Engineering topics

Smith, B. F.

Publications and source records attributed to Smith, B. F..

At least 19 records

DOE OSTI2024

PETSc/TAO Users Manual Revision 3.22

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Toolkit for Advanced Optimization (TAO) for the numerical solution of partial differential equations (PDEs) and related problems on high-performance computers. PETSc/TAO is a suite of data structures and routines that provide the building blocks for implementing large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1997

Modelling the Centers of Galaxies

The key to studying central regions by means of nobody numerical experiments is to concentrate on the central few parsecs of a galaxy, replacing the remainder of the galaxy by a suitable boundary condition, rather after the manner in which stellar interiors can be studied without a detailed stellar atmosphere by replacing the atmosphere with a boundary condition. Replacements must be carefully designed because the long range gravitational force means that the core region is sensitive to mass outside that region and because particles can exchange between the outer galaxy and the core region. We use periodic boundary conditions, coupled with an iterative procedure to generate initial particle loads in isothermal equilibrium. Angular momentum conservation is ensured for problems including systematic rotation by a circular reflecting boundary and by integrating in a frame that rotates with the mean flow. Mass beyond the boundary contributes to the gravitational potential, but does not participate in the dynamics. A symplectic integration scheme has been developed for rotating coordinate systems. This combination works well, leading to robust configurations. Some preliminary results with this combination show that: (1) Rotating systems are extremely sensitive to non-axisymmetric external potentials, and (2) that a second core, orbiting near the main core (like the M31 second core system), shows extremely rapid orbital decay. The experimental setups will be discussed, along with preliminary results.

Smith, B. F.↗

NASA NTRS1995

Disruption of the Globular Cluster Pal 5

Orbit calculations suggest that the sparse globular cluster, Pal 5, will pass within 7 kpc of the Galactic center the next time it crosses the plane, where it might be destroyed by tidal stresses. We study this problem, treating Pal 5 as a self-consistent dynamical system orbiting through an external potential that represents the Galaxy. The first part of the problem is to find suitable analytic approximations to the Galactic potential. They must be valid in all regions the cluster is likely to explore. Observed velocity and positional data for Pal 5 are used as initial conditions to determine the orbit. Methods we used for a different problem some 12 years ago have been adapted to this problem. Three experiments have been run, with M/L= 1, 3, and 10, for the cluster model. The cluster blew up shortly after passing through the Galactic plane (about 130 Myrs after the beginning of the run) with M/L=1. At M/L = 3 and 10 the cluster survived, although it got quite a kick in the fundamental mode on passing through the plane. But the fundamental mode oscillation died out in a couple of oscillation cycles at M/L=10. Pal 5 will probably be destroyed on its next crossing of the Galactic plane if M/L=1, but it can survive (albeit with fairly heavy damage) if NI/L=3. We haven't tried to trap the mass limits more closely than that. Pal 5 comes through pretty well unscathed at M/L=10. An interesting follow-up experiment would be to back the cluster up along its orbit to look at its previous passage through the Galactic plane, to see what kind of object it might have been at earlier times.

Miller, R. H.↗

NASA NTRS1995

On M31's Double Nucleus

The recent HST discovery of a double nucleus in M31 brings into prominence the question how long, a second core can survive within the nuclear regions of a galaxy. Physical conditions in the nuclear regions of a typical galaxy help a second core survive, so it can orbit for a long time. possibly for thousands of orbits. Given the nearly uniform mass density in a core, tidal forces within a core radius are compressive in all directions and help the core survive the buffeting it takes as it orbits near the center of the galaxy. We use numerical experiments to illustrate these physical principles. Our method allows the full power of the experiments to be concentrated on the nuclear regions. Spatial resolution of about 0.2 pc comfortably resolves detail within the 1.4 parsec core radius of the second, but brighter core (P1) in M31. We use these physical principles to discuss M31's double nucleus, but they apply to other galaxies as well. and in other astronomical situations such as dumbbell galaxies. galaxies orbiting near the center of a galaxy cluster, and subclustering in galaxy clusters. The experiments also illustrate that galaxy encounters and merging are quite sensitive to external tidal forces, such as those produced by the gravitational potential in a group or cluster of galaxies.

