems show chaotic behaviour. We consequently investigated the effects of the number of planets and their parameters on the system stability. A comparison of results obtained using the MEGNO indicator and machine-learning algorithm SPOCK suggests that the SPOCK could be used as an effective tool for reviewing the stability of multiplanetary systems. A similar study was already published by Laskar and Petit in 2017. We compared their analysis based on the AMD criterion with our results. The possible discrepancies are discussed.

Read this paper on arXiv…

P. Gajdoš and M. Vaňko
Fri, 4 Nov 22
45/84

Comments: 8 pages, 5 figures; MNRAS accepted

Clusters of heavy particles in two-dimensional Keplerian turbulence [EPA]

Posted on by

http://arxiv.org/abs/2210.13147


Protoplanetary disks are gaseous systems in Keplerian rotation around young stars, known to be turbulent. They include a small fraction of dust from which planets form. In the incremental scenario for planet growth, the formation of kilometer-size objects (planetesimals) from pebbles is a major open question. Clustering of particles is necessary for solids to undergo a local gravitational collapse. To address this question, the dynamic of inertial particles in turbulent flows with Keplerian rotation and shear is studied. Two-dimensional direct numerical simulations are performed to explore systematically two physical parameters: the rotation rate, which depends on the distance to the star, and the particle response time, which relates to their size. Shear is found to drastically affect the characteristics of the turbulent flow destroying cyclones and favoring the survival of anticyclones. Faster rotation enhances clustering of particles in anticyclones, especially for intermediate particles sizes. These clusters form in a hierarchical manner and merge together with time. For parameter values falling outside this regime, solids still concentrate on fractal sets. The mass distribution of particles is then found to be multifractal with small dimensions at large orders, intriguing for triggering their gravitational collapse. Such results are promising for a precise description and better understanding of planetesimal formation.

Read this paper on arXiv…

F. Gerosa, H. Meheut and J. Bec
Tue, 25 Oct 22
78/111

Comments: 16 pages, 21 figures

Stability analysis of planetary systems via second-order Rényi entropy [EPA]

Posted on by

http://arxiv.org/abs/2210.09417


The long-term dynamical evolution is a crucial point in recent planetary research. Although the amount of observational data is continuously growing and the precision allows us to obtain accurate planetary orbits, the canonical stability analysis still requires N-body simulations and phase space trajectory investigations. We propose a method for stability analysis of planetary motion based on the generalized R\’enyi entropy obtained from a scalar measurement. The radial velocity data of the central body in the gravitational three-body problem is used as the basis of a phase space reconstruction procedure. Then, Poincar\’e’s recurrence theorem contributes to finding a natural partitioning in the reconstructed phase space to obtain the R\’enyi entropy. It turns out that the entropy-based stability analysis is in good agreement with other chaos detection methods, and it requires only a few tens of thousands of orbital period integration time.

Read this paper on arXiv…

T. Kovács, M. Pszota, E. Kővári, et. al.
Wed, 19 Oct 22
15/87

Comments: 7 pages, 7 figures, accepted for publication in MNRAS

A database of high precision trivial choreographies for the planar three-body problem [CL]

Posted on by

http://arxiv.org/abs/2210.00594


Trivial choreographies are special periodic solutions of the planar three-body problem. In this work we use a modified Newton’s method based on the continuous analog of Newton’s method and a high precision arithmetic for a specialized numerical search for new trivial choreographies. As a result of the search we computed a high precision database of 462 such orbits, including 397 new ones. The initial conditions and the periods of all found solutions are given with 180 correct decimal digits. 108 of the choreographies are linearly stable, including 99 new ones. The linear stability is tested by a high precision computing of the eigenvalues of the monodromy matrices.

Read this paper on arXiv…

I. Hristov, R. Hristova, I. Puzynin, et. al.
Tue, 4 Oct 22
37/71

Comments: 10 pages, 3 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:2203.02793

The Phase Space Structure in the vicinity of vertical Lyapunov orbits around L1,2 in a barred galaxy model [GA]

Posted on by

http://arxiv.org/abs/2209.10249


We study the phase space structure and the orbital diffusion from the vicinity of the vertical Lyapunov periodic orbits around the unstable Lagrangian points L1,2 in a 3D barred galaxy model. By perturbing the initial conditions of these periodic orbits, we detected the following five types of orbital structures in the 4D spaces of section: (i) Ring-like structures, sticky for large time intervals to the unstable invariant manifolds of the simple and double unstable vertical Lyapunov periodic orbits. (ii) 2D tori belonging to quasi-periodic orbits around stable periodic orbits existing in the region. They are associated either with vertical stable periodic orbits around L4,5 or with “stable anomalous” periodic orbits. (iii) Orbits sticky for large time intervals to these tori, forming “sticky tori”, before they slowly depart from them. (iv) Clouds of points that have a strong chaotic behavior. Such clouds of consequents have slow diffusion speeds, because they are hindered by the presence of the tori around the “stable anomalous” periodic orbits. (v) Toroidal zones consisting of points that stick for long time on the unstable invariant manifolds of the “unstable anomalous” periodic orbits. By continuing the integration, we find that eventually they become strongly chaotic, retaining however small diffusion speeds, due to the presence of the tori around the stable anomalous periodic orbits.

Read this paper on arXiv…

M. M.Katsanikas and P. P.Patsis
Thu, 22 Sep 22
5/65

Comments: 13 pages, accepted for publication in MNRAS

The paradox of infinitesimal granularity: Chaos and the reversibility of time in Newton's theory of gravity [CL]

Posted on by

http://arxiv.org/abs/2209.03347


The fundamental laws of physics are time-symmetric, but our macroscopic experience contradicts this. The time reversibility paradox is partly a consequence of the unpredictability of Newton’s equations of motion. We measure the dependence of the fraction of irreversible, gravitational N-body systems on numerical precision and find that it scales as a power law. The stochastic wave packet reduction postulate then introduces fundamental uncertainties in the Cartesian phase space coordinates that propagate through classical three-body dynamics to macroscopic scales within the triple’s lifetime. The spontaneous collapse of the wave function then drives the global chaotic behavior of the Universe through the superposition of triple systems (and probably multi-body systems). The paradox of infinitesimal granularity then arises from the superposition principle, which states that any multi-body system is composed of an ensemble of three-body problems.

Read this paper on arXiv…

S. Zwart and T. Boekholt
Fri, 9 Sep 22
48/76

Comments: Accepted for publication in IC M2 Physical Sciences AIP Conference Proceedings

A direct N-body integrator for modelling the chaotic, tidal dynamics of multi-body extrasolar systems: TIDYMESS [IMA]

Posted on by

http://arxiv.org/abs/2209.03955


Tidal dissipation plays an important role in the dynamical evolution of moons, planets, stars and compact remnants. The interesting complexity originates from the interplay between the internal structure and external tidal forcing. Recent and upcoming observing missions of exoplanets and stars in the Galaxy help to provide constraints on the physics of tidal dissipation. It is timely to develop new N-body codes, which allow for experimentation with various tidal models and numerical implementations. We present the open-source N-body code TIDYMESS, which stands for “TIdal DYnamics of Multi-body ExtraSolar Systems”. This code implements a creep deformation law for the bodies, parametrized by their fluid Love numbers and fluid relaxation times. Due to tidal and centrifugal deformations, we approximate the general shape of a body to be an ellipsoid. We calculate the associated gravitational field to quadruple order, from which we derive the gravitational accelerations and torques. The equations of motion for the orbits, spins and deformations are integrated directly using a fourth-order integration method based on a symplectic composition. We implement a novel integration method for the deformations, which allows for a time step solely dependent on the orbits, and not on the spin periods or fluid relaxation times. This feature greatly speeds up the calculations, while also improving the consistency when comparing different tidal regimes. We demonstrate the capabilities and performance of TIDYMESS, particularly in the niche regime of parameter space where orbits are chaotic and tides become non-linear.

Read this paper on arXiv…

T. Boekholt and A. Correia
Fri, 9 Sep 22
50/76

Comments: 17 pages, 6 figures

New families of periodic orbits for the planar three-body problem computed with high precision [CL]

Posted on by

http://arxiv.org/abs/2205.14709


In this paper we use a Modified Newton’s method based on the Continuous analog of Newton’s method and high precision arithmetic for a general numerical search of periodic orbits for the planar three-body problem. We consider relatively short periods and a relatively coarse search-grid. As a result, we found 123 periodic solutions belonging to 105 new topological families that are not included in the database in [Science China Physics, Mechanics and Astronomy 60.12 (2017)]. The extensive numerical search is achieved by a parallel solving of many independent tasks using many cores in a computational cluster.

Read this paper on arXiv…

I. Hristov, R. Hristova, I. Puzynin, et. al.
Tue, 31 May 22
71/89

Comments: 5 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:2203.02793

Three-dimensional direct numerical simulation of free-surface magnetohydrodynamic wave turbulence [CL]

Posted on by

http://arxiv.org/abs/2205.11516


We report on three-dimensional direct numerical simulation of wave turbulence on the free surface of a magnetic fluid subjected to an external horizontal magnetic field. A transition from capillarywave turbulence to anisotropic magneto-capillary wave turbulence is observed for an increasing field. At high enough field, wave turbulence becomes highly anisotropic, cascading mainly perpendicularly to the field direction, in good agreement with the prediction of a phenomenological model, and with anisotropic Alfv{\’e}n wave turbulence. Although surface waves on a magnetic fluid are different from Alfv{\’e}n waves in plasma, a strong analogy is found with similar wave spectrum scalings and similar magnetic-field dependent dispersionless wave velocities.

Read this paper on arXiv…

E. Kochurin, G. Ricard, N. Zubarev, et. al.
Wed, 25 May 22
32/56

Comments: in press in Phys. Rev E (Letter). For Supplemental Material, see this http URL

Long-term instability of the inner Solar System: numerical experiments [EPA]

Posted on by

http://arxiv.org/abs/2205.04170


Apart from being chaotic, the inner planets in the Solar System constitute an open system, as they are forced by the regular long-term motion of the outer ones. No integrals of motion can bound a priori the stochastic wanderings in their high-dimensional phase space. Still, the probability of a dynamical instability is remarkably low over the next 5 billion years, a timescale thousand times longer than the Lyapunov time. The dynamical half-life of Mercury has indeed been estimated recently at 40 billion years. By means of the computer algebra system TRIP, we consider a set of dynamical models resulting from truncation of the forced secular dynamics recently proposed for the inner planets at different degrees in eccentricities and inclinations. Through ensembles of $10^3$ to $10^5$ numerical integrations spanning 5 to 100 Gyr, we find that the Hamiltonian truncated at degree 4 practically does not allow any instability over 5 Gyr. The destabilisation is mainly due to terms of degree 6. This surprising result suggests an analogy to the Fermi-Pasta-Ulam-Tsingou problem, in which tangency to Toda Hamiltonian explains the very long timescale of thermalisation, which Fermi unsuccessfully looked for.

Read this paper on arXiv…

N. Hoang, F. Mogavero and J. Laskar
Tue, 10 May 22
30/70

Comments: Accepted for publication in MNRAS. 9 pages, 7 figures

The origin of chaos in the Solar System through computer algebra [EPA]

Posted on by

http://arxiv.org/abs/2205.03298


The discovery of the chaotic motion of the planets in the Solar System dates back more than 30 years. Still, no analytical theory has satisfactorily addressed the origin of chaos so far. Implementing canonical perturbation theory in the computer algebra system TRIP, we systematically retrieve the secular resonances at work along the orbital solution of a forced long-term dynamics of the inner planets. We compare the time statistic of their half-widths to the ensemble distribution of the maximum Lyapunov exponent and establish dynamical sources of chaos in an unbiased way. New resonances are predicted by the theory and checked against direct integrations of the Solar System. The image of an entangled dynamics of the inner planets emerges.

Read this paper on arXiv…

F. Mogavero and J. Laskar
Mon, 9 May 22
20/63

Comments: 16 pages, 8 figures. Astronomy & Astrophysics Letters

Chaotic Behaviour of the Earth System in the Anthropocene [EPA]

Posted on by

http://arxiv.org/abs/2204.08955


It is shown that the Earth System (ES) can, due to the impact of human activities, behave in a chaotic fashion. Our arguments are based on the assumption that the ES can be described by a Landau-Ginzburg model, which on its own allows for predicting that the ES evolves, through regular trajectories in the phase space, towards a Hothouse Earth scenario for a finite amount of human-driven impact. Furthermore, we find that the equilibrium point for temperature fluctuations can exhibit bifurcations and a chaotic pattern if the human impact follows a logistic map.

Read this paper on arXiv…

A. Bernardini, O. Bertolami and F. Francisco
Wed, 20 Apr 22
27/62

Comments: 18 pages, 6 figures. arXiv admin note: text overlap with arXiv:1811.05543

Characterization of planar symmetric central configurations of four bodies, models, and an application [EPA]

Posted on by

http://arxiv.org/abs/2203.14993


We overview angle-based models to study planar symmetric central configurations of four bodies. We present models to determine the masses given the shape of the configuration and the shape-type of the configuration given the masses. We also describe a diagram-based method for the counting of the shape-types in the case of the concave configurations. As an application, we determine planar symmetric central configurations containing bodies of Earth’s and Moon’s masses.

