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Results for “methods: N-body simulations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1975

N-body simulations of disks

The methods used in large-scale n-body simulations are discussed. However, the present review concentrates on results already obtained in n-body simulations using systems containing up to 200,000 simulation stars. Results are presented which show that the stability criterion developed for flattened systems applies only to truly axisymmetric instabilities. Purely stellar disks acquire rather large velocity dispersions, generally two or more times the velocity dispersion required by Toomre (1964) for axisymmetric stability. In computer simulations, the bar-forming instability can be prevented only by comparatively large velocity dispersions. However, simulations including the effects of the galactic halo and core as a fixed background field show that bar formation can be prevented for fixed halo components as large or larger than the self-consistent disk component. Experiments performed to determine the collisional relaxation time for large-scale gravitational n-body calculations show that these models are indeed 'collisionless'.

Hohl, F.↗
NASA NTRS1993

Galaxy tracers in N-body simulations

Using the method of smoothed particle hydrodynamics, we have modeled the formation of a compact group of galaxies with sufficient resolution to trace galaxies. Radiative cooling allows the baryons to dissipate their thermal energy and collapse to overdensities characteristic of real galaxies. With their cross section greatly reduced, these galaxy tracers remain distinct during cluster formation while their dark matter halos merge. In addition, the number density, the mass distribution function, and even the morphology of these objects are similar to those of observed galaxies. A viable population of galaxy tracers can be unambiguously defined.

Summers, F. J.↗
NASA NTRS1989

Recovering the full velocity and density fields from large-scale redshift-distance samples

A new method for extracting the large-scale three-dimensional velocity and mass density fields from measurements of the radial peculiar velocities is presented. Galaxies are assumed to trace the velocity field rather than the mass. The key assumption made is that the Lagrangian velocity field has negligible vorticity, as might be expected from perturbations that grew by gravitational instability. By applying the method to cosmological N-body simulations, it is demonstrated that it accurately reconstructs the velocity field. This technique promises a direct determination of the mass density field and the initial conditions for the formation of large-scale structure from galaxy peculiar velocity surveys.

Bertschinger, Edmund↗
NASA NTRS1993

An improved reconstruction method for cosmological density fields

This paper proposes some improvements to existing reconstruction methods for recovering the initial linear density and velocity fields of the universe from the present large-scale density distribution. We derive the Eulerian continuity equation in the Zel'dovich approximation and show that, by applying this equation, we can trace the evolution of the gravitational potential of the universe more exactly than is possible with previous approaches based on the Zel'dovich-Bernoulli equation. The improved reconstruction method is tested using N-body simulations. When the Zel'dovich-Bernoulli equation describes the formation of filaments, then the Zel'dovich continuity equation also follows the clustering of clumps inside the filaments. Our reconstruction method recovers the true initial gravitational potential with an rms error about 3 times smaller than previous methods. We examine the recovery of the initial distribution of Fourier components and find the scale at which the recovered phases are scrambled with respect their true initial values. Integrating the Zel'dovich continuity equation back in time, we can improve the spatial resolution of the reconstruction by a factor of about 2.

Gramann, Mirt↗
NASA NTRS1993

Quantitative analysis of voids in percolating structures in two-dimensional N-body simulations

We present in this paper a quantitative method for defining void size in large-scale structure based on percolation threshold density. Beginning with two-dimensional gravitational clustering simulations smoothed to the threshold of nonlinearity, we perform percolation analysis to determine the large scale structure. The resulting objective definition of voids has a natural scaling property, is topologically interesting, and can be applied immediately to redshift surveys.

Harrington, Patrick M.↗
NASA NTRS1990

Potential, velocity, and density fields from sparse and noisy redshift-distance samples - Method

A method for recovering the three-dimensional potential, velocity, and density fields from large-scale redshift-distance samples is described. Galaxies are taken as tracers of the velocity field, not of the mass. The density field and the initial conditions are calculated using an iterative procedure that applies the no-vorticity assumption at an initial time and uses the Zel'dovich approximation to relate initial and final positions of particles on a grid. The method is tested using a cosmological N-body simulation 'observed' at the positions of real galaxies in a redshift-distance sample, taking into account their distance measurement errors. Malmquist bias and other systematic and statistical errors are extensively explored using both analytical techniques and Monte Carlo simulations.

Dekel, Avishai↗
NASA NTRS1983

Numerical simulations of the decay of satellite galaxy orbits

A multiple three-body technique is used to study the orbital evolution of satellite galaxies which is similar to the N-body method but neglects two-body forces between stars in the halo of the parent galaxy. It is found that, for satellites orbiting within the halo, Chandrasekhar's (1960) dynamical friction formula accurately describes the orbital decay rate, including its variation with satellite mass and size and with the number density and mass of halo stars. Significant frictional forces are present even outside the halo, and the orbital decay rate, instead of depending on the procedure used to place the satellite in its orbit, is determined only by the current orbital parameters. This semirestricted N-body method is sufficiently fast to have permitted the running of 200 simulations to date, many more than would have been possible by means of the conventional N-body technique.

