On Hurty/Craig-Bampton Substructuring with Interface Reduction on Contacting Surfaces.
Abstract not provided.
Kuether, Robert J.↗
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Substructure Interface Reduction Techniques to Capture Nonlinearities in Bolted Structures.
Abstract not provided.
Singh, Aabhas↗
Substructuring on Combinations of Steel and Aluminum Components of the Benchmark Structure of the Technical Division on Dynamic Substructures.
Abstract not provided.
Roettgen, Daniel↗
Substructuring of a nonlinear beam using modal Iwan framework Part II: Nonlinear Modal Substructuring.
Abstract not provided.
Mayes, Randall L.↗
TEM investigations on lath martensite substructure in quenched Fe-0.2C alloys
Highlights: • Twin can be lath martensite substructure in low-carbon steels. • Detwinning behavior occurs in an auto-tempering process during quenching. • Detwinning may result in the formation of twinned laths. • Detwinning may result in the laths with dislocation-like contrast as substructure. - Abstract: Lath martensite in low-carbon steels is the main microstructural feature in the quenched state, and dislocations have been generally recognized as the substructure of lath martensite. However, the effects of quenching conditions on the quenched substructure have not yet been fully understood. In the present work, a Fe-0.2C (wt%) alloy was selected for detailed investigations on the microstructural evolution at various austenitizing temperatures. Microstructural characterization was carried out by using a conventional transmission electron microscope (TEM). The substructure of lath martensite was found to vary with austenitizing temperature. In the 1200 °C-water-quenched (WQ) samples, twinned laths (two specific variants having a {112}<111>-type twin relationship) and a twinned region (laths with the twin structure as their substructure) can be observed. Almost all lath martensite with a high density of fine twins as its substructure can be obtained in the 1300 °C-WQ samples. The twins gradually disappear or detwinning-occurs during TEM observations carried out with in situ heating. A further increase in temperature results in the formation of twinned laths and then lath with dislocation-like contrasts or lines appears as the substructure. These results suggested that a completely twin structure can be the initial substructure of lath martensite, and lath with dislocation-like contrasts or lines as its substructure is most likely the auto-tempering result of twinning.
36 MATERIALS SCIENCE↗
Substructure in the stellar halo near the Sun: II. Characterisation of independent structures
In an accompanying paper, we present a data-driven method for clustering in ‘integrals of motion’ space and apply it to a large sample of nearby halo stars with 6D phase-space information. The algorithm identified a large number of clusters, many of which could tentatively be merged into larger groups. The goal here is to establish the reality of the clusters and groups through a combined study of their stellar populations (average age, metallicity, and chemical and dynamical properties) to gain more insights into the accretion history of the Milky Way. To this end, we developed a procedure that quantifies the similarity of clusters based on the Kolmogorov–Smirnov test using their metallicity distribution functions, and an isochrone fitting method to determine their average age, which is also used to compare the distribution of stars in the colour–absolute magnitude diagram. Also taking into consideration how the clusters are distributed in integrals of motion space allows us to group clusters into substructures and to compare substructures with one another. We find that the 67 clusters identified by our algorithm can be merged into 12 extended substructures and 8 small clusters that remain as such. The large substructures include the previously known Gaia-Enceladus, Helmi streams, Sequoia, and Thamnos 1 and 2. We identify a few over-densities that can be associated with the hot thick disc and host a small metal-poor population. Especially notable is the largest (by number of member stars) substructure in our sample which, although peaking at the metallicity characteristic of the thick disc, has a very well populated metal-poor component, and dynamics intermediate between the hot thick disc and the halo. We also identify additional debris in the region occupied by Sequoia with clearly distinct kinematics, likely remnants of three different accretion events with progenitors of similar masses. Although only a small subset of the stars in our sample have chemical abundance information, we are able to identify different trends of [Mg/Fe] versus [Fe/H] for the various substructures, confirming our dissection of the nearby halo. We find that at least 20% of the halo near the Sun is associated to substructures. When comparing their global properties, we note that those substructures on retrograde orbits are not only more metal-poor on average but are also older. We provide a table summarising the properties of the substructures, as well as a membership list that can be used for follow-up chemical abundance studies for example.
