Shadowing-based Reliability Decay in Softened
                    <i>n</i>
                    -Body Simulations

Hayes, Wayne B.

doi:10.1086/375263

Cited by 10 publications

(8 citation statements)

References 8 publications

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“…A resimulation of an object with higher resolution may not reproduce its structure in detail, but it can still be viewed as the result of evolution from a nearby set of initial conditions (e.g. Hayes 2003).…”

Section: A Convergence Study Of Subhalo Populationsmentioning

confidence: 99%

The subhalo populations of ΛCDM dark haloes

Gao¹,

White²,

Jenkins³

et al. 2004

Monthly Notices of the Royal Astronomical Society

658

150

874

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We investigate the subhalo populations of dark matter haloes in the concordance Λ cold dark matter (ΛCDM) cosmology. We use a large cosmological simulation and a variety of high‐resolution resimulations of individual cluster and galaxy haloes to study the systematics of subhalo populations over ranges of 1000 in halo mass and 1000 in the ratio of subhalo to parent halo mass. The subhalo populations of different haloes are not scaled copies of each other, but vary systematically with halo properties. On average, the amount of substructure increases with halo mass. At fixed mass, it decreases with halo concentration and with halo formation redshift. These trends are comparable in size to the scatter in subhalo abundance between similar haloes. Averaged over all haloes of given mass, the abundance of low‐mass subhaloes per unit parent halo mass is independent of parent mass. It is very similar to the abundance per unit mass of low‐mass haloes in the Universe as a whole, once differing boundary definitions for subhaloes and haloes are accounted for. The radial distribution of subhaloes within their parent haloes is substantially less centrally concentrated than that of the dark matter. It varies at most weakly with the mass (or concentration) of the parent halo and not at all with subhalo mass. It does depend on the criteria used to define the subhalo population considered. About 90 per cent of present‐day subhaloes were accreted after z= 1 and about 70 per cent after z= 0.5. Only about 8 per cent of the total mass of all haloes accreted at z= 1 survives as bound subhaloes at z= 0. For haloes accreted at z= 2, the survival mass fraction is just 2 per cent. Subhaloes seen near the centre of their parent typically were accreted earlier and retain less of their original mass than those seen near the edge. These strong systematics mean that comparison with galaxies in real clusters is only possible if the formation of the luminous component is modelled appropriately.

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Section: A Convergence Study Of Subhalo Populationsmentioning

confidence: 99%

The subhalo populations of ΛCDM dark haloes

Gao¹,

White²,

Jenkins³

et al. 2004

Monthly Notices of the Royal Astronomical Society

658

150

874

View full text Add to dashboard Cite

show abstract

“…On the other hand, analytical estimations give severe limits on the reliability of N-body calculations. For instance, it was shown that the orbits of particles diverge exponentially with time from their original trajectories (Goodman et al 1993;Hayes 2003).…”

Section: Introductionmentioning

confidence: 99%

The influence of numerical parameters on tidally triggered bar formation

Gabbasov

Rodríguez‐Meza²,

Klapp

et al. 2006

A&A

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The joint influence of numerical parameters such as the number of particles N, the gravitational softening length ε and the time-step ∆t is investigated in the context of galaxy simulations. For isolated galaxy models we have performed a convergence study and estimated the numerical parameters ranges for which the relaxed models do not deviate significantly from its initial configuration. By fixing N, we calculate the range of the mean interparticle separation λ(r) along the disc radius. Uniformly spaced values of λ are used as ε in numerical tests of disc heating. We have found that in the simulations with N = 1 310 720 particles λ varies by a factor of 6, and the corresponding final Toomre's parameters Q change by only about 5 per cent. By decreasing N, the λ and Q ranges broaden. Large ε and small N cause an earlier bar formation. In addition, the numerical experiments indicate, that for a given set of parameters the disc heating is smaller with the Plummer softening than with the spline softening. For galaxy collision models we have studied the influence of the selected numerical parameters on the formation of tidally triggered bars in galactic discs and their properties, such as their dimensions, shape, amplitude and rotational velocity. Numerical simulations indicate that the properties of the formed bars strongly depend upon the selection of N and ε. Large values of the gravitational softening parameter and a small number of particles result in the rapid formation of a well defined, slowly rotating bar. On the other hand, small values of ε produce a small, rapidly rotating disc with tightly wound spiral arms, and subsequently a weak bar emerges. We have found that by increasing N, the bar properties converge and the effect of the softening parameter diminishes. Finally, in some cases short spiral arms are observed at the ends of the bar that change periodically from trailing to leading and vice-versa -the wiggle.

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“…First, in a large system, the motion of particles is governed far more by the global potential than by the positions of nearby particles, 16 and second, individual particles appear to encounter glitches independently of one another. 36,38 These observations suggest that if one particle encounters a glitch, then it will have a negligible effect on the motion of the others, at least at first, because one errant particle does not appreciably change the global gravitational potential created by the ͑millions of͒ other particles. In fact, the global potential will remain substantially valid as long as most particles are on valid trajectories.…”

Section: Shadowing the Gravitational N-body Problemmentioning

confidence: 99%

“…Figure 2 plots this fraction of nonglitched ͑that is, shadowed͒ particles as a function of time for a set of parameters described more fully in Ref. 38. As Fig.…”

Section: Shadowing the Gravitational N-body Problemmentioning

confidence: 99%

Computer simulations, exact trajectories, and the gravitational N-body problem

Hayes

2004

American Journal of Physics

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Many physical systems of current interest are chaotic, which means that numerical errors in their simulation are exponentially magnified with the passage of time. This could mean that a numerical solution of a chaotic system is the result of nothing but magnified noise, which calls into question the value of such simulations. Although this fact has been well known for a long time, its impact on the validity of simulations is not well understood. The study of shadowing may provide an answer. A shadow is an exact trajectory of a chaotic map or ordinary differential equation that remains close to an approximate solution for a nontrivial duration of time. If it can be shown that a numerical solution has a shadow, then the validity of the solution is strong, in the sense that it can be viewed as an experimental observation of the shadow, which is an exact solution. We present a discussion of shadowing, including an algorithm to find shadows, using the gravitational N-body problem as an example.

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Shadowing-based Reliability Decay in Softened n -Body Simulations

Cited by 10 publications

References 8 publications

The subhalo populations of ΛCDM dark haloes

The subhalo populations of ΛCDM dark haloes

The influence of numerical parameters on tidally triggered bar formation

Computer simulations, exact trajectories, and the gravitational N-body problem

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