Lin, D. N. C.↗
NASA NTRS1993

Cluster evolution as a probe of primordial density fluctuations

Although COBE's detection of large angle microwave background anisotropies fixes the amplitude of density fluctuations on length scales k exp -1 approximately = (300-6000) h(exp -1)Mpc, what is crucial for the level of large scale clustering is the amplitude of density fluctuations on scales (5-50) h(exp -1)Mpc. The level of dynamical clustering is usually parameterized by the size of the mass fluctuations in 8 h exp -1 Mpc spheres, sigma sub 8. For the cold dark matter model, COBE gives sigma sub 8 approximately = 1, while models with extra large scale power give sigma sub 8 approximately = 1/2. The most massive clusters of galaxies (greater than or approximately = 10 exp 15 solar mass) form from rare 'peak patches' found in the initial mass density distribution. Their abundance as a function of redshift is a sensitive probe of the wave number band k(exp -1) approx. (3-8) h(exp -1)Mpc, hence of sigma sub 8, and so cluster evolution can discriminate among models allowed by the COBE results. We use our Hierarchical Peaks Method, which accurately reproduces the results of P3M N-body simulations, to calculate the evolution of cluster x-ray flux counts, luminosity, and temperature functions as a function of sigma sub 8 for CDM models and those with more large scale power. We find that the EMSS and Edge et al. cluster samples support sigma sub 8 in the range from approx. 0.6-0.9, and that models with more large scale power (and hence flatter fluctuation spectra in the cluster regime) fit the x-ray bright end better.

Bond, J. Richard↗
NASA NTRS1992

Ambiguities in the identification of giant molecular cloud complexes from longitude-velocity diagrams

Techniques which use longitude-velocity diagrams to identify molecular cloud complexes in the disk of the Galaxy are investigated by means of model Galactic disks generated from N-body cloud-particle simulations. A procedure similar to the method used to reduce the low-level emission in Galactic l-v diagrams is employed to isolate complexes of emission in the model l-v diagram (LVCs) from the 'background'clouds. The LVCs produced in this manner yield a size-line-width relationship with a slope of 0.58 and a mass spectrum with a slope of 1.55, consistent with Galactic observations. It is demonstrated that associations identified as LVCs are often chance superpositions of clouds spread out along the line of sight in the disk of the model system. This indicates that the l-v diagram cannot be used to unambiguously determine the location of molecular cloud complexes in the model Galactic disk. The modeling results also indicate that the existence of a size-line-width relationship is not a reliable indicator of the physical nature of cloud complexes, in particular, whether the complexes are gravitationally bound objects.

Adler, David S.↗
NASA NTRS1993

A new method to simulate vertical and horizontal structure in galactic disks

We have modified the particles in an N-body treecode to have different softening lengths in the horizontal and vertical directions. This allows us to simultaneously have thin enough particles to resolve the vertical structure in galactic disks, and horizontally large enough particles to suppress the vertical heating due to two-body effects.

Dalcanton, Julianne J.↗
NASA NTRS1978

Space construction base control system

Aspects of an attitude control system were studied and developed for a large space base that is structurally flexible and whose mass properties change rather dramatically during its orbital lifetime. Topics of discussion include the following: (1) space base orbital pointing and maneuvering; (2) angular momentum sizing of actuators; (3) momentum desaturation selection and sizing; (4) multilevel control technique applied to configuration one; (5) one-dimensional model simulation; (6) N-body discrete coordinate simulation; (7) structural analysis math model formulation; and (8) discussion of control problems and control methods.

Source record↗
NASA NTRS1993

The large-scale morphology of IRAS galaxies

At present, visual inspection is the only method for comparing the large-scale morphologies in the distribution of galaxies to those in model universes generated by N-body simulations. To remedy the situation, we have developed a set of three structure functions (S1, S2, S3) that quantify the degree of large-scale prolateness, oblateness, and sphericity/uniformity of a 3-D particle distribution and have applied them to a volume-limited (less than = 4000 km/s) sample of 699 IRAS galaxies with f sub 60 greater than 1.2 Jy. To determine the structure functions, we randomly select 500 galaxies as origins of spherical windows of radius R sub w, locate the centroid of the galaxies in the window (assuming all galaxies have equal mass) and then, compute the principal moments of inertia (I sub 1, I sub 2, I sub 3) about the centroid. Each S sub i is a function of (I sub 2)/(I sub 1) and (I sub 3)/I sub 1). S1, S2, and S3 tend to unity for highly prolate, oblate, and uniform distributions, respectively and tend to zero otherwise. The resulting 500 values of S sub i at each scale R sub w are used to construct a histogram.