79 ASTRONOMY AND ASTROPHYSICS↗
IDENTIFICATION OF GALAXY CLUSTER SUBSTRUCTURES WITH THE CAUSTIC METHOD
We investigate the power of the caustic technique for identifying substructures of galaxy clusters from optical redshift data alone. The caustic technique is designed to estimate the mass profile of galaxy clusters to radii well beyond the virial radius, where dynamical equilibrium does not hold. Two by-products of this technique are the identification of the cluster members and the identification of the cluster substructures. We test the caustic technique as a substructure detector on two samples of 150 mock redshift surveys of clusters; the clusters are extracted from a large cosmological N-body simulation of a ΛCDM model and have masses of M{sub 200}∼10{sup 14}h{sup −1}M{sub ⊙} and M{sub 200}∼10{sup 15}h{sup −1}M{sub ⊙} in the two samples. We limit our analysis to substructures identified in the simulation with masses larger than 10{sup 13}h{sup −1}M{sub ⊙}. With mock redshift surveys with 200 galaxies within 3R{sub 200}, (1) the caustic technique recovers ∼30%–50% of the real substructures, and (2) ∼15%–20% of the substructures identified by the caustic technique correspond to real substructures of the central cluster, the remaining fraction being low-mass substructures, groups or substructures of clusters in the surrounding region, or chance alignments of unrelated galaxies. These encouraging results show that the caustic technique is a promising approach for investigating the complex dynamics of galaxy clusters.
79 ASTRONOMY AND ASTROPHYSICS↗
Probing the Galactic halo with RR Lyrae stars – II. The substructures of the Milky Way
ABSTRACT We identify substructures of the Galactic halo using 3003 type ab RR Lyrae stars with six-dimensional position–velocity information from the Sloan Digital Sky Survey, the Large Sky Area Multi-Object Fiber Spectroscopic Telescope and the Gaia Early Data Release 3. Based on this information, we define the separation of any two of the stars in the integrals of motion space and we identify substructures by utilizing the friends-of-friends algorithm. We identify members belonging to several known substructures: the Sagittarius stream, the Gaia-Enceladus-Sausage (GES), the Sequoia and the Helmi streams. In addition to these known substructures, there are three other substructures possibly associated with globular clusters NGC 5272, 6656 and 5024, respectively. Finally, we also find three remaining unknown substructures, one of which has large angular momentum and a mean metallicity −2.13 dex, which may be a new substructure. As for the GES, we find that it accounts for a large part of substructures in the inner halo and the apocentre distance is in the range 10–34 kpc, which suggests that the GES is mainly distributed in the inner halo. The near one-third proportion of the GES and the peak value of 20 kpc of the apocentre distance suggest that the GES could account for the break in the density profile of the Galactic halo at the Galactocentric distance ~20–25 kpc. The similarity when comparing the kinematic properties of the GES with the Hercules–Aquila Cloud and Virgo Overdensity suggests that the three substructures may have similar origins.
79 ASTRONOMY AND ASTROPHYSICS↗
Free-interface methods of substructure coupling for dynamic analysis
Benfield, et al. (1972) showed that among fixed-interface, free-interface, and hybrid substructure coupling methods, the fixed-interface methods as the most accurate and the free-interface methods are the least accurate. In the present note, a substructure coupling method is proposed which employs free-interface substructure modes supplemented by 'reduced flexibility.' Substructure coupling based on the improved substructure model is discussed, and a numerical comparison with Hou's free-interface method is given. To simplify representation of the method proposed, the substructure equations are developed first for constrained substructures, and then the equations representing substructures with rigid-body modes are given. Finally, the equations for coupling of substructures are derived. Example calculations are included.
