JANUS: a bit-wise reversible integrator for N-body dynamics

Rein, Hanno; Tamayo, Daniel

doi:10.1093/mnras/stx2479

Cited by 39 publications

(13 citation statements)

References 18 publications

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“…The same authors presented a different solution to the problem of reproducibility in Rein & Tamayo (2018). This paper introduces a new integration scheme, JANUS, a highorder leap-frog integrator operating on 64-bit integers.…”

Section: Numerical Considerations For Reproducibilitymentioning

confidence: 99%

Chaos and variance in galaxy formation

Keller

Wadsley

Wang

et al. 2018

Monthly Notices of the Royal Astronomical Society

102

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The evolution of galaxies is governed by equations with chaotic solutions: gravity and compressible (magneto-)hydrodynamics. While this micro-scale chaos and stochasticity has been well studied, it is poorly understood how it couples to macro-scale properties examined in simulations of galaxy formation. In this paper, we use tiny perturbations introduced by floating-point roundoff, random number generators, and seemingly trivial differences in algorithmic behaviour as seeds for chaotic behaviour. These can ultimately grow to produce non-trivial differences in star formation histories, circumgalactic medium (CGM) properties, and the distribution of stellar mass. We examine the importance of stochasticity due to discreteness noise, variations in merger timings and how self-regulation moderates the effects of this stochasticity. We show that chaotic variations in stellar mass can be suppressed through gas exhaustion, or be maintained at a roughly constant variance through stellar feedback. We also find that galaxy mergers are critical points from which large (as much as a factor of 2) variations can grow in global quantities such as the total stellar mass. These variations can grow and persist for Gyrs before regressing towards the mean. These results show that detailed comparisons of simulations require serious consideration of the magnitude of effects compared to run-to-run chaotic variation, and may significantly complicate interpreting the impact of different physical models. Understanding the results of simulations requires us to understand that the process of simulation is not a mapping of an infinitesimal point in configuration space to another, final infinitesimal point. Instead, simulations map a point in a space of possible initial conditions points to a volume of possible final states.

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Section: Numerical Considerations For Reproducibilitymentioning

confidence: 99%

Chaos and variance in galaxy formation

Keller

Wadsley

Wang

et al. 2018

Monthly Notices of the Royal Astronomical Society

102

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“…In the long-term regime, the dynamics become irreversible in a practical sense, even when they are formally reversible. Even codes especially designed to ensure reversibility (Portegies Zwart & Boekholt 2018;Rein & Tamayo 2018) will fail irreversibility tests eventually. Note that irreversibility in of itself is not problematic (Heggie 1991), although it can be an indication of erroneous dynamics as Hernandez (2016) found in investigations of MERCURY.…”

Section: Introductionmentioning

confidence: 99%

Are long-term N-body simulations reliable?

Hernández

Hadden

Makino

2020

Monthly Notices of the Royal Astronomical Society

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N-body integrations are used to model a wide range of astrophysical dynamics, but they suffer from errors which make their orbits diverge exponentially in time from the correct orbits. Over long time-scales, their reliability needs to be established. We address this reliability by running a three-body planetary system over about 200 e-folding times. Using nearby initial conditions, we can construct statistics of the long-term phase-space structure and compare to rough estimates of resonant widths of the system. Our statistics are approximately consistent for a wide range of numerical methods, including a Runge-Kutta method, Wisdom-Holman method, symplectic corrector methods, and a method by Laskar & Robutel. "Improving" an integrator did not affect the phase space accuracy, but simply increasing the number of initial conditions did.

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“…We therefore chose to exclude the Earth-Moon interaction in our model, preferring to work with a Hamiltonian whose dependence on eccentricities and inclinations is exact, as compared to a non-decisive increase in precision on the orbit precession frequencies. Moreover, we know that the N-body Hamiltonian (1), corrected for general relativity, reproduces the maximum Lyapunov exponent of the inner Solar System (Rein & Tamayo 2018). Therefore, apart from irrelevant constant terms only depending on the semi-major axes in Eqs.…”

Section: Secular Dynamicsmentioning

confidence: 95%

Long-term dynamics of the inner planets in the Solar System

Mogavero

Laskar

2021

A&A

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Although the discovery of the chaotic motion of the inner planets in the Solar System (Mercury to Mars) was made more than 30 years ago, the secular chaos of their orbits still demands more analytical analyses. In addition to the high-dimensional structure of the motion, this is probably related to the lack of an adequately simple dynamical model. We consider a new secular dynamics for the inner planets, with the aim of retaining a fundamental set of interactions that explains their chaotic behaviour and at the same time is consistent with the predictions of the most precise orbital solutions currently available. We exploit the regularity in the secular motion of the outer planets (Jupiter to Neptune) 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. In addition, the low masses of the inner planets and the absence of strong mean-motion resonances permits us 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 an analytical inspection of planet interactions when the Hamiltonian is truncated at a given total degree in eccentricities and inclinations. The new model matches reference orbital solutions of the Solar System over timescales shorter than or comparable to the Lyapunov time very satisfactorily. 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 g1 − g5 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.

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JANUS: a bit-wise reversible integrator for N-body dynamics

Cited by 39 publications

References 18 publications

Chaos and variance in galaxy formation

Chaos and variance in galaxy formation

Are long-term N-body simulations reliable?

Long-term dynamics of the inner planets in the Solar System

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