Babul, Arif↗
NASA NTRS1993

When clusters collide - A numerical Hydro/N-body simulation of merging galaxy clusters

A 3D numerical simulation of two merging clusters of galaxies, using a hybrid Hydro/N-body code, is presented. The hydrodynamics of the code is solved by an Eulerian finite difference method. Initial results disclose that the X-ray emission of the dominant cluster becomes elongated and broadened; heating occurs at the core of the dominant cluster as a result of multiple shocks, and high velocity gas motions within the intracluster medium. It is predicted that clusters which have undergone recent mergers and do not have cooling flows will have high peculiar gas velocities and that the shocks and turbulence generated during the merger may power cluster-wide radio halos. Prolonged high-velocity gas motions through the dominant cluster core possibly play a major role in the formation and shaping of wide-angle tailed radio sources associated with central dominant galaxies. The N-body component of the simulation reveals the subcluster to be dispersed as it passes through the dominant cluster.

Roettiger, Kurt↗
NASA NTRS1985

Rotation and flattening of globular clusters

Methods for measuring globular cluster ellipticities and the results of such measurements are reviewed, and the processes that determine the shapes of globular clusters and the ways in which they change with time are discussed. The use of the virial tensor theorem to study the connection between the global rotation, velocity anisotropy, and the shape of a self-gravitating system is addressed, and the employment of N-body models to simulate the evolution of globular clusters with initially anisotropic velocity distributions is examined. The application of a simple evaporation model and Fokker-Planck integrations to study the two-body diffusion in globular clusters is reviewed.

Fall, S. M.↗
NASA NTRS1985

Numerical techniques for large cosmological N-body simulations

Techniques for carrying out large N-body simulations of the gravitational evolution of clustering in the fundamental cube of an infinite periodic universe are described and compared. The accuracy of the forces derived from several commonly used particle mesh schemes is examined, showing how submesh resolution can be achieved by including short-range forces between particles by direct summation techniques. The time integration of the equations of motion is discussed, and the accuracy of the codes for various choices of 'time' variable and time step is tested by considering energy conservation as well as by direct analysis of particle trajectories. Methods for generating initial particle positions and velocities corresponding to a growing mode representation of a specified power spectrum of linear density fluctuations are described. The effects of force resolution are studied and different simulation schemes are compared. An algorithm is implemented for generating initial conditions by varying the number of particles, the initial amplitude of density fluctuations, and the initial peculiar velocity field.

Efstathiou, G.↗
NASA NTRS1992

Percolation analysis of nonlinear structures in scale-free two-dimensional simulations

Results are presented of applying percolation analysis to several two-dimensional N-body models which simulate the formation of large-scale structure. Three parameters are estimated: total area (a(c)), total mass (M(C)), and percolation density (rho(c)) of the percolating structure at the percolation threshold for both unsmoothed and smoothed (with different scales L(s)) nonlinear with filamentary structures, confirming early speculations that this type of model has several features of filamentary-type distributions. Also, it is shown that, by properly applying smoothing techniques, many problems previously considered detrimental can be dealt with and overcome. Possible difficulties and prospects with the use of this method are discussed, specifically relating to techniques and methods already applied to CfA deep sky surveys. The success of this test in two dimensions and the potential for extrapolation to three dimensions is also discussed.

Dominik, Kurt G.↗
NASA NTRS1994

Weakly damped modes in star clusters and galaxies

A perturber may excite a coherent mode in a star cluster or galaxy. If the stellar system is stable, it is commonly assumed that such a mode will be strongly damped and therefore of little practical consequence other than redistributing momentum and energy deposited by the perturber. This paper demonstrates that this assumption is false; weakly damped modes exist and may persist long enough to have observable consequences. To do this, a method for investigating the dispersion relation for spherical stellar systems and for locating weakly damped modes in particular is developed and applied to King models of varying concentration. This leads to a following remarkable result: King models exhibit very weakly damped m = 1 modes over a wide range of concentration (0.67 less than or equal to c less than or equal to 1.5 have been examined). The predicted damping time is tens of hundreds of crossing times. This mode causes the peak density to shift from and slowly revolve about the initial center. The existence of the mode is supported by n-body simulation. Higher order modes and possible astronomical consequences are discussed. Weakly damped modes, for example, may provide a neutral explanation for observed discrepancies between density and kinematic centers in galaxies, off-center nuclei, the location of velocity cusps due to massive black holes, and both m = 1 and barlike disturbances of disks enbedded in massive halos or spheroids. Gravitational shocking may excite the m = 1 mode in globular clusters, which could modify their subsequent evolution and displace the positions of exotic remnants.

Weinberg, Martin D.↗