Craig, R. R., Jr.↗
A NEW METHOD TO QUANTIFY X-RAY SUBSTRUCTURES IN CLUSTERS OF GALAXIES
We present a new method to quantify substructures in clusters of galaxies, based on the analysis of the intensity of structures. This analysis is done in a residual image that is the result of the subtraction of a surface brightness model, obtained by fitting a two-dimensional analytical model ({beta}-model or Sersic profile) with elliptical symmetry, from the X-ray image. Our method is applied to 34 clusters observed by the Chandra Space Telescope that are in the redshift range z in [0.02, 0.2] and have a signal-to-noise ratio (S/N) greater than 100. We present the calibration of the method and the relations between the substructure level with physical quantities, such as the mass, X-ray luminosity, temperature, and cluster redshift. We use our method to separate the clusters in two sub-samples of high- and low-substructure levels. We conclude, using Monte Carlo simulations, that the method recuperates very well the true amount of substructure for small angular core radii clusters (with respect to the whole image size) and good S/N observations. We find no evidence of correlation between the substructure level and physical properties of the clusters such as gas temperature, X-ray luminosity, and redshift; however, analysis suggest a trend between the substructure level and cluster mass. The scaling relations for the two sub-samples (high- and low-substructure level clusters) are different (they present an offset, i.e., given a fixed mass or temperature, low-substructure clusters tend to be more X-ray luminous), which is an important result for cosmological tests using the mass-luminosity relation to obtain the cluster mass function, since they rely on the assumption that clusters do not present different scaling relations according to their dynamical state.
79 ASTRONOMY AND ASTROPHYSICS↗
THE SEGUE K GIANT SURVEY. III. QUANTIFYING GALACTIC HALO SUBSTRUCTURE
We statistically quantify the amount of substructure in the Milky Way stellar halo using a sample of 4568 halo K giant stars at Galactocentric distances ranging over 5–125 kpc. These stars have been selected photometrically and confirmed spectroscopically as K giants from the Sloan Digital Sky Survey’s Sloan Extension for Galactic Understanding and Exploration project. Using a position–velocity clustering estimator (the 4distance) and a model of a smooth stellar halo, we quantify the amount of substructure in the halo, divided by distance and metallicity. Overall, we find that the halo as a whole is highly structured. We also confirm earlier work using blue horizontal branch (BHB) stars which showed that there is an increasing amount of substructure with increasing Galactocentric radius, and additionally find that the amount of substructure in the halo increases with increasing metallicity. Comparing to resampled BHB stars, we find that K giants and BHBs have similar amounts of substructure over equivalent ranges of Galactocentric radius. Using a friends-of-friends algorithm to identify members of individual groups, we find that a large fraction (∼33%) of grouped stars are associated with Sgr, and identify stars belonging to other halo star streams: the Orphan Stream, the Cetus Polar Stream, and others, including previously unknown substructures. A large fraction of sample K giants (more than 50%) are not grouped into any substructure. We find also that the Sgr stream strongly dominates groups in the outer halo for all except the most metal-poor stars, and suggest that this is the source of the increase of substructure with Galactocentric radius and metallicity.
79 ASTRONOMY AND ASTROPHYSICS↗
Substructuring techniques
The substructure function generator program is discussed. Input to this program consists of a definition of a finite element model of a substructure, and specification of the type and number of displacement functions to be generated. Primary output is a substructure data file containing the substructure mass and stiffness matrices expressing kinetic and potential energies as quadratic forms in coefficients of the displacement functions, etc. The substructure synthesis program forms complete system mass, stiffness, and damping matrices, computes system modes and frequencies, and executes transient response calculations. Input to this program consists of the array of substructure data files generated by the function generator program for individual substructures, and data cards defining the position and interconnection of the substructures, damping data, forcing function details, and function control parameters.
Whetstone, W. D.↗
A substructure coupling procedure applicable to general linear time-invariant dynamic systems
A substructure synthesis procedure applicable to structural systems containing general nonconservative terms is presented. In their final form, the non-self-adjoint substructure equations of motion are cast in state vector form through the use of a variational principle. A reduced-order model for each substructure is implemented by representing the substructure as a combination of a small number of Ritz vectors. For the method presented, the substructure Ritz vectors are identified as a truncated set of substructure eigenmodes, which are typically complex, along with a set of generalized real attachment modes. The formation of the generalized attachment modes does not require any knowledge of the substructure flexible modes; hence, only the eigenmodes used explicitly as Ritz vectors need to be extracted from the substructure eigenproblem. An example problem is presented to illustrate the method.