Miller, R. H.↗

NASA NTRS1994

Galactic oscillations

A stable galaxy, if excited above its ground state, oscillates about that ground state. If it is resonably robust, it can support oscillations of large amplitude. Normal mode oscillations, with surprisingly large amplitudes, have been seen in numerical experiments. Observational evidence shows that real galaxies also oscillate. Galaxies ring like a bell in the experiments, and ringing continues undamped long after initial transients have died out. Their total kinetic energy oscillates with an amplitude as large as 10% of the mean. A fundamental mode dominates. It is homologous expansion/contraction of the entire galaxy (no nodes). Inward or outward velocities due to this mode are sufficiently large in the outer reaches of a galaxy to account for kinematic warps in observed velocity fields. A second spherically symmetrical mode has one node and is important near the center of the galaxy. It may be the driving force behind bulges in spiral galaxies. Two other normal modes have been identified as well. This appears to be the first experimental demonstration of normal mode oscillations within stable galaxy models.

Miller, R. H.↗

NASA NTRS1994

Multiple Core Galaxies: Implications for M31

It is generally perceived that two cores cannot survive very long within the nuclear regions of a galaxy. The recent HST discovery of a double nucleus in M31 brings this question into prominence. Physical conditions in the nuclear regions of a typical galaxy help a second core survive so it can orbit for a long time, possibly for thousands of orbits. Given the nearly uniform mass density in a core, tidal forces within a core radius are compressive in all directions and help the core survive the buffeting it takes as it orbits near the center of the galaxy. We use numerical experiments to illustrate these physical principles. Modifications to the experimental method allow the full power of the experiments to be concentrated on the nuclear regions. Spatial resolution of about 0.2 parsec comfortably resolves detail within the 1.4 parsec core radius of the second, but brighter, core (P1) in M31. The same physical principles apply in other astronomical situations, such as dumbbell galaxies, galaxies orbiting near the center of a galaxy cluster, and subclustering in galaxy clusters. The experiments also illustrate that galaxy encounters and merging are quite sensitive to external tidal forces, such as those produced by the gravitational potential in a group or cluster of galaxies.

Smith, B. F.↗

NASA NTRS1993

Galactic oscillations

Several oscillations have been identified in spherical galaxy models. These are normal mode oscillations in a stable galaxy. Each has its own distinct period and spatial form, and each rings without detectable damping through a Hubble time. The most important are: (1) a simple radial pulsation (fundamental mode), in which all parts of the galaxy move inward or outward with the same phase; and (2) a second spherically symmetrical radial mode with one node, so material inside the node moves outward when material outside moves inward. Numerical experiments suggest that normal mode oscillations may be present in nearly all galaxies at a considerably higher amplitude than has previously been thought. Amplitudes typically run a few percent of equilibrium values, and periods are around 50-300 Myrs in typical galaxies. These time scales are long enough that gas trapped near the center could cool during an oscillation cycle, allowing star formation activity. The second mode oscillations could cause bursts of star formation.

Smith, B. F.↗

NASA NTRS1992

Off-center nuclei in galaxies

The nucleus of a galaxy orbits around the mass centroid. Orbital motions appear overstable in numerical experiments started with a galaxy's nucleus at rest atop its mass centroid. The amplitude doubles in 6-10 orbital periods. Orbits precess, nutate, and change their amplitudes, but they keep fairly constant periods. Orbital periods are in resonance with local particle motions, and amplitudes reach a core radius. This resonance suggests that center motions are a local, rather than a global, phenomenon. The overstability implies that a galaxy cannot be formed in nature with its nucleus at rest atop its mass centroid, and that nuclei orbit the mass centroid in real galaxies. These center motions should show up observationally as a shift of the nucleus away from the center defined by nearby isophotes. Off-center nuclei have been reported in many galaxies (e.g., M33, M101, NGC 3379, NGC 3384). Other kinds of observations confirmed the picture of nonsteady galactic centers as well. Gas trapped in moving nuclear regions of a galaxy should show strange flow patterns with possible shocks. The nuclear regions of galaxies including Milky Way and of globular clusters are not likely to be in a static steady state.