Read this paper on arXiv…

Z. Czirják, B. Érdi and E. Forgács-Dajka
Wed, 30 Mar 22
20/77

Comments: 15 pages, submitted to Physical Review E

The Fractality and Size Distributions of Astrophysical Self-Organized Criticality Systems [SSA]

Posted on by

http://arxiv.org/abs/2203.12484


The statistics of nonlinear processes in avalanching systems, based on the {\sl self-organized criticality (SOC)} concept of Bak et al.~(1987), predicts power law-like size (or occurrence frequency) distribution functions. Following up on previous work we define a {\sl standard SOC model} in terms of six assumptions: (i) multi-fractality; (ii) the length-area-volume relationship of Mandelbrot (1977); (iii) the flux-volume relationship, (iv) classical diffusion, (v) the Euclidean volume limit at the event peak time, and (vi) the spatio-temporal fluence or energy of an avalanche event. We gather data of the fractal dimension and power law slopes from 162 publications and assemble them in 28 groups (e.g., solar and stellar flare energies), from which we find that 75\% of the groups are consistent with the standard SOC model. Alternative SOC models (Levy-flight, flat-world, non-fractal) are slightly less correlated with the data. The remaining discrepancies are attributed to outliers caused by small-number statistics, background subtraction problems, inadequate fitting ranges, and deviations from ideal power laws.

Read this paper on arXiv…

M. Aschwanden
Thu, 24 Mar 22
12/56

Comments: 51 pages, 6 Figures, 16 Tables

On the Jacobi capture origin of binaries with applications to the Earth-Moon system and black holes in galactic nuclei [EPA]

Posted on by

http://arxiv.org/abs/2203.09646


Close encounters between two bodies in a disk often result in a single orbital deflection. However, within their Jacobi volumes, where the gravitational forces between the two bodies and the central body become competitive, temporary captures with multiple close encounters become possible outcomes: a Jacobi capture. We perform 3-body simulations in order to characterise the dynamics of Jacobi captures in the plane. We find that the phase space structure resembles a Cantor set with a fractal dimension of 0.4. The lifetime distribution decreases exponentially, while the distribution of the closest separation follows a power law with index 0.5. In our first application, we consider the Jacobi capture of the Moon. We demonstrate that both tidal captures and giant impacts are possible outcomes. Their respective 1D cross sections differ within an order of magnitude, evaluated at a heliocentric distance of 1 AU. The impact speed is well approximated by a parabolic encounter, while the impact angles follow that of a uniform beam on a circular target. In our second application, we find that Jacobi captures with gravitational wave dissipation can result in the formation of binary black holes in galactic nuclei. The eccentricity distribution is approximately super-thermal and includes both prograde and retrograde orientations. We estimate a cosmic rate density of 0.083 < R < 14 Gpc^-3 yr^-1. We conclude that dissipative Jacobi captures form an efficient channel for binary formation, which motivates further research into establishing the universality of Jacobi captures across multiple astrophysical scales.

Read this paper on arXiv…

T. Boekholt, C. Rowan and B. Kocsis
Mon, 21 Mar 22
8/60

Comments: Submitted to MNRAS. 18 pages, 16 figures

Periodic orbits in the 1:2:3 resonant chain and their impact on the orbital dynamics of the planetary system Kepler-51 [EPA]

Posted on by

http://arxiv.org/abs/2203.03349


Many exoplanets evolving in (or close) to MMRs and resonant chains have been discovered by space missions. Oftentimes, the published data possess very large uncertainties, due to observational limitations, which deem the system chaotic in short or large timescales. We propose a study of the dynamics of such systems by exploring particular regions in phase space. We exemplify our method by studying the long-term orbital stability of the three-planet system Kepler-51 and either favor or constrain its data. It is a dual process which breaks down in two steps: the computation of the families of periodic orbits in the 1:2:3 resonant chain and the visualization of the phase space through maps of dynamical stability. We present novel results in the General 4-Body Problem. Stable periodic orbits were found only in the low-eccentricity regime. We demonstrate three possible scenarios safeguarding Kepler-51, each followed by constraints. Firstly, the 2/1 and 3/2 two-body MMRs, in which $e_b<0.02$, so that such two-body MMRs last for long-time spans. Secondly, the 1:2:3 three-body Laplace-like resonance, in which $e_c<0.016$ and $e_d<0.006$ for such a chain to be viable. Thirdly, the combination comprising an 1/1 secondary resonance inside 2/1 MMR for the inner pair of planets and an apsidal difference oscillation for the outer pair of planets in which the observational eccentricities $e_b$ and $e_c$ are favored as long as $e_d\approx 0$. Aiming to the optimum deduction of the orbital elements, this study showcases the need for dynamical analyses based on periodic orbits being performed in parallel to the fitting processes.

Read this paper on arXiv…

K. Antoniadou and G. Voyatzis
Tue, 8 Mar 22
56/100

Comments: Accepted for publication in A&A

New satellites of figure-eight orbit computed with high precision [CL]

Posted on by

http://arxiv.org/abs/2203.02793


In this paper we use a Modified Newton’s method based on the Continuous analog of Newton’s method and high precision arithmetic for a search of new satellites of the famous figure-eight orbit. By making a purposeful search for such satellites, we found over 300 new satellites, including 7 new stable choreographies.

Read this paper on arXiv…

I. Hristov, R. Hristova, I. Puzynin, et. al.
Tue, 8 Mar 22
63/100

Comments: 11 pages, 9 figures, 1 table

Assessing Planetary Complexity and Potential Agnostic Biosignatures using Epsilon Machines [EPA]

Posted on by

http://arxiv.org/abs/2202.03699


We present a new approach to exoplanet characterisation using techniques from complexity science, with potential applications to biosignature detection. This agnostic method makes use of the temporal variability of light reflected or emitted from a planet. We use a technique known as epsilon machine reconstruction to compute the statistical complexity, a measure of the minimal model size for time series data. We demonstrate that statistical complexity is an effective measure of the complexity of planetary features. Increasing levels of qualitative planetary complexity correlate with increases in statistical complexity and Shannon entropy, demonstrating that our approach can identify planets with the richest dynamics. We also compare Earth time series with Jupiter data, and find that for the three wavelengths considered, Earth’s average complexity and entropy rate are approximately 50% and 43% higher than Jupiter’s, respectively. The majority of schemes for the detection of extraterrestrial life rely upon biochemical signatures and planetary context. However, it is increasingly recognised that extraterrestrial life could be very different to life on Earth. Under the hypothesis that there is a correlation between the presence of a biosphere and observable planetary complexity, our technique offers an agnostic and quantitative method for the measurement thereof.

Read this paper on arXiv…

S. Bartlett, J. Li, L. Gu, et. al.
Wed, 9 Feb 22
16/48

Comments: N/A

Machine learning prediction for mean motion resonance behaviour — The planar case [EPA]

Posted on by

http://arxiv.org/abs/2201.06743


Most recently, machine learning has been used to study the dynamics of integrable Hamiltonian systems and the chaotic 3-body problem. In this work, we consider an intermediate case of regular motion in a non-integrable system: the behaviour of objects in the 2:3 mean motion resonance with Neptune. We show that, given initial data from a short 6250 yr numerical integration, the best-trained artificial neural network (ANN) can predict the trajectories of the 2:3 resonators over the subsequent 18750 yr evolution, covering a full libration cycle over the combined time period. By comparing our ANN’s prediction of the resonant angle to the outcome of numerical integrations, the former can predict the resonant angle with an accuracy as small as of a few degrees only, while it has the advantage of considerably saving computational time. More specifically, the trained ANN can effectively measure the resonant amplitudes of the 2:3 resonators, and thus provides a fast approach that can identify the resonant candidates. This may be helpful in classifying a huge population of KBOs to be discovered in future surveys.

Read this paper on arXiv…

X. Li, J. Li, Z. Xia, et. al.
Wed, 19 Jan 22
88/121

Comments: 12 pages, 9 figures, accepted for pubblication on Monthly Notices of the Royal Astronomical Society

Collisionless relaxation of a Lynden-Bell plasma [CL]

Posted on by

http://arxiv.org/abs/2201.03376


A plasma whose Coulomb-collision rate is very small may relax on a shorter time scale to non-Maxwellian quasi-equilibria, which, nevertheless, have a universal form, with dependence on initial conditions retained only via an infinite set of Casimir invariants enforcing phase-volume conservation. These are distributions derived by Lynden-Bell (1967) via a statistical-mechanical entropy-maximisation procedure, assuming perfect mixing of phase-space elements. To show that these equilibria are reached dynamically, one must derive an effective `collisionless collision integral’ for which they are fixed points — unique and inevitable provided the integral has an appropriate H-theorem. We describe how such collision integrals are derived and what assumptions are required for them to have a closed form, how to prove the H-theorems for them, and why, for a system carrying sufficiently large electric-fluctuation energy, collisionless relaxation should be fast. It is suggested that collisionless dynamics may favour maximising entropy locally in phase space before converging to global maximum-entropy states.

Read this paper on arXiv…

R. Ewart, A. Brown, T. Adkins, et. al.
Tue, 11 Jan 22
19/95

Comments: 35 pages, submitted to JPP

Dynamical Friction, Buoyancy and Core-Stalling — I. A Non-perturbative Orbit-based Analysis [GA]

Posted on by

http://arxiv.org/abs/2112.06944


We examine the origin of dynamical friction using a non-perturbative, orbit-based approach. Unlike the standard perturbative approach, in which dynamical friction arises from the LBK torque due to pure resonances, this alternative, complementary view nicely illustrates how a massive perturber significantly changes the energies and angular momenta of field particles on near-resonant orbits, with friction arising from an imbalance between particles that gain energy and those that lose energy. We treat dynamical friction in a spherical host system as a restricted three-body problem. This treatment is applicable in the `slow’ regime, in which the perturber sinks slowly and the standard perturbative framework fails due to the onset of non-linearities. Hence it is especially suited to investigate the origin of core-stalling: the cessation of dynamical friction in central constant-density cores. We identify three different families of near-co-rotation-resonant orbits that dominate the contribution to dynamical friction. Their relative contribution is governed by the Lagrange points (fixed points in the co-rotating frame). In particular, one of the three families, which we call Pac-Man orbits because of their appearance in the co-rotating frame, is unique to cored density distributions. When the perturber reaches a central core, a bifurcation of the Lagrange points drastically changes the orbital make-up, with Pac-Man orbits becoming dominant. In addition, due to relatively small gradients in the distribution function inside a core, the net torque from these Pac-Man orbits becomes positive (enhancing), thereby effectuating a dynamical buoyancy. We argue that core stalling occurs where this buoyancy is balanced by friction.

Read this paper on arXiv…

U. Banik and F. Bosch
Wed, 15 Dec 21
81/85

Comments: Accepted for publication in ApJ; 12 figures, 1 table

Evidence for dynamical changes in Betelgeuse using multi-wavelength data [SSA]

Posted on by

http://arxiv.org/abs/2111.09218


The reasons behind the Great Dimming and subsequent rising in the brightness of Betelgeuse between October 2019 and March 2020 still continue to baffle astronomers. It has been shown by George et. al. (2020) that critical slowing down preceded the dimming event. This suggested that the dimming was a result of the change in the nature of the nonlinear dynamics of the star. In this work we present additional evidence for dynamical changes in Betelgeuse prior to the Great Dimming event, using nonlinear time series analysis. We study the relations between the different bands in the photometry data collected from the Wing photometry (IR/near-IR) and Wasatonic observatory (V-band). We also analyse how the early warning signals studied previously changed during and after the Great Dimming.

Read this paper on arXiv…

S. Kachhara, S. George, R. Misra, et. al.
Thu, 18 Nov 21
20/92

Comments: 9 pages, 4 figures, Contribution to the Proceedings of the Sixteenth Marcel Grossmann Meeting (MG16), July 5-10, 2021

Resolving pericenter: explaining inconsistencies in Solar System simulations [EPA]

Posted on by

http://arxiv.org/abs/2111.08835


We compare the evolution of Mercury’s eccentricity in published Solar System integrations. These data sets are affected to different degrees by numerical chaos, because of how well they resolve Mercury’s pericenter passage. We find statistically significant differences between two data sets, in the eccentricity distribution of Mercury over time. We also study pericenter resolution in a variety of symplectic maps used in the literature.

Read this paper on arXiv…

D. Hernandez, R. Zeebe and S. Hadden
Thu, 18 Nov 21
32/92

Comments: 6 pages, 6 figures, submitted to MNRAS, comments welcome

Stochastic diffusion of electrons interacting with whistler-mode waves in the solar wind [SSA]

Posted on by

http://arxiv.org/abs/2111.06341


Effects of increasing whistler amplitude and propagation angle are studied through a variational test particle simulation and calculations of the resonance width. While high amplitude and oblique whistlers in typical 1 AU solar wind parameters are capable of forming an isotropic population without any additional processes, anomalous interactions with quasi-parallel whistlers are essential for the process of halo formation near the Sun. Without high amplitude and quasi-parallel whistlers, strahl electrons cannot be scattered to low velocities (less than the wave phase velocity) to form a halo population. We also present in detail a careful treatment of errors in phase space volume, which is necessary for numerical calculations when the motion is highly stochastic due to resonant interactions with large amplitude waves. These calculations of errors have a wide application in both PIC and test particle simulations.