Howsman, T. G.↗
A substructure coupling procedure applicable to general linear time-invariant dynamic systems
A substructure synthesis procedure applicable to structural systems containing general nonconservative terms is presented. In their final form, the nonself-adjoint substructure equations of motion are cast in state vector form through the use of a variational principle. A reduced-order mode for each substructure is implemented by representing the substructure as a combination of a small number of Ritz vectors. For the method presented, the substructure Ritz vectors are identified as a truncated set of substructure eigenmodes, which are typically complex, along with a set of generalized real attachment modes. The formation of the generalized attachment modes does not require any knowledge of the substructure flexible modes; hence, only the eigenmodes used explicitly as Ritz vectors need to be extracted from the substructure eigenproblem. An example problem is presented to illustrate the method.
Howsman, T. G.↗
THE EFFECTS OF HALO-TO-HALO VARIATION ON SUBSTRUCTURE LENSING
We explore the halo-to-halo variation of dark matter (DM) substructure in galaxy-sized DM halos, focusing on its implications for strongly gravitational lensed systems. We find that the median value for projected substructure mass fractions within projected radii of 3% of the host halo virial radius is approximately f{sub sub} Almost-Equal-To 0.25%, but that the variance is large with a 95 percentile range of 0 {<=} f{sub sub} {<=} 1%. We quantify possible effects of substructure on quadruply imaged lens systems using the cusp relation and the simple statistic, R{sub cusp}. We estimate that the probability of obtaining the large values of the R{sub cusp} which have been observed from substructure effects is roughly {approx}10{sup -3} to {approx}10{sup -2}. We consider a variety of possible correlations between host halo properties and substructure properties in order to probe possible sample biases. In particular, low-concentration host DM halos have more large substructures and give rise to large values of R{sub cusp} more often. However, there is no known observational bias that would drive observed quadruply imaged quasars to be produced by low-concentration lens halos. Finally, we show that the substructure mass fraction is a relatively reliable predictor of the value of R{sub cusp}.
79 ASTRONOMY AND ASTROPHYSICS↗
Galaxy Cluster Mass Reconstruction Project – III. The impact of dynamical substructure on cluster mass estimates
With the advent of wide-field cosmological surveys, we are approaching samples of hundreds of thousands of galaxy clusters. While such large numbers will help reduce statistical uncertainties, the control of systematics in cluster masses is crucial. Here we examine the effects of an important source of systematic uncertainty in galaxy-based cluster mass estimation techniques: the presence of significant dynamical substructure. Dynamical substructure manifests as dynamically distinct subgroups in phase-space, indicating an ‘unrelaxed’ state. This issue affects around a quarter of clusters in a generally selected sample. We employ a set of mock clusters whose masses have been measured homogeneously with commonly used galaxy-based mass estimation techniques (kinematic, richness, caustic, radial methods). We use these to study how the relation between observationally estimated and true cluster mass depends on the presence of substructure, as identified by various popular diagnostics. We find that the scatter for an ensemble of clusters does not increase dramatically for clusters with dynamical substructure. However, we find a systematic bias for all methods, such that clusters with significant substructure have higher measured masses than their relaxed counterparts. This bias depends on cluster mass: the most massive clusters are largely unaffected by the presence of significant substructure, but masses are significantly overestimated for lower mass clusters, by ~ 10 percent at 10 14 and ≳ 20 percent for ≲ 10 13.5 . Finally, the use of cluster samples with different levels of substructure can therefore bias certain cosmological parameters up to a level comparable to the typical uncertainties in current cosmological studies.
79 ASTRONOMY AND ASTROPHYSICS↗
NASTRAN multipartitioning and one-shot substructuring
For intermediate size problems where all the data is accessible, the present method of substructuring in three separate phases (for static analysis) is unneccessarily cumbersome. The versatility of NASTRAN's DMAP and internal logic lends itself to finding a practical alternative to these procedures whereby self-contained special-purpose ALTER packages can be written to be run in one pass. Two examples are presented here under the titles of multipartitioning and one-shot substructuring. The flow of multipartitioning resembles that of the present three-phase substructuring. The basic effect is to partition the structure into substructures and operate on each substructure separately. This can be used to reduce the bandwidth of a given problem as well as to store information which will allow a change to be made in one of the substructures in a later run. This latter procedure is carried out in a second program titled one-shot substructuring.
Levy, A.↗