Miller, R. H.↗

NASA NTRS1990

An experimental study of counter-rotating cores in elliptical galaxies

Recent observational studies (Franx and Illingworth 1987; Jedrzejewski and Schechter 1988; Bender 1988; Illingworth and Franx 1989) have shown that some elliptical galaxies have a small region near the center that rotates in the opposite direction from the outer parts of the galaxy. Often the rotation in the central part is much faster than that in the outer part. A few other galaxies show a small region near the center that rotates in the same direction as the rest of the galaxy, but much faster. Either way, the part near the center that shows a strange pattern of rotation (the 'core') has been interpreted as a distinct dynamical subsystem. Very briefly, the observational data seem to be that anomalies show up in rotation curves near the centers of some elliptical galaxies and that galaxies with these strange rotational properties do not show a photometric signature: there are no noticeable bumps in the brightness profile and no unusual shapes of isophotal contours that would suggest an excess of matter concentrated near the center. No strong color variations have been reported. The puzzle is to learn what we can about elliptical galaxies in general, and about galaxies with strange central regions in particular, from these observational facts. The authors' approach is experimental. They make a guess about the form of the dynamically distinct subsystem, and then build a galaxy model to test experimental consequences such as the amount of matter required to produce observable effects and the length of time over which these effects would remain observable. They sidestep questions about how the galaxy might have gotten to be that way in the first place. That gives them more freedom to explore a variety of suggestions about what kind of dynamical system might give rise to the observed rotational patterns.

Miller, R. H.↗

NASA NTRS1989

Numerical experiments on the oscillations of a rotating, axisymmetric galaxy

Modes of oscillation in six rotating, axisymmetric N-body systems are studied in a sequence of self-consistent, three-dimensional numerical experiments. The experimental systems are realizations of theoretical models of galaxies which are stellar-dynamical counterparts of uniformly rotating polytropes of index equal to 0.5. The ratio of the rotational kinetic energy to the gravitational potential energy ranges from 0.13 to 0.20. The systems oscillate axisymmetrically; the oscillations are interpreted as superpositions of a mode of radial pulsation and a Kelvin-like mode of oscillation. The experimental frequencies of these modes agree very well with theoretical predictions. When these modes are suppressed, the states of the experimental systems are very steady. The systems are dynamically unstable with respect to a toroidal mode when the ratio of the rotational kinetic energy to the gravitational potential energy exceeds a value lying between 0.16 and 0.17.

Miller, R. H.↗

NASA NTRS1988

Cluster influences on the internal dynamics of a galaxy

As part of a study of cluster influences, an attempt is made to map out damage to a galaxy under several different kinds of buffeting a galaxy suffers as it sweeps along its orbit through a cluster. It is shown that a cluster's observational characteristics are determined by the shape of its gravitational potential. It is noted the model galaxy must have full freedom to do whatever the physical galaxy wants to do.

Miller, R. H.↗

NASA NTRS1986

On the formation of galaxies with flat rotation curves

The dynamical development of a gravitationally unstable, initially uniform, collision-free medium has been studied by means of fully self-consistent three-dimensional numerical experiments. The system is encouraged to form just one blob by means of a small density bump, and its collapse is followed until a steady state has been reached. That blob may be interpreted as a galaxy, complete with halo. The galaxies that form have flat 'rotation curves'. Particles with initial speeds in excess of the velocity (V0) in that flat rotation curve remain unaffected by the collapse; those with speeds less than V0 join the collapse and have their speeds increased to V0. A quasi-virial argument yields correct estimates for V0.

Smith, B. F.↗

NASA NTRS1984

Gravitational spurs and resonances - Effects of small mass disturbers in spiral galaxy disks

In the present simulations of a disturber in a complete stellar disk without the restrictive assumption, the disturber parameters of the NGC 206 cloud in M 31 were assumed as a realistic example. The resulting spur around the disturber was comparable in shape, size, and strength to Julian and Toomre's (1966) results. In addition, a complicated evolving pattern of strong density peaks appeared well inside and outside the disturber's orbit. Simulation with a ten-times-more-massive disturber showed a more clearly defined version of the same initial pattern, two spiral arms of density peaks rotating with the disturber in the stronger arm. The orbital radii of the density peaks correspond to those of epicyclic resonances with the orbiting disturber potential.