Read this paper on arXiv…

T. Vo, R. Lysak and C. Cattell
Fri, 12 Nov 21
51/53

Comments: 11 pages, 5 figures, submitted to Physics of Plasmas

The Stability Boundary of the Distant Scattered Disk [EPA]

Posted on by

http://arxiv.org/abs/2111.00305


The scattered disk is a vast population of trans-Neptunian minor bodies that orbit the sun on highly elongated, long-period orbits. The stability of scattered disk objects is primarily controlled by a single parameter – their perihelion distance. While the existence of a perihelion boundary that separates chaotic and regular motion of long-period orbits is well established through numerical experiments, its theoretical basis as well as its semi-major axis dependence remain poorly understood. In this work, we outline an analytical model for the dynamics of distant trans-Neptunian objects and show that the orbital architecture of the scattered disk is shaped by an infinite chain of $2:j$ resonances with Neptune. The widths of these resonances increase as the perihelion distance approaches Neptune’s semi-major axis, and their overlap drives chaotic motion. Within the context of this picture, we derive an analytic criterion for instability of long-period orbits, and demonstrate that rapid dynamical chaos ensues when the perihelion drops below a critical value, given by $q_{\rm{crit}}=a_{\rm{N}}\,\big(\ln((24^2/5)\,(m_{\rm{N}}/M_{\odot})\,(a/a_{\rm{N}})^{5/2})\big)^{1/2}$. This expression constitutes a boundary between the “detached” and actively “scattering” sub-populations of distant trans-Neptunian minor bodies. Additionally, we find that within the stochastic layer, the Lyapunov time of scattered disk objects approaches the orbital period, and show that the semi-major axis diffusion coefficient is approximated by $\mathcal{D}a\sim(8/(5\,\pi))\,(m{\rm{N}}/M_{\odot})\,\sqrt{\mathcal{G}\,M_{\odot}\,a_{\rm{N}}}\,\exp\big[-(q/a_{\rm{N}})^2/2\big]$. We confirm our results with numerical simulations and highlight the connections between scattered disk dynamics and the Chirikov Standard Map. Implications of our results for the long-term evolution of the distant solar system are discussed.

Read this paper on arXiv…

K. Batygin, R. Mardling and D. Nesvorny
Tue, 2 Nov 21
45/93

Comments: 14 pages, 3 figures, published in ApJ

Dynamics Near the Three-Body Libration Points via Koopman Operator Theory [CL]

Posted on by

http://arxiv.org/abs/2110.12119


This paper investigates the application of the Koopman Operator theory to the motion of a satellite about a libration point in the Circular Restricted Three-Body Problem. Recently, the Koopman Operator has emerged as a promising alternative to the geometric perspective for dynamical systems, where the Koopman Operator formulates the analysis and dynamical systems in terms of observables. This paper explores the use of the Koopman Operator for computing both 2D and 3D periodic orbits near libration points. Further, simulation results show that the Koopman Operator provides analytical solutions with high accuracy for both Lyapunov and Halo orbits, which are then applied to a station-keeping application.

Read this paper on arXiv…

S. Servadio, D. Arnas and R. Linares
Tue, 26 Oct 21
65/109

Comments: N/A

Application of the Shannon entropy in the planar (non-restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system [EPA]

Posted on by

http://arxiv.org/abs/2110.05971


In this paper, we present an application of the Shannon entropy in the case of the planar (non-restricted) four-body problem. Specifically, the Kepler-60 extrasolar system is being investigated with a primary interest in the resonant configuration of the planets that exhibit a chain of mean-motion commensurabilities with the ratios 5:4:3. In the dynamical maps provided, the Shannon entropy is utilized to explore the general structure of the phase space, while, based on the time evolution of the entropy, we determine also the extent and rate of the chaotic diffusion as well as the characteristic times of stability for the planets. Two cases are considered: (i) the pure Laplace resonance when the critical angles of the 2-body resonances circulate and that of the 3-body resonance librates; and (ii) the chain of two 2-body resonances when all the critical angles librate. Our results suggest that case (ii) is the more favourable configuration but we state too that, in either case, the relevant resonance plays an important role to stabilize the system. The derived stability times are no shorter than $10^8$ yrs in the central parts of the resonances.

Read this paper on arXiv…

E. Kővári, B. Érdi and Z. Sándor
Wed, 13 Oct 21
60/80

Comments: 10 pages, 8 figures, accepted for publication in the open-access journal MNRAS

The Criterion for Chaos in Three-Planet Systems [EPA]

Posted on by

http://arxiv.org/abs/2110.02956


We establish the criterion for chaos in three-planet systems, for systems similar to those discovered by the Kepler spacecraft. Our main results are as follows: (i) The simplest criterion, which is based on overlapping mean motion resonances MMR’s), only agrees with numerical simulations at a very crude level. (ii) Much greater accuracy is attained by considering neighboring MMR’s that do not overlap. We work out the width of the chaotic zones around each of the neighbors, and also provide simple approximate expressions for the widths. (iii) Even greater accuracy is provided by the overlap of three-body resonances (3BR’s), which accounts for fine-grained structure seen in maps from N-body simulations, and also predicts the Lyapunov times. Previous studies conflict on whether overlap of MMR’s or of 3BR’s drive interplanetary chaos. We show that both do, and in fact they are merely different ways of looking at the same effect. (iv) We compare both criteria with high-resolution maps of chaos from N-body simulations, and show that they agree at a high level of detail.

Read this paper on arXiv…

J. Rath, S. Hadden and Y. Lithwick
Fri, 8 Oct 21
61/70

Comments: N/A

Chaos in self-gravitating many-body systems: Lyapunov time dependence of $N$ and the influence of general relativity [CL]

Posted on by

http://arxiv.org/abs/2109.11012


In self-gravitating $N$-body systems, small perturbations introduced at the start, or infinitesimal errors produced by the numerical integrator or due to limited precision in the computer, grow exponentially with time. For Newton’s gravity, we confirm earlier results by \cite{1992ApJ…386..635K} and \cite{1993ApJ…415..715G}, that for relatively homogeneous systems, this rate of growth per crossing time increases with $N$ up to $N \sim 30$, but that for larger systems, the growth rate has a weaker dependency with $N$. For concentrated systems, however, the rate of exponential growth continues to scale with $N$. In relativistic self-gravitating systems, the rate of growth is almost independent of $N$. This effect, however, is only noticeable when the system’s mean velocity approaches the speed of light to within three orders of magnitude. The chaotic behavior of systems with $\apgt 10$ bodies for the usually adopted approximation of only solving the pairwise interactions in the Einstein-Infeld-Hoffmann equation of motion, is qualitatively different than when the interaction terms (or cross terms) are taken into account. This result provides a strong motivation for follow-up studies on the microscopic effect of general relativity on orbital chaos, and the influence of higher-order cross-terms in the Taylor-series expansion of the EIH equations of motion.

Read this paper on arXiv…

S. Zwart, T. Boekholt, E. Por, et. al.
Fri, 24 Sep 21
80/81

Comments: Submitted to A&A

Chaoticity in the vicinity of complex unstable periodic orbits in galactic type potentials [GA]

Posted on by

http://arxiv.org/abs/2109.09656


We investigate the evolution of phase space close to complex unstable periodic orbits in two galactic type potentials. They represent characteristic morphological types of disc galaxies, namely barred and normal (non-barred) spiral galaxies. These potentials are known for providing building blocks to support observed features such as the peanut, or X-shaped bulge, in the former case and the spiral arms in the latter. We investigate the possibility that these structures are reinforced, apart by regular orbits, also by orbits in the vicinity of complex unstable periodic orbits. We examine the evolution of the phase space structure in the immediate neighbourhood of the periodic orbits in cases where the stability of a family presents a successive transition from stability to complex instability and then to stability again, as energy increases. We find that we have a gradual reshaping of invariant structures close to the transition points and we trace this evolution in both models. We conclude that for time scales significant for the dynamics of galaxies, there are weakly chaotic orbits associated with complex unstable periodic orbits, which should be considered as structure-supporting, since they reinforce the morphological features we study.

Read this paper on arXiv…

P. Patsis, T. Manos, L. Chaves-Velasquez, et. al.
Tue, 21 Sep 21
64/85

Comments: 21 pages, 16 figures (accepted for publication in Physica D: Nonlinear Phenomena)

Applying explicit symplectic integrator to study chaos of charged particles around magnetized Kerr black hole [CL]

Posted on by

http://arxiv.org/abs/2109.02295


In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving around the Kerr black hole embedded in an external magnetic field. Its successful construction is due to the contribution of a time transformation. The algorithm exhibits a good long-term numerical performance in stable Hamiltonian errors and computational efficiency. As its application, the dynamics of order and chaos of charged particles is surveyed. In some circumstances, an increase of the dragging effects of the spacetime seems to weaken the extent of chaos from the global phase-space structure on Poincare sections. However, an increase of the magnetic parameter strengthens the chaotic properties. On the other hand, fast Lyapunov indicators show that there is no universal rule for the dependence of the transition between different dynamical regimes on the black hole spin. The dragging effects of the spacetime do not always weaken the extent of chaos from a local point of view.

Read this paper on arXiv…

W. Sun, Y. Wang, F. Liu, et. al.
Tue, 7 Sep 21
29/89

Comments: 10 pages,20 figures

Tadpole type motion of charged dust in the Lagrange problem with planet Jupiter [EPA]

Posted on by

http://arxiv.org/abs/2109.00800


We investigate the dynamics of charged dust interacting with the interplanetary magnetic field in a Parker spiral type model and subject to the solar wind and Poynting-Robertson effect in the vicinity of the 1:1 mean motion resonance with planet Jupiter. We estimate the shifts of the location of the minimum libration amplitude solutions close to the location of the L4 and L5 points of the classical – gravitational – problem and provide the extension of the ‘librational regimes of motion’ and the width of the resonance in dependency of the nongravitational parameters related to the dust grain size and surface potential of the particles. Our study is based on numerical simulations in the framework of the spatial, elliptic restricted three-body problem and semi-analytical estimates obtained by averaging of Gauss’ planetary equations of motion.

Read this paper on arXiv…

C. Lhotka and L. Zhou
Fri, 3 Sep 21
3/52

Comments: Accepted manuscript in Communications in Nonlinear Science and Numerical Simulation Available online 1 September 2021, 106024, 32 pages, 14 figures

Jammed Keplerian gas leads to the formation and disappearance of spiral arms in a coupled map lattice for astronomical objects [CL]

Posted on by

http://arxiv.org/abs/2109.00458


The formation and disappearance of spiral arms are studied by focusing on jammed Keplerian gas in a coupled map lattice (CML) with a minimal set of procedures for simulating diverse patterns in astronomical objects. The CML shows that a spiral arm is a type of traffic jam, and its motion is governed by both a gas inflow into and outflow from the jam. In particular, a new mechanism for the disappearance of spiral arms is found. It is caused not by conventional differential rotation, but by the gas flow rate difference between the light inflow and heavy outflow, here called “light-in and heavy-out”, leading to the disappearance of traffic jams. Furthermore, we propose a general approximate formula for the lifetime of spiral arms, which is simply derived from the mechanism of the “light-in and heavy-out”. The proposed formula is successfully applied to the CML simulations, and moreover, to the observational data of the spiral galaxy M51.

Read this paper on arXiv…

E. Nozawa
Thu, 2 Sep 21
43/59

Comments: 8 pages, 4 figures

Structures of secular resonances for inner test particles in hierarchical planetary systems [EPA]

Posted on by

http://arxiv.org/abs/2108.11532


In this study, dynamics of secular resonances for inner test particles are investigated under the octupole-level approximation by taking non-perturbative approaches. In practice, webs of the major secular resonances are produced by identifying families of stable periodic orbits and the associated stable libration zones are obtained by analysing Poincar\’e surfaces of section. By taking different values of the factor $\epsilon$ ($\epsilon$ measures the contribution of octupole terms), the influences of the octupole-order terms upon the dynamical structures are evaluated. Under the condition of $\epsilon = 0$ (no octupole-order contribution), the dynamical model is totally integrable and there is only Kozai resonance arising in the phase space. When the factor $\epsilon$ is different from zero, the dynamical structure in the phase space becomes complicated due to varieties of secular resonances appearing. Numerical results further indicate that (a) distributions of libration centres and stable libration zones remain qualitatively similar with different values of $\epsilon$, (b) Kozai resonance disappears due to the chaotic motion in the low-eccentricity region, and (c) the chaotic area arising in the low-eccentricity region increases with the factor $\epsilon$. Secular resonances are the source of many important dynamical phenomena, such as chaos, orbit alignment and orbit flipping, and thus the results presented in this work could be useful to understand the secular dynamics for those high-eccentricity and/or high-inclination objects in hierarchical planetary systems.

Read this paper on arXiv…

H. Lei
Fri, 27 Aug 21
47/67

Comments: 23 pages, 12 figures, Accepted for publication in CM&DA

Chaos in the vicinity of a singularity in the Three-Body Problem: The equilateral triangle experiment in the zero angular momentum limit [CL]

Posted on by

http://arxiv.org/abs/2108.06335


We present numerical simulations for the three-body problem, in which three particles lie at rest at the vertex of a perturbed equilateral triangle. In the unperturbed problem, the three particles fall towards the center of mass of the system to form a three-body collision, or singularity, where the particles overlap in space and time. By perturbing the initial positions of the particles, we are able to study chaos in the vicinity of the singularity. Here we cover the full range in parameter space for binary formation due to three-body interactions of isolated single stars, covering the singular region corresponding to an equilateral triangle and extending to sufficiently deformed triangles that we enter the binary-single scattering regime (i.e., one side of the triangle is very short and the other two are very long). We make phase space plots to study the regular and ergodic subsets of our simulations independently and derive the expected properties of the left-over binaries from three-body binary formation in isotropic cluster environments. We further provide fits to the ergodic subset to characterize the properties of the left-over binaries. We identify the discrepancy between the statistical theory and the simulations to the regular subset of interactions, which exhibit only weak chaos. As we decrease the scale of the perturbations in the initial positions, the phase space becomes entirely dominated by regular interactions, according to our metric for chaos.

Read this paper on arXiv…

H. Parischewsky, G. Ceballos, A. Trani, et. al.
Mon, 16 Aug 21
26/34

Comments: 18 pages, 8 figures, 1 table, submitted

Orbit classification in a disk galaxy model with a pseudo-Newtonian central black hole [GA]

Posted on by

http://arxiv.org/abs/2108.05209


We numerically investigate the motion of stars on the meridional plane of an axially symmetric disk galaxy model, containing a central supermassive black hole, represented by the Paczynski-Wiita potential. By using this pseudo-Newtonian potential we can replicate important relativistic properties, such as the existence of the Schwarzschild radius. After classifying extensive samples of initial conditions of trajectories, we manage to distinguish between collisional, ordered, and chaotic motion. Besides, all starting conditions of regular orbits are further classified into families of regular orbits. Our results are presented through modern color-coded basin diagrams on several types of two-dimensional planes. Our analysis reveals that both the mass of the black hole (in direct relation with the Schwarzschild radius) as well as the angular momentum play an important role in the character of orbits of stars. More specifically, the trajectories of low angular momentum stars are highly affected by the mass of the black hole, while high angular momentum stars seem to be unaffected by the central black hole. Comparison with previous related outcomes, using Newtonian potentials for the central region of the galaxy, is also made.

Read this paper on arXiv…

E. Zotos, F. Dubeibe, A. Steklain, et. al.
Thu, 12 Aug 21
58/62

Comments: 10 pages, 10 figures

Gravitational-wave glitches: resonant islands and frequency jumps in non-integrable extreme-mass-ratio inspirals [CL]

Posted on by

http://arxiv.org/abs/2108.02782


The detection of gravitational waves from extreme-mass-ratio inspirals with upcoming space-borne detectors will allow for unprecedented tests of general relativity in the strong-field regime. Aside from assessing whether black holes are unequivocally described by the Kerr metric, such detections may place constraints on the degree of spacetime symmetry. In particular, depending on exactly how a hypothetical departure from the Kerr metric manifests, the Carter symmetry, which implies the integrability of the geodesic equations, may be broken. Here, we examine the gravitational waveforms associated with non-integrable extreme-mass-ratio inspirals involving a small-mass companion and a supermassive compact object of general relativity, namely the Manko-Novikov spacetime. We show that the waveforms displays sudden frequency jumps, when the companion transverses resonant islands. These findings demonstrate that such abrupt manifestations in the gravitational-wave frequencies are generic, have a genuine astrophysical origin and function as a distinctive signature of chaotic phenomena in extreme-mass-ratio binaries.

Read this paper on arXiv…

K. Destounis and K. Kokkotas
Mon, 9 Aug 21
4/51

Comments: 13 pages, 4 figures, accepted for publication in Phys. Rev. D

Coupling and recoupling of binaries in chaotic three body systems [CL]

Posted on by

http://arxiv.org/abs/2107.14627


Three body systems where one of the bodies is ejected without escaping the binary system have previously been studied in various restricted forms. However, none of these studies dwells on the problem in a general setting. Thus, to study this phenomenon qualitatively, we try to expand this problem’s scope to unequal mass systems and generalize them by considering various configurations of fixed initial points with precisely calculated initial velocities, some zero velocity models, and some optimized models. We will see the use of terminology similar to the previous studies done in this domain, but incorporate different analytical and evaluation methods.

Read this paper on arXiv…

T. Venkatesh
Mon, 2 Aug 21
18/82

Comments: 4 pages, 3 figures, A technical report on a specific case of three body systems

A deep dive into the $2g+h$ resonance: separatrices, manifolds and phase space structure of navigation satellites [EPA]

Posted on by

http://arxiv.org/abs/2107.14507


Despite extended past studies, several questions regarding the resonant structure of the medium-Earth orbit (MEO) region remain hitherto unanswered. This work describes in depth the effects of the $2g+h$ lunisolar resonance. In particular, (i) we compute the correct forms of the separatrices of the resonance in the inclination-eccentricity space for fixed semi-major axis. This allows to compute the change in the width of the $2g+h$ resonance as the altitude increases. (ii) We discuss the crucial role played by the value of the inclination of the Laplace plane, $i_{L}$. Since $i_L$ is comparable to the resonance’s separatrix width, the parametrization of all resonance bifurcations has to be done in terms of the proper inclination $i_{p}$, instead of the mean one. (iii) The subset of circular orbits constitutes an invariant subspace embedded in the full phase space, the center manifold $\mathcal{C}$. Using $i_p$ as a label, we compute its range of values for which $\mathcal{C}$ becomes a normally hyperbolic invariant manifold (NHIM). The structure of invariant tori in $\mathcal{C}$ allows to explain the role of the initial phase $h$ noticed in several works. (iv) Through Fast Lyapunov Indicator (FLI) cartography, we portray the stable and unstable manifolds of the NHIM as the altitude increases. Manifold oscillations dominate in phase space between $a=24,000$ km and $a=30,000$ km as a result of the sweeping of the $2g+h$ resonance by the $h-\Omega_{\rm{Moon}}$ and $2h-\Omega_{\rm{Moon}}$ resonances. The noticeable effects of the latter are explained as a consequence of the relative inclination of the Moon’s orbit with respect to the ecliptic. The role of the phases $(h,\Omega_{\rm{Moon}})$ in the structures observed in the FLI maps is also clarified. Finally,(v) we discuss how the understanding of the manifold dynamics could inspire end-of-life disposal strategies.

Read this paper on arXiv…

J. Daquin, E. Legnaro, I. Gkolias, et. al.
Mon, 2 Aug 21
51/82

Comments: 26 pages, 8 figures, 4 tables. Comments and feedback are most welcome

Bridges and gaps at low-eccentricity first-order resonances [EPA]

Posted on by

http://arxiv.org/abs/2107.10678


Previous works on the divergence of first-order mean-motion resonances (MMRs) have studied in detail the extent of the pericentric and apocentric libration zones of adjacent first-order MMRs, highlighting possible bridges between them in the low-eccentricity circular restricted three-body problem. Here, we describe the previous results in the context of periodic orbits and show that the so-called circular family of periodic orbits is the path that can drive the passage between neighbouring resonances under dissipative effects. We illustrate that the circular family can bridge first and higher order resonances while its gaps at first-order MMRs can serve as boundaries that stop transitions between resonances. In particular, for the Sun-asteroid-Jupiter problem, we show that, during the migration of Jupiter in the protoplanetary disc, a system initially evolving below the apocentric branch of a first-order MMR follows the circular family and can either be captured into the pericentric branch of an adjacent first-order MMR if the orbital migration is rapid or in a higher order MMR in case of slow migration. Radial transport via the circular family can be extended to many small body and planetary system configurations undergoing dissipative effects (e.g., tidal dissipation, solar mass-loss and gas drag).

Read this paper on arXiv…

K. Antoniadou and A. Libert
Fri, 23 Jul 21
38/63

Comments: Accepted for publication in MNRAS

A Criterion for the Onset of Chaos in Compact, Eccentric Multiplanet Systems [EPA]

Posted on by

http://arxiv.org/abs/2106.14863


We derive a semi-analytic criterion for the presence of chaos in compact, eccentric multiplanet systems. Beyond a minimum semimajor-axis separation, below which the dynamics are chaotic at all eccentricities, we show that (i) the onset of chaos is determined by the overlap of two-body mean motion resonances (MMRs), like it is in two-planet systems; (ii) secular evolution causes the MMR widths to expand and contract adiabatically, so that the chaotic boundary is established where MMRs overlap at their greatest width. For closely spaced two-planet systems, a near-symmetry strongly suppresses this secular modulation, explaining why the long-term stability of two-planet systems is qualitatively different from cases with more than two planets. We use these results to derive an improved angular-momentum-deficit (AMD) stability criterion, i.e., the critical system AMD below which stability should be guaranteed. This introduces an additional factor to the expression from Laskar and Petit (2017) that is exponential in the interplanetary separations, which corrects the AMD threshold toward lower eccentricities by a factor of several for tightly packed configurations. We make routines for evaluating the chaotic boundary available to the community through the open-source SPOCK package.

Read this paper on arXiv…

D. Tamayo, N. Murray, S. Tremaine, et. al.
Tue, 29 Jun 21
15/101

Comments: submitted to AJ. Routines for estimating whether compact planetary configurations are chaotic, together with example notebooks are available as part of the SPOCK package: this https URL

Construction of explicit symplectic integrators in general relativity. IV. Kerr black holes [CL]

Posted on by

http://arxiv.org/abs/2106.12356


In previous papers, explicit symplectic integrators were designed for nonrotating black holes, such as a Schwarzschild black hole. However, they fail to work in the Kerr spacetime because not all variables can be separable, or not all splitting parts have analytical solutions as explicit functions of proper time. To cope with this difficulty, we introduce a time transformation function to the Hamiltonian of Kerr geometry so as to obtain a time-transformed Hamiltonian consisting of five splitting parts, whose analytical solutions are explicit functions of the new coordinate time. The chosen time transformation function can cause time steps to be adaptive, but it is mainly used to implement the desired splitting of the time transformed Hamiltonian. In this manner, new explicit symplectic algorithms are easily available. Unlike Runge Kutta integrators, the newly proposed algorithms exhibit good long term behavior in the conservation of Hamiltonian quantities when appropriate fixed coordinate time steps are considered. They are better than same order implicit and explicit mixed symplectic algorithms and extended phase space explicit symplectic like methods in computational efficiency. The proposed idea on the construction of explicit symplectic integrators is suitable for not only the Kerr metric but also many other relativistic problems, such as a Kerr black hole immersed in a magnetic field, a Kerr Newman black hole with an external magnetic field, axially symmetric core shell systems, and five dimensional black ring metrics.

Read this paper on arXiv…

X. Wu, Y. Wang, W. Sun, et. al.
Thu, 24 Jun 21
25/54

Comments: 12pages,12figures

Long-term dynamics of the solar system inner planets [EPA]

Posted on by

http://arxiv.org/abs/2105.14976


Although the discovery of the chaotic motion of the inner planets in the solar system dates back to more than thirty years ago, the secular chaos of their orbits still dares more analytical analyses. Apart from the high-dimensional structure of the motion, this is probably related to the lack of an adequately simple dynamical model. Here, we consider a new secular dynamics for the inner planets, with the aim of retaining a fundamental set of interactions responsible for their chaotic behaviour, while being consistent with the predictions of the most precise orbital solutions currently available. We exploit the regularity in the secular motion of the outer planets, to predetermine a quasi-periodic solution for their orbits. This reduces the secular phase space to the degrees of freedom dominated by the inner planets. On top of that, the smallness of the inner planet masses and the absence of strong mean-motion resonances permits to restrict ourselves to first-order secular averaging. The resulting dynamics can be integrated numerically in a very efficient way through Gauss’s method, while computer algebra allows for analytical inspection of planet interactions, once the Hamiltonian is truncated at a given total degree in eccentricities and inclinations. The new model matches very satisfactorily reference orbital solutions of the solar system over timescales shorter than or comparable to the Lyapunov time. It correctly reproduces the maximum Lyapunov exponent of the inner system and the statistics of the high eccentricities of Mercury over the next five billion years. The destabilizing role of the $g_1-g_5$ secular resonance also arises. A numerical experiment, consisting of a thousand orbital solutions over one hundred billion years, reveals the essential properties of the stochastic process driving the destabilization of the inner solar system and clarifies its current metastable state.

Read this paper on arXiv…

F. Mogavero and J. Laskar
Tue, 1 Jun 21
19/72

Comments: 25 pages, 10 figures. Accepted for publication in Astronomy & Astrophysics

An Empirical Proxy for the Second Integral of Motion in Rotating Barred or Tri-axial Potentials [GA]

Posted on by

http://arxiv.org/abs/2105.15116


We identify an effective proxy for the analytically-unknown second integral of motion (I_2) for rotating barred or tri-axial potentials. Planar orbits of a given energy follow a tight sequence in the space of the time-averaged angular momentum and its amplitude of fluctuation. The sequence monotonically traces the main orbital families in the Poincare map, even in the presence of resonant and chaotic orbits. This behavior allows us to define the “Calibrated Angular Momentum,” the average angular momentum normalized by the amplitude of its fluctuation, as a numerical proxy for I_2. It also implies that the amplitude of fluctuation in L_z, previously under-appreciated, contains valuable information. This new proxy allows one to classify orbital families easily and accurately, even for real orbits in N-body simulations of barred galaxies. It is a good diagnostic tool of dynamical systems, and may facilitate the construction of equilibrium models.

Read this paper on arXiv…

Y. Qin and J. Shen
Tue, 1 Jun 21
48/72

Comments: 7 pages, 4 figure. Published on ApJL

Oort cloud Ecology II: The chronology of the formation of the Oort cloud [EPA]

Posted on by

http://arxiv.org/abs/2105.12816


We present a chronology on the formation and early evolution of the Oort cloud, and test the sequence of events of its formation by simulating the formation process in subsequent amalgamated steps. These simulations start with the Solar system being born with planets and asteroids in a stellar cluster orbiting the Galactic center. Upon ejection from its birth environment, we continue to follow the Solar system’s evolution while it sojourns the Galaxy as an isolated planetary system. We conclude that the range in semi-major axis between $\sim 100$\,au and several $\sim 10^3$\,au still bears the signatures of the Sun being born in a $\apgt 1000$\,\Msun/pc$^3$ star cluster, and that most of the outer Oort cloud formed after the Solar system escaped. The escape, we argue, happened between $\sim 20$\,Myr and $50$\,Myr after birth of the Solar system. Today, the bulk of the material in the Oort cloud ($\sim 70$\%) originates from the region in the circumstellar disk that was located between $\sim 15$\,au and $\sim 35$\,au, near the current location of the ice-giants and the Centaur family of asteroids. This population is eradicated if the ice-giant planets were born in orbital resonance. Planet migration or chaotic orbital reorganization, occurring while the Solar system is still a cluster member is, according to our model, inconsistent with the presence of the Oort cloud. About half the inner Oort cloud, between $100$ and $10^4$\,au, and a quarter of the material in the outer Oort cloud $\apgt 10^4$\,au could be non-native to the Solar system but was captured from free-floating derbis in the cluster or from the circumstellar disk of other stars in the birth cluster. Characterizing this population will help us to reconstruct the Solar system’s history.

Read this paper on arXiv…

S. Zwart, S. Torres, M. Cai, et. al.
Fri, 28 May 21
2/56

Comments: Accepted for publication in A&A (17 pages)

Non-linear effects in EMRI dynamics and their imprints on gravitational waves [CL]

Posted on by

http://arxiv.org/abs/2103.06724


The largest part of any gravitational-wave inspiral of a compact binary can be understood as a slow, adiabatic drift between the trajectories of a certain referential conservative system. In many contexts, the phase space of this conservative system is smooth and there are no “topological transitions” in the phase space, meaning that there are no sudden qualitative changes in the character of the orbital motion during the inspiral. However, in this chapter we discuss the cases where this assumption fails and non-linear and/or non-smooth transitions come into play. In integrable conservative systems under perturbation, topological transitions suddenly appear at resonances, and we sketch how to implement the passage through such regions in an inspiral model. Even though many of the developments of this chapter apply to general inspirals, we focus on a particular scenario known as the Extreme mass ratio inspiral (EMRI). An EMRI consists of a compact stellar-mass object inspiralling into a supermassive black hole. At leading order, the referential conservative system is simply geodesic motion in the field of the supermassive black hole and the rate of the drift is given by radiation reaction. In Einstein gravity the supermassive black hole field is the Kerr space-time in which the geodesic motion is integrable. However, the equations of motion can be perturbed in various ways so that prolonged resonances and chaos appear in phase space as well as the inspiral, which we demonstrate in simple physically motivated examples.

Read this paper on arXiv…

G. Lukes-Gerakopoulos and V. Witzany
Fri, 12 Mar 21
5/59

Comments: 44 pages, 9 figures, 1 table. Invited chapter for “Handbook of Gravitational Wave Astronomy” (Eds. C. Bambi, S. Katsanevas, and K. Kokkotas; Springer, Singapore, 2021)

Gravitational-wave glitches in chaotic extreme-mass-ratio inspirals [CL]

Posted on by

http://arxiv.org/abs/2103.05643


The Kerr geometry admits the Carter symmetry, which ensures that the geodesic equations are integrable. It is shown that gravitational waveforms associated with extreme-mass-ratio inspirals involving a non-integrable compact object display `glitch’ phenomena, where the frequencies of gravitational waves increase abruptly, when the orbit crosses certain spacetime regions known as Birkhoff islands. The presence or absence of these features in data from upcoming space-borne detectors will therefore allow not only for tests of general relativity, but also of fundamental spacetime symmetries.

Read this paper on arXiv…

K. Destounis, A. Suvorov and K. Kokkotas
Thu, 11 Mar 21
27/62

Comments: 5 pages, 2 figures, accepted for publication in Physical Review Letters

Dynamical properties of the Molniya satellite constellation: long-term evolution of the semi-major axis [CL]

Posted on by

http://arxiv.org/abs/2103.06251


We describe the phase space structures related to the semi-major axis of Molniya-like satellites subject to tesseral and lunisolar resonances. In particular, we dissect the indirect interplay of the critical inclination resonance on the semi-geosynchronous resonance using a hierarchy of more realistic dynamical systems, thus discussing the dynamics beyond the integrable approximation. By introducing \textit{ad hoc} tractable models averaged over the fast angles, we numerically demarcate the hyperbolic structures organising the long-term dynamics via the computation of finite-time variational indicators. Based on the publicly available two-line elements space orbital data, we identify two satellites, namely M1-69 and M1-87, displaying fingerprints consistent with the dynamics associated to the hyperbolic set. The computations of the associated dynamical maps highlight that the spacecraft are trapped within the hyperbolic tangle.

Read this paper on arXiv…

J. Daquin, E. Alessi, J. O’Leary, et. al.
Thu, 11 Mar 21
45/62

Comments: 26 pages, 9 figures. Comments and feedback appreciated

Nonlinear superfluidity and time-delay based chaotic spin-down in pulsars [HEAP]

Posted on by

http://arxiv.org/abs/2103.05421


We investigate the chaotic spin-down behavior seen from some pulsars in terms of the nonlinear superfluid dynamics. To this end, we numerically solve the set of equations for the superfluid-normal matter system whose coupling is mediated by creep of the vortex lines. We show that glitch perturbations which introduce a time-delay to the steady-state dynamics leave behind a remnant in the third time derivative of the rotational phase. This time-delay induces a hyper-chaotic spin-down for pulsars. We find that glitch-induced changes in the rotational parameters lead to non-closing cyclic patterns in the time-delayed phase difference diagram. We observe that the number of cycles, $N$, in the diagram results from $N+1$ glitches occurred in total observation time.

Read this paper on arXiv…

E. Gügercinoğlu, M. Doğan and K. Ekşi
Wed, 10 Mar 21
5/56

Comments: 6 pages with 5 figures

Construction of explicit symplectic integrators in general relativity. II. Reissner-Nordstrom black holes [CL]

Posted on by

http://arxiv.org/abs/2103.02864


In a previous paper, second- and fourth-order explicit symplectic integrators were designed for a Hamiltonian of the Schwarzschild black hole. Following this work, we continue to trace the possibility of the construction of explicit symplectic integrators for a Hamiltonian of charged particles moving around a Reissner-Nordstrom black hole with an external magnetic field. Such explicit symplectic methods are still available when the Hamiltonian is separated into five independently integrable parts with analytical solutions as explicit functions of proper time. Numerical tests show that the proposed algorithms share the desirable properties in their long-term stability, precision and efficiency for appropriate choices of step sizes. For the applicability of one of the new algorithms, the effects of the black hole’s charge, the Coulomb part of the electromagnetic potential and the magnetic parameter on the dynamical behavior are surveyed. Under some circumstances, the extent of chaos gets strong with an increase of the magnetic parameter from a global phase-space structure. No the variation of the black hole’s charge but the variation of the Coulomb part is considerably sensitive to affect the regular and chaotic dynamics of particles’ orbits. A positive Coulomb part is easier to induce chaos than a negative one.

Read this paper on arXiv…

Y. Wang, W. Sun, F. Liu, et. al.
Fri, 5 Mar 21
44/64

Comments: 8 pages,20 figures

The Manifold Of Variations: impact location of short-term impactors [EPA]

Posted on by

http://arxiv.org/abs/2102.11399


The interest in the problem of small asteroids observed shortly before a deep close approach or an impact with the Earth has grown a lot in recent years. Since the observational dataset of such objects is very limited, they deserve dedicated orbit determination and hazard assessment methods. The currently available systems are based on the systematic ranging, a technique providing a 2-dimensional manifold of orbits compatible with the observations, the so-called Manifold Of Variations. In this paper we first review the Manifold Of Variations method, to then show how this set of virtual asteroids can be used to predict the impact location of short-term impactors, and compare the results with those of already existent methods.

Read this paper on arXiv…

A. Vigna, L. Dimare and D. Cioci
Wed, 24 Feb 21
7/64

Comments: N/A

Normal forms for the Laplace resonance [EPA]

Posted on by

http://arxiv.org/abs/2102.07671


We describe a comprehensive model for systems locked in the Laplace resonance. The framework is based on the simplest possible dynamical structure provided by the Keplerian problem perturbed by the resonant coupling truncated at second order in the eccentricities. The reduced Hamiltonian, constructed by a transformation to resonant coordinates, is then submitted to a suitable ordering of the terms and to the study of its equilibria. Henceforth, resonant normal forms are computed. The main result is the identification of two different classes of equilibria. In the first class, only one kind of stable equilibrium is present: the paradigmatic case is that of the Galilean system. In the second class, three kinds of stable equilibria are possible and at least one of them is characterised by a high value of the forced eccentricity for the `first planet’: here the paradigmatic case is the exo-planetary system GJ-876,
in which the combination of libration centers admits triple conjunctions otherwise not possible in the Galilean case. The normal form obtained by averaging with respect to the free eccentricity oscillations, describes the libration of the Laplace argument for arbitrary amplitudes and allows us to determine the libration width of the resonance. The agreement of the analytic predictions with the numerical integration of the toy models is very good.

Read this paper on arXiv…

G. Pucacco
Tue, 16 Feb 21
44/63

Comments: Accepted for publication on Celestial Mechanics and Dynamical Astronomy

Construction of Explicit Symplectic Integrators in General Relativity. I. Schwarzschild Black Holes [CL]

Posted on by

http://arxiv.org/abs/2102.00373


Symplectic integrators that preserve the geometric structure of Hamiltonian flows and do not exhibit secular growth in energy errors are suitable for the long-term integration of N-body Hamiltonian systems in the solar system. However, the construction of explicit symplectic integrators is frequently difficult in general relativity because all variables are inseparable. Moreover, even if two analytically integrable splitting parts exist in a relativistic Hamiltonian, all analytical solutions are not explicit functions of proper time. Naturally, implicit symplectic integrators, such as the midpoint rule, are applicable to this case. In general, these integrators are numerically more expensive to solve than same-order explicit symplectic algorithms. To address this issue, we split the Hamiltonian of Schwarzschild spacetime geometry into four integrable parts with analytical solutions as explicit functions of proper time. In this manner, second- and fourth-order explicit symplectic integrators can be easily made available. The new algorithms are also useful for modeling the chaotic motion of charged particles around a black hole with an external magnetic field. They demonstrate excellent long-term performance in maintaining bounded Hamiltonian errors and saving computational cost when appropriate proper time steps are adopted.

Read this paper on arXiv…

Y. Wang, W. Sun, F. Liu, et. al.
Tue, 2 Feb 21
11/86

Comments: 10 pages,2 figures

Impact of non-gravitational effects on chaotic properties of retrograde orbits [EPA]

Posted on by

http://arxiv.org/abs/2101.04364


Dynamical studies of asteroid populations in retrograde orbits, that is with orbital inclinations greater than 90 degrees, are interesting because the origin of such orbits is still unexplained. Generally, the population of retrograde asteroids includes mostly Centaurs and transneptunian objects (TNOs). A special case is the near-Earth object (343158) 2009 HC82 from the Apollo group. Another interesting object is the comet 333P/LINEAR, which for several years was considered the second retrograde object approaching Earth. Another comet in retrograde orbit, 161P Hartley/IRAS appears to be an object of similar type. Thanks to the large amount of observational data for these two comets, we tested various models of cometary non-gravitational forces applied to their dynamics.
The goal was to estimate which of non-gravitational perturbations could affect the stability of retrograde bodies. In principle, we study the local stability by measuring the divergence of nearby orbits.
We numerically determined Lyapunov characteristic indicators (LCI) and the associated Lyapunov times (LT). This time, our calculations were extended by more advanced models of non-gravitational perturbations (i.e. Yarkovsky drift and in selected cases cometary forces). This allowed us to estimate chaos in the Lyapunov sense.
We found that the Yarkovsky effect for obliquities of $\gamma=0^{\circ}$ and $\gamma=180^{\circ}$ can change the LT substantially. In most cases, for the prograde rotation, we received more stable solutions. Moreover, we confirmed the role of retrograde resonances in this process. Additionally, the studied cometary effects also significantly influence the long-term behaviour of the selected comets. The LT can reach values from 100 to over 1000 years. Conclusions. All of our results indicate that the use of models with non-gravitational effects for retrograde bodies is clearly justified.

Read this paper on arXiv…

P. Kankiewicz and I. Włodarczyk
Wed, 13 Jan 21
33/70

Comments: Accepted for publication in Astronomy and Astrophysics, Dec 19, 2020

Testing the Flux-based statistical prediction of the Three-Body Problem [EPA]

Posted on by

http://arxiv.org/abs/2101.03661


We present an extensive comparison between the statistical properties of non-hierarchical three-body systems and the corresponding three-body theoretical predictions. We perform and analyze 1 million realizations for each different initial condition considering equal and unequal mass three-body systems to provide high accuracy statistics. We measure 4 quantities characterizing the statistical distribution of ergodic disintegrations: escape probability of each body, the characteristic exponent for escapes by a narrow margin, predicted absorptivity as a function of binary energy and binary angular momentum, and, finally, the lifetime distribution. The escape probabilities are shown to be in agreement down to the 1% level with the emissivity-blind, flux-based theoretical prediction. This represents a leap in accuracy compared to previous three-body statistical theories. The characteristic exponent at the threshold for marginally unbound escapes is an emissivity-independent flux-based prediction, and the measured values are found to agree well with the prediction. We interpret both tests as strong evidence for the flux-based three-body statistical formalism. The predicted absorptivity and lifetime distributions are measured to enable future tests of statistical theories.

Read this paper on arXiv…

V. Manwadkar, B. Kol, A. Trani, et. al.
Tue, 12 Jan 21
44/90

Comments: 17 pages, 11 figures

Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries [CL]

Posted on by

http://arxiv.org/abs/2011.12533


The dynamics of the planar circular restricted three-body problem with Kerr-like primaries in the context of a beyond-Newtonian approximation is studied. The beyond-Newtonian potential is developed by using the Fodor-Hoenselaers-Perj\’es procedure. An expansion in the Kerr potential is performed and terms up-to the first non-Newtonian contribution of both the mass and spin effects are included. With this potential, a model for a test particle of infinitesimal mass orbiting in the equatorial plane of the two primaries is examined. The introduction of a parameter, $\epsilon$, allows examination of the system as it transitions from the Newtonian to the beyond-Newtonian regime. The evolution and stability of the fixed points of the system as a function of the parameter $\epsilon$ is also studied. The dynamics of the particle is studied using the Poincar\’e map of section and the Maximal Lyapunov Exponent as indicators of chaos. Intermediate values of $\epsilon$ seem to be the most chaotic for the two cases of primary mass-ratios ($=0.001,0.5$) examined. The amount of chaos in the system remains higher than the Newtonian system as well as for the planar circular restricted three-body problem with Schwarzschild-like primaries for all non-zero values of $\epsilon$.

Read this paper on arXiv…

S. De, S. Roychowdhury and R. Banerjee
Thu, 26 Nov 20
56/65

Comments: 19 pages, 11 figures; Accepted for publication in MNRAS

Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries [CL]

Posted on by

http://arxiv.org/abs/2011.12533


The dynamics of the planar circular restricted three-body problem with Kerr-like primaries in the context of a beyond-Newtonian approximation is studied. The beyond-Newtonian potential is developed by using the Fodor-Hoenselaers-Perj\’es procedure. An expansion in the Kerr potential is performed and terms up-to the first non-Newtonian contribution of both the mass and spin effects are included. With this potential, a model for a test particle of infinitesimal mass orbiting in the equatorial plane of the two primaries is examined. The introduction of a parameter, $\epsilon$, allows examination of the system as it transitions from the Newtonian to the beyond-Newtonian regime. The evolution and stability of the fixed points of the system as a function of the parameter $\epsilon$ is also studied. The dynamics of the particle is studied using the Poincar\’e map of section and the Maximal Lyapunov Exponent as indicators of chaos. Intermediate values of $\epsilon$ seem to be the most chaotic for the two cases of primary mass-ratios ($=0.001,0.5$) examined. The amount of chaos in the system remains higher than the Newtonian system as well as for the planar circular restricted three-body problem with Schwarzschild-like primaries for all non-zero values of $\epsilon$.

Read this paper on arXiv…

S. De, S. Roychowdhury and R. Banerjee
Thu, 26 Nov 20
49/65

Comments: 19 pages, 11 figures; Accepted for publication in MNRAS

Variable energy flux in turbulence [CL]

Posted on by

http://arxiv.org/abs/2011.07291


In three-dimensional hydrodynamic turbulence forced at large length scales, a constant energy flux $ \Pi_u $ flows from large scales to intermediate scales, and then to small scales. It is well known that for multiscale energy injection and dissipation, the energy flux $\Pi_u$ varies with scales. In this review we describe this principle and show how this general framework is useful for describing a variety of turbulent phenomena. Compared to Kolmogorov’s spectrum, the energy spectrum steepens in turbulence involving quasi-static magnetofluid, Ekman friction, stable stratification, magnetohydrodynamics, and solution with dilute polymer. However, in turbulent thermal convection, in unstably stratified turbulence such as Rayleigh-Taylor turbulence, and in shear turbulence, the energy spectrum has an opposite behaviour due to an increase of energy flux with wavenumber. In addition, we briefly describe the role of variable energy flux in quantum turbulence, in binary-fluid turbulence including time-dependent Landau-Ginzburg and Cahn-Hillianrd equations, and in Euler turbulence.

Read this paper on arXiv…

M. Verma
Wed, 18 Nov 20
66/79

Comments: 69 pages

The Stationary Points of the Hierarchical Three Body Problem [EPA]

Posted on by

http://arxiv.org/abs/2011.07103


We study the stationary points of the hierarchical three body problem in the planetary limit (m_2, m_3 << m_1) at both the quadrupole and octupole orders. We demonstrate that the extension to octupole order preserves the principal stationary points of the quadrupole solution in the limit of small outer eccentricity e_2 but that new families of stable fixed points occur in both prograde and retrograde cases.
The most important new equilibria are those that branch off from the quadrupolar solutions and extend to large e_2. The apsidal alignment of these families is a function of mass and inner planet eccentricity, and is determined by the relative directions of precession of omega_1 and omega_2 at the quadrupole level.
These new equilibria are also the most resilient to the destabilizing effects of relativistic precession.
We find additional equilibria that enable libration of the inner planet argument of pericentre in the limit of radial orbits and recover the non-linear analogue of the Laplace-Lagrange solutions in the coplanar limit. Finally, we show that the chaotic diffusion and orbital flips identified with the Eccentric Kozai Lidov mechanism and its variants can be understood in terms of the stationary points discussed here.

Read this paper on arXiv…

B. Hansen and S. Naoz
Tue, 17 Nov 20
62/83

Comments: 27 pages, 36 figures

MHD Turbulence: A Biased Review [CL]

Posted on by

http://arxiv.org/abs/2010.00699


This review puts the developments of the last few years in the context of the canonical time line (Kolmogorov to Iroshnikov-Kraichnan to Goldreich-Sridhar to Boldyrev). It is argued that Beresnyak’s objection that Boldyrev’s alignment theory violates the RMHD rescaling symmetry can be reconciled with alignment if the latter is understood as an intermittency effect. Boldyrev’s scalings, recovered in this interpretation, are thus an example of a physical theory of intermittency in a turbulent system. Emergence of aligned structures brings in reconnection physics, so the theory of MHD turbulence intertwines with the physics of tearing and current-sheet disruption. Recent work on this by Loureiro, Mallet et al. is reviewed and it is argued that we finally have a reasonably complete picture of MHD cascade all the way to the dissipation scale. This picture appears to reconcile Beresnyak’s Kolmogorov scaling of the dissipation cutoff with Boldyrev’s aligned cascade. These ideas also enable some progress in understanding saturated MHD dynamo, argued to be controlled by reconnection and to contain, at small scales, a tearing-mediated cascade similar to its strong-mean-field counterpart. On the margins of this core narrative, standard weak-MHD-turbulence theory is argued to require adjustment—and a scheme for it is proposed—to take account of the part that a spontaneously emergent 2D condensate plays in mediating the Alfven-wave cascade. This completes the picture of the MHD cascade at large scales. A number of outstanding issues are surveyed, concerning imbalanced MHD turbulence, residual energy, subviscous and decaying regimes of MHD turbulence (where reconnection again features prominently). Some new ideas about them are proposed. Finally, it is argued that the natural direction of research is now away from MHD and into kinetic territory.

Read this paper on arXiv…

A. Schekochihin
Mon, 5 Oct 20
53/61

Comments: 160 pages, 45 figures; submitted to JPP

Violation of the zeroth law of turbulence in space plasmas [CL]

Posted on by

http://arxiv.org/abs/2009.02828


The zeroth law of turbulence states that, for fixed energy input into large-scale motions, the statistical steady state of a turbulent system is independent of microphysical dissipation properties. The behavior, which is fundamental to nearly all fluid-like systems from industrial processes to galaxies, occurs because nonlinear processes generate smaller and smaller scales in the flow, until the dissipation—no matter how small—can thermalize the energy input. Using direct numerical simulations and theoretical arguments, we show that in strongly magnetized plasma turbulence such as that recently observed by the Parker Solar Probe (PSP) spacecraft, the zeroth law is routinely violated. Namely, when such turbulence is “imbalanced”—when the large-scale energy input is dominated by Alfvén waves propagating in one direction (the most common situation in space plasmas)—nonlinear conservation laws imply the existence of a “barrier” at scales near the ion gyroradius. This causes energy to build up over time at large scales. The resulting magnetic-energy spectra bear a strong similarity to those observed in situ, exhibiting a sharp, steep kinetic transition range above and around the ion-Larmor scale, with flattening at yet smaller scales, thus resolving the decade-long puzzle of the position and variability of ion-kinetic spectral breaks in plasma turbulence. The “barrier” effect also suggests that how a plasma is forced at large scales (the imbalance) may have a crucial influence on thermodynamic properties such as the ion-to-electron heating ratio.

Read this paper on arXiv…

R. Meyrand, J. Squire, A. Schekochihin, et. al.
Thu, 24 Sep 2020
50/61

Comments: N/A

Dynamical properties of the Molniya satellite constellation: long-term evolution of orbital eccentricity [EPA]

Posted on by

http://arxiv.org/abs/2007.04341


The aim of this work is to analyze the orbital evolution of the mean eccentricity given by the Two-Line Elements (TLE) set of the Molniya satellites constellation. The approach is bottom-up, aiming at a synergy between the observed dynamics and the mathematical modeling. Being the focus the long-term evolution of the eccentricity, the dynamical model adopted is a doubly-averaged formulation of the third-body perturbation due to Sun and Moon, coupled with the oblateness effect on the orientation of the satellite. The numerical evolution of the eccentricity, obtained by a two-degree-of-freedom model assuming different orders in the series expansion of the third-body effect, is compared against the mean evolution given by the TLE. The results show that, despite being highly elliptical orbits, the second order expansion catches extremely well the behavior. Also, the lunisolar effect turns out to be non-negligible for the behavior of the longitude of the ascending node and the argument of pericenter. The role of chaos in the timespan considered is also addressed. Finally, a frequency series analysis is proposed to show the main contributions that can be detected from the observational data.

Read this paper on arXiv…

E. Alessi, A. Buzzoni, J. Daquin, et. al.
Fri, 10 Jul 20
-76/76

Comments: N/A

Dynamical taxonomy of the coupled solar radiation pressure and oblateness problem and analytical deorbiting configurations [EPA]

Posted on by

http://arxiv.org/abs/2007.04945


Recent works demonstrated that the dynamics caused by the planetary oblateness coupled with the solar radiation pressure can be described through a model based on singly-averaged equations of motion. The coupled perturbations affect the evolution of the eccentricity, inclination and orientation of the orbit with respect to the Sun–Earth line. Resonant interactions lead to non-trivial orbital evolution that can be exploited in mission design. Moreover, the dynamics in the vicinity of each resonance can be analytically described by a resonant model that provides the location of the central and hyperbolic invariant manifolds which drive the phase space evolution. The classical tools of the dynamical systems theory can be applied to perform a preliminary mission analysis for practical applications. On this basis, in this work we provide a detailed derivation of the resonant dynamics, also in non-singular variables, and discuss its properties, by studying the main bifurcation phenomena associated to each resonance. Last, the analytical model will provide a simple analytical expression to obtain the area-to-mass ratio required for a satellite to deorbit from a given altitude in a feasible timescale.

Read this paper on arXiv…

I. Gkolias, E. Alessi and C. Colombo
Fri, 10 Jul 20
-69/76

Comments: N/A

The analysis of restricted five-body problem within frame of variable mass [CL]

Posted on by

http://arxiv.org/abs/2005.11261


In the framework of restricted five bodies problem, the existence and stability of the libration points are explored and analysed numerically, under the effect of non–isotropic mass variation of the fifth body (test particle or infinitesimal body). The evolution of the positions of these points and the possible regions of motion are illustrated, as a function of the perturbation parameter. We perform a systematic investigation in an attempt to understand how the perturbation parameter due to variable mass of the fifth body, affects the positions, movement and stability of the libration points. In addition, we have revealed how the domain of the basins of convergence associated with the libration points are substantially influenced by the perturbation parameter.

Read this paper on arXiv…

M. SanamSuraj, E. I.Abouelmagd, R. Aggarwal, et. al.
Mon, 25 May 20
36/39

Comments: N/A

The perturbed restricted three-body problem with angular velocity: Analysis of basins of convergence linked to the libration points [CL]

Posted on by

http://arxiv.org/abs/2005.10715


The analysis of the affect of angular velocity on the geometry of the basins of convergence (BoC) linked to the equilibrium points in the restricted three-body problem is illustrated when the primaries are source of radiation. The bivariate scheme of the Newton-Raphson (N-R) iterative method has been used to discuss the topology of the basins of convergence. The parametric evolution of the fractality of the convergence plane is also presented where the degree of fractality is illustrated by evaluating the basin entropy of the convergence plane.

Read this paper on arXiv…

M. Suraj, R. Aggarwal, A. Mittal, et. al.
Fri, 22 May 20
4/64

Comments: N/A

On the spatial collinear restricted four-body problem with non-spherical primaries [CL]

Posted on by

http://arxiv.org/abs/2005.10751


In the present work a systematic study has been presented in the context of the existence of libration points, their linear stability, the regions of motion where the third particle can orbit and the domain of basins of convergence linked to libration points in the spatial configuration of the collinear restricted four-body problem with non-spherical primaries (i.e., the primaries are oblate or prolate spheroid). The parametric evolution of the positions of the libration points as function of the oblateness and prolateness parameters of the primaries and the stability of these points in linear sense are illustrated numerically. Moreover, the numerical investigation shows that the only libration points which lie on either of the axes are linearly stable for several combinations of the oblateness parameter and mass parameter whereas the non-collinear libration points are found linearly unstable, consequently unstable in nonlinear sense also, for studied value of mass parameter and oblateness parameter. Moreover, the regions of possible motion are also depicted, where the infinitesimal mass is free to orbit, as function of Jacobian constant. In addition, the basins of convergence (BoC) linked to the libration points are illustrated by using the multivariate version of the Newton-Raphson (NR) iterative scheme.

Read this paper on arXiv…

M. Suraj, R. Aggarwal, A. Mittal, et. al.
Fri, 22 May 20
25/64

Comments: Chaos, Solitons & Fractals, 2020

The Lyapunov exponents and the neighbourhood of periodic orbits [CL]

Posted on by

http://arxiv.org/abs/2004.14234


We show that the Lyapunov exponents of a periodic orbit can be easily obtained from the eigenvalues of the monodromy matrix. It turns out that the Lyapunov exponents of simply stable periodic orbits are all zero, simply unstable periodic orbits have only one positive Lyapunov exponent, doubly unstable periodic orbits have two different positive Lyapunov exponents and the two positive Lyapunov exponents of complex unstable periodic orbits are equal. We present a numerical example for periodic orbits in a realistic galactic potential. Moreover, the center manifold theorem allowed us to show that stable, simply unstable and doubly unstable periodic orbits are the mothers of families of, respectively, regular, partially and fully chaotic orbits in their neighbourhood.

Read this paper on arXiv…

D. Carpintero and J. Muzzio
Thu, 30 Apr 20
6/71

Comments: 5 pages, 1, figure. Accepted for publication in MNRAS

Phase reconstruction with iterated Hilbert transforms [CL]

Posted on by

http://arxiv.org/abs/2004.13461


We present a study dealing with a novel phase reconstruction method based on iterated Hilbert transform embeddings. We show results for the Stuart-Landau oscillator observed by generic observables. The benefits for reconstruction of the phase response curve a presented and the method is applied in a setting where the observed system is pertubred by noise.

Read this paper on arXiv…

E. Gengel and A. Pikovsky
Wed, 29 Apr 20
66/75

Comments: The manuscript is based on findings presented in the poster presentation at the Dynamics days Europe in 2019

Euler Turbulence and thermodynamic equilibrium [CL]

Posted on by

http://arxiv.org/abs/2004.09053


We perform a unique direct numerical simulation of Euler turbulence using delta-correlated velocity field as an initial condition, and report a full range of $k^2$ and $k$ energy spectra for 3D and 2D flows respectively, zero energy flux, and Maxwell-Boltzmann distribution for the velocity field. These are direct verification of the predictions of the absolute equilibrium theory of turbulence. For a coherent vortex as an initial condition, Euler turbulence transitions from a mixture of nonequilibrium-equilibrium state to a equilibrium state through a process called thermalization. In this letter, we present a model for thermalization in Euler turbulence.

Read this paper on arXiv…

M. Verma, S. Bhattacharya and S. Chatterjee
Tue, 21 Apr 20
23/90

Comments: 5 pages

Cassini states of a rigid body with a liquid core [EPA]

Posted on by

http://arxiv.org/abs/2004.00242


The purpose of this work is to determine the location and stability of the Cassini states of a celestial body with an inviscid fluid core surrounded by a perfectly rigid mantle. Both situations where the rotation speed is either non-resonant or trapped in a p:1 spin-orbit resonance where p is a half integer are addressed. The rotation dynamics is described by the Poincar\’e-Hough model which assumes a simple motion of the core. The problem is written in a non-canonical Hamiltonian formalism. The secular evolution is obtained without any truncation in obliquity, eccentricity nor inclination. The condition for the body to be in a Cassini state is written as a set of two equations whose unknowns are the mantle obliquity and the tilt angle of the core spin-axis. Solving the system with Mercury’s physical and orbital parameters leads to a maximum of 16 different equilibrium configurations, half of them being spectrally stable. In most of these solutions the core is highly tilted with respect to the mantle. The model is also applied to Io and the Moon.

Read this paper on arXiv…

G. Boué
Thu, 2 Apr 20
29/56

Comments: 25 pages, 3 figures. To be published in Celestial Mechanics and Dynamical Astronomy

Global Evolution of Solar Magnetic Fields and Prediction of Activity Cycles [SSA]

Posted on by

http://arxiv.org/abs/2003.04563


Prediction of solar activity cycles is challenging because physical processes inside the Sun involve a broad range of multiscale dynamics that no model can reproduce and because the available observations are highly limited and cover mostly surface layers. Helioseismology makes it possible to probe solar dynamics in the convective zone, but variations in differential rotation and meridional circulation are currently available for only two solar activity cycles. It has been demonstrated that sunspot observations, which cover over 400 years, can be used to calibrate the Parker-Kleeorin-Ruzmaikin dynamo model, and that the Ensemble Kalman Filter (EnKF) method can be used to link the modeled magnetic fields to sunspot observations and make reliable predictions of a following activity cycle. However, for more accurate predictions, it is necessary to use actual observations of the solar magnetic fields, which are available only for the last four solar cycles. In this paper I briefly discuss the influence of the limited number of available observations on the accuracy of EnKF estimates of solar cycle parameters, the criteria to evaluate the predictions, and application of synoptic magnetograms to the prediction of solar activity.

Read this paper on arXiv…

I. Kitiashvili
Wed, 11 Mar 20
3/65

Comments: 10 pages, 6 figures, submitted to Proceedings of IAUS #354

Non-intrusive hierarchical coupling strategies for multi-scale simulations in gravitational dynamics [IMA]

Posted on by

http://arxiv.org/abs/2002.11206


Hierarchical code coupling strategies make it possible to combine the results of individual numerical solvers into a self-consistent symplectic solution. We explore the possibility of allowing such a coupling strategy to be non-intrusive. In that case, the underlying numerical implementation is not affected by the coupling itself, but its functionality is carried over in the interface. This method is efficient for solving the equations of motion for a self-gravitating system over a wide range of scales. We adopt a dedicated integrator for solving each particular part of the problem and combine the results to a self-consistent solution. In particular, we explore the possibilities of combining the evolution of one or more microscopic systems that are embedded in a macroscopic system. The here presented generalizations of Bridge include higher-order coupling strategies (from the classic 2nd order up to 10th-order), but we also demonstrate how multiple bridges can be nested and how additional processes can be introduced at the bridge time-step to enrich the physics, for example by incorporating dissipative processes. Such augmentation allows for including additional processes in a classic Newtonian N-body integrator without alterations to the underlying code. These additional processes include for example the Yarkovsky effect, dynamical friction or relativistic dynamics. Some of these processes operate on all particles whereas others apply only to a subset.
The presented method is non-intrusive in the sense that the underlying methods remain operational without changes to the code (apart from adding the get- and set-functions to enable the bridge operator). As a result, the fundamental integrators continue to operate with their internal time step and preserve their local optimizations and parallelism.
… abridged …

Read this paper on arXiv…

S. Zwart, I. Pelupessy, C. Martinez-Barbosa, et. al.
Thu, 27 Feb 20
51/51

Comments: Accepted for publication in Communications in Nonlinear Science and Numerical Simulation (CNSNS) The associated software is part of the AMUSE framework and can be downloaded from http:www.amusecode.org

On a method for the analysis of compulsive phase mixing and its application in cosmogony of galaxy superclusters [GA]

Posted on by

http://arxiv.org/abs/2002.09310


In this paper, we study the strong non-stationary stochastic processes that take place in the phase space of self-gravitating systems at the initial non-stationary stage of their evolution. The numerical calculations of the compulsive phase mixing process were carried out based on the model of chaotic impacts, according to which the initially selected phase volume experiences random impacts of a different and complex nature.

Read this paper on arXiv…

S. Nuritdinov and A. Muminov
Mon, 24 Feb 20
14/49

Comments: N/A

On linear and non-linear hydromagnetic stability in laminar and turbulent flows [CL]

Posted on by

http://arxiv.org/abs/2002.08275


We derive several equations that determine the stability of purely hydrodynamic flow of an electrically conducting fluid with respect to creation of magnetic field. One equation determines the evolution of arbitrarily large disturbances of the hydrodynamic flow and provides extension of the Reynolds-Orr equation that includes the magnetic degrees of freedom. This equation allows to demonstrate that, for hydrodynamic and magnetic Reynolds numbers below a threshold, the purely hydrodynamic flow is non-linearly stable and magnetic field of an arbitrary initial amplitude decays. In the case of high Reynolds number turbulence, the non-linear stability bound is provided via properties of ordinary hydrodynamic turbulence and an unknown constant of order one. In the case where the perturbations of magnetic field are small, the so-called kinematic dynamo, we revisit Childress and Backus bounds and provide equation for logarithmic growth rate of the magnetic energy. This equation demonstrates that the rate has the form of infinite-dimensional generalization of the Lyapunov exponent. Thus it is plausible that the rate can be determined from a single realization of evolution similarly to the Lyapunov exponents. The form could also provide a shortcut to the numerical determination of the growth rate. We illustrate its usage by providing an estimate for the critical magnetic Reynolds number below which the magnetic field decays in turbulence exponentially.

Read this paper on arXiv…

I. Fouxon, J. Feinberg and M. Mond
Thu, 20 Feb 20
57/61

Comments: N/A

Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length [IMA]

Posted on by

http://arxiv.org/abs/2002.04029


Chaos is present in most stellar dynamical systems and manifests itself through the exponential growth of small perturbations. Exponential divergence drives time irreversibility and increases the entropy in the system. A numerical consequence is that integrations of the N-body problem unavoidably magnify truncation and rounding errors to macroscopic scales. Hitherto, a quantitative relation between chaos in stellar dynamical systems and the level of irreversibility remained undetermined. In this work we study chaotic three-body systems in free fall initially using the accurate and precise N-body code Brutus, which goes beyond standard double-precision arithmetic. We demonstrate that the fraction of irreversible solutions decreases as a power law with numerical accuracy. This can be derived from the distribution of amplification factors of small initial perturbations. Applying this result to systems consisting of three massive black holes with zero total angular momentum, we conclude that up to five percent of such triples would require an accuracy of smaller than the Planck length in order to produce a time-reversible solution, thus rendering them fundamentally unpredictable.

Read this paper on arXiv…

T. Boekholt, S. Zwart and M. Valtonen
Tue, 11 Feb 20
60/81

Comments: Accepted for publication in MNRAS. 7 pages, 4 figures

Design and performance of low-energy orbits for the exploration of Enceladus [EPA]

Posted on by

http://arxiv.org/abs/2002.01672


The icy moons are in the focus of the exploration plans of the leading space agencies because of the indications of water-based life and geological activity observed in a number of these objects. In particular, the presence of geyser-like jets of water near Enceladus’ south pole has turned this moon of Saturn into a priority candidate to search for life and habitability features. This investigation proposes a set of trajectories between Halo orbits about Lagrangian points L1 and L2 in the Saturn-Enceladus Circular Restricted Three-Body Problem as science orbits for a future in situ mission at Enceladus. The methodology adopted to design these heteroclinics is presented and discussed. This is followed by the analysis of the observational performance of the solutions, including orbital periods, distance ranges from the surface of Enceladus, orbital elements, speeds in the moon-centered inertial reference frame, instantaneous surface coverage, times of overflight and ground tracks. The conclusion of the analysis is that the proposed orbits exhibit suitable features for their use in the scientific exploration of Enceladus, i.e., long transfer times, low altitudes, wide surface visibility windows and long times of overflight.

Read this paper on arXiv…

E. Fantino, F. Salazar and E. Alessi
Thu, 6 Feb 20
50/57

Comments: N/A

Effects of Observational Data Shortage on Accuracy of Global Solar Activity Forecast [SSA]

Posted on by

http://arxiv.org/abs/2001.09376


Building a reliable forecast of solar activity is a long-standing problem that requires to accurately describe past and current global dynamics. However, synoptic observations of magnetic fields and subsurface flows became available relatively recently. In this paper, we present an investigation of effects of short observational data series on accuracy of solar cycle prediction. This analysis is performed using the annual sunspot number time-series applied to the Parker-Kleeorin-Ruzmaikin dynamo model and employing the Ensemble Kalman Filter (EnKF) data assimilation method. The testing of the cycle prediction accuracy is performed for the last six cycles (from Solar Cycle 19 to 24) by sequentially shortening the observational data series that are used for prediction of a target cycle, and evaluating the prediction accuracy according to specified criteria. According to the analysis, reliable activity predictions can be made using relatively short time-series of the sunspot number. It demonstrated that even two cycles of available observations allow us to obtain reasonable forecasts.

Read this paper on arXiv…

I. Kitiashvili
Tue, 28 Jan 20
18/63

Comments: 24 pages, 13 figures, 1 table, submitted to ApJ

Yang-Mills Classical and Quantum Mechanics and Maximally Chaotic Dynamical Systems [CL]

Posted on by

http://arxiv.org/abs/2001.04902


The maximally chaotic dynamical systems (DS) are the systems which have nonzero Kolmogorov entropy. The Anosov C-condition defines a reach class of hyperbolic dynamical systems that have exponential instability of the phase trajectories and positive Kolmogorov entropy and are therefore maximally chaotic. The interest in Anosov-Kolmogorov systems is associated with the attempts to understand the relaxation phenomena, the foundation of the statistical mechanics, the appearance of turbulence in fluid dynamics, the non-linear dynamics of the Yang-Mills field, the N-body system in Newtonian gravity and the relaxation phenomena in stellar systems and the Black hole thermodynamics. The classical- and quantum-mechanical properties of maximally chaotic dynamical systems, the application of the C-K theory to the investigation of the Yang-Mills dynamics and gravitational systems as well as their application in the Monte Carlo method will be presented.

Read this paper on arXiv…

G. Savvidy
Wed, 15 Jan 20
54/66

Comments: 13 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2001.01785

Discreteness effects, $N-$body chaos and the onset of radial-orbit instability [GA]

Posted on by

http://arxiv.org/abs/1912.07406


We study the stability of a family of spherical equilibrium models of self-gravitating systems, the so-called $\gamma-$models with Osipkov-Merritt velocity anisotropy, by means of $N-$body simulations. In particular, we analyze the effect of self-consistent $N-$body chaos on the onset of radial-orbit instability (ROI). We find that degree of chaoticity of the system associated to its largest Lyapunov exponent $\Lambda_{\rm max}$ has no appreciable relation with the stability of the model for fixed density profile and different values of radial velocity anisotropy. However, by studying the distribution of the Lyapunov exponents $\lambda_{\rm m}$ of the individual particles in the single-particle phase space, we find that more anisotropic systems have a larger fraction of orbits with larger $\lambda_{\rm m}$.

Read this paper on arXiv…

P. Cintio and L. Casetti
Tue, 17 Dec 19
39/89

Comments: 8 pages, 7 figures. Submitted to MNRAS, comments welcome

Effects of chaos on the detectability of stellar streams [GA]

Posted on by

http://arxiv.org/abs/1912.05592


Observations show that stellar streams originating in satellite dwarf galaxies are frequent in the Universe. While such events are predicted by theory, it is not clear how many of the streams that are generated are washed out afterwards to the point in which it is imposible to detect them. Here we study how these diffusion times are affected by the fact that typical gravitational potentials of the host galaxies can sustain chaotic orbits. We do this by comparing the behaviour of simulated stellar streams that reside in chaotic or non-chaotic regions of the phase-space. We find that chaos does reduce the time interval in which streams can be detected. By analyzing detectability criteria in configuration and velocity space, we find that the impact of these results on the observations depends on the quality of both the data and the underlying stellar halo model. For all the stellar streams, we obtain a similar upper limit to the detectable mass.

Read this paper on arXiv…

M. Mestre, C. Llinares and D. Carpintero
Fri, 13 Dec 19
13/75

Comments: N/A

Stellar migration in galaxy discs using the Chirikov diffusion rate [GA]

Posted on by

http://arxiv.org/abs/1912.03218


We are re-examining the problem of stellar migration in disc galaxies from a diffusion perspective. We use for the first time the formulation of the diffusion rates introduced by \citet{1979PhR….52..263C}, applied to both energy $E$ and angular momentum $L_\mathrm{z}$ in self-consistent N$-$body experiments. We limit our study to the evolution of stellar discs well after the formation of the bar, in a regime of adiabatic evolution. We show that distribution functions of Chirikov diffusion rates have similar shapes regardless the simulations, but different slopes for energy and angular momentum. Distribution functions of derived diffusion time scales $T_D$ have also the same form for all simulations, but are different for $T_D(E)$ and $T_D(L_\mathrm{z})$. Diffusion time scales are strongly dependent on $L_\mathrm{z}$. $T_D(E) \lesssim 1$~Gyr in a $L_\mathrm{z}$ range roughly delimited by the set of stellar bar resonances (between the Ultra Harmonic Resonance and the Outer Lindblad Resonance). Only particles with low $L_\mathrm{z}$ have $T_D(L_\mathrm{z}) \lesssim 10$ Gyr, i.e. the simulation length. In terms of mass fraction, 35 to 42% turn out to diffuse energy in a characteristic time scale shorter than 10 Gyr, i.e. simulations length, while 60 to 64% undergo the diffusion of the angular momentum on the same time scale. Both the diffusion of $L_\mathrm{z}$ and $E$ are important in order to grasp the full characterisation of the radial migration process, and we showed that depending on the spatial region considered, one or the other of the two diffusions dominates.

Read this paper on arXiv…

H. Wozniak
Mon, 9 Dec 19
46/53

Comments: 15 pages, 17 figures, Accepted for publication to ApJ

Stability of exoplanetary systems retrieved from scalar time series [EPA]

Posted on by

http://arxiv.org/abs/1911.07957


We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time series are used to build up the high-dimensional phase space trajectory representing the dynamical evolution of planetary motion. The framework of nonlinear time series analysis and Poincar\’e recurrences allows us to transform the obtained univariate signals into complex networks whose topology carries the dynamical properties of the underlying system. The network-based analysis is able to distinguish the regular and chaotic behaviour not only for synthetic inputs but also for noisy and irregularly sampled real world observations. The proposed scheme does not require neither n-body integration nor best fitting planetary model to perform the stability investigation, therefore, the computation time can be reduced drastically compared to those of the standard numerical methods.

Read this paper on arXiv…

T. Kovacs
Wed, 20 Nov 19
47/73

Comments: 19 pages, 20 figures, accepted for publication in mnras

Transfer Learning in Spatial-Temporal Forecasting of the Solar Magnetic Field [SSA]

Posted on by

http://arxiv.org/abs/1911.03193


Machine learning techniques have been widely used in attempts to forecast several solar datasets. Most of these approaches employ supervised machine learning algorithms which are, in general, very data hungry. This hampers the attempts to forecast some of these data series, particularly the ones that depend on (relatively) recent space observations. Here we focus on an attempt to forecast the solar surface longitudinally averaged radial magnetic field distribution using a form of spatial-temporal neural networks. Given that the recording of these spatial-temporal datasets only started in 1975 and are therefore quite short, the forecasts are predictably quite modest. However, given that there is a potential physical relationship between sunspots and the magnetic field, we employ another machine learning technique called transfer learning which has recently received considerable attention in the literature. Here, this approach consists in first training the source spatial-temporal neural network on the much longer time/latitude sunspot area dataset, which starts in 1874, then transferring the trained set of layers to a target network, and continue training the latter on the magnetic field dataset. The employment of transfer learning in the field of computer vision is known to obtain a generalized set of feature filters that can be reused for other datasets and tasks. Here we obtain a similar result, whereby we first train the network on the spatial-temporal sunspot area data, then the first few layers of the neural network are able to identify the two main features of the solar cycle, i.e. the amplitude variation and the migration to the equator, and therefore can be used to train on the magnetic field dataset and forecast better than a prediction based only on the historical magnetic field data.

Read this paper on arXiv…

E. Covas
Mon, 11 Nov 19
35/105

Comments: N/A

Charged dust close to outer mean-motion resonances in the heliosphere [EPA]

Posted on by

http://arxiv.org/abs/1911.02778


We investigate the dynamics of charged dust close to outer mean-motion resonances with planet Jupiter. The importance of the interplanetary magnetic field on the orbital evolution of dust is clearly demonstrated. New dynamical phenomena are found that do not exist in the classical problem of uncharged dust. We find changes in the orientation of the orbital planes of dust particles, an increased amount of chaotic orbital motions, sudden ‘jumps’ in the resonant argument, and a decrease in time of temporary capture due to the Lorentz force. Variations in the orbital planes of dust grain orbits are found to be related to the angle between the orbital angular momentum and magnetic axes of the heliospheric field and the rotation rate of the Sun. These variations are bound using a simplified model derived from the full dynamical problem using first order averaging theory. It is found that the interplanetary magnetic field does not affect the capture process, that is still dominated by the other non-gravitational forces. Our study is based on a dynamical model in the framework of the inclined circular restricted three-body problem. Additional forces include solar radiation pressure, solar wind drag, the Poynting-Robertson effect, and the influence of a Parker spiral type interplanetary magnetic field model. The analytical estimates are derived on the basis of Gauss’ form of planetary equations of motion. Numerical results are obtained by simulations of dust grain orbits together with the system of variational equations. Chaotic regions in phase space are revealed by means of Fast Lyapunov Chaos Indicators.

Read this paper on arXiv…

C. Lhotka and C. Gales
Mon, 11 Nov 19
81/105

Comments: 31 pages, 13 figures, 1 table

Orbital dynamics in the photogravitational restricted four-body problem: Lagrange configuration [CL]

Posted on by

http://arxiv.org/abs/1910.09757


We study the effect of the radiation parameter in the location, stability and orbital dynamics in the Lagrange configuration of the restricted four-body problem when one of the primaries is a radiating body. The equations of motion for the test particle are derived by assuming that the primaries revolve in the same plane with uniform angular velocity, and regardless of their mass distribution, they will always lie at the vertices of an equilateral triangle. The insertion of the radiation factor in the restricted four-body problem, let us model more realistically the dynamics of a test particle orbiting an astrophysical system with an active star. The dynamical mechanisms responsible for the smoothening on the basin structures of the configuration space is related to the decrease in the total number of fixed points with increasing values of the radiation parameter. In our model of the Sun-Jupiter-Trojan Asteroid system, it is found that despite the repulsive character of the solar radiation pressure, there exist two stable libration points roughly located at the position of L4 and L5 in the Sun-Jupiter system.

Read this paper on arXiv…

J. Osorio-Vargas, F. Dubeibe and G. González
Wed, 23 Oct 19
28/64

Comments: 14 pages, 10 figures

Periodic orbits of the retrograde coorbital problem [EPA]

Posted on by

http://arxiv.org/abs/1910.09042


Asteroid (514107) Kaepaokaawela is the first example of an object in the 1/1 mean motion resonance with Jupiter with retrograde motion around the Sun. Its orbit was shown to be stable over the age of the Solar System which implies that it must have been captured from another star when the Sun was still in its birth cluster. Kaepaokaawela orbit is also located at the peak of the capture probability in the coorbital resonance. Identifying the periodic orbits that Kaepaokaawela and similar asteroids followed during their evolution is an important step towards precisely understanding their capture mechanism. Here, we find the families of periodic orbits in the two-dimensional retrograde coorbital problem and analyze their stability and bifurcations into three-dimensional periodic orbits. Our results explain the radical differences observed in 2D and 3D coorbital capture simulations. In particular, we find that analytical and numerical results obtained for planar motion are not always valid at infinitesimal deviations from the plane.

Read this paper on arXiv…

M. Morais and F. Namouni
Tue, 22 Oct 19
13/91

Comments: 7 pages, to appear in Monthly Notices of the Royal Astronomical Society

Instantons for the destabilization of the inner Solar System [CL]

Posted on by

http://arxiv.org/abs/1910.04005


For rare events, path probabilities often concentrate close to a predictable path, called instanton. First developed in statistical physics and field theory, instantons are action minimizers in a path integral representation. For chaotic deterministic systems, where no such action is known, shall we expect path probabilities to concentrate close to an instanton? We address this question for the dynamics of the terrestrial bodies of the Solar System. It is known that the destabilization of the inner Solar System might occur with a low probability, within a few hundred million years, or billion years, through a resonance between the motions of Mercury and Jupiter perihelia. In a simple deterministic model of Mercury dynamics, we show that the first exit time of such a resonance can be computed. We predict the related instanton and demonstrate that path probabilities actually concentrate close to this instanton, for events which occur within a few hundred million years. We discuss the possible implications for the actual Solar System.

Read this paper on arXiv…

F. Bouchet and E. Woillez
Thu, 10 Oct 19
13/63

Comments: Physical Review Letters, American Physical Society, In press

Application of Synoptic Magnetograms to Global Solar Activity Forecast [SSA]

Posted on by

http://arxiv.org/abs/1910.00820


Synoptic magnetograms provide us with knowledge about the evolution of magnetic fields on the solar surface and present important information for forecasting future solar activity. In this work, poloidal and toroidal magnetic field components derived from synoptic magnetograms are assimilated, using the Ensemble Kalman Filter method, into a mean-field dynamo model based on Parker’s migratory dynamo theory complemented by magnetic helicity conservation. It was found that the predicted toroidal field is in good agreement with observations for almost the entire following solar cycle. However, poloidal field predictions agree with observations only for the first 2 – 3 years of the predicted cycle. The results indicate that the upcoming Solar Maximum of Cycle 25 (SC25) is expected to be weaker than the current Cycle 24. The model results show that a deep extended solar activity minimum is expected during 2019 – 2021, and that the next solar maximum will occur in 2024 – 2025. The sunspot number at the maximum will be about 50 with an error estimate of 15 – 30 %. The maximum will likely have a double peak or show extended periods (for 2 – 2.5 years) of high activity. According to the hemispheric prediction results, SC25 will start in 2020 in the Southern hemisphere, and will have a maximum in 2024 with a sunspot number of about 28. In the Northern hemisphere the cycle will be delayed for about 1 year (with an error of $\pm 0.5$ year), and reach a maximum in 2025 with a sunspot number of about 23.

Read this paper on arXiv…

I. Kitiashvili
Thu, 3 Oct 19
2/59

Comments: 15 figures, 1 table, 29 pages, submitted to ApJ

Chaotic transport of navigation satellites [EPA]

Posted on by

http://arxiv.org/abs/1909.11531


Navigation satellites are known from numerical studies to reside in a dynamically sensitive environment, which may be of profound importance for their long-term sustainability. We derive the fundamental Hamiltonian of GNSS dynamics and show analytically that near-circular trajectories lie in the neighborhood of a Normally Hyperbolic Invariant Manifold (NHIM), which is the primary source of hyperbolicity. Quasi-circular orbits escape through chaotic transport, regulated by the NHIM’s stable and unstable manifolds, following a power-law escape time distribution $P(t) \sim t^{-\alpha}$, with $\alpha \sim 0.8 – 1.5$. Our study is highly relevant for the design of satellite disposal trajectories, using manifold dynamics.

Read this paper on arXiv…

I. Gkolias, J. Daquin, D. Skoulidou, et. al.
Thu, 26 Sep 19
23/61

Comments: Accepted for publication in Chaos: An Interdisciplinary Journal of Nonlinear Science