Byrd, G. G.↗

NASA NTRS1983

Stochastic self-propagating star formation in three-dimensional disk galaxy simulations

The behavior of stochastic self-propagating star formation (SSPSF) in three dimensions is examined in simulation for the first time, emphasizing the effect of the added dimension on the sensitivity of spiral structure to the probability of star formation. The model produces global equilibrium spiral structure over a much more restricted range of star formation probabilities and relaxation times than in two dimensions. Spiral structure also occurs as a transient phenomenon in the runs which eventually fill or evolve to structured nonspiral states. The equilibrium spirals are not as distinctive as those produced by two-dimensional models. However, there are refinements which may modify these results, such as allowing for the depletion of gas in the interstellar medium due to conversion to long-lived low mass stars.

Statler, T.↗

NASA NTRS1983

Collisions and merging of disk galaxies

The stable disks required as initial states for an experiment are produced by embedding the disk (which is visible) in a halo (invisible). The disk is a luminous tracer that represents only 1 percent of the total mass of the system. The stability of the initial state of the model is confirmed experimentally. Collisions with various combinations of initial orbital energy and angular momentum and of disk orientations are investigated. Two initially parabolic cases with different impact parameters are followed in time until the interactions lead to a merger. The interpenetration of the two galaxies gives rise to a contraction and subsequent disruption of the entire system. A variety of responses is found for the visible disks, ranging from stretched-out nearly linear features to rapidly propagating ringlike patterns. It is noted that these forms depend critically on initial disk orientations but do not depend strongly on the sense of disk rotation. The ringlike patterns are found even for collisions with significant impact parameters.

Smith, B. F.↗

NASA NTRS1982

A numerical experiment on the equilibrium and stability of a rotating galactic bar

A self-consistent, three-dimensional numerical experiment is performed on an N-body system whose initial state is a realization of a certain theoretical model of a rotating triaxial galaxy. The model is a stellar-dynamical counterpart of a uniformly rotating polytrope of index equal to 0.5. The aim of the experiment is to study the equilibrium of the system and, in particular, to test its stability. The experimental system behaves in the mean like a realization of the theoretical model for at least seven crossing times. The principal departure of the system from equilibrium is an oscillation which is identified as a radial pulsation. There is no indication in its behavior that the system is unstable with respect to anu mode with an e-folding time shorter than or of the order of two crossing times. Certain changes that occur in the state of the system are interpreted, with the aid of the theoretical model, as secular changes which result from a slight failure of our numerical methods to conserve the mass, energy, and angular momentum of the system; these effects are small enough that they do not vitiate the experiment on a dynamical time scale.

Miller, R. H.↗

NASA NTRS1982

On the stability of Schwarzschild's triaxial galaxy model

The numerical model for a triaxial galaxy constructed by Schwartzschild (1979) has been tested by means of fully self-consistent three-dimensional n-body numerical experiments that use a representation of this model to start the integration. The integration, study models, initial load, and correcting potential of the experiment are detailed. Preliminary checks included density values, potential values, and integration in potential of an ideal model. The results showed some particle loss and no significant shape change. The model is rugged and robust, and no growing disturbances with growth rate in excess of 0.5 per crossing time could be detected. Runs were done at 50 percent excess halo and with tube orbits reversed.

Smith, B. F.↗

NASA NTRS1982

Environmental effects on galaxies in clusters

Influences from the cluster environment build up steadily over long times so that the internal dynamics of a galaxy in a cluster change appreciably over a cluster crossing time. The galaxy can no longer be considered as an isolated object. Slow rotation of elliptical galaxies and observations on galaxy alignment within clusters of galaxies provide two independent pieces of observational evidence for cluster influence. A first cut at studying cluster influences on the internal dynamics of galaxies is presented by means of numerical experiments started from a rotating barlike galaxy placed in an external force field like that which a galaxy sees in a cluster. Both pattern motion and observable rotation are tidally braked by the cluster force field. The experiments verify that the braking rate scales inversely as the square of the cluster crossing time. Systematic internal motions are reduced so that observational V/sigma is less than 0.2, in agreement with observations on elliptical galaxies but sharply reduced from V/sigma of approximately 1.0 for the original model. The final shapes of tidally braked galaxies need not be spherical.

Miller, R